From a42061bdf5b8974baa21a0a4097bbc9de3a0da1c Mon Sep 17 00:00:00 2001
From: Ali Romman <226877337+aliromman@users.noreply.github.com>
Date: Thu, 22 Oct 2026 14:24:08 -0500
Subject: [PATCH] Add native centre capture and complete fixed-reader services

---
 .../native-centre-capture/CLAIM-INDEX.json    |    457 +
 research/native-centre-capture/COSTS.md       |     82 +
 .../EXTERNAL-NOTICES.json                     |     40 +
 .../HISTORICAL-BUDGETS.md                     |     94 +
 research/native-centre-capture/LICENSE        |    201 +
 .../LOCAL-LINK-CHECK.json                     |     54 +
 research/native-centre-capture/NOTICE.md      |     88 +
 .../native-centre-capture/OPEN-QUESTIONS.md   |     26 +
 .../PACKAGE-MANIFEST.json                     |   1965 +
 research/native-centre-capture/PROOF.md       |    246 +
 research/native-centre-capture/README.md      |    117 +
 .../SOURCE-MANIFEST.json                      |   3787 +
 .../native-centre-capture/VALIDATION.json     |     34 +
 .../adapters/ADAPTATIONS.json                 |     23 +
 ...clean-exchange-budget-review-20261020.diff |     26 +
 .../clean-exchange-budget-review-20261020.py  |    255 +
 ...w-displacement-budget-review-20261020.diff |     32 +
 ...low-displacement-budget-review-20261020.py |    387 +
 .../check_bridge_access.py                    |    399 +
 .../involution-reader-20261020/FREEZE.json    |     14 +
 .../INVOLUTION-READER.md                      |    204 +
 .../involution-reader-20261020/emit_query.py  |    282 +
 .../final-normal/CHECKS.json                  |    131 +
 .../final-normal/INVOLUTION-READER.json.gz    |    Bin 0 -> 210767 bytes
 .../final-optimized/CHECKS.json               |    131 +
 .../final-optimized/INVOLUTION-READER.json.gz |    Bin 0 -> 210767 bytes
 .../COMPLETE-DUAL.md                          |    215 +
 .../FREEZE.json                               |     19 +
 .../emit_dual.py                              |    433 +
 .../final-normal/CHECKS.json                  |    134 +
 .../final-normal/COMPLETE-DUAL.json.gz        |    Bin 0 -> 210319 bytes
 .../final-optimized/CHECKS.json               |    134 +
 .../final-optimized/COMPLETE-DUAL.json.gz     |    Bin 0 -> 210319 bytes
 .../DIMENSION25-VIEWS.json                    |  12810 ++
 .../TRIPLE25-PROGRAMS.json.gz                 |    Bin 0 -> 307661 bytes
 .../check_matched_access.py                   |    237 +
 .../check_triple25.py                         |    273 +
 .../rank9-completion-20261020/CHECKS.json     |     70 +
 .../rank9-completion-20261020/FREEZE.json     |     13 +
 .../RANK9-PROGRAMS.json.gz                    |    Bin 0 -> 45831 bytes
 .../rank9-completion-20261020/RANK9.md        |    206 +
 .../rank9-completion-20261020/check_rank9.py  |    313 +
 .../row-capture-access-20261020/ACCESS.md     |    163 +
 .../row-capture-access-20261020/FREEZE.json   |     13 +
 .../INTEGRATION-FREEZE.json                   |     12 +
 .../INTEGRATION.md                            |    218 +
 .../REUSE-FREEZE.json                         |     14 +
 .../row-capture-access-20261020/REUSE.md      |    197 +
 .../check_access.py                           |    249 +
 .../check_integration.py                      |    341 +
 .../check_reuse.py                            |    321 +
 .../integration-v2-normal/CHECKS.json         |    100 +
 .../integration-v2-normal/DISPATCHER.json     |  32749 +++++
 .../integration-v2-optimized/CHECKS.json      |    100 +
 .../integration-v2-optimized/DISPATCHER.json  |  32749 +++++
 .../reuse-normal/REUSE-CHECKS.json            |     49 +
 .../reuse-normal/REUSE-PROGRAM.json           | 102701 +++++++++++++++
 .../reuse-optimized/REUSE-CHECKS.json         |     49 +
 .../reuse-optimized/REUSE-PROGRAM.json        | 102701 +++++++++++++++
 .../run-normal/ACCESS-PROGRAM.json            |  10064 ++
 .../run-normal/CHECKS.json                    |     39 +
 .../run-optimized/ACCESS-PROGRAM.json         |  10064 ++
 .../run-optimized/CHECKS.json                 |     39 +
 .../FREEZE.json                               |     14 +
 .../PEER-REVIEW.md                            |     29 +
 .../REPRODUCTION.json                         |     11 +
 .../REVIEW.md                                 |    236 +
 .../check_review.py                           |    258 +
 .../normal/REVIEW-CHECKS.json                 |    580 +
 .../optimized/REVIEW-CHECKS.json              |    580 +
 .../FREEZE.json                               |     11 +
 .../REVIEW.md                                 |     44 +
 .../check_budget.py                           |     72 +
 .../normal.json                               |     57 +
 .../optimized.json                            |     57 +
 .../FREEZE.json                               |     15 +
 .../GENERAL-READER.md                         |    111 +
 .../PEER-REVIEW.md                            |     27 +
 .../REPRODUCTION.json                         |     11 +
 .../REVIEW.md                                 |    283 +
 .../check_review.py                           |    680 +
 .../normal/REVIEW-CHECKS.json                 |    635 +
 .../optimized/REVIEW-CHECKS.json              |    635 +
 .../FREEZE.json                               |     13 +
 .../REPRODUCTION.json                         |     11 +
 .../REVIEW.md                                 |    199 +
 .../check_service.py                          |    378 +
 .../normal/REVIEW-CHECKS.json                 |    172 +
 .../optimized/REVIEW-CHECKS.json              |    172 +
 .../FREEZE.json                               |     16 +
 .../GENERAL-QUERY.md                          |    105 +
 .../PEER-REVIEW.md                            |     26 +
 .../REPRODUCTION.json                         |     11 +
 .../REVIEW.md                                 |    240 +
 .../check_review.py                           |    273 +
 .../normal/REVIEW-CHECKS.json                 |    523 +
 .../optimized/REVIEW-CHECKS.json              |    523 +
 .../FREEZE.json                               |     13 +
 .../REPRODUCTION.json                         |     12 +
 .../REVIEW.json                               |   3073 +
 .../REVIEW.md                                 |    216 +
 .../check_review.py                           |    387 +
 .../CHECKS.json                               |     77 +
 .../FREEZE.json                               |     11 +
 .../NORMAL-HASHES.json                        |      3 +
 .../REVIEW.md                                 |    214 +
 .../check_rank9.py                            |    339 +
 .../BUDGET.json                               |    555 +
 .../FREEZE.json                               |     14 +
 .../clean-exchange-budget-20261020/PROOF.md   |    113 +
 .../REPRODUCTION.json                         |     11 +
 .../check_budget.py                           |    210 +
 .../BUDGET.json                               |    244 +
 .../BUDGET.json                               |   1868 +
 .../FREEZE.json                               |     14 +
 .../low-displacement-budget-20261020/PROOF.md |    122 +
 .../REPRODUCTION.json                         |     11 +
 .../check_budget.py                           |    274 +
 .../MATCHED-NATIVE-BUDGET.json                |   1410 +
 .../mixed-exit-budget-20261020/FREEZE.json    |     13 +
 .../MIXED-BUDGET.json                         |    265 +
 .../mixed-exit-budget-20261020/PROOF.md       |     52 +
 .../REPRODUCTION.json                         |      9 +
 .../check_mixed_budget.py                     |     91 +
 .../matching-geometry-20261018/GEOMETRY.json  |   1523 +
 .../row-capture-20261020/FREEZE.json          |     12 +
 .../row-capture-20261020/ROW-CAPTURE.md       |    258 +
 .../row-capture-20261020/check_row_capture.py |    269 +
 .../run-normal/CHECKS.json                    |     32 +
 .../run-normal/ROW-CAPTURE.json               |  10667 ++
 .../COMPLETION-LIMITS.md                      |    187 +
 .../row-involution-20261020/FREEZE.json       |     11 +
 .../LIMITS-FREEZE.json                        |     12 +
 .../row-involution-20261020/ROW-INVOLUTION.md |    219 +
 .../check_completion_limits.py                |    179 +
 .../check_row_involution.py                   |    297 +
 .../limits-normal/CHECKS.json                 |     23 +
 .../limits-normal/COMPLETION-LIMITS.json      |   9144 ++
 .../limits-optimized/CHECKS.json              |     23 +
 .../limits-optimized/COMPLETION-LIMITS.json   |   9144 ++
 .../run-normal/CHECKS.json                    |     23 +
 .../run-normal/ROW-INVOLUTION.json            |  29746 +++++
 .../run-optimized/CHECKS.json                 |     23 +
 .../run-optimized/ROW-INVOLUTION.json         |  29746 +++++
 .../PROGRAM.json                              |      1 +
 .../PERMUTATION64-PROGRAMS.json.gz            |    Bin 0 -> 72000 bytes
 .../CYCLIC-FLAGS.json                         |  27210 ++++
 .../FULL-GAUGE.json                           |   3353 +
 .../rank-thirty-review-20261020/CHECKS.json   |     59 +
 .../rank-thirty-review-20261020/FREEZE.json   |     10 +
 .../REPRODUCTION.json                         |     15 +
 .../rank-thirty-review-20261020/REVIEW.md     |    158 +
 .../check_review.py                           |    233 +
 .../FREEZE.json                               |     11 +
 .../REPRODUCTION.json                         |      7 +
 .../route32-capture-review-20261020/REVIEW.md |    229 +
 .../check_review.py                           |    393 +
 .../run-normal/CHECKS.json                    |    183 +
 .../run-optimized/CHECKS.json                 |    183 +
 .../FREEZE.json                               |     12 +
 .../REPRODUCTION.md                           |     28 +
 .../row-involution-review-20261020/REVIEW.md  |    414 +
 .../check_review.py                           |    318 +
 .../verified-normal/CHECKS.json               |     79 +
 .../verified-optimized/CHECKS.json            |     79 +
 .../interface-proof/verify_native_lift.py     |    336 +
 .../CLEAN-J-PROGRAMS.json.gz                  |    Bin 0 -> 583358 bytes
 .../CODED-EXITS-FREEZE.json                   |     13 +
 .../low-displacement-20261020/CODED-EXITS.md  |    115 +
 .../EXTENSIONS-FREEZE.json                    |     14 +
 .../low-displacement-20261020/EXTENSIONS.md   |    190 +
 .../NATIVE-FREEZE.json                        |     12 +
 .../low-displacement-20261020/NATIVE.md       |    149 +
 .../RESPONSE-FREEZE.json                      |     11 +
 .../low-displacement-20261020/RESPONSE.md     |    165 +
 .../check_response.py                         |    339 +
 .../CLEAN-DUAL.md                             |    190 +
 .../CLEAN-LATE-EXCHANGE.md                    |    192 +
 .../DUAL-FREEZE.json                          |     14 +
 .../clean-late-exchange-20261020/FREEZE.json  |     26 +
 .../dual-normal/CHECKS.json                   |    140 +
 .../dual-normal/CLEAN-DUAL.json.gz            |    Bin 0 -> 293926 bytes
 .../dual-optimized/CHECKS.json                |    140 +
 .../dual-optimized/CLEAN-DUAL.json.gz         |    Bin 0 -> 293926 bytes
 .../emit_clean_exchange.py                    |    242 +
 .../clean-late-exchange-20261020/emit_dual.py |    229 +
 .../run-normal/CHECKS.json                    |    127 +
 .../run-normal/CLEAN-LATE-EXCHANGE.json.gz    |    Bin 0 -> 287881 bytes
 .../run-optimized/CHECKS.json                 |    127 +
 .../run-optimized/CLEAN-LATE-EXCHANGE.json.gz |    Bin 0 -> 287881 bytes
 .../coded-normal/CODED-EXITS-CHECKS.json      |    430 +
 .../coded-normal/CODED-EXITS-PROGRAM.json.gz  |    Bin 0 -> 948891 bytes
 .../emit_coded_exits.py                       |    140 +
 .../emit_followthrough.py                     |    227 +
 .../low-displacement-20261020/emit_native.py  |    279 +
 .../CARRIER-PREFIX.md                         |     40 +
 .../PREFIX-FREEZE.json                        |     12 +
 .../QUERY-FREEZE.json                         |     14 +
 .../ROUTED-QUERY.md                           |    152 +
 .../SERVICE-FREEZE.json                       |     14 +
 .../fixed-reader-reuse-20261020/SERVICES.md   |    117 +
 .../emit_prefix.py                            |     97 +
 .../emit_routed_query.py                      |    330 +
 .../emit_service.py                           |    187 +
 .../prefix-normal/CARRIER-PREFIX.json.gz      |    Bin 0 -> 142430 bytes
 .../prefix-normal/CHECKS.json                 |     65 +
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 .../query-normal/ROUTED-QUERY.json.gz         |    Bin 0 -> 305210 bytes
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 .../FIXED-READER-SERVICES.json.gz             |    Bin 0 -> 341332 bytes
 .../service-optimized/CHECKS.json             |    135 +
 .../FIXED-READER-SERVICES.json.gz             |    Bin 0 -> 341332 bytes
 .../native-normal-v2/NATIVE-CHECKS.json       |     78 +
 .../native-normal-v2/NATIVE-PROGRAM.json.gz   |    Bin 0 -> 233723 bytes
 .../odd16-normal-v2/EXTENSION-CHECKS.json     |     51 +
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 .../route32/FREEZE.json                       |     14 +
 .../route32/ROUTE32.md                        |    209 +
 .../route32/emit_model.py                     |    244 +
 .../route32/emit_native.py                    |    130 +
 .../route32/model-normal/CHECKS.json          |     76 +
 .../route32/model-normal/ROUTE32-MODEL.json   |      1 +
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 .../FREEZE.json                               |     14 +
 .../ROW-INVOLUTION-NATIVE.md                  |    187 +
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 .../LINE-ENTRY-REUSE-FREEZE.json              |     14 +
 .../LINE-ENTRY-REUSE.md                       |     86 +
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 .../direct-optimized/CHECKS.json              |     71 +
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 .../row-only-capture-20261020/emit_capture.py |    291 +
 .../emit_direct_full.py                       |     79 +
 .../emit_line_entry_reuse.py                  |    132 +
 .../reuse-normal/CHECKS.json                  |     71 +
 .../reuse-normal/LINE-ENTRY-REUSE.json.gz     |    Bin 0 -> 144819 bytes
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 .../run-normal/RESPONSE-CHECKS.json           |     46 +
 .../run-normal/RESPONSE-PROGRAM.json          |  22900 ++++
 .../simple-clean-native-20261020/FREEZE.json  |     14 +
 .../SIMPLE-CLEAN-NATIVE.md                    |    172 +
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 .../NATIVE-LIFT.md                            |    140 +
 .../SOURCE-PINS.json                          |     10 +
 .../DERIVATION.md                             |    101 +
 .../FREEZE.json                               |     15 +
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 .../REVIEW.md                                 |    166 +
 .../check.py                                  |    211 +
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 .../normal/REVIEW.json                        |   1064 +
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 .../clean-dual-review-20261020/FREEZE.json    |     14 +
 .../REPRODUCTION.json                         |      8 +
 .../clean-dual-review-20261020/REVIEW.md      |    198 +
 .../clean-dual-review-20261020/check.py       |    217 +
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 .../check.py                                  |    450 +
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 .../isotropic-pair-review-20261018/check.py   |    593 +
 .../FREEZE.json                               |     14 +
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 .../REVIEW.md                                 |    199 +
 .../line-entry-reuse-review-20261020/check.py |    200 +
 .../normal/INPUTS.json                        |    110 +
 .../normal/REVIEW.json                        |    185 +
 .../optimized/INPUTS.json                     |    110 +
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 .../EXTENSIONS-REPRODUCTION.json              |      8 +
 .../EXTENSIONS-REVIEW-FREEZE.json             |     15 +
 .../EXTENSIONS-REVIEW.md                      |    177 +
 .../NATIVE-REPRODUCTION.json                  |      8 +
 .../NATIVE-REVIEW-FREEZE.json                 |     14 +
 .../REVIEW.md                                 |    193 +
 .../check_extensions.py                       |    158 +
 .../check_native.py                           |    268 +
 .../extensions-normal/EXTENSIONS-INPUTS.json  |     74 +
 .../extensions-normal/EXTENSIONS-REVIEW.json  |   8068 ++
 .../EXTENSIONS-INPUTS.json                    |     74 +
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 .../FREEZE.json                               |     17 +
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 .../route32-native-review-20261020/REVIEW.md  |    182 +
 .../route32-native-review-20261020/check.py   |    148 +
 .../normal/INPUTS.json                        |     89 +
 .../normal/REVIEW.json                        |  11681 ++
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 .../DERIVATION.md                             |     98 +
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 .../sources/vendor/clifford/clifford_exact.py |    149 +
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 .../certificates/selected-result.json         |    222 +
 .../ASSEMBLY.json                             |    345 +
 .../notices/PR2226-NOTICE.md                  |     22 +
 .../notices/PR2588-NOTICE                     |     10 +
 .../notices/PR2588-NOTICE-PR2226.md           |     21 +
 .../notices/PR3133-CREDITS.md                 |     19 +
 .../notices/PR3133-NOTICE                     |     28 +
 research/native-centre-capture/replay.py      |     75 +
 .../native-centre-capture/replay_budgets.py   |     69 +
 .../validation/normal/BUDGET-REPLAY.json      |     28 +
 .../validation/normal/NATIVE-REPLAY.json      |     74 +
 .../normal/budget-clean-exchange.json         |    580 +
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 .../normal/budget-low-displacement.json       |   3073 +
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 .../validation/normal/clean-dual.json         |    137 +
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 .../validation/normal/involution-model.json   |     79 +
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 .../validation/normal/reader-forward.json     |    523 +
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 .../validation/normal/route32-model.json      |    183 +
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 .../validation/normal/route32-native.json     |  11681 ++
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 .../cold/main-optimized/REPLAY.json           |     74 +
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diff --git a/research/native-centre-capture/CLAIM-INDEX.json b/research/native-centre-capture/CLAIM-INDEX.json
new file mode 100644
index 0000000000..ca82e13da6
--- /dev/null
+++ b/research/native-centre-capture/CLAIM-INDEX.json
@@ -0,0 +1,457 @@
+{
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+        },
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+        },
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+          "role": "proof",
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+        },
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+        },
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+        },
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+          "role": "checker",
+          "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+        },
+        {
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+          "role": "frozen_receipt",
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+        }
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+          "path": "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE.md",
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+        },
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+        }
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+    },
+    {
+      "claim": "Clean selected centres with the old arbitrary baseline retained in selected X.",
+      "expected_status": "PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE",
+      "files": [
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+      "claim": "Complete same-chronology inverse-adjoint and selected-field conjugate for the actual Q-entry word.",
+      "expected_status": "PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE",
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+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal/REVIEW.json",
+          "role": "frozen_receipt",
+          "sha256": "c9abd280df35e3fa2270c8853a5e5f32d380e3d87a5ca0337e99e7bc400fcda2"
+        }
+      ],
+      "id": "clean-dual",
+      "replay_stage": "clean-dual"
+    },
+    {
+      "claim": "Actual row involution and transpose, dyadic scalar words, general rank(A-I) statement, and fixed-E sixteen-row replacement bound.",
+      "expected_status": "PASS",
+      "files": [
+        {
+          "path": "frozen/lanes/controller-followthrough-20261017/row-involution-20261020/ROW-INVOLUTION.md",
+          "role": "proof",
+          "sha256": "c8470cc2280a057cbebf4a31ee679495990b200a6d6c033cc39e459eb2cf139f"
+        },
+        {
+          "path": "frozen/lanes/controller-followthrough-20261017/row-involution-20261020/COMPLETION-LIMITS.md",
+          "role": "proof",
+          "sha256": "91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/row-involution-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "a136f1ae9960a93b9e399d84853c4899eb6a39fd42d1464a97a1c32bbdfb6f31"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/row-involution-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "0bc6af49367a6e9cab21e8c4069fc12cb39b8d1210d4554d7f55f9894ddb4f41"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/row-involution-review-20261020/check_review.py",
+          "role": "checker",
+          "sha256": "2b5f8c6231e42d6299c6dba249d0c86d6dab1a9db97cadcf8e902c3d01a8a2e3"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/row-involution-review-20261020/verified-normal/CHECKS.json",
+          "role": "frozen_receipt",
+          "sha256": "57039f8f9603f4b101a3960bfca4472f9617855213c8247c2470d84f31171f92"
+        }
+      ],
+      "id": "involution-model",
+      "replay_stage": "involution-model"
+    },
+    {
+      "claim": "Eight complete mixed-FULL/hole native A and A-transpose words.",
+      "expected_status": "PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS",
+      "files": [
+        {
+          "path": "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/ROW-INVOLUTION-NATIVE.md",
+          "role": "proof",
+          "sha256": "3cb445c5216f9a3371ad938da1f663408c6db6b8d3f66875d86d83e830bd7e86"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "3d7c72015cde33add3f2287aa4ed58e6b90c2e51c73bbe851eafb7c3ca4d274c"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "7f03bff5bdf98cdaf7b098c4bdbacc2ee571738198ec2e2e8fdf9f5ff9c4d35a"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/check.py",
+          "role": "checker",
+          "sha256": "b411d3eb6352b71a0e8200cac88c8a01569e254cbbeaba9acb04edf6441134bf"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/normal/REVIEW.json",
+          "role": "frozen_receipt",
+          "sha256": "5c2bbc8076679da2e14db052c9445a42c60f71fefadf05bb7f09c007187a9b10"
+        }
+      ],
+      "id": "involution-native",
+      "replay_stage": "involution-native"
+    },
+    {
+      "claim": "Six complete D25 forward services for actual past readers and current involution responses.",
+      "expected_status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER",
+      "files": [
+        {
+          "path": "frozen/lanes/bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md",
+          "role": "proof",
+          "sha256": "718829c1842c856d5694abbcd6ebd509cafbb8901b4225be218f45abd2844dab"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "e8862531740470b3bb4f45b421c0ab100c07f00bed71271b398ee7bdb89d834d"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "b4770cbd56bc8b115728529ab218d60ca2bd1a385896ba78cfdf374f04370c97"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/check_review.py",
+          "role": "checker",
+          "sha256": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json",
+          "role": "frozen_receipt",
+          "sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830"
+        }
+      ],
+      "id": "reader-forward",
+      "replay_stage": "reader-forward"
+    },
+    {
+      "claim": "Six complete typed inverse-adjoint services, including native prefix, DATA views, barrier, and late query.",
+      "expected_status": "PASS_INDEPENDENT_COMPLETE_READER_DUAL",
+      "files": [
+        {
+          "path": "frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/COMPLETE-DUAL.md",
+          "role": "proof",
+          "sha256": "37a3a187acf93cad2048f9147457bf8925cf53ce61836b5e899dd13bc4239c5e"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "613fc0bc8d4d2470d05e2d1325a647f6da35d3a785e2ae834b1829094cf81fb1"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "03220af20f51c283bdd4593c9a368d94dd741e0c6bcb3609f5a0b85ee1d38821"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/check.py",
+          "role": "checker",
+          "sha256": "363b69d3b32ea8d5b1b9511c72224a5a32ada7dffc552dae16abf1b0b8387489"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/normal/REVIEW-CHECKS.json",
+          "role": "frozen_receipt",
+          "sha256": "6107e7fe7f9e7821774a80cab51961147cbfaa81d325f95d4644fc57d4c4d80d"
+        }
+      ],
+      "id": "reader-dual",
+      "replay_stage": "reader-dual"
+    },
+    {
+      "claim": "Rank32 route-homogeneous response, rational inverse, dyadic capture codes, and restricted partition minimum.",
+      "expected_status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE",
+      "files": [
+        {
+          "path": "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md",
+          "role": "proof",
+          "sha256": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/route32-capture-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "e4a287d477eff6a8fd8ad672350b3898add189428bd28b7688822de715370f96"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/route32-capture-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "3b3ec8891902261ad22a82c5d0922c2ae6c96ad00c0cc5f82598a1a227865421"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py",
+          "role": "checker",
+          "sha256": "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89"
+        },
+        {
+          "path": "frozen/lanes/independent-review-20261017/route32-capture-review-20261020/run-normal/CHECKS.json",
+          "role": "frozen_receipt",
+          "sha256": "42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596"
+        }
+      ],
+      "id": "route32-model",
+      "replay_stage": "route32-model"
+    },
+    {
+      "claim": "Direct Fsimple and Bcustom local pair at 2912 scalar primitives, 320 children, and native mass 1984.",
+      "expected_status": "PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE",
+      "files": [
+        {
+          "path": "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/SIMPLE-CLEAN-NATIVE.md",
+          "role": "proof",
+          "sha256": "8c64af43d7f43c5fc28056715c5cc277d8580ca4cf05dcabb7ff4bd0911738e7"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "06b782821db7d45cc05aecb8eff34ca2732202c9e32948be6b5c8f7952b0716f"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "b3544043aab76f8966d903e662c345edd390f64c151cbeb4b5062d329a5bd5d4"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/check.py",
+          "role": "checker",
+          "sha256": "637db7eba7629a522e41e96333cda9a1af713c0d1403b1caada2827c2e3447f9"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/REVIEW-CHECKS.json",
+          "role": "frozen_receipt",
+          "sha256": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784"
+        }
+      ],
+      "id": "simple-clean",
+      "replay_stage": "simple-clean"
+    },
+    {
+      "claim": "Four complete raw native words with 297 new exact phase recipes; no common-W lift or whole-W decoder.",
+      "expected_status": "PASS_INDEPENDENT_ROUTE32_NATIVE",
+      "files": [
+        {
+          "path": "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md",
+          "role": "proof",
+          "sha256": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "d272e97e8b2d68fae87163c83308da4c6f81f5310cf568f04323f77ffd01bb8c"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "bb1bb2fabea06c9a1de93f5def491bcadbeee997c42921e6f08f75a4bafaf9f1"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/check.py",
+          "role": "checker",
+          "sha256": "a0f6fed3b062f53d3d7237b7bc1ac95518a27eb94abaf1c9b731473547beb3c6"
+        },
+        {
+          "path": "frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal/REVIEW.json",
+          "role": "frozen_receipt",
+          "sha256": "9161f559d162d008e3927aa4cffcff9205f141f2d140596056681f031e3eae1f"
+        }
+      ],
+      "id": "route32-native",
+      "replay_stage": "route32-native"
+    },
+    {
+      "claim": "Conditional fixed-profile inequalities at the retained historical exponent only.",
+      "files": [
+        {
+          "path": "frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "9b2c0661a9764fb9cbdb8b7218c0f0f929bd962f44b3a07555a1ef7f357f8e68"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.json",
+          "role": "frozen_receipt",
+          "sha256": "e0047b4e85e3d93f765e9fb453a74b269a5cd5aeef03f88579998391b843bf52"
+        }
+      ],
+      "id": "budget-low-displacement",
+      "runner": "replay_budgets.py"
+    },
+    {
+      "claim": "Conditional fixed-profile inequalities at the retained historical exponent only.",
+      "files": [
+        {
+          "path": "frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "fabb4fec8bf52fef4fc3c873c00dad2f0b7ee5dc6804be3426062d6c262d759c"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "f229e0ba034cc40d3f7ebf4a7f60835cd183df6aa6bdf19a26b495a2a35e250e"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/normal/REVIEW-CHECKS.json",
+          "role": "frozen_receipt",
+          "sha256": "b76233f91b441dc680db0df7bb2d889364d269222b3f0a711be31f96c461d0b2"
+        }
+      ],
+      "id": "budget-clean-exchange",
+      "runner": "replay_budgets.py"
+    },
+    {
+      "claim": "Conditional fixed-profile inequalities at the retained historical exponent only.",
+      "files": [
+        {
+          "path": "frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/REVIEW.md",
+          "role": "independent_review",
+          "sha256": "f398499be52193a8c7f0f7a44a306086873cf6adddc3d7d6b5d398a0d2dfda2f"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/FREEZE.json",
+          "role": "review_freeze",
+          "sha256": "b414db0a70d02ea10e546979ecf2210e08ff1587d6614fca25ebd15ad59daab3"
+        },
+        {
+          "path": "frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/normal.json",
+          "role": "frozen_receipt",
+          "sha256": "13335f11799d34af003fbb7dc76eddc27423ee1d1ff54d473b49dd0030da4db6"
+        }
+      ],
+      "id": "budget-coalesced",
+      "runner": "replay_budgets.py"
+    }
+  ],
+  "excluded": [
+    "route32 common-W lift",
+    "route32 whole-W reflection decoder",
+    "complete recursive helper host",
+    "complete caller and supplier",
+    "complete kappa improvement",
+    "global response or native optimality"
+  ],
+  "schema": "native-centre-capture-claim-index-v1"
+}
diff --git a/research/native-centre-capture/COSTS.md b/research/native-centre-capture/COSTS.md
new file mode 100644
index 0000000000..18057457b8
--- /dev/null
+++ b/research/native-centre-capture/COSTS.md
@@ -0,0 +1,82 @@
+# Literal local costs and bounds
+
+The scalar unit is the source model's real primitive tariff. A unit
+complex ADD costs eight. A complex sign costs two; a double or half
+costs two more when present. A monomial map count is not a finite price.
+Native mass is sum r H_r. Recursive cost depends on the full histogram,
+not only its mass.
+
+Define the two shared profiles:
+
+```text
+P9 = 1392 H1 + 64 H2 + 48 H3 + 16 H9;
+P8 = 1392 H1 + 64 H2 + 48 H3 + 16 H8.
+```
+
+Both have 1520 children. Their masses are 1808 and 1792.
+
+| Complete local word | Real scalars | Profile | Input views | Output views | Native side-map upper bound |
+| --- | ---: | --- | ---: | ---: | ---: |
+| Row formation, direct FULL | 11640 | P9 | 112 | 96 | 3008 |
+| Same-reader line-entry reuse | 9880 | P8 | 128 | 96 | 3040 |
+| Clean exchange, I entry | 8600 | P9 | 112 | 96 | 3008 |
+| Clean exchange, Q entry | 8600 | P8 | 128 | 96 | 3040 |
+| Clean Q inverse-adjoint or selected conjugate | 8600 | P8 | 128 | 96 | 3040 |
+| A native forward or backward | 9416 | P9 | 112 | 96 | 3008 |
+| A^T native forward or backward | 8936 | P9 | 112 | 96 | 3008 |
+| Complete D25 fixed-reader forward or dual | 14896 | P8 | 128 | 96 | 3040 |
+| Route32 raw forward or backward | 4312 | 944 H1 + 48 H3 + 64 H5 + 64 H6 | 112 | 112 | 2240 |
+| Direct Fsimple or Bcustom | 2912 | 96 H1 + 128 H8 + 96 H9 | 0 | 0 | 448 |
+
+The route32 raw word has 1120 children and mass 1792. The direct clean
+word has 320 children and mass 1984. The direct word changes the old
+native paths; it is not a cheaper scalar suffix with the old profile.
+
+The D25 row also has 448 DATA maps and 672 query maps. Its complete
+map-call bound is 448+224+3040+672=4384. The local rows above contain no
+implicit DATA charge. The generic formation before the direct-FULL
+refinement has 3040 side maps; the refinement removes the 32 identity
+maps on its sixteen H9 children. H8 side maps remain charged.
+
+The main scalar splits are:
+
+```text
+formation:        6456 retained + 1760 precode + 3424 query = 11640;
+line entry:       6456 retained + 3424 query = 9880;
+clean exchange:   6456 retained + 1760 source code + 384 exchange = 8600;
+A native:         6456 retained + 2960 late query = 9416;
+A^T native:       6952 retained + 1984 late query = 8936;
+D25 reader:       6456 carrier + 8440 routed query = 14896;
+direct clean:     768 self ADDs + 1760 source code + 384 exchange = 2912.
+```
+
+The separate common-frame A and A^T words each cost 3276 scalars. They
+are used twice in the complete fixed-reader query. Route32's pivot code
+and inverse each cost 1870; its reflection capture code and inverse each
+cost 2486. These code costs are not included in its raw native bill.
+The literal route32 entry adds 112 explicit Q^2 translation maps.
+
+| Emitted word | Maximum content row one-norm | Additional binary denominator height |
+| --- | ---: | ---: |
+| Formation | 132 | 1 |
+| Line-entry reuse | 112 | 1 |
+| Clean exchange | 22 | 1 |
+| Clean dual or selected conjugate | 12 | 2 |
+| A native forward / backward | 70 / 22 | 1 |
+| A^T native forward / backward | 30 / 62 | 1 |
+| Complete D25 forward | 202 | 2 |
+| Complete D25 dual | 40 | 2 |
+| Route32 raw, either direction | 14 | Not reported in the native review |
+| Route32 pivot code / inverse | 8 / 4 | 0 / 3 |
+| Route32 reflection code / inverse | 8 / 4 | 1 / 2 |
+| Direct Fsimple / Bcustom | 22 / 4 | 1 |
+
+These are ideal content bounds at emitted operation boundaries. They do
+not bound scalar primitive interiors, recursive child interiors, or the
+full roundoff error. For the routed reader, the complete dual prefix has
+norm 12 and its isolated late query has norm 30; the complete word reaches
+40. The forward routed query reaches 202 on the stated regular cover.
+
+All native rows preserve 416 arbitrary outside values. A scalar code on
+X alone preserves the other 528 fields. Neither statement creates a
+recursive parking schedule or gives productive progress to those values.
diff --git a/research/native-centre-capture/EXTERNAL-NOTICES.json b/research/native-centre-capture/EXTERNAL-NOTICES.json
new file mode 100644
index 0000000000..de2d746073
--- /dev/null
+++ b/research/native-centre-capture/EXTERNAL-NOTICES.json
@@ -0,0 +1,40 @@
+{
+  "files": [
+    {
+      "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb",
+      "file": "notices/PR2588-NOTICE",
+      "sha256": "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b",
+      "source": "research/gmx-t74-borrow43-handoff/NOTICE",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/NOTICE"
+    },
+    {
+      "commit": "f2927a4b8afcf0701a6b945e14f30de1d94f5176",
+      "file": "notices/PR3133-NOTICE",
+      "sha256": "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661",
+      "source": "research/coupled-carrier-cap740/vendor/PR3133-NOTICE",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/vendor/PR3133-NOTICE"
+    },
+    {
+      "commit": "f2927a4b8afcf0701a6b945e14f30de1d94f5176",
+      "file": "notices/PR3133-CREDITS.md",
+      "sha256": "1d9d8f56d8899f55878e4cb2c4e052b22506444016a51c2e678773505f5189e6",
+      "source": "research/coupled-carrier-cap740/vendor/PR3133-CREDITS.md",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/vendor/PR3133-CREDITS.md"
+    },
+    {
+      "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb",
+      "file": "notices/PR2588-NOTICE-PR2226.md",
+      "sha256": "6b6730303818f6edc2a253eb4d05471eee58f28b5815fb250c32ae376f774c8a",
+      "source": "research/gmx-t74-borrow43-handoff/new/code/borrow/NOTICE-PR2226.md",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/NOTICE-PR2226.md"
+    },
+    {
+      "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb",
+      "file": "notices/PR2226-NOTICE.md",
+      "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422",
+      "source": "research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/PR2226-NOTICE.md",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/PR2226-NOTICE.md"
+    }
+  ],
+  "scope": "Unchanged notices from verified historical GitHub file objects."
+}
diff --git a/research/native-centre-capture/HISTORICAL-BUDGETS.md b/research/native-centre-capture/HISTORICAL-BUDGETS.md
new file mode 100644
index 0000000000..f82bb18226
--- /dev/null
+++ b/research/native-centre-capture/HISTORICAL-BUDGETS.md
@@ -0,0 +1,94 @@
+# Conditional historical budget appendix
+
+These are strict inequalities for specified histograms. They do not admit
+a routed composition, a changed output, a cleanup service, or a terminal
+decoder. They do not change the complete kappa calculation.
+
+The retained selected certificate and assembly at commit
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f` give
+
+```text
+b = 67018507072324140917 / 40000000000000000000000.
+```
+
+For D=25, productive width W=224, three calls, and no idle jobs, use
+
+```text
+M(H) = sum_r H[r] * r/5600 * (25/r)^b.
+```
+
+The current publication base is different. No threshold below is a
+recalculation at the current selected rate.
+
+## Literal invoice and exact interval checks
+
+The low-displacement review recounts all 24 raw and changed words. It
+checks sixteen unchanged scalar sequences and 176 complete profile
+intervals. These include raw rank30/rank16, W48/I64 and W112 changed exits,
+mixed exits, and a separate H9 comparator. The clean review recounts all
+eight I/Q/dual local words. The coalesced review takes its frozen histogram
+as a premise; it does not recount the twelve earlier native words.
+
+The independent numerical engine uses rational arithmetic only. It reduces
+logarithms to 1<=y<2 and uses 64 terms of the atanh series, with its positive
+tail bounded above. It uses the degree-20 exponential polynomial with an
+upper tail. Outward rounding keeps valid intervals. Every reported
+maximum has an upper endpoint below one, and its successor has a lower
+endpoint above one. No floating-point value decides a sign.
+
+## Useful strict thresholds
+
+The columns are alternative allowances for all added native work. They
+cannot both be spent.
+
+| Fixed three-call profile | Extra H1 limit | Extra H2 limit |
+| --- | ---: | ---: |
+| Raw rank30 | 199 | 99 |
+| Raw rank16 | 195 | 97 |
+| Clean Q + Q + Q | 196 | 98 |
+| Clean I + Q + Q | 180 | 90 |
+| Coalesced fixed profile | 198 | 99 |
+| Coalesced with stipulated 64 H1 cleanup | 134 | 67 |
+
+The coalesced profile is exactly
+
+```text
+{1:2913, 2:711, 3:138, 4:36, 5:15, 6:33, 7:30}.
+```
+
+For the clean Q+Q+Q profile, every H1/H2 mixture passes exactly when
+n1+2n2<=196. For I+Q+Q the condition is n1+2n2<=180. The cheapest mixture
+at the next rank fails. This classifies the specified numerical mixtures;
+it does not construct the physical children.
+
+For arbitrary legal extra ranks 1 through 17, strict concavity of
+r^(1-b) makes the cheapest profile at a fixed total rank consist of as
+many rank17 children as possible and at most one remainder. The maximum
+added rank is 197 for three Q calls and 181 for I+Q+Q. The passing profiles
+are 11 H17+H10 and 10 H17+H11. Increasing the remainder by one fails.
+This at most one-rank gain is a fact of these fixed base histograms.
+
+A full 224-H1 terminal fails for both clean profiles. In the Q case the
+total mass is 5600 and every child rank is less than 25, so M>1 for b>0.
+The I case has mass 5616 and fails already at b=0. At the pinned exponent,
+a terminal with all other work fixed must save at least 28 or 44 H1 calls.
+The number 224 is a comparator, not an admitted decoder.
+
+For the earlier W48/I64 changed exits, each changed call replaces
+48(H1+H3) by 48H2. Its saving in H1 moment units is strictly between
+95.846609456084463 and 95.846609456084464. With one, two, or three changed
+calls and the hypothetical 224-H1 terminal, the extra H1/H2 limits are:
+
+| Family | Changed calls | Extra H1 | Extra H2 |
+| --- | ---: | ---: | ---: |
+| Rank30 | 1 | 71 | 35 |
+| Rank30 | 2 | 167 | 83 |
+| Rank30 | 3 | 263 | 131 |
+| Rank16 | 1 | 66 | 33 |
+| Rank16 | 2 | 162 | 81 |
+| Rank16 | 3 | 258 | 129 |
+
+These bounds give necessary cost targets for later constructions. They
+supply no stage access, owner dispatcher, helper host, terminal, or
+precision proof. In particular, the direct clean comparator's mass 1984
+profile is not assigned any of these smaller-profile allowances.
diff --git a/research/native-centre-capture/LICENSE b/research/native-centre-capture/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/native-centre-capture/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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+   4. Redistribution. You may reproduce and distribute copies of the
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+      meet the following conditions:
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+      (a) You must give any other recipients of the Work or
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+
+      (b) You must cause any modified files to carry prominent notices
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+      (c) You must retain, in the Source form of any Derivative Works
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+      (d) If the Work includes a "NOTICE" text file as part of its
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+          of the NOTICE file are for informational purposes only and
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+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
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+   7. Disclaimer of Warranty. Unless required by applicable law or
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+      Contributor provides its Contributions) on an "AS IS" BASIS,
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+      risks associated with Your exercise of permissions under this License.
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+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
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+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
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+   9. Accepting Warranty or Additional Liability. While redistributing
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+      on Your own behalf and on Your sole responsibility, not on behalf
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diff --git a/research/native-centre-capture/LOCAL-LINK-CHECK.json b/research/native-centre-capture/LOCAL-LINK-CHECK.json
new file mode 100644
index 0000000000..a8f7212699
--- /dev/null
+++ b/research/native-centre-capture/LOCAL-LINK-CHECK.json
@@ -0,0 +1,54 @@
+{
+  "checked": [
+    [
+      "README.md",
+      "PROOF.md"
+    ],
+    [
+      "README.md",
+      "COSTS.md"
+    ],
+    [
+      "README.md",
+      "CLAIM-INDEX.json"
+    ],
+    [
+      "README.md",
+      "SOURCE-MANIFEST.json"
+    ],
+    [
+      "README.md",
+      "VALIDATION.json"
+    ],
+    [
+      "README.md",
+      "adapters/ADAPTATIONS.json"
+    ],
+    [
+      "README.md",
+      "HISTORICAL-BUDGETS.md"
+    ],
+    [
+      "README.md",
+      "NOTICE.md"
+    ],
+    [
+      "README.md",
+      "OPEN-QUESTIONS.md"
+    ],
+    [
+      "NOTICE.md",
+      "frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md"
+    ],
+    [
+      "NOTICE.md",
+      "frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json"
+    ],
+    [
+      "NOTICE.md",
+      "EXTERNAL-NOTICES.json"
+    ]
+  ],
+  "scope": "New package Markdown only. Historical frozen links are preserved. GitHub publication links require the final commit.",
+  "status": "PASS_LOCAL_WRAPPER_LINK_TARGETS"
+}
diff --git a/research/native-centre-capture/NOTICE.md b/research/native-centre-capture/NOTICE.md
new file mode 100644
index 0000000000..fbbf093c50
--- /dev/null
+++ b/research/native-centre-capture/NOTICE.md
@@ -0,0 +1,88 @@
+# Source credit, license, and extraction scope
+
+This package extracts completed work from the October 2026 centre-encoding
+campaign. SOURCE-MANIFEST.json records each original path, byte hash, size,
+and decompressed hash where needed. The original proofs, scripts, freezes,
+and receipts in frozen/ are unchanged. They describe historical local
+inputs, not the current selected supplier.
+
+## Campaign contributions
+
+The controller-followthrough lane supplied the row reader, source code,
+row-involution completion, literal scalar words, and completion limits.
+The new-core-transfer lane supplied productive capture, direct FULL,
+line-entry reuse, clean exchange, clean dual, the native row involutions,
+route32 model and native words, and the direct clean pair.
+
+The bridge-access lane supplied the actual D25 views, forward involution
+reader, and complete inverse-adjoint splice. The bridge-review lane
+supplied the independent matrix, owner-route, forward-service, and late
+query checks. The new-native-recipes lane supplied separate complete
+word, physical phase, direct-clean, and complete-dual checks. The
+independent-review lane supplied the cyclic flags and separate
+row-involution and route32 model checks.
+
+The coordinating researcher supplied the route split and reflection
+formula. The budget-geometry lane supplied conditional native budgets.
+The bridge-review lane supplied the independent invoice reader, third
+rational interval engine, and strict mixed-rank consequences. Those
+numerical checks remain conditional on the stated profiles and do not
+admit their proposed caller or decoder.
+
+The new extraction adds a portable exact input closure, two explicit
+budget I/O adapters, an adopted-claim index, unified scope and cost notes,
+and fresh cold replays. The independent publication review is a separate
+agent calculation. It is not a maintainer acceptance or a formal proof of
+the full multiplication theorem.
+
+## Historical external lineage
+
+The retained [native source notice](frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md)
+and [source pins](frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json)
+identify the earlier native tools and providers:
+
+- [PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133),
+  at commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`, supplied the core
+  used by the native lane.
+- [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148),
+  at commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`, retained the
+  byte-equal provider words. The source copies are
+  [base](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz)
+  and [extra](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz).
+- [PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588),
+  at commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`, supplied the
+  exact native recipe tools used in the producer lineage. Its
+  [source notice](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/NOTICE)
+  and [PR #2226 port notice](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/NOTICE-PR2226.md)
+  retain the earlier compiler, wrapper, and warp credit.
+
+The fresh independent replay imports no producer compiler. It reads the
+frozen recipe records and uses the retained independent exact interpreters.
+The source compiler is provenance, not a runtime requirement here.
+No contributor handle is inferred from a submitter account.
+
+The exact predecessor notices and credits are retained in notices/.
+[EXTERNAL-NOTICES.json](EXTERNAL-NOTICES.json) gives their historical
+GitHub paths and hashes from the earlier verified publication closure.
+Those files include the PR #2226 notice that the PR #2588 notice requires.
+The extraction retains those bytes and does not substitute moving heads.
+
+The historical budget snapshot comes from
+[the selected certificate](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/certificates/selected-result.json)
+and [its assembly](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1094-audit/ASSEMBLY.json)
+at `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The publication base is
+`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. Its
+[selected record](https://github.com/CrocSwap/integer-mult-bounds/blob/b58ad9ef4d4e861b0eaa5dba41742bdc072dca51/certificates/selected-result.json)
+names [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470).
+The contracts are different. No current-frontier replay or transfer is
+claimed.
+
+## License and AI assistance
+
+The package uses the repository's Apache-2.0 license. The exact license
+text is in LICENSE. The retained notices keep their original wording.
+
+OpenAI Codex gave substantial assistance with the construction, proofs,
+code, exact checks, independent agent reviews, and package extraction.
+The source lane names identify contributions within this campaign; they
+are not verified individual contributor identities.
diff --git a/research/native-centre-capture/OPEN-QUESTIONS.md b/research/native-centre-capture/OPEN-QUESTIONS.md
new file mode 100644
index 0000000000..4213c50764
--- /dev/null
+++ b/research/native-centre-capture/OPEN-QUESTIONS.md
@@ -0,0 +1,26 @@
+# Open construction obligations
+
+The local data and reader words are complete within their stated types.
+The following steps remain open for a complete multiplication supplier:
+
+- Supply the recursive child helpers at their exact event times and frames.
+  Unchanged arbitrary top-level fields do not prove a recursive host.
+- Bind a closed routed caller with the required entrance, intermediate,
+  and exit types. A selected-field role partition does not price a bank
+  permutation or identify readers from different stages.
+- Price each finite owner and monomial map implementation. The map counts
+  in this package are upper bounds on calls, not finite arithmetic costs.
+- Give a terminal decoder and any required odd-denominator representation.
+  The route32 rational inverse contains factors of one third; its dyadic
+  capture codes do not remove those factors from the inverse response.
+- Prove precision through scalar primitive interiors, recursive children,
+  and the complete caller. The recorded row norms apply only at emitted
+  ideal-content boundaries.
+- Recalculate a complete supplier at the intended selected rate after the
+  construction obligations are met. The historical budget tests do not
+  perform this calculation.
+
+The route32 common-W lift and whole-W reflection decoder remain outside
+the adopted scope. This package makes no claim that a proposed decoder is
+necessary, that a search found a global optimum, or that native mass alone
+determines recursive cost.
diff --git a/research/native-centre-capture/PACKAGE-MANIFEST.json b/research/native-centre-capture/PACKAGE-MANIFEST.json
new file mode 100644
index 0000000000..39883063c1
--- /dev/null
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+    {
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+    },
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+    },
+    {
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+    },
+    {
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+    },
+    {
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+    }
+  ],
+  "schema": "native-centre-capture-package-manifest-v1"
+}
diff --git a/research/native-centre-capture/PROOF.md b/research/native-centre-capture/PROOF.md
new file mode 100644
index 0000000000..b055e4b7aa
--- /dev/null
+++ b/research/native-centre-capture/PROOF.md
@@ -0,0 +1,246 @@
+# Adopted constructions and exact scope
+
+This note joins the reviewed local results. It does not alter their frozen
+proofs. CLAIM-INDEX.json points to each original proof and independent
+review. Every field below can have an arbitrary input value.
+
+## 1. The actual row reader
+
+The fixed 112-port response has E=I+UV, with 16 centre coordinates. Its
+selected ports, in order, are
+
+```text
+0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23.
+```
+
+The actual signed pivot Gram matrix is V_P V_P^T=diag(2I8,I8).
+Thus V_P is a unit over Z[1/2]. Put L=V_P^-1 V=[I,B] in P,R order.
+The code C has selected rows L and ordinary rows I:
+
+```text
+C = [[I,B],[0,I]],       C^-1 = [[I,-B],[0,I]].
+```
+
+The off-diagonal correction squares to zero. The literal scalar code and
+its inverse each cost 1760 real primitives and use existing fields only.
+For the actual response, LE=Hc L with Hc=diag(-5I8,-7I8). This equality
+does not require division by five or seven in any word below.
+
+For row formation, start with X=Qx,Y=y. Precode Y by C at I. Remove the
+250 selected-target events from the old native word; these contain 128 H1
+calls. The retained core never reads a removed selected Y field. Complete
+the entire core, advance the sixteen selected Y fields from I to FULL,
+and then execute the literal late query. The endpoint is
+
+```text
+X'   = F9 x,
+Y'_R = F9 q_R (y+Ex)_R,
+Y'_P = F9 [C(y+Ex)]_P = F9 (Ly+Hc Lx).
+```
+
+The arbitrary Ly baseline remains. The direct-FULL refinement uses the
+exact F9 kernel with identity side maps for the sixteen H9 children.
+It changes the side-map count, not the scalar bill or native profile.
+
+The line-entry variant starts with Y_P=Q_P z for independent z. It omits
+the precode and uses sixteen H8 children to reach FULL. Its selected
+output is F9(z+Hc Lx), with the same ordinary output. If z=Ly, the same
+reader is retained. This is not an implementation of a different past
+reader L_s E_t. That routed query has a separate word and cost.
+
+## 2. Clean exchange and its exact dual
+
+After the retained core and selected FULL advance, apply C to X. For each
+selected pair, execute Y+=X, X-=Y, Y+=X. This maps (a,b) to (-b,a).
+For I-entry let b=y_P; for Q-entry let b=z. The complete endpoint is
+
+```text
+X'_P = -F9 b,               X'_R = F9 x_R,
+Y'_P =  F9 Lx,              Y'_R = F9 q_R (y+Ex)_R.
+```
+
+The old baseline moves into X_P. No field is erased. The code and three
+ADDs give an algebraic inverse on all 224 data fields. A formula for that
+inverse alone would not price a native inverse service.
+
+For the Q-entry content, put J=-B^T. The actual symmetric response has
+E_PP=0 and E_R=[J,I+JB]. In P,R bank order, write an input as (a,u,z,v).
+Then the clean content map and its inverse transpose are
+
+```text
+M(a,u,z,v)     = (-z,u,a+Bu,v+u+J(a+Bu)),
+M^-T(a,u,z,v)  = (-z,u+Ja-v,a+Bv,v).
+```
+
+The selected-conjugate word has content
+
+```text
+S M^-T S(a,u,z,v) = (z+Bv,u+Jz-v,-a,v).
+```
+
+Here S exchanges X_P and Y_P. This uses J=-B^T for the actual source.
+A routed substitution needs its own adjoint relation.
+
+If a physical word is W=Aout M Ain^-1 and Ain,Aout are unitary, then
+W^-*=Aout M^-T Ain^-1. In chronological order, replace each real ADD by
+its negative transpose and each SCALE by its reciprocal. Keep each
+unitary native or monomial operator, including its phase, in the same
+chronological position. This gives the physical inverse-adjoint. It does
+not reverse chronology. For the selected conjugate, both selected input
+types are Q and both output types are FULL. Rename every selected field
+in each instruction; adjacent S factors cancel. No runtime swap is used.
+This fact does not permit a free bank permutation in an arbitrary caller.
+
+## 3. Row involutions and native words
+
+Over a ring in which two is a unit, let V_P be invertible. Keep U_R and set
+
+```text
+U'_P = V_P^-1(-2I-V_R U_R),       A = I+U'V.
+```
+
+Then VU'=-2I and A^2=I. The ordinary rows of E are unchanged. Over a
+field of characteristic different from two, rank(A-I)=16 and det(A)=1.
+The actual source also has rank(A-E)=16 and trace(A)=80. The first rank
+identity is the general statement; the second is source-specific.
+The frozen COMPLETION-LIMITS.md and independent review retain this
+clarification.
+
+The independent signed-block construction uses eight blocks of size six
+and eight of size eight. In each block d_p=1 and
+A_k=I+((k-2)e_p-d)d^T. Its contraction is -2. The actual physical pair
+metric is checked when the transpose is formed; H is not assumed to be
+an orthogonal matrix of unit scale.
+
+The 3276-scalar common-frame A and A^T words use no new field or odd
+division. The native words use explicit changed transfer coefficients,
+complete their retained cores, and execute the selected FULL queries.
+For M=A or A^T, their exact content maps are
+
+```text
+forward:   (x,y) -> (x,y+Mx),
+backward:  (x,y) -> (x-M^T y,y).
+```
+
+The physical input is X=Qx,Y=y. The output types are FULL on X and Y_P,
+and F9 q_R on Y_R. The complete emitted lists, both providers, both M,
+and both directions are checked on all 640 inputs. The physical boundary
+conversions remain part of any composition; A^2=I alone does not close a
+reciprocal caller.
+
+The independent model review also proves that sixteen changed rows are
+necessary for a dyadic-unit row replacement of this fixed E. Its large
+component has left-nullity eight modulo five and its small component has
+left-nullity eight modulo seven. If fewer than eight rows change in one
+component, a nonzero old left-null vector can vanish on all changed rows
+and still annihilate the new matrix. A dyadic unit must stay invertible
+modulo those odd primes. The actual A attains eight changed rows in each
+component. This is a common-scalar row-replacement bound, not a native or
+computation lower bound.
+
+## 4. Complete D25 fixed-reader pair
+
+Let A_t be the actual current response with its owner routes, and L_s the
+retained past reader. At the completed FULL cut, apply A_t to X, add L_s X
+to selected Y, and apply A_t again to X. Since the routed A_t is itself
+an involution, the endpoint is (x,y)->(x,y+L_s A_t x). The old target
+baseline is retained and X is restored. No reader commutes through A_t.
+
+The literal query costs 8440 scalars and 672 monomial maps: two
+3276-scalar/224-map A applications, one 1760-scalar/224-map complement
+reader, and sixteen same-port copies at cost 128. It uses no child or
+extra field. Omitting the second A or substituting the current reader
+fails for each checked pair.
+
+Put G_R=diag(I_P,q_R). Let F_l act on the first 9+8l axes. Set
+(D_st)_P=L_s A_t and (D_st)_R=(A_t)_R. For (s,t)=(0,1),(0,2),(1,2),
+both providers have complete typed services
+
+```text
+forward:
+(F_(t-1)x,F_(t-1)G_R w) -> (F_t x,F_t G_R(w+D_st x)),
+
+dual:
+(F_(t-1)x,F_(t-1)G_R w) -> (F_t(x-D_st* w),F_t G_R w).
+```
+
+The input level is t-1, including pair (0,2). The star includes transpose
+and inverse owner route. The replay keeps the complete native prefix,
+all DATA entry/exit views, the full cover barrier, and the late query.
+It checks 896 DATA phase equations and the ordered D25 owner paths.
+There are 3824 selected field/path terms per pair. Both inverse products
+of the complete dual with the forward adjoint are identity on all 640
+fields. This is a complete local backward service with stated boundary
+types; it does not supply a recursive host or a closed outer caller.
+
+## 5. Route32 raw response and scalar codes
+
+Split the old signed blocks by the least valid shared-root label. The
+actual classes have 64,32,16 ports, with labels 30,45,75. The split gives
+eight large four-mode blocks, eight large two-mode blocks, and sixteen
+small four-mode blocks. With the actual pair code H, use
+
+```text
+E32 = H^-1 direct_sum(I-dd^T) H.
+```
+
+The response has rank(E32-I)=32, zero physical diagonal, and determinant
+3^24. Its inverse is rational with no odd denominator except three. It
+is not a dyadic inverse. The old selected-eight principal block is zero;
+the reviewed raw packet instead has empty selection.
+
+One pivot code sends d to k e_p and has pivot row d^T. It conjugates each
+I-dd^T to I-k e_p e_p^T. The complete code costs 1870 scalars in each
+direction, including H. A second code uses S=I-ss^T/2 on each four-mode
+block, where s=d-2d_p e_p. Since s^T s=4 and s^T d=2, S is an involution
+and S d=2d_p e_p. Its complete price is 2486 in each direction. Both use
+existing fields and dyadic units only. Their common diagonal response is
+-3 on 24 pivots, -1 on eight pivots, and +1 on 80 complements.
+
+All scalar transfers preserve the route class. Thus the codes commute
+with diag(A_r) when each class has one exact spatial operator. The actual
+unshifted D11 advances have identical ordered circuits within each class.
+This does not move Q through C or admit a field-dependent view. The
+literal entry C Q^2 includes 112 maps before the scalar code. The formal
+q C q code diagonalizes Q E32 q, not E32 alone, and is not a raw decoder.
+
+The rank32 minimum is restricted to the same H, route-homogeneous
+partitions within each large vertex, small monochromatic cliques, and no
+cross-sector mixing. Each large vertex needs two blocks. The small sector
+needs sixteen cliques because its largest monochromatic clique has four
+ports. The total is at least 32, and this construction attains it.
+
+The raw native forward/backward words have content (x,y+E32 x) and
+(x-E32^T y,y), with input (Qx,y) and output types (F9,F9 q). Their 297
+new spatial kernels are checked on every 512-column input basis. Exact
+ordered-record equality retains 752 accepted kernels. The whole-W lift
+and reflection decoder are not part of the adopted result.
+
+## 6. Direct clean comparator
+
+A separate direct word applies F9 q_p to all X and selected Y, F9 to
+ordinary Y, adds each ordinary X to its Y partner, and applies q_p to
+ordinary Y. It then applies C to FULL X and the same selected rotations.
+This gives
+
+```text
+Fsimple(a,u,z,v) = (-z,u,a+Bu,v+u).
+```
+
+The selected-conjugate inverse-adjoint gives
+
+```text
+Bcustom(a,u,z,v) = (z,u-B^T z-v,-a,v).
+```
+
+Both have input (Q(a,u),Q_P z,v) and output types (F9,F9,F9 q_R).
+All 209 distinct kernels are checked on all 512 spatial columns, with
+exact Gaussian-integer coefficients and global phase. These are complete
+one-alphabet operator identities. Their full tensor powers give the same
+field transitions at every width; no one-bit polynomial is substituted
+for a tensor-power line operator.
+
+Each complete word costs 2912 scalars, with 320 children and mass 1984.
+This is a different profile and interface from the old 8600-scalar clean
+word and from the separate 4632-scalar phase-coded caller word. It is a
+local comparator, not a better complete recursive supplier.
diff --git a/research/native-centre-capture/README.md b/research/native-centre-capture/README.md
new file mode 100644
index 0000000000..3ec9010d20
--- /dev/null
+++ b/research/native-centre-capture/README.md
@@ -0,0 +1,117 @@
+# Native centre capture and complete fixed-reader services
+
+This package gives exact local native constructions that place sixteen
+centre records in existing data fields. It includes productive row capture,
+a clean selected exchange and its dual, native row involutions, a complete
+D25 fixed-reader forward/dual pair, and a route-preserving rank32 response
+with two scalar capture codes. A direct clean pair gives a separate
+2,912-scalar comparator with a larger native profile.
+
+The result is a construction and a set of scoped exact checks. It does not
+improve the complete kappa calculation. A recursive helper host, a closed
+caller, a finite price for the physical maps, terminal decoding, and the
+complete precision argument remain open.
+
+Start with [PROOF.md](PROOF.md), [COSTS.md](COSTS.md), and the
+[claim and source index](CLAIM-INDEX.json). Each claim keeps its original
+producer proof, independent review, frozen input, and exact checker.
+[SOURCE-MANIFEST.json](SOURCE-MANIFEST.json) binds the retained bytes.
+[VALIDATION.json](VALIDATION.json) records the new cold checks.
+
+## The common contract
+
+There are 112 X fields, 112 Y fields, and 416 outside fields. All 640 input
+fields are arbitrary. The local words preserve the 416 outside values.
+They neither require a zero field nor give productive progress to those
+outside fields. The retained recursive child contract remains a premise.
+
+Let P be the fixed sixteen ports. Let R be the other 96 ports. Let Q be
+the diagonal positive line operator, q=Q^-1, and F9 the full nine-axis
+operator. The row reader L has L_P=I and the code C has selected rows L
+and ordinary rows I. Physical types are part of each result. A selected
+FULL output, a selected Q input, and an ordinary hole output are different
+types; the counts do not pay for a caller conversion between them.
+
+The clean exchange puts Lx in selected Y and the arbitrary old selected
+baseline in selected X with a minus sign. Thus the centres are clean of
+that baseline, and the baseline remains in the complete state.
+
+## Replay
+
+Use Python 3.11 or later and its standard library. The fresh runs used
+Python 3.14.7. No network, Git object,
+producer compiler, or third-party Python package is needed. Each runner
+uses one child process at a time and requires at least 3 GiB of free disk.
+Use absent output directories:
+
+```sh
+python3 -I -B replay.py --out /tmp/native-centre-capture-normal
+python3 -I -B replay_budgets.py --out /tmp/native-centre-capture-budgets-normal
+```
+
+Expected final lines:
+
+```text
+PASS_NATIVE_CENTRE_CAPTURE_REPLAY
+PASS_NATIVE_CAPTURE_HISTORICAL_BUDGETS
+```
+
+Add `--optimized` to either command to run its child checks with Python
+`-O`. The eleven native/model review scripts are byte-exact originals.
+Their new receipts must equal the frozen receipts. The runner also checks
+the original input receipts where these exist. All checks run from a copied
+source tree and write only into the chosen output directory.
+
+The two budget I/O adapters replace historical `git show` reads with exact
+retained files. One also receives an output path. Their original files,
+full diffs, hashes, and unchanged helper-function counts are in
+[adapters/ADAPTATIONS.json](adapters/ADAPTATIONS.json). Their complete
+mathematical receipts must equal the originals after replacing only the
+adapter's self-hash. The third budget checker is unchanged.
+
+## What the fresh checks establish
+
+The native/model runner executes eleven prior independent reviews. It
+rechecks full arbitrary-input maps, physical types, actual owner paths,
+inverse identities, scalar tariffs, native profiles, and negative controls.
+It performs fresh complete spatial checks for the new formation and
+line-entry kernels, all 297 new route32 kernels, and all 209 direct-clean
+kernels. Global phases remain in every operator comparison.
+
+The retained native recipes also use earlier accepted phase tables. The
+checks bind their exact ordered frames and recipe records. They do not
+rerun every earlier spatial phase census or regenerate the historical
+producer compilers. Those earlier review freezes remain explicit premises.
+
+The budget runner recounts 24 earlier raw/changed words and eight clean
+words. It reproduces 176 exact low-displacement profile intervals, the
+clean-exchange strict thresholds and mixed-rank bounds, and four coalesced
+thresholds. These calculations use a historical exponent and conditional
+profiles. They do not admit the stage access or terminal decoder assumed
+by a budget comparison. See [HISTORICAL-BUDGETS.md](HISTORICAL-BUDGETS.md).
+
+## Source and scope boundaries
+
+The publication base is `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`.
+Its selected construction is PR #4470. This package uses earlier campaign
+inputs and proves no transfer to that selected construction. The budget
+appendix uses the selected certificate at
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`.
+
+Only the listed local raw, code, and reader claims are adopted. The route32
+common-W lift and whole-W reflection decoder are producer proposals and
+are excluded. The reviewed four-mode reflection capture code is a
+separate scalar construction and is included. The rank32 minimum concerns
+only the stated route-homogeneous clique partition family. No global
+response minimum follows.
+
+The frozen formation DERIVATION.md contains preliminary prices 2048 and
+3696. Use the final review, checker, and receipt: the actual chosen pivot
+code costs 1760 and the formation late query costs 3424. The original text
+is retained unchanged. The row-completion review also clarifies that the
+general rank statement is rank(A-I)=16; rank(A-E)=16 is an additional fact
+of this actual source.
+
+[NOTICE.md](NOTICE.md) gives source credit, license details, and AI
+assistance. [OPEN-QUESTIONS.md](OPEN-QUESTIONS.md) lists the remaining
+construction obligations.
diff --git a/research/native-centre-capture/SOURCE-MANIFEST.json b/research/native-centre-capture/SOURCE-MANIFEST.json
new file mode 100644
index 0000000000..aea67566b1
--- /dev/null
+++ b/research/native-centre-capture/SOURCE-MANIFEST.json
@@ -0,0 +1,3787 @@
+{
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+        "payload source pin: lanes/bridge-access-20261017/row-capture-access-20261020/run-optimized/ACCESS-PROGRAM.json",
+        "payload source pin: lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/CHECKS.json",
+        "payload source pin: lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/ACCESS-PROGRAM.json",
+        "payload source pin: lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/DISPATCHER.json",
+        "payload source pin: lanes/bridge-access-20261017/row-capture-access-20261020/reuse-optimized/REUSE-PROGRAM.json",
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+        "payload source pin: lanes/bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-PROGRAM.json",
+        "payload source pin: lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/CHECKS.json",
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+      "sha256": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784",
+      "source": "work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/REVIEW-CHECKS.json"
+    },
+    {
+      "bytes": 3729,
+      "path": "frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/optimized/INPUTS.json",
+      "reasons": [
+        "exact freeze closure: lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/FREEZE.json"
+      ],
+      "sha256": "3afffef723776daea5f8de1f9e4a0c45de8d8294517f17173efc63350caa46fd",
+      "source": "work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/optimized/INPUTS.json"
+    },
+    {
+      "bytes": 39775,
+      "path": "frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/optimized/REVIEW-CHECKS.json",
+      "reasons": [
+        "exact freeze closure: lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/FREEZE.json"
+      ],
+      "sha256": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784",
+      "source": "work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/optimized/REVIEW-CHECKS.json"
+    },
+    {
+      "bytes": 6824,
+      "path": "frozen/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py",
+      "reasons": [
+        "consumed review input: lanes/new-native-recipes-20261017/low-displacement-review-20261020/optimized/INPUTS.json",
+        "consumed review input: lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json"
+      ],
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+      "source": "work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py"
+    },
+    {
+      "bytes": 127346,
+      "decompressed_sha256": "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025",
+      "path": "frozen/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz",
+      "reasons": [
+        "payload source pin: lanes/bridge-review-20261017/rank9-completion-review-20261020/CHECKS.json",
+        "payload source pin: lanes/bridge-access-20261017/rank9-completion-20261020/RANK9-PROGRAMS.json.gz",
+        "payload source pin: lanes/bridge-access-20261017/rank9-completion-20261020/CHECKS.json"
+      ],
+      "sha256": "61fd6d0283de4af6ad53c013cd8220d8ea55d971c6980ce5259053ce31d366bd",
+      "source": "work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz"
+    },
+    {
+      "bytes": 10725,
+      "path": "historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/certificates/selected-result.json",
+      "reasons": [
+        "exact historical selected exponent"
+      ],
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+      "source": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/completed-prefix-outer/sources/upstream/certificates/selected-result.json"
+    },
+    {
+      "bytes": 85147,
+      "path": "historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1094-audit/ASSEMBLY.json",
+      "reasons": [
+        "exact historical selected exponent"
+      ],
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+      "source": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/completed-prefix-outer/sources/upstream/research/community-frontier1094-audit/ASSEMBLY.json"
+    },
+    {
+      "bytes": 1279,
+      "path": "notices/PR2226-NOTICE.md",
+      "reasons": [
+        "historical license and source credit"
+      ],
+      "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422",
+      "source": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/reciprocal-native-responses/notices/PR2226-NOTICE.md"
+    },
+    {
+      "bytes": 1439,
+      "path": "notices/PR2588-NOTICE",
+      "reasons": [
+        "historical license and source credit"
+      ],
+      "sha256": "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b",
+      "source": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/reciprocal-native-responses/notices/PR2588-NOTICE"
+    },
+    {
+      "bytes": 1754,
+      "path": "notices/PR2588-NOTICE-PR2226.md",
+      "reasons": [
+        "historical license and source credit"
+      ],
+      "sha256": "6b6730303818f6edc2a253eb4d05471eee58f28b5815fb250c32ae376f774c8a",
+      "source": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/reciprocal-native-responses/notices/PR2588-NOTICE-PR2226.md"
+    },
+    {
+      "bytes": 5030,
+      "path": "notices/PR3133-CREDITS.md",
+      "reasons": [
+        "historical license and source credit"
+      ],
+      "sha256": "1d9d8f56d8899f55878e4cb2c4e052b22506444016a51c2e678773505f5189e6",
+      "source": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/reciprocal-native-responses/notices/PR3133-CREDITS.md"
+    },
+    {
+      "bytes": 3234,
+      "path": "notices/PR3133-NOTICE",
+      "reasons": [
+        "historical license and source credit"
+      ],
+      "sha256": "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661",
+      "source": "work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/reciprocal-native-responses/notices/PR3133-NOTICE"
+    }
+  ],
+  "schema": "native-centre-capture-source-manifest-v1"
+}
diff --git a/research/native-centre-capture/VALIDATION.json b/research/native-centre-capture/VALIDATION.json
new file mode 100644
index 0000000000..34d458be6c
--- /dev/null
+++ b/research/native-centre-capture/VALIDATION.json
@@ -0,0 +1,34 @@
+{
+  "budgets": {
+    "comparison": "All fields equal the historical receipts except the two declared adapter checker_sha256 fields.",
+    "mode": "normal",
+    "receipt": "validation/normal/BUDGET-REPLAY.json",
+    "receipt_sha256": "ead9c8aa018d3fedc47ce6488bec1f6514e5098516b301c677478bc4179d1239",
+    "runner_sha256": "eb04df858d4182ed3a607bc79f5c72cbf032bcc4de39560847aa748261bad128"
+  },
+  "fresh_independent_review": "A separate publication reviewer ran a relocated optimized main replay and all three budget stages with PATH=/nonexistent. Its report is published separately.",
+  "historical_runs": "The retained independent freezes record normal and optimized runs.",
+  "main": {
+    "comparison": "All eleven receipts and all emitted input manifests equal the frozen bytes.",
+    "mode": "normal",
+    "receipt": "validation/normal/NATIVE-REPLAY.json",
+    "receipt_sha256": "0625b367451f7569f1303e1b8fb80b6d141e36df8e0c4295f115ecfba3158bb2",
+    "runner_sha256": "086c1542083d8c5d2120b38df97139bde26fc7f2a0f26129e42e303106df8c97"
+  },
+  "not_adopted": [
+    "route32 common-W lift and whole-W reflection decoder"
+  ],
+  "not_run": [
+    "complete historical producer/compiler regeneration",
+    "all inherited spatial phase censuses",
+    "current selected-supplier replay",
+    "complete host or caller admission",
+    "complete precision and kappa calculation"
+  ],
+  "python": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
+  "repair_note": "The first extraction lacked one inherited reader-service input. The exact frozen dependency was added. The final full normal replay passed; no source checker or mathematical input changed.",
+  "schema": "native-centre-capture-validation-v1",
+  "source_files": 345,
+  "source_manifest_sha256": "f5ce04e8e029fcbe8eadfaa1b20ef823586732777815544fe25aaaaee32827f8",
+  "status": "PASS_ALL_ELEVEN_NATIVE_AND_THREE_BUDGET_STAGES"
+}
diff --git a/research/native-centre-capture/adapters/ADAPTATIONS.json b/research/native-centre-capture/adapters/ADAPTATIONS.json
new file mode 100644
index 0000000000..b25b180558
--- /dev/null
+++ b/research/native-centre-capture/adapters/ADAPTATIONS.json
@@ -0,0 +1,23 @@
+{
+  "files": [
+    {
+      "adapter": "adapters/low-displacement-budget-review-20261020.py",
+      "adapter_sha256": "07a55ce0b090630f4efcd735810cd5de4a7dbdd02a3509ee60165eaeffe3dc37",
+      "diff": "adapters/low-displacement-budget-review-20261020.diff",
+      "original": "frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/check_review.py",
+      "original_sha256": "1c0d4bd42ec556b0a2b866feb65d47ba864d2874963d2b43fd3ef276180de091",
+      "scope": "Only historical input reads and output destination change. Every arithmetic operation and check is retained.",
+      "unchanged_non_main_function_count": 18
+    },
+    {
+      "adapter": "adapters/clean-exchange-budget-review-20261020.py",
+      "adapter_sha256": "1d55f32fa742bc79a395ae7b7b0d3d727ec4f1ca751189cc6b80130677c49c82",
+      "diff": "adapters/clean-exchange-budget-review-20261020.diff",
+      "original": "frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/check_review.py",
+      "original_sha256": "1908fe146d5dd006e84bf3c067509ba1b51e7d95af815f0fa84247939bc39264",
+      "scope": "Only historical input reads and output destination change. Every arithmetic operation and check is retained.",
+      "unchanged_non_main_function_count": 8
+    }
+  ],
+  "schema": "native-capture-budget-io-adaptations-v1"
+}
diff --git a/research/native-centre-capture/adapters/clean-exchange-budget-review-20261020.diff b/research/native-centre-capture/adapters/clean-exchange-budget-review-20261020.diff
new file mode 100644
index 0000000000..3b9eb82002
--- /dev/null
+++ b/research/native-centre-capture/adapters/clean-exchange-budget-review-20261020.diff
@@ -0,0 +1,26 @@
+--- original/check_review.py
++++ portable/check_review.py
+@@ -8,7 +8,6 @@
+ import importlib.util
+ import json
+ from pathlib import Path
+-import subprocess
+ 
+ 
+ HERE = Path(__file__).resolve().parent
+@@ -156,13 +155,11 @@
+     need(Q(receipt["historical_selected_b"]) == B == math.B and 0 < B < 1,
+          "Exact positive historical exponent")
+     need(receipt["engine_commit"] == COMMIT, "Historical certificate commit")
+-    selected_raw = subprocess.check_output(
+-        ["git", "-C", str(REPO), "show", COMMIT + ":certificates/selected-result.json"])
++    selected_raw = (CAMPAIGN.parent / "historical" / COMMIT / "certificates/selected-result.json").read_bytes()
+     need(digest(selected_raw) == receipt["selected_result_sha256"] == math.PINS["selected"],
+          "Selected certificate source")
+     selected = json.loads(selected_raw)
+-    assembly_raw = subprocess.check_output(
+-        ["git", "-C", str(REPO), "show", COMMIT + ":" + selected["certificate"]])
++    assembly_raw = (CAMPAIGN.parent / "historical" / COMMIT / selected["certificate"]).read_bytes()
+     need(digest(assembly_raw) == selected["certificate_sha256"]
+          == receipt["assembly_sha256"] == math.PINS["assembly"], "Selected assembly source")
+     need(Q(json.loads(assembly_raw)["complex_lower"]) == B, "Selected exponent from assembly")
diff --git a/research/native-centre-capture/adapters/clean-exchange-budget-review-20261020.py b/research/native-centre-capture/adapters/clean-exchange-budget-review-20261020.py
new file mode 100644
index 0000000000..5d23fdcf2c
--- /dev/null
+++ b/research/native-centre-capture/adapters/clean-exchange-budget-review-20261020.py
@@ -0,0 +1,255 @@
+"""Check the clean words and bound their conditional native budgets."""
+
+import argparse
+from collections import Counter
+from fractions import Fraction as Q
+import gzip
+from hashlib import sha256
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+CAMPAIGN = HERE.parents[2]
+REPO = CAMPAIGN.parents[1]
+PRODUCER = CAMPAIGN / "lanes/budget-geometry-20261017/clean-exchange-budget-20261020"
+ENGINE = HERE.parent / "low-displacement-budget-review-20261020"
+ENGINE_PIN = "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87"
+FREEZE_PIN = "c2ee7b116d5b177c06b94fffb167354c3e6b49d759f2df16a4599eefded121d5"
+RECEIPT_PIN = "30a59c5cda0ff3c6f9e6ad7f9f38ec98fbfe71d34c58ddf768964cda304ba30d"
+COMMIT = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f"
+LOCAL = "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/"
+B = Q(67018507072324140917, 40000000000000000000000)
+
+
+def need(test, reason):
+    if not test:
+        raise ValueError(reason)
+
+
+def digest(raw):
+    return sha256(raw).hexdigest()
+
+
+def read(path, pin, compressed=False):
+    raw = path.read_bytes()
+    if compressed:
+        raw = gzip.decompress(raw)
+    need(digest(raw) == pin, "Source pin: " + str(path))
+    return json.loads(raw)
+
+
+def freeze(path, pin):
+    result = read(path, pin)
+    for name, expected in result["files"].items():
+        need(digest((path.parent / name).read_bytes()) == expected, "Frozen file: " + name)
+    return result
+
+
+freeze(ENGINE / "FREEZE.json", ENGINE_PIN)
+spec = importlib.util.spec_from_file_location("third_exact_budget_engine", ENGINE / "check_review.py")
+math = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(math)
+
+
+def encode(interval):
+    return [str(value) for value in interval]
+
+
+def enclosure(interval, outer, label):
+    a, b = map(Q, outer)
+    need(a <= interval[0] <= interval[1] <= b, "Independent interval: " + label)
+
+
+def census(word, initial):
+    profile = Counter()
+    field_ranks = Counter()
+    tariffs = Counter()
+    recipe_identity = {
+        "matrix_rows": [1 << i for i in range(9)],
+        "linear_Z4": [0] * 9,
+        "quadratic_rows": [0] * 9,
+        "offset": 0,
+        "phase": 0,
+    }
+    direct = 0
+    for event in word["events"]:
+        if event[0] == "native":
+            _, field, _, _, rank, key = event
+            need(0 <= field < 224 and 0 < rank <= 17 and 2 * rank * rank < 25 * 25,
+                 "Native data role and size")
+            recipe = word["native_recipes"][key]
+            need(recipe["rank"] == rank and recipe["left"] is not None
+                 and recipe["right"] is not None, "Complete native recipe")
+            profile[rank] += 1
+            field_ranks[field] += rank
+            if initial and rank == 9:
+                need(recipe["left"] == recipe_identity == recipe["right"], "Direct H9 has identity sides")
+                direct += 1
+        else:
+            need(event[0] == "scalar" and len(event[1]) == 4, "Every event is counted")
+            op, target, source, value = event[1]
+            value = Q(value)
+            need(0 <= target < 224 and op in ("add", "scale"), "Scalar data role")
+            if op == "add":
+                need(0 <= source < 224 and abs(value) == 1, "Unit complex data ADD")
+                price = 8
+            else:
+                need(source is None and value in (-1, 2, Q(1, 2), -2, Q(-1, 2)),
+                     "Power-of-two SCALE")
+                price = 2 * ((abs(value) != 1) + (value < 0))
+            tariffs[price] += 1
+    expected = Counter({1: 1392, 2: 64, 3: 48, 9 if initial else 8: 16})
+    need(profile == expected, "Native histogram")
+    need(set(field_ranks) == set(range(224)), "Every productive field is counted")
+    need(Counter(field_ranks.values()) == (Counter({8: 208, 9: 16}) if initial else Counter({8: 224})),
+         "Per-field rank sum")
+    need(tariffs == Counter({8: 1032, 2: 96, 4: 38}), "Complete scalar tariff census")
+    need(len(word["input_views"]) == (112 if initial else 128)
+         and len(word["output_views"]) == 96 and direct == (16 if initial else 0),
+         "All external and direct views are counted")
+    side_maps = 2 * sum(profile.values()) - 2 * direct
+    return {
+        "profile": dict(sorted(profile.items())),
+        "children": sum(profile.values()),
+        "native_mass": sum(rank * n for rank, n in profile.items()),
+        "scalar_primitives": sum(price * n for price, n in tariffs.items()),
+        "scalar_tariff_census": dict(sorted(tariffs.items())),
+        "input_maps": len(word["input_views"]),
+        "output_maps": len(word["output_views"]),
+        "native_side_map_bound": side_maps,
+        "total_map_bound": len(word["input_views"]) + len(word["output_views"]) + side_maps,
+        "field_rank_census": dict(sorted(Counter(field_ranks.values()).items())),
+    }
+
+
+def check_threshold(profile, row):
+    expected = Counter({int(r): n for r, n in row["profile"].items()})
+    need(profile == expected, "Complete histogram binding")
+    need(sum(r * n for r, n in profile.items()) == row["mass"], "Complete native mass")
+    value = math.moment(profile)
+    enclosure(value, row["moment"], "base")
+    need(value[1] < 1, "Positive conditional allowance")
+    result = {"profile": dict(sorted(profile.items())), "moment": encode(value), "limits": {}}
+    for rank in (1, 2):
+        old = row["limits"][str(rank)]
+        n = old["children"]
+        yes = math.moment(profile + Counter({rank: n}))
+        no = math.moment(profile + Counter({rank: n + 1}))
+        enclosure(yes, old["accepted"], "accepted H" + str(rank))
+        enclosure(no, old["next"], "next H" + str(rank))
+        need(yes[1] < 1 < no[0] and old["rank_mass"] == rank * n, "Strict threshold")
+        result["limits"][str(rank)] = {"children": n, "accepted": encode(yes), "next": encode(no)}
+    return result
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "normal")
+    args = parser.parse_args()
+    freeze(PRODUCER / "FREEZE.json", FREEZE_PIN)
+    receipt = read(PRODUCER / "BUDGET.json", RECEIPT_PIN)
+    need(receipt["dimension"] == 25 and receipt["productive_width"] == 224
+         and receipt["calls"] == 3 and receipt["idle_profile"] == {}, "Exact conditional model")
+    need(Q(receipt["historical_selected_b"]) == B == math.B and 0 < B < 1,
+         "Exact positive historical exponent")
+    need(receipt["engine_commit"] == COMMIT, "Historical certificate commit")
+    selected_raw = (CAMPAIGN.parent / "historical" / COMMIT / "certificates/selected-result.json").read_bytes()
+    need(digest(selected_raw) == receipt["selected_result_sha256"] == math.PINS["selected"],
+         "Selected certificate source")
+    selected = json.loads(selected_raw)
+    assembly_raw = (CAMPAIGN.parent / "historical" / COMMIT / selected["certificate"]).read_bytes()
+    need(digest(assembly_raw) == selected["certificate_sha256"]
+         == receipt["assembly_sha256"] == math.PINS["assembly"], "Selected assembly source")
+    need(Q(json.loads(assembly_raw)["complex_lower"]) == B, "Selected exponent from assembly")
+    source = {}
+    for path, pin in receipt["source_pins"].items():
+        source[path] = read(CAMPAIGN / path, pin, path.endswith(".gz"))
+        if path.endswith("FREEZE.json"):
+            freeze(CAMPAIGN / path, pin)
+    invoices = {}
+    for name, suffix in (("clean", "run-normal/CLEAN-LATE-EXCHANGE.json.gz"),
+                         ("dual", "dual-normal/CLEAN-DUAL.json.gz")):
+        payload = source[LOCAL + suffix]
+        need(set(payload["providers"]) == {"base", "extra"}, "Both native providers")
+        for provider, variants in payload["providers"].items():
+            need(set(variants) == ({"I", "Q"} if name == "clean"
+                                   else {"inverse_adjoint", "selected_swap_conjugate"}),
+                 "All clean and dual variants")
+            for variant, word in variants.items():
+                key = name + "/" + provider + "/" + variant
+                bill = census(word, name == "clean" and variant == "I")
+                old = receipt["literal"][name][provider + "/" + variant]
+                need(bill["profile"] == {int(k): n for k, n in old["profile"].items()}
+                     and bill["children"] == old["children"]
+                     and bill["native_mass"] == old["mass"]
+                     and bill["scalar_primitives"] == old["scalar"]
+                     and bill["native_side_map_bound"] == old["native_side_map_bound"]
+                     and bill["total_map_bound"] == old["total_map_bound"], "Independent literal invoice")
+                invoices[key] = bill
+    need(len(invoices) == 8, "All eight literal words")
+    results = {}
+    for name, initial in (("three_Q", 0), ("one_I_two_Q", 1)):
+        local_q = Counter(invoices["clean/base/Q"]["profile"])
+        local_i = Counter(invoices["clean/base/I"]["profile"])
+        profile = Counter({r: (3 - initial) * n for r, n in local_q.items()})
+        profile.update({r: initial * n for r, n in local_i.items()})
+        profile = +profile
+        old = receipt["results"][name]
+        result = check_threshold(profile, old)
+        result["cleanup"] = {}
+        for size in (112, 128, 144):
+            result["cleanup"][str(size)] = check_threshold(
+                profile + Counter({1: size}), old["hypothetical_H1_cleanup"][str(size)])
+        need(old["three_call_scalar_subtotal"] == 3 * 8600 == 25800, "Three scalar calls")
+        maps = (3 - initial) * invoices["clean/base/Q"]["total_map_bound"]
+        maps += initial * invoices["clean/base/I"]["total_map_bound"]
+        need(maps == old["three_call_map_bound"] == 9792 - 48 * initial, "Three map counts")
+        narrow = 196 - 16 * initial
+        yes = math.moment(profile + Counter({1: narrow}))
+        next_two = Counter({2: (narrow + 1) // 2, 1: (narrow + 1) % 2})
+        no = math.moment(profile + next_two)
+        need(yes[1] < 1 < no[0], "All mixtures of H1 and H2 have the stated sharp rank budget")
+        result["all_H1_H2_mixtures"] = {
+            "total_rank_limit": narrow, "all_H1_at_limit": encode(yes),
+            "cheapest_next_profile": dict(sorted(next_two.items())),
+            "cheapest_next_moment": encode(no),
+        }
+        broad = narrow + 1
+        need(2 * 17**2 < 25**2 < 2 * 18**2, "Largest legal child rank")
+        yes = math.moment(profile + math.packed(broad))
+        no = math.moment(profile + math.packed(broad + 1))
+        need(yes[1] < 1 < no[0], "Sharp total-rank budget over all legal child ranks")
+        result["all_legal_ranks"] = {
+            "largest_child_rank": 17, "total_rank_limit": broad,
+            "best_profile": dict(sorted(math.packed(broad).items())),
+            "accepted": encode(yes),
+            "next_best_profile": dict(sorted(math.packed(broad + 1).items())),
+            "next": encode(no),
+        }
+        terminal = math.moment(profile + Counter({1: 224}))
+        need(terminal[0] > 1, "The complete 224-H1 terminal fails")
+        result["full_terminal"] = {"moment": encode(terminal), "minimum_H1_removal": 224 - narrow}
+        results[name] = result
+    result = {
+        "status": "PASS_INDEPENDENT_CLEAN_EXCHANGE_BUDGET",
+        "checker_sha256": digest(Path(__file__).read_bytes()),
+        "producer_freeze_sha256": FREEZE_PIN,
+        "third_engine_review_sha256": ENGINE_PIN,
+        "third_engine_imported_from_producer": False,
+        "historical_certificate_commit": COMMIT,
+        "historical_b": str(B),
+        "invoices": invoices,
+        "results": results,
+        "scope": "Literal invoice and strict conditional native arithmetic only. No new phase review or routed caller.",
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(result, sort_keys=True, indent=2) + "\n").encode()
+    (args.output / "REVIEW-CHECKS.json").write_bytes(raw)
+    print(result["status"])
+    print(digest(raw))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/adapters/low-displacement-budget-review-20261020.diff b/research/native-centre-capture/adapters/low-displacement-budget-review-20261020.diff
new file mode 100644
index 0000000000..fab990571d
--- /dev/null
+++ b/research/native-centre-capture/adapters/low-displacement-budget-review-20261020.diff
@@ -0,0 +1,32 @@
+--- original/check_review.py
++++ portable/check_review.py
+@@ -7,7 +7,7 @@
+ from pathlib import Path
+ import gzip
+ import json
+-import subprocess
++import sys
+ 
+ 
+ HERE = Path(__file__).resolve().parent
+@@ -212,9 +212,9 @@
+     mixed = read(MIXED / "MIXED-BUDGET.json", PINS["mixed_receipt"])
+     read(HERE.parent / "rank9-completion-review-20261020/FREEZE.json", PINS["rank9_review"])
+     selected_path = "certificates/selected-result.json"
+-    selected = pinned(subprocess.check_output(["git", "-C", str(REPO), "show", BASE + ":" + selected_path]),
++    selected = pinned((CAMPAIGN.parent / "historical" / BASE / selected_path).read_bytes(),
+                       PINS["selected"], selected_path)
+-    assembly = pinned(subprocess.check_output(["git", "-C", str(REPO), "show", BASE + ":" + selected["certificate"]]),
++    assembly = pinned((CAMPAIGN.parent / "historical" / BASE / selected["certificate"]).read_bytes(),
+                       PINS["assembly"], selected["certificate"])
+     need(selected["certificate_sha256"] == PINS["assembly"], "Selected certificate binding")
+     need(Q(assembly["complex_lower"]) == B == Q(low["selected_b_snapshot"])
+@@ -379,7 +379,7 @@
+         "discrete_packing_steps_checked": 136,
+         "scope": "Literal event invoices and conditional D25 histograms. No native phase replay, routed caller, recursive admission, finite map cost, precision, or kappa claim.",
+     }
+-    (HERE / "REVIEW.json").write_text(json.dumps(out, indent=2, sort_keys=True) + "\n")
++    Path(sys.argv[1]).write_text(json.dumps(out, indent=2, sort_keys=True) + "\n")
+     print("PASS", len(certificates), "exact profile intervals; 24 literal words; 16 unchanged scalar sequences")
+ 
+ 
diff --git a/research/native-centre-capture/adapters/low-displacement-budget-review-20261020.py b/research/native-centre-capture/adapters/low-displacement-budget-review-20261020.py
new file mode 100644
index 0000000000..5fd2363e32
--- /dev/null
+++ b/research/native-centre-capture/adapters/low-displacement-budget-review-20261020.py
@@ -0,0 +1,387 @@
+"""Check the literal invoices and the conditional native budgets."""
+
+from collections import Counter
+from fractions import Fraction as Q
+from functools import cache
+from hashlib import sha256
+from pathlib import Path
+import gzip
+import json
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+CAMPAIGN = HERE.parents[2]
+REPO = CAMPAIGN.parents[1]
+BUDGET = CAMPAIGN / "lanes/budget-geometry-20261017"
+LOW = BUDGET / "low-displacement-budget-20261020"
+MIXED = BUDGET / "mixed-exit-budget-20261020"
+SOURCE = "lanes/new-core-transfer-20261017/low-displacement-20261020/"
+BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f"
+PINS = {
+    "low_freeze": "c730e61f7446b072c60411f9cb6af903e5b252b12ce9a4d9bce906990303fbef",
+    "low_receipt": "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2",
+    "mixed_freeze": "99f084410fcba6228d396d8c547dd4ed74835dc97de7fce004387b6de6ab92a5",
+    "mixed_receipt": "7359fbab24858a21ea9879fff0b61883134ee3bb754916085689136f6d833224",
+    "selected": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+    "assembly": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+    "rank9_review": "50f2e168cdbf08e2bdad445bf2aa28f96d699cbc669a39892927bf94593e3b51",
+}
+B = Q(67018507072324140917, 40000000000000000000000)
+D, W = 25, 224
+GRID = 10**60
+LOG_TERMS = 64
+EXP_DEGREE = 20
+
+
+def need(value, reason):
+    if not value:
+        raise ValueError(reason)
+
+
+def pinned(raw, digest, label):
+    need(sha256(raw).hexdigest() == digest, "Source pin: " + label)
+    return json.loads(raw)
+
+
+def read(path, digest):
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    return pinned(raw, digest, str(path.relative_to(CAMPAIGN)))
+
+
+def floor(value):
+    return Q((value * GRID).__floor__(), GRID)
+
+
+def ceil(value):
+    return -floor(-value)
+
+
+def log_series(z):
+    need(0 <= z <= Q(1, 3), "Reduced logarithm argument")
+    term, total = z, Q(0)
+    for j in range(LOG_TERMS):
+        total += 2 * term / (2 * j + 1)
+        term *= z * z
+    tail = 2 * term / ((2 * LOG_TERMS + 1) * (1 - z * z))
+    return total, total + tail
+
+
+@cache
+def logarithm(value):
+    need(value >= 1, "Positive logarithm")
+    k = 0
+    while value >= 2:
+        value /= 2
+        k += 1
+    a, b = log_series((value - 1) / (value + 1))
+    c, d = log_series(Q(1, 3))
+    return floor(a + k * c), ceil(b + k * d)
+
+
+def exponential(lo, hi):
+    need(0 <= lo <= hi < Q(1, 100), "Small positive exponential")
+
+    def partial(value):
+        total = term = Q(1)
+        for j in range(1, EXP_DEGREE + 1):
+            term *= value / j
+            total += term
+        return total, term
+
+    low, _ = partial(lo)
+    high, last = partial(hi)
+    tail = last * hi / (EXP_DEGREE + 1) / (1 - hi / (EXP_DEGREE + 2))
+    return floor(low), ceil(high + tail)
+
+
+@cache
+def unit(rank):
+    a, b = logarithm(Q(D, rank))
+    c, d = exponential(B * a, B * b)
+    return Q(rank, D * W) * c, Q(rank, D * W) * d
+
+
+def counts(value):
+    return Counter({int(r): n for r, n in value.items() if n})
+
+
+def mass(value):
+    return sum(r * n for r, n in value.items())
+
+
+def moment(profile):
+    answer = [Q(0), Q(0)]
+    for r, n in profile.items():
+        need(0 < r < D and n > 0, "Positive child multiplicity")
+        low, high = unit(r)
+        answer[0] += n * low
+        answer[1] += n * high
+    return tuple(answer)
+
+
+def encode(value):
+    return [str(x) for x in value]
+
+
+def enclosure(inner, outer, label):
+    a, b = map(Q, outer)
+    need(a <= inner[0] <= inner[1] <= b, "Independent interval is enclosed: " + label)
+
+
+def scalar_word(word):
+    answer = []
+    for event in word["events"]:
+        if event[0] != "scalar":
+            continue
+        gate = event[1]
+        if isinstance(gate[-1], str):
+            op, target, source, coefficient = gate
+            coefficient = Q(coefficient)
+        else:
+            op, target = gate[:2]
+            source = gate[2] if op == "add" else None
+            coefficient = Q(*gate[-2:])
+        need(op in ("add", "scale") and 0 <= target < W, "Data scalar target")
+        need(op != "add" or 0 <= source < W, "Data scalar source")
+        answer.append((op, target, source if op == "add" else None, coefficient))
+    return answer
+
+
+def scalar_price(gate):
+    op, _, _, coefficient = gate
+    if op == "add":
+        need(abs(coefficient) in (1, 2, 3), "Integer ADD tariff")
+        return {1: 8, 2: 10, 3: 12}[abs(coefficient)]
+    need(coefficient in (-1, 2, Q(1, 2), -2, Q(-1, 2)), "Dyadic scale tariff")
+    return 2 * ((abs(coefficient) != 1) + (coefficient < 0))
+
+
+def invoice(word):
+    profile, field_mass = Counter(), Counter()
+    inline = 0
+    for event in word["events"]:
+        kind = event[0]
+        need(kind in ("scalar", "native", "monomial"), "Known local event")
+        if kind == "scalar":
+            continue
+        need(0 <= event[1] < W, "Data native or map owner")
+        recipe = word["native_recipes"][event[-1]]
+        if kind == "native":
+            rank = event[4]
+            need(0 < rank <= 17 and recipe["rank"] == rank, "Native rank and recipe")
+            need(recipe["left"] is not None and recipe["right"] is not None, "Two native side maps")
+            profile[rank] += 1
+            field_mass[event[1]] += rank
+        else:
+            need(recipe["rank"] == 0 and recipe["left"] is not None
+                 and recipe["right"] is None, "One inline monomial map")
+            inline += 1
+    for endpoint in word["endpoint_adapters"]:
+        need(endpoint["rank"] == 0 and endpoint["left"] is not None
+             and endpoint["right"] is None, "One endpoint map")
+    need(set(field_mass) == set(range(W)), "All data fields occur")
+    scalars = scalar_word(word)
+    census = Counter((op, coefficient) for op, _, _, coefficient in scalars)
+    return {
+        "profile": dict(sorted(profile.items())),
+        "native_mass": mass(profile),
+        "children": sum(profile.values()),
+        "scalar_primitives": sum(map(scalar_price, scalars)),
+        "endpoint_maps": len(word["endpoint_adapters"]),
+        "inline_maps": inline,
+        "map_bound": 2 * sum(profile.values()) + len(word["endpoint_adapters"]) + inline,
+        "field_rank_census": dict(sorted(Counter(field_mass.values()).items())),
+        "scalar_census": {op + ":" + str(c): n for (op, c), n in sorted(census.items())},
+    }
+
+
+def packed(total):
+    q, r = divmod(total, 17)
+    return Counter({17: q}) + (Counter({r: 1}) if r else Counter())
+
+
+def main():
+    for directory, key in ((LOW, "low"), (MIXED, "mixed")):
+        freeze = read(directory / "FREEZE.json", PINS[key + "_freeze"])
+        for name, pin in freeze["files"].items():
+            need(sha256((directory / name).read_bytes()).hexdigest() == pin, "Frozen file: " + name)
+    low = read(LOW / "BUDGET.json", PINS["low_receipt"])
+    mixed = read(MIXED / "MIXED-BUDGET.json", PINS["mixed_receipt"])
+    read(HERE.parent / "rank9-completion-review-20261020/FREEZE.json", PINS["rank9_review"])
+    selected_path = "certificates/selected-result.json"
+    selected = pinned((CAMPAIGN.parent / "historical" / BASE / selected_path).read_bytes(),
+                      PINS["selected"], selected_path)
+    assembly = pinned((CAMPAIGN.parent / "historical" / BASE / selected["certificate"]).read_bytes(),
+                      PINS["assembly"], selected["certificate"])
+    need(selected["certificate_sha256"] == PINS["assembly"], "Selected certificate binding")
+    need(Q(assembly["complex_lower"]) == B == Q(low["selected_b_snapshot"])
+         == Q(mixed["selected_b_snapshot"]), "Historical selected exponent")
+    need(0 < B < 1 and (low["dimension"], low["productive_width"], low["calls"]) == (D, W, 3)
+         and low["idle_profile"] == {}, "Conditional schedule")
+
+    sources = {name: read(CAMPAIGN / name, digest) for name, digest in low["source_pins"].items()}
+    raw = {
+        "rank30": sources[SOURCE + "native-normal-v2/NATIVE-PROGRAM.json.gz"]["providers"],
+        "odd_rank16": sources[SOURCE + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz"]["providers"],
+    }
+    changed = sources[SOURCE + "coded-normal/CODED-EXITS-PROGRAM.json.gz"]["providers_by_response_and_code"]
+    words = dict(raw)
+    for family, local in (("rank30", "rank30"), ("odd_rank16", "rank16")):
+        for code in ("W48_I64", "W112"):
+            words[family + "_" + code] = changed[local][code]
+    invoices = {}
+    for name, providers in words.items():
+        need(set(providers) == {"base", "extra"}, "Both providers")
+        invoices[name] = {}
+        for provider, directions in providers.items():
+            need(set(directions) == {"forward", "backward"}, "Both orientations")
+            for direction, word in directions.items():
+                bill = invoice(word)
+                retained = low["literal_native_invoices"][name][provider + "/" + direction]
+                for key, value in bill.items():
+                    expected = retained[key]
+                    if key in ("profile", "field_rank_census"):
+                        expected = {int(k): v for k, v in expected.items()}
+                    need(value == expected, "Literal invoice: " + name + "/" + key)
+                if "_W" in name:
+                    family = name.split("_W")[0]
+                    need(scalar_word(word) == scalar_word(raw[family][provider][direction]),
+                         "The changed exit preserves the complete scalar sequence")
+                invoices[name][provider + "/" + direction] = bill
+    need(sum(len(x) for x in invoices.values()) == 24, "All raw and changed words")
+
+    certificates = {}
+
+    def check_profile(profile, retained, label):
+        interval = moment(profile)
+        enclosure(interval, retained, label)
+        certificates[label] = {"profile": dict(sorted(profile.items())), "moment": encode(interval)}
+        return interval
+
+    def allowance(row, label):
+        profile = counts(row["profile"])
+        need(mass(profile) == row["native_mass"], "Native mass")
+        need(check_profile(profile, row["moment"], label)[1] < 1, "Base passes")
+        for rank, entry in row["limits"].items():
+            rank, n = int(rank), entry["children"]
+            yes = check_profile(profile + Counter({rank: n}), entry["accepted"], label + "/H" + str(rank))
+            no = check_profile(profile + Counter({rank: n + 1}), entry["next"], label + "/H" + str(rank) + "+1")
+            need(yes[1] < 1 < no[0], "Strict threshold")
+            need(entry["rank_mass"] == rank * n, "Threshold rank mass")
+        entry = row["all_legal_ranks"]
+        n = entry["total_rank_limit"]
+        need(entry["maximum_child_rank"] == 17 and 2 * 17**2 < D**2 < 2 * 18**2, "Strict size guard")
+        need(counts(entry["best_profile"]) == packed(n)
+             and counts(entry["next_best_profile"]) == packed(n + 1), "Packed rank optimum")
+        yes = check_profile(profile + packed(n), entry["accepted"], label + "/packed")
+        no = check_profile(profile + packed(n + 1), entry["next"], label + "/packed+1")
+        need(yes[1] < 1 < no[0], "Strict total-rank threshold")
+
+    for family in ("rank30", "odd_rank16"):
+        row = low["results"][family]
+        profile = counts(invoices[family]["base/forward"]["profile"])
+        need(counts(row["profile"]) == Counter({r: 3 * n for r, n in profile.items()}), "Three raw calls")
+        allowance(row, family)
+        full = counts(row["profile"]) + Counter({1: 224})
+        need(mass(full) == D * W and check_profile(full, row["unfused_terminal_moment"], family + "/full")[0] > 1,
+             "Raw terminal comparator fails")
+        need(row["H1_removal_from_unfused_terminal"] == 224 - row["limits"]["1"]["children"], "Raw terminal saving")
+        for n, target in row["hypothetical_H1_terminal_targets"].items():
+            check_profile(counts(row["profile"]) + Counter({1: int(n)}), target["moment"], family + "/target" + n)
+            need(target["remaining_H1"] == row["limits"]["1"]["children"] - int(n), "Hypothetical remainder")
+        for code in ("W48_I64", "W112"):
+            name = family + "_" + code
+            row = low["results"][name]
+            local = counts(invoices[name]["base/forward"]["profile"])
+            three = Counter({r: 3 * n for r, n in local.items()})
+            need(counts(row["local_profile"]) == local
+                 and counts(row["preterminal"]["profile"]) == three, "Three changed calls")
+            allowance(row["preterminal"], name + "/preterminal")
+            full = three + Counter({1: 224})
+            check_profile(full, row["with_terminal_comparator_moment"], name + "/full")
+            need(mass(full) == row["with_terminal_comparator_rank_mass"], "Changed complete mass")
+            if code == "W48_I64":
+                need(counts(row["all_other_debt_after_terminal"]["profile"]) == full, "Changed debt profile")
+                allowance(row["all_other_debt_after_terminal"], name + "/debt")
+                need(mass(full) + row["full_per_call_restoration_rank"] == D * W, "Full restoration mass")
+            else:
+                need(mass(full) == D * W + 96, "Uniform exit excess")
+
+    fusion = low["results"]["matched_H7_H2_fusion"]
+    allowance(fusion, "matched_H9")
+    full = counts(fusion["profile"]) + Counter({1: 96})
+    check_profile(full, fusion["complete_moment"], "matched_H9/full")
+    need(full == Counter({1: 576, 2: 144, 5: 144, 7: 272, 8: 192, 9: 64})
+         and mass(full) == 5600 and fusion["minimum_H1_saving"] == 15, "Reviewed H9 profile")
+
+    mixed_limits = {}
+    for family, rows in mixed["rows"].items():
+        old = counts(invoices[family]["base/forward"]["profile"])
+        new = counts(invoices[family + "_W48_I64"]["base/forward"]["profile"])
+        difference = {r: new[r] - old[r] for r in old.keys() | new.keys() if new[r] != old[r]}
+        need(difference == {1: -48, 2: 48, 3: -48}, "The common changed-exit histogram")
+        mixed_limits[family] = {}
+        for k, row in rows.items():
+            k = int(k)
+            profile = Counter({r: (3 - k) * n for r, n in old.items()})
+            profile.update({r: k * n for r, n in new.items()})
+            profile[1] += 224
+            profile += Counter()
+            need(profile == counts(row["profile"]) and mass(profile) == 5600 - 96 * k, "Mixed word histogram")
+            label = family + "/mixed" + str(k)
+            need(check_profile(profile, row["moment"], label)[1] < 1, "Mixed base passes")
+            for rank, entry in row["limits"].items():
+                rank, n = int(rank), entry["children"]
+                yes = check_profile(profile + Counter({rank: n}), entry["accepted"], label + "/H" + str(rank))
+                no = check_profile(profile + Counter({rank: n + 1}), entry["next"], label + "/H" + str(rank) + "+1")
+                need(yes[1] < 1 < no[0], "Mixed strict threshold")
+            saving = 96 * k - row["limits"]["1"]["children"]
+            need(row["H1_saving_from_full_restoration"] == saving == (25 if family == "rank30" else 30),
+                 "Full all-H1 restoration saving")
+            mixed_limits[family][str(k)] = {rank: entry["children"] for rank, entry in row["limits"].items()}
+
+    u1, u2, u3 = (unit(r) for r in (1, 2, 3))
+    saving = (48 * (u1[0] + u3[0] - u2[1]) / u1[1],
+              48 * (u1[1] + u3[1] - u2[0]) / u1[0])
+    enclosure(saving, ["95.846609456084463", "95.846609456084464"], "Common H1-equivalent saving")
+    need(Q("95.846609456084463") < saving[0] <= saving[1] < Q("95.846609456084464"),
+         "Strict common saving enclosure")
+
+    # These checks cover the discrete steps in the packing proof.
+    for small in range(1, 17):
+        for large in range(small, 17):
+            before = moment(Counter([small, large]))
+            after = moment(Counter([large + 1]) + (Counter([small - 1]) if small > 1 else Counter()))
+            need(after[1] < before[0], "Moving rank to the larger child lowers the cost")
+
+    out = {
+        "status": "PASS_INDEPENDENT_LITERAL_AND_RATIONAL_BUDGET_REVIEW",
+        "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "source_pins": PINS,
+        "upstream_source_pins": low["source_pins"],
+        "selected_commit": BASE,
+        "selected_certificate": selected_path,
+        "selected_assembly": selected["certificate"],
+        "selected_b_snapshot": str(B),
+        "literal_words_checked": 24,
+        "unchanged_changed_scalar_sequences": 16,
+        "literal_invoices": invoices,
+        "exact_method": {"log_series": "64 positive atanh terms after binary reduction",
+                         "exp_degree": EXP_DEGREE, "outward_grid": str(GRID),
+                         "producer_imports": 0, "retained_engine_imports": 0},
+        "profile_intervals_checked": len(certificates),
+        "certificates": certificates,
+        "mixed_limits": mixed_limits,
+        "common_changed_exit_H1_equivalent_saving": encode(saving),
+        "discrete_packing_steps_checked": 136,
+        "scope": "Literal event invoices and conditional D25 histograms. No native phase replay, routed caller, recursive admission, finite map cost, precision, or kappa claim.",
+    }
+    Path(sys.argv[1]).write_text(json.dumps(out, indent=2, sort_keys=True) + "\n")
+    print("PASS", len(certificates), "exact profile intervals; 24 literal words; 16 unchanged scalar sequences")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/check_bridge_access.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/check_bridge_access.py
new file mode 100644
index 0000000000..5a13b62b8b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/check_bridge_access.py
@@ -0,0 +1,399 @@
+"""Check future projection bridges at the actual supplier cuts."""
+
+import argparse
+from bisect import bisect_left
+from collections import Counter, defaultdict
+from fractions import Fraction
+from functools import cache
+from hashlib import sha256
+import gzip
+import json
+from pathlib import Path
+import tarfile
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent
+ROOT = HERE.parents[3]
+ARCHIVE = ROOT / "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz"
+ARCHIVE_PIN = "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6"
+MEMBERS = {
+    "template": ("candidate/strict/global/hosted/GLOBAL-TEMPLATE.json.gz", "2acf02b418078e37090495c601fe550448751d4f35912757b13a1f778efc7760"),
+    "phases": ("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"),
+    "word": ("candidate/strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz", "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219"),
+}
+PINS = {
+    "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3",
+    "cover-algebra/BRIDGES.md": "0db4e1e4589da903e50057b2d8657512c1185159a9ee18e605ad54c027c7dc80",
+    "interface-proof/BRIDGE-OPERATOR-REVIEW.json": "c905a19d70f34c435c5f5454c6190bbfb1ce4594b1513bf76156acf620d7c6fc",
+    "interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json": "8b8c4d814b44c2fc42cf9ad995f8451512309fcfc46bea9317ebe4b4d79e8a4d",
+}
+SELECTED = [0, 7, 20, 27, 36, 46, 57, 111]
+ORDINARY = [p for p in range(112) if p not in SELECTED]
+UNIT = [1 << j for j in range(73)]
+ZERO = (0, 0, 0)
+
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def owner(replica, pair, side, port):
+    return 896 * replica + 224 * pair + 112 * side + port
+
+
+def act(columns, vector):
+    result = 0
+    while vector:
+        low = vector & -vector
+        result ^= columns[low.bit_length() - 1]
+        vector ^= low
+    return result
+
+
+def add_phase(a, b):
+    return a[0] ^ b[0], a[1] ^ b[1] ^ (a[0] & b[0]), a[2] ^ b[2]
+
+
+def negative(a):
+    return a[0], a[1] ^ a[0], a[2]
+
+
+@cache
+def line(vector, exponent=1):
+    cross = 0
+    for j in range(73):
+        if vector >> j & 1:
+            cross ^= (vector & ((1 << j) - 1)) << (j * (j - 1) // 2)
+    return (vector if exponent & 1 else 0,
+            vector if exponent & 2 else 0, cross if exponent & 1 else 0)
+
+
+def product(terms):
+    result = ZERO
+    for vector, exponent in terms:
+        result = add_phase(result, line(vector, exponent % 4))
+    return result
+
+
+def canonical(q, level, side):
+    if level == -1:
+        return line(q) if side == 0 else ZERO
+    frame = ((1 << (9 + 8 * level)) - 1, 0, 0)
+    return add_phase(frame, line(q, 3)) if side else frame
+
+
+def chart(q):
+    hole = next(i for i in range(9) if not q >> i & 1)
+    v = q ^ (1 << hole)
+    order = list(range(9))
+    order[0], order[hole] = order[hole], order[0]
+    basis = [(1 << j) ^ (v if v >> j & 1 else 0) for j in order] + UNIT[9:]
+    need(basis[0] == q and all((a & b).bit_count() % 2 == int(i == j)
+         for i, a in enumerate(basis) for j, b in enumerate(basis)), "Actual orthogonal port chart")
+    return basis
+
+
+def route(basis, stage):
+    columns = list(UNIT)
+    if stage:
+        swaps = [basis[j + 1] ^ UNIT[9 + 8 * (stage - 1) + j] for j in range(8)]
+        columns = [v ^ sum_xor(a for a in swaps if (a & v).bit_count() & 1) for v in columns]
+    need([act(columns, v) for v in columns] == UNIT, "Stage route is an involution")
+    return columns
+
+
+def sum_xor(values):
+    result = 0
+    for value in values:
+        result ^= value
+    return result
+
+
+def phases_and_views(data):
+    views, checks, controls = {}, Counter(), Counter()
+    for p, recipe in enumerate(data["phases"]["recipes"]):
+        q, basis = recipe["q"], chart(recipe["q"])
+        need(basis[1:9] == recipe["idle_children"][0]["orthogonal_axes"][:8], "Source port basis")
+        beta = sum((((v.bit_count() - 1) // 2) & 1) << j for j, v in enumerate(basis[1:9]))
+        local_beta = act(basis[1:9], beta)
+        for t in range(1, 9):
+            rho = route(basis, t)
+            lifted_beta = beta << (9 + 8 * (t - 1))
+            delta_y = q ^ lifted_beta
+            delta_x = local_beta ^ lifted_beta
+            need(act(rho, recipe["stage_alignment"][t]["entry_Y"]) == delta_y,
+                 "Future view has the literal supplier entry translation")
+            need(recipe["stage_alignment"][t]["exit_X"] == delta_x,
+                 "Past view has the literal supplier exit translation")
+            for level in range(t):
+                terms = [(act(rho, e), 1) for e in UNIT[:9 + 8 * level]] + [(q, -1)]
+                actual = product(terms)
+                common_axes = list(range(9, 9 + 8 * level)) + list(range(9 + 8 * (t - 1), 9 + 8 * t))
+                expected = product([(UNIT[j], 1) for j in common_axes])
+                need(add_phase(actual, line(delta_y, 2)) == expected, "Full future-Y phase identity")
+                checks["future_Y"] += 1
+                controls["omitted_Y_translation"] += actual != expected
+                controls["wrong_Y_translation_order"] += add_phase(actual, line(act(rho, delta_y), 2)) != expected
+            for level in range(t, 9):
+                actual = product([(act(rho, e), 1) for e in UNIT[:9 + 8 * level]])
+                expected = canonical(q, level, 0)
+                need(add_phase(actual, line(delta_x, 2)) == expected, "Full past-X phase identity")
+                checks["past_X"] += 1
+                controls["omitted_X_translation"] += actual != expected
+            views[p, t, "Y"] = dict(port=p, stage=t, side="Y", route_columns=rho,
+                translation_after_route=delta_y, translation_before_route=act(rho, delta_y))
+            views[p, t, "X"] = dict(port=p, stage=t, side="X", route_columns=rho,
+                translation_after_route=delta_x, translation_before_route=act(rho, delta_x))
+    need(checks == {"future_Y": 4032, "past_X": 4032}, "Full cone coverage")
+    need(controls == {"omitted_Y_translation": 4032, "wrong_Y_translation_order": 4032,
+                      "omitted_X_translation": 4032}, "All exact phase controls fail")
+    return views, dict(checks), dict(controls)
+
+
+def scalar_word(B, sign):
+    word = [["add", 112 + p, p, str(sign)] for p in ORDINARY]
+    word += [["add", 112 + a, p, str(-sign * B[i][j])]
+             for i, a in enumerate(SELECTED) for j, p in enumerate(ORDINARY) if B[i][j]]
+    return word
+
+
+def scalar_check(B):
+    receipts = {}
+    for sign in (-1, 1):
+        word = scalar_word(B, sign)
+        rows = [{j: Fraction(1)} for j in range(224)]
+        max_norm = Fraction(1)
+        for _, target, source, coefficient in word:
+            coefficient = Fraction(coefficient)
+            need(source < 112 and target >= 112 and source in ORDINARY, "No changed or selected source is read")
+            for origin, value in rows[source].items():
+                rows[target][origin] = rows[target].get(origin, 0) + coefficient * value
+            max_norm = max(max_norm, sum(abs(x) for x in rows[target].values()))
+        expected = [{j: Fraction(1)} for j in range(224)]
+        for p in ORDINARY:
+            expected[112 + p][p] = Fraction(sign)
+        for i, a in enumerate(SELECTED):
+            for j, p in enumerate(ORDINARY):
+                if B[i][j]:
+                    expected[112 + a][p] = -sign * B[i][j]
+        need(rows == expected and len(word) == 520 and max_norm == 27, "Exact arbitrary-data U bridge")
+        need(rows[:112] == [{j: Fraction(1)} for j in range(112)], "Every source is unchanged")
+        receipts[str(sign)] = dict(program=word, arbitrary_input_columns=224,
+            unit_adds=104, half_adds=416, real_scalar_bound=4992,
+            maximum_intermediate_row_one_norm=str(max_norm), native_children=0,
+            private_fields=0, unchanged_source_rows=112)
+    return receipts
+
+
+def schedule_audit(data, views, mixed):
+    template, phases, word = data["template"], data["phases"]["recipes"], data["word"]
+    events, calls = template["execution_schedule"], template["calls"]
+    bases = [chart(r["q"]) for r in phases]
+    positions = {e["time"]: i for i, e in enumerate(events) if e["kind"] == "local_cover_sweep"}
+    touches, deadline = defaultdict(list), {}
+    for i, e in enumerate(events):
+        if e["kind"] == "local_cover_sweep":
+            c = calls[e["time"]]
+            touches[c["replica"], c["pair"]].append(i)
+        elif e["kind"] == "bridge":
+            for pair in (e["src"], e["dst"]):
+                touches[e["replica"], pair].append(i)
+        elif e["kind"] == "idle_cover_sweep":
+            for side, child in enumerate(e["child_indices"]):
+                deadline[e["replica"], child] = (i, side)
+    jobs, suffixes, partition = defaultdict(list), defaultdict(list), defaultdict(set)
+    for index, job in enumerate(template["hosting"]["pooled_slots"]):
+        end, side = deadline[job["owner_replica"], job["child"]]
+        e = events[end]
+        used = touches[job["owner_replica"], e["pair"]]
+        offset = bisect_left(used, end)
+        release = used[offset - 1] if offset else -1
+        need(release < positions[job["time"]] < end, "Old complete helper strict window")
+        family = owner(job["owner_replica"], e["pair"], side, job["port"])
+        role = 224 + job["helper"]
+        width = len(word["frames"][word["final"][role]]) - len(word["frames"][word["start"][role]])
+        begin = 8 * (e["from_level"] + 1) + 1 + job["offset"]
+        axes = list(range(begin, begin + width))
+        spectators = [j for j in range(73) if j not in axes][:9 - width]
+        descriptor = [3, job["child"], job["offset"]] if width == 9 else [4, job["child"], job["offset"], width, spectators]
+        need(job["family"] == family and job["width"] == width
+             and calls[job["time"]]["owners"][role] == [family, descriptor], "Literal helper role and route")
+        key = job["owner_replica"], job["child"], job["port"]
+        need(not partition[key].intersection(axes), "No helper axis repeats")
+        partition[key].update(axes)
+        jobs[job["time"]].append((family, product([(bases[job["port"]][j], 1) for j in axes])))
+    for job in template["idle_children"]:
+        end, side = deadline[job["replica"], job["child"]]
+        e = events[end]
+        begin = 8 * (e["from_level"] + 1) + 1 + job["pending_offset"]
+        stop = 8 * (e["to_level"] + 1) + 1
+        axes = list(range(begin, stop))
+        family = owner(job["replica"], e["pair"], side, job["port"])
+        need(job["family"] == family and len(axes) == job["rank"], "Literal idle suffix")
+        key = job["replica"], job["child"], job["port"]
+        need(not partition[key].intersection(axes), "No suffix axis repeats")
+        partition[key].update(axes)
+        suffixes[end].append((family, product([(bases[job["port"]][j], 1) for j in axes])))
+    for (replica, child), (end, _) in deadline.items():
+        e = events[end]
+        expected = set(range(8 * (e["from_level"] + 1) + 1, 8 * (e["to_level"] + 1) + 1))
+        for p in range(112):
+            need(partition[replica, child, p] == expected, "Every pending axis is used once")
+    frames = [canonical(phases[f % 112]["q"], -1, (f // 112) % 2) for f in range(14336)]
+    retired, cuts, counts = set(), [], Counter()
+    bridge_count = Counter()
+
+    def complete(replica, pair, level):
+        for side in (0, 1):
+            for p in range(112):
+                f = owner(replica, pair, side, p)
+                expected = canonical(phases[p]["q"], level, side)
+                if f in retired:
+                    expected = add_phase(expected, line(phases[p]["q"]))
+                need(frames[f] == expected, "Actual complete bank phase")
+
+    for position, event in enumerate(events):
+        kind, replica = event["kind"], event.get("replica")
+        if kind == "local_cover_sweep":
+            call = calls[event["time"]]
+            pair, stage = call["pair"], call["stage"]
+            need(len(call["owners"]) == len({o[0] for o in call["owners"]}) == 704, "No local owner alias")
+            complete(replica, pair, stage - 1)
+            for side in (0, 1):
+                for p in range(112):
+                    f = owner(replica, pair, side, p)
+                    need(call["owners"][112 * side + p] == [f, [1, stage, p]], "Actual active route")
+                    frames[f] = canonical(phases[p]["q"], stage, side)
+                    if mixed and side == 1 and p in SELECTED and stage in (2, 4, 6, 8):
+                        retired.add(f)
+                        frames[f] = add_phase(frames[f], line(phases[p]["q"]))
+            for f, phase in jobs[event["time"]]:
+                frames[f] = add_phase(frames[f], phase)
+                counts["helper_jobs"] += 1
+            complete(replica, pair, stage)
+            counts["local_calls"] += 1
+        elif kind == "idle_cover_sweep":
+            for f, phase in suffixes[position]:
+                frames[f] = add_phase(frames[f], phase)
+                counts["idle_suffixes"] += 1
+            for side, child in enumerate(event["child_indices"]):
+                for p in range(112):
+                    f = owner(replica, event["pair"], side, p)
+                    frames[f] = add_phase(frames[f], line(phases[p]["idle_children"][child]["translation_after"], 2))
+            complete(replica, event["pair"], event["to_level"])
+            counts["idle_events"] += 1
+        elif kind == "bridge":
+            index = bridge_count[replica]
+            bridge_count[replica] += 1
+            if index < 6:
+                src_pair, dst_pair, side = event["dst"], event["src"], 1
+                stage = 2 * dst_pair + 1
+                level = 2 * src_pair + 1 + (index % 2)
+                sign = -event["coefficient"]
+                need(src_pair + 1 == dst_pair and level < stage, "Future Y bridge order")
+                counts["future_Y_cuts"] += 1
+            else:
+                src_pair, dst_pair, side = event["src"], event["dst"], 0
+                stage, level, sign = 2 * dst_pair + 1, 8, 1
+                need(src_pair + 1 == dst_pair and stage <= level, "Past X tail order")
+                counts["past_X_tail_cuts"] += 1
+            families = [owner(replica, src_pair, side, p) for p in ORDINARY]
+            families += [owner(replica, dst_pair, side, p) for p in range(112)]
+            need(len(families) == len(set(families)) == 216, "No bridge source/target owner alias")
+            for p in ORDINARY:
+                source = owner(replica, src_pair, side, p)
+                target = owner(replica, dst_pair, side, p)
+                expected = canonical(phases[p]["q"], level, side)
+                need(frames[source] == frames[target] == expected, "Exact same-port ordinary bridge phase")
+            for p in SELECTED:
+                target = owner(replica, dst_pair, side, p)
+                need(target not in retired and frames[target] == canonical(phases[p]["q"], level, side),
+                     "Every selected target has the required unmodified phase")
+            name = "Y" if side else "X"
+            cuts.append(dict(position=position, source_event=event["source_event"], replica=replica,
+                source_pair=src_pair, target_pair=dst_pair, side=name, stage=stage,
+                completed_level=level, sign=sign,
+                source_ordinary_families=[owner(replica, src_pair, side, p) for p in ORDINARY],
+                target_families=[owner(replica, dst_pair, side, p) for p in range(112)],
+                aligned_source_ports=ORDINARY, aligned_target_ports=SELECTED,
+                scalar_word_key=str(sign), new_affine_view_maps=224,
+                retained_X_bridge=(index < 6), removed_Y_tail=(index >= 6)))
+            counts["all_bridge_frame_pairs"] += 224
+        elif kind == "terminal_Y_translations":
+            for pair in range(4):
+                complete(replica, pair, 8)
+            counts["preterminal_endpoints"] += 1
+        elif kind == "terminal":
+            counts["terminal_events"] += 1
+        else:
+            need(kind in ("bank_padding_cover_sweep", "translate_every_live_family"), "Known source event")
+    need(all(v == 9 for v in bridge_count.values()) and len(cuts) == 144, "All new bridge cuts")
+    need(counts["helper_jobs"] == 69120 and counts["idle_suffixes"] == 7526
+         and counts["future_Y_cuts"] == 96 and counts["past_X_tail_cuts"] == 48, "Complete source schedule")
+    need(len(retired) == (512 if mixed else 0), "Selected FULL exceptions")
+    return dict(mixed_selected_outputs=mixed, checked_counts=dict(counts), cuts=cuts,
+                retired_selected_fields_not_read=512 if mixed else 0)
+
+
+def main(args):
+    raw = ARCHIVE.read_bytes()
+    need(sha256(raw).hexdigest() == ARCHIVE_PIN, "Selected archive pin")
+    data = {}
+    with tarfile.open(ARCHIVE) as stream:
+        for key, (path, pin) in MEMBERS.items():
+            raw = stream.extractfile(path).read()
+            need(sha256(raw).hexdigest() == pin, "Archive member pin: " + key)
+            data[key] = json.loads(gzip.decompress(raw) if path.endswith(".gz") else raw)
+    for path, pin in PINS.items():
+        need(sha256((LANES / path).read_bytes()).hexdigest() == pin, "Premise pin: " + path)
+    interface = json.loads((LANES / "circuit-interface/INTERFACE.json").read_bytes())
+    R = [[Fraction(row.get(str(p), "0")) for p in range(112)] for row in interface["R"]]
+    need(interface["ports"] == [r["q"] for r in data["phases"]["recipes"]], "Actual port order")
+    need(all(sum(R[k][a] * R[k][b] for k in range(8)) == 4 * int(i == j)
+         for i, a in enumerate(SELECTED) for j, b in enumerate(SELECTED)), "Selected square minor")
+    B = [[sum(R[k][a] * R[k][p] for k in range(8)) / 4 for p in ORDINARY] for a in SELECTED]
+    need(sum(bool(c) for row in B for c in row) == 416
+         and all(sum(bool(c) for c in row) == 52 for row in B)
+         and all(abs(c) == Fraction(1, 2) for row in B for c in row if c), "Exact sparse B matrix")
+    views, checks, controls = phases_and_views(data)
+    scalar = scalar_check(B)
+    uniform, mixed = [schedule_audit(data, views, setting) for setting in (False, True)]
+    need(uniform["cuts"] == mixed["cuts"], "One program handles both retirement phase policies")
+    payload = dict(format="future-projection-bridge-v1", views=list(views.values()),
+                   scalar_words={k: v["program"] for k, v in scalar.items()}, cuts=uniform["cuts"],
+                   operation_order=["104 same-port ordinary ADDs", "Align 104 source U and 8 target A fields",
+                                    "416 half ADDs", "Undo 112 affine views"],
+                   inverse_view_order="Undo translation, then undo the route; rho is its own inverse")
+    payload_raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    args.program.write_bytes(gzip.compress(payload_raw, mtime=0))
+    for row in scalar.values():
+        del row["program"]
+    receipt = dict(status="PASS_ACTUAL_FUTURE_PROJECTION_BRIDGES", archive_sha256=ARCHIVE_PIN,
+        source_member_sha256={k: v[1] for k, v in MEMBERS.items()}, premise_sha256=PINS,
+        checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(),
+        payload_sha256=sha256(payload_raw).hexdigest(), phase_checks=checks, phase_controls=controls,
+        scalar_words=scalar, uniform_schedule=uniform["checked_counts"], mixed_schedule=mixed["checked_counts"],
+        mixed_retired_selected_fields_not_read=512, new_native_children=0, new_private_fields=0,
+        unchanged_original_helper_jobs=69120, unchanged_original_idle_suffixes=7526,
+        complete_T_equals_W_bridge_invoice=dict(U_updates=144, real_scalar_bound=718848,
+            retained_X_unit_adds=10752, retained_X_real_scalar_bound=86016,
+            total_real_scalar_bound=804864, new_affine_view_maps=32256,
+            native_profile_delta={}, live_delta=0, physical_stock_delta=0),
+        complete_T_zero_bridge_invoice=dict(U_updates=96, real_scalar_bound=479232,
+            retained_X_real_scalar_bound=86016, total_real_scalar_bound=565248,
+            new_affine_view_maps=21504, native_profile_delta={}, live_delta=0, physical_stock_delta=0),
+        tensor_scope="All phase polynomials are exact modulo four and have zero constant. The identities tensor to every positive width.",
+        scope="Literal source-bound bridge macros and exact phase/owner admission. This is not a complete supplier, precision invoice, or kappa claim.",
+        open_costs=["Compile affine view maps in the complete finite invoice", "Bind the selected controller and all new local maps", "Price complete controller growth and recursive supplier"])
+    args.out.write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n", encoding="utf-8")
+    print(receipt["status"])
+    print(json.dumps(dict(cuts=144, new_native_children=0, scalar=804864, affine_views=32256), sort_keys=True))
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--out", type=Path, default=HERE / "ACCESS.json")
+    parser.add_argument("--program", type=Path, default=HERE / "BRIDGE-PROGRAMS.json.gz")
+    main(parser.parse_args())
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/FREEZE.json
new file mode 100644
index 0000000000..7f772907b2
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "INVOLUTION-READER.md": "718829c1842c856d5694abbcd6ebd509cafbb8901b4225be218f45abd2844dab",
+    "emit_query.py": "29afc86c918f428d9562b02e2017a1eebc38b1cf2dcae2b2d6bf53c5473be14b",
+    "final-normal/CHECKS.json": "fe484b746a1a3f3c7d54e40afeb3f3f9e3493fd7fc7ff350ac91920a8ab38c6f",
+    "final-normal/INVOLUTION-READER.json.gz": "6fd5d6df96582aeaeef9a3295289d239586de3a1420ae7f8e99679e9ef96b810",
+    "final-optimized/CHECKS.json": "fe484b746a1a3f3c7d54e40afeb3f3f9e3493fd7fc7ff350ac91920a8ab38c6f",
+    "final-optimized/INVOLUTION-READER.json.gz": "6fd5d6df96582aeaeef9a3295289d239586de3a1420ae7f8e99679e9ef96b810"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091",
+  "scope": "Actual fixed-reader forward service for routed row involution. Backward caller, inherited helper hosting and complete supplier remain separate.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md
new file mode 100644
index 0000000000..587107b820
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md
@@ -0,0 +1,204 @@
+# A restored-source query for the routed involution
+
+The actual dyadic row involution permits a shorter fixed-reader service.
+At the completed FULL cut, apply the current involution to X, query
+the past reader from X, and apply the involution again. The last step
+restores every source field. The target can have an arbitrary baseline.
+
+The emitted query has 8,440 real scalar primitives, 672 monomial maps,
+and no native child or extra field. With the existing carrier prefix,
+the complete typed forward service has 14,896 real scalar primitives
+and native rank 1,792. This result does not close a backward caller,
+the helper host, or the full supplier.
+
+## The reversible-source query lemma
+
+Let X be a complete source bank. Let Y be a distinct target bank.
+Let T be a unit on X, and let L be a reader from X to Y. Assume that
+the following three operations are admitted at their actual frames:
+
+1. Apply T to X.
+2. Add LX to Y.
+3. Apply \(T^{-1}\) to X.
+
+On arbitrary independent x and y, this word gives
+
+\[
+(x,y)\longmapsto (x,y+LTx).
+\tag{1}
+\]
+
+The first operation gives \(Tx\). The second adds \(LTx\) to the
+unchanged target baseline. The last restores x. No condition on
+\(LJ\), no zero source, and no zero target is needed. In particular,
+the selected target records need not be a separate owned workspace.
+
+If the three words restore their own borrowed fields, the complete
+word restores them as well. The price is
+\(a(T)+c(L)+a(T^{-1})\), with the actual view and storage costs included.
+If both source words cost at most a, this is at most \(2a+c(L)\).
+The lemma does not make T or L admissible at a new frame.
+
+Several target readers can be used between steps 1 and 3 if each
+reader preserves X and the other target baselines. In that case the
+two source transformations are shared. This is an algebraic extension;
+this packet emits one sixteen-row reader.
+
+## The actual current source unit
+
+The source is the controller lane's 112-port physical row involution A.
+The emitter pins its exact matrix and its 3,276-scalar common-frame
+word. It checks both the complete word and \(A^2=I\).
+
+The pivot set P has sixteen ports. Its complement R has 96 ports.
+The source response E and A have exactly the same R rows:
+
+\[
+A[R,*]=E[R,*].
+\tag{2}
+\]
+
+Thus the frozen carrier prefix for E remains a valid carrier prefix
+for A. It emits the ordinary increment \((A_tx)_R\), leaves the selected
+records independent, and completes all X and selected Y fields to
+FULL. No native transfer or native phase recipe is changed.
+
+Let \(A_t\) be the current routed operator. Let \(L_s\) be the retained
+past reader. Use (1) with \(T=A_t=T^{-1}\) and \(L=L_s\).
+The result is the required selected increment \(L_sA_tx\).
+
+This argument does not replace \(A_t\) by a scalar matrix in the
+global chart. It does not commute the reader through the response.
+The map \(L_sA_t\) has 3,824 actual owner paths in each checked case.
+The implementation does not enumerate those paths as separate ADDs.
+
+## Literal current and past views
+
+The three checked pairs are
+\((s,t)=(0,1),(0,2),(1,2)\). The physical input level is always \(t-1\).
+The label s identifies the carried reader, not that physical level.
+
+At the completed level t, the current A word has this order:
+
+1. Apply the literal current FULL view to each of the 112 X fields.
+2. Execute the pinned 3,276-scalar A word.
+3. Undo those 112 views.
+
+The word therefore uses 224 map calls and has the exact global action
+\(A_t\). The emitter checks every view's complete Z4 phase polynomial.
+Each route is orthogonal and fixes every uncompleted axis.
+The current view arrays equal the current DATA exit arrays in the
+frozen dispatcher.
+
+For the old reader, write \(L_s=J^{\mathsf T}+B_s\). Use the old FULL
+views on 96 ordinary X fields and sixteen selected Y fields. Run
+the 1,760-scalar complement reader and undo its views. This costs
+224 maps. Then make the sixteen same-port selected copies, at a
+cost of 128 scalar primitives and no further map.
+
+All maps act only on FULL fields. The ordinary Y hole fields are
+neither read nor changed by this late query. The second A word uses
+the same current views and the same scalar word as the first.
+
+The exact order is:
+
+```text
+current A on X
+past B_s complement query into Y_P
+sixteen selected copies into Y_P
+current A on X
+```
+
+The two current A words restore X as a complete routed operator.
+They do not restore X by identifying different owner paths.
+
+## The complete typed forward service
+
+Use the frozen carrier prefix before the query. It has 2,406 events
+and the profile
+
+```text
+1392 H1 + 64 H2 + 48 H3 + 16 H8.
+```
+
+Its native rank is 1,792, and it has 1,520 native children. Its
+scalar price is 6,456. All 416 arbitrary helper fields are restored.
+The existing native phase checks and the current DATA phase checks
+remain unchanged.
+
+Let \(F_\ell\) be FULL on the first \(9+8\ell\) axes, and put
+\(G_R=\operatorname{diag}(I_P,q_R)\). For independent target records w,
+the complete service is
+
+\[
+(F_{t-1}x,\ F_{t-1}G_Rw)
+\longmapsto
+(F_tx,\ F_tG_R(w+D_{s,t}x)),
+\tag{3}
+\]
+
+where
+
+\[
+(D_{s,t})_P=L_sA_t,\qquad
+(D_{s,t})_R=(A_t)_R.
+\]
+
+If \(w=C_sy\), the selected records after the service are
+\(L_s(y+A_tx)\). Thus the reader from stage s is retained.
+
+The native cover sweep and all DATA exits precede the late query.
+The program contains both native provider prefixes, all actual stage
+view records, and all six provider/pair invocations. It preserves
+the whole-cover barrier in the previous dispatcher.
+
+The query invoice is:
+
+| Part | Real scalar primitives | Maps |
+| --- | ---: | ---: |
+| First current A | 3,276 | 224 |
+| Past complement reader | 1,760 | 224 |
+| Selected copies | 128 | 0 |
+| Second current A | 3,276 | 224 |
+| Total | 8,440 | 672 |
+
+Adding the carrier prefix gives 14,896 scalar primitives. A conservative
+bound for this word is 4,384 monomial calls: 448 DATA calls, 224 local
+endpoint adapters, at most 3,040 native side maps, and 672 query maps.
+This is a call count, not a finite real-operation price for those maps.
+Helper acquisition, recursive parking, and the outer caller remain
+separate.
+
+The exact query row-sum maximum at the emitted gate boundaries is
+202, and its binary denominator height is at most two. These values
+hold for all three pairs. The bound also holds after the complete
+carrier prefix. It does not cover internal arithmetic in a lowered
+ADD, a native child, or a recursive caller.
+
+## Checks, scope, and credit
+
+The emitter uses exact rational coefficients and the pinned route
+algebra engine. It checks all 640 formal input columns of the joined
+prefix and query. Each coefficient retains its input field and its
+complete \(O(25,2)\) owner route. It compares the result with the
+direct \(L_sA_t\) product. Every X field, ordinary Y field, and helper
+has the required endpoint.
+
+Omitting the second A word fails. Replacing the past reader by the
+current reader also fails. Both controls fail for every checked pair.
+
+Run `emit_query.py --output <new-directory>` with normal Python and
+with `python3 -O`. The payloads and receipts must be byte equal.
+The emitter rejects an existing output directory.
+
+The reversible-source argument supplies the selected query. It does
+not prove that the complete response \(D_{s,t}\) is reciprocal or
+stage independent. A backward service, the complete controller,
+raw output restoration, recursive hosting, and a final exponent
+remain open.
+
+The work uses the controller lane's dyadic row involution, the native
+lane's carrier prefix, and the bridge-access and review lanes' fixed
+reader and literal view calculations. OpenAI Codex assisted the work.
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/emit_query.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/emit_query.py
new file mode 100644
index 0000000000..ec79601de6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/emit_query.py
@@ -0,0 +1,282 @@
+"""Emit a restored-source query for the actual routed involution."""
+
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import argparse
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+PINS = {
+    "involution": (
+        "controller-followthrough-20261017/row-involution-20261020/"
+        "run-normal/ROW-INVOLUTION.json",
+        "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+    ),
+    "capture": (
+        "controller-followthrough-20261017/row-capture-20261020/"
+        "run-normal/ROW-CAPTURE.json",
+        "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7",
+    ),
+    "prefix": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz",
+        "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e",
+    ),
+    "view_query": (
+        "bridge-access-20261017/row-capture-access-20261020/"
+        "reuse-normal/REUSE-PROGRAM.json",
+        "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b",
+    ),
+    "dispatcher": (
+        "bridge-access-20261017/row-capture-access-20261020/"
+        "integration-v2-normal/DISPATCHER.json",
+        "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24",
+    ),
+    "dispatcher_freeze": (
+        "bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json",
+        "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331",
+    ),
+    "operator_engine": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "fixed-reader-reuse-20261020/emit_routed_query.py",
+        "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900",
+    ),
+}
+
+
+def need(test, label):
+    if not test:
+        raise ValueError(label)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = (LANES / path).read_bytes()
+    if path.endswith(".gz"):
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source: " + name)
+    return raw
+
+
+def load_engine():
+    read("operator_engine")
+    spec = importlib.util.spec_from_file_location(
+        "involution_reader_engine", LANES / PINS["operator_engine"][0])
+    engine = importlib.util.module_from_spec(spec)
+    sys.modules[spec.name] = engine
+    spec.loader.exec_module(engine)
+    return engine
+
+
+def emit_word(engine, pair, involution, capture, pivots):
+    events, maps, registry, ranges = [], [], {}, {}
+    stage = pair["service_stage"]
+    full_axes = engine.UNIT[:9 + 8 * stage]
+    full = engine.phase.product([(v, 1) for v in full_axes])
+
+    def register(columns, translation):
+        columns = tuple(columns)
+        key = columns, translation
+        if key not in registry:
+            inverse = engine.transpose(columns)
+            need(engine.compose(columns, inverse) == engine.compose(inverse, columns)
+                 == engine.UNIT, "The route is orthogonal")
+            need(columns[9 + 8 * stage:] == engine.UNIT[9 + 8 * stage:],
+                 "The route fixes all future axes")
+            transformed = engine.phase.product(
+                [(engine.act(columns, v), 1) for v in full_axes])
+            need(engine.phase.add_phase(transformed, engine.phase.line(translation, 2)) == full,
+                 "The complete FULL phase equation")
+            registry[key] = len(maps)
+            maps.append({
+                "columns": columns, "translation": translation,
+                "inverse_columns": inverse,
+                "inverse_translation": engine.act(inverse, translation),
+            })
+        return registry[key]
+
+    def view(field, record, inverse=False):
+        route, delta = tuple(record["route_columns"]), record["translation"]
+        if inverse:
+            route = engine.transpose(route)
+            delta = engine.act(route, delta)
+        events.append(["map", field, register(route, delta)])
+
+    current = {v["port"]: v for v in pair["current_code_views"]}
+    old = {v["port"]: v for v in pair["old_reader_views"]}
+    ordinary = sorted(set(range(112)) - set(pivots))
+
+    def apply_current(name):
+        begin = len(events)
+        for p in range(112):
+            view(p, current[p])
+        for op, target, source, coefficient in involution["common_frame_words"]["A"]:
+            events.append(["scalar", op, target, source, coefficient])
+        for p in reversed(range(112)):
+            view(p, current[p], inverse=True)
+        ranges[name] = [begin, len(events)]
+
+    apply_current("apply_current_involution")
+    begin = len(events)
+    fields = [(p, p) for p in ordinary] + [(112 + p, p) for p in pivots]
+    for field, p in fields:
+        view(field, old[p])
+    for op, target, source, coefficient in capture["scalar_word"]:
+        need(target in pivots and (source is None or source in ordinary),
+             "The old complement reader is unchanged")
+        events.append(["scalar", op, 112 + target, source, coefficient])
+    for field, p in reversed(fields):
+        view(field, old[p], inverse=True)
+    ranges["old_reader_complement"] = [begin, len(events)]
+    begin = len(events)
+    for p in pivots:
+        events.append(["scalar", "add", 112 + p, p, "1"])
+    ranges["selected_reader_copy"] = [begin, len(events)]
+    apply_current("restore_current_involution")
+    return {"reader_stage": pair["reader_stage"], "service_stage": stage,
+            "events": events, "maps": maps, "stage_ranges": ranges}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    source = {name: read(name) for name in PINS}
+    inv, capture, prefix, access, dispatch = (
+        json.loads(source[name])
+        for name in ("involution", "capture", "prefix", "view_query", "dispatcher"))
+    engine = load_engine()
+    pivots = inv["pivots"]
+    selected = set(pivots)
+    need(pivots == prefix["selected_ports"] == capture["pivots"] == access["pivots"],
+         "All packets use the same physical selected ports")
+    matrix = engine.base.n.rows(inv["response"])
+    old_response = engine.base.n.rows(prefix["response"])
+    reader = engine.base.n.rows(capture["centre_reader"])
+    need(all(matrix[p] == old_response[p] for p in range(112) if p not in selected),
+         "The retained ordinary native response is exactly A_R")
+    need(engine.base.n.r.product(matrix, matrix) == engine.base.n.r.identity(112),
+         "The actual physical response is an involution")
+    scalar_state = engine.base.n.r.identity(112)
+    for op, target, origin, value in inv["common_frame_words"]["A"]:
+        coefficient = F(value)
+        if op == "add":
+            engine.base.n.r.add(scalar_state[target], scalar_state[origin], coefficient)
+        else:
+            need(op == "scale", "Only scalar ADD and SCALE")
+            scalar_state[target] = {j: coefficient * v for j, v in scalar_state[target].items()}
+    need(scalar_state == matrix, "The complete 112-column current scalar A word")
+    need(engine.base.n.r.price(inv["common_frame_words"]["A"]) == 3276,
+         "The exact scalar price of A")
+    prefix_reports = {}
+    for provider, word in prefix["providers"].items():
+        prefix_reports[provider] = engine.base.verify(
+            word, engine.base.n.r.identity(112), matrix, [{} for _ in range(112)], selected)
+    words, reports = {}, {}
+    for pair in access["pairs"]:
+        s, t = pair["reader_stage"], pair["service_stage"]
+        key = f"{s}:{t}"
+        stage_view = dispatch["stage_views"][t - 1]
+        data_exits = {v["port"]: v for v in stage_view["DATA_exit"] if v["side"] == "X"}
+        for view in pair["current_code_views"]:
+            expected = data_exits[view["port"]]
+            need(view["route_columns"] == expected["route_columns"]
+                 and view["translation"] == expected["translation_after_route"],
+                 "Current query views equal the actual DATA exits")
+        at = engine.routed(matrix, range(112), pair["current_code_views"])
+        ls = engine.routed(reader, pivots, pair["old_reader_views"])
+        direct = engine.product(ls, at)
+        word = emit_word(engine, pair, inv, capture, pivots)
+        initial = engine.initial_prefix(at, selected)
+        expected = [dict(row) for row in initial]
+        for p, row in zip(pivots, direct):
+            engine.add(expected[112 + p], row)
+        actual, complete_report = engine.replay(
+            word["events"], word["maps"], initial, selected)
+        need(actual == expected, "All 640 columns after the complete native prefix")
+        query_initial = [{(i, engine.UNIT): F(1)} for i in range(640)]
+        query_expected = [dict(row) for row in query_initial]
+        for p, row in zip(pivots, direct):
+            engine.add(query_expected[112 + p], row)
+        query_actual, query_report = engine.replay(
+            word["events"], word["maps"], query_initial, selected)
+        need(query_actual == query_expected, "All independent FULL query inputs")
+        need(query_actual[:112] == query_initial[:112]
+             and query_actual[224:] == query_initial[224:],
+             "Every source and arbitrary helper is restored")
+        need(query_report["scalar_primitives"] == 8440
+             and query_report["monomial_maps"] == 672, "The complete query invoice")
+        cutoff = word["stage_ranges"]["restore_current_involution"][0]
+        bad, _ = engine.replay(word["events"][:cutoff], word["maps"], query_initial, selected)
+        need(bad != query_expected, "Omitting the source restoration fails")
+        wrong_pair = deepcopy(pair)
+        wrong_pair["old_reader_views"] = wrong_pair["current_code_views"]
+        wrong_word = emit_word(engine, wrong_pair, inv, capture, pivots)
+        bad, _ = engine.replay(wrong_word["events"], wrong_word["maps"], query_initial, selected)
+        need(bad != query_expected, "Replacing the old reader by the current reader fails")
+        words[key] = word
+        reports[key] = {
+            "query": query_report, "after_native_prefix": complete_report,
+            "direct_owner_paths": sum(map(len, direct)),
+            "negative_controls": ["omitted_restore", "current_reader_substitution"],
+        }
+    invocations = deepcopy(dispatch["invocations"])
+    for call in invocations:
+        query_block = call["ordered_blocks"][-1]
+        need(query_block["op"] == "fixed_past_reader_query",
+             "The query follows the full native sweep and DATA exits")
+        query_block.update({
+            "source": "queries",
+            "literal_source": "queries",
+            "literal_key": f"{call['reader_stage']}:{call['service_stage']}",
+            "map_calls": 672,
+        })
+        query_block.pop("pair_record")
+        call["query_key"] = query_block["literal_key"]
+        call.pop("query_pair_record")
+        call["scalar_primitives"] = 14896
+        call["map_call_bound"]["late_query"] = 672
+        call["map_call_bound"]["total"] = 4384
+    payload = {
+        "schema": "involution-fixed-reader-service-v1", "source_pins": PINS,
+        "pivots": pivots, "response": inv["response"],
+        "native_prefixes": prefix["providers"], "queries": words,
+        "stage_views": dispatch["stage_views"], "invocations": invocations,
+        "physical_contract": {
+            "input": "(Fprev*x, Fprev*diag(I_P,q_R)*w)",
+            "output": "(Fnew*x, Fnew*diag(I_P,q_R)*(w+D_st*x))",
+            "response_rows_P": "L_s*A_t",
+            "response_rows_R": "(A_t)_R",
+            "arbitrary_selected_baselines": True,
+            "physical_input_level": "t-1, independent of reader stage s",
+        },
+        "helper_hosting": dispatch["owner_contract"],
+        "backward_or_complete_caller_claimed": False,
+    }
+    args.output.mkdir(parents=True, exist_ok=False)
+    raw = (json.dumps(payload, separators=(",", ":"), sort_keys=True) + "\n").encode()
+    (args.output / "INVOLUTION-READER.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {
+        "status": "PASS_ACTUAL_INVOLUTION_FIXED_READER_SERVICE",
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_decompressed_sha256": sha256(raw).hexdigest(),
+        "prefix_reports": prefix_reports, "query_reports": reports,
+        "query_scalar_primitives": 8440, "query_maps": 672,
+        "complete_word_scalar_primitives": 14896,
+        "own_word_monomial_call_bound": 4384,
+        "native_mass": 1792, "native_children": 1520,
+        "backward_or_complete_caller_claimed": False,
+    }
+    (args.output / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(receipt["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json
new file mode 100644
index 0000000000..854518cab3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json
@@ -0,0 +1,131 @@
+{
+  "backward_or_complete_caller_claimed": false,
+  "complete_word_scalar_primitives": 14896,
+  "native_children": 1520,
+  "native_mass": 1792,
+  "own_word_monomial_call_bound": 4384,
+  "payload_decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091",
+  "prefix_reports": {
+    "base": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "explicit_input_monomial_views": 128,
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/INVOLUTION-READER.json.gz b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/INVOLUTION-READER.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-optimized/CHECKS.json
new file mode 100644
index 0000000000..854518cab3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-optimized/CHECKS.json
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-optimized/INVOLUTION-READER.json.gz b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-20261020/final-optimized/INVOLUTION-READER.json.gz
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literal 0
HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/COMPLETE-DUAL.md b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/COMPLETE-DUAL.md
new file mode 100644
index 0000000000..c85a124027
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+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/COMPLETE-DUAL.md
@@ -0,0 +1,215 @@
+# The complete inverse-adjoint reader service
+
+This packet completes the physical inverse-adjoint of the fixed-reader
+forward service. It includes the native carrier prefix, all DATA maps,
+the whole-cover barrier, and the late query. The old-reader label can be
+0 or 1. The current service stage can be 1 or 2. The three pairs are
+\((s,t)=(0,1),(0,2),(1,2)\). Both native providers are included.
+
+The complete word costs 14,896 real scalar primitives and has native
+rank 1,792. It has no extra field and no odd division. All 416 borrowed
+helper fields can have arbitrary input values and are restored.
+The map count is an upper bound of 4,384 calls. This packet does not
+give a finite real-operation price for these maps, a new helper host,
+a closed caller, or a multiplication exponent.
+
+## The exact types
+
+Let P be the pinned set of sixteen selected ports. Let R be its
+96-port complement. Put
+
+\[
+G_R=\operatorname{diag}(I_P,q_R),\qquad
+F_\ell=\operatorname{FULL}_{9+8\ell}.
+\]
+
+The physical input level is \(t-1\), independent of the reader label s.
+The old reader is the actual routed \(L_s\). The current response is
+the actual routed dyadic involution \(A_t\). Define the complete
+112-row operator \(D_{s,t}\) by
+
+\[
+(D_{s,t})_P=L_sA_t,\qquad (D_{s,t})_R=(A_t)_R.
+\tag{1}
+\]
+
+The emitted inverse-adjoint service is
+
+\[
+(F_{t-1}x,\ F_{t-1}G_Rw)
+\longmapsto
+(F_t(x-D_{s,t}^{*}w),\ F_tG_Rw).
+\tag{2}
+\]
+
+The selected records and all ordinary records in w are arbitrary.
+The word preserves their logical contents. It does not set a borrowed
+baseline to zero. The star includes the inverse owner route of every
+coefficient, as well as the matrix transpose.
+
+For comparison, the frozen forward service has the same physical
+types and the content map \((x,w)\mapsto(x,w+D_{s,t}x)\).
+Equation (2) is its exact inverse-adjoint, with its unitary input and
+output frames retained.
+
+## Same chronology, complete physical operation
+
+For chronological gates \(g_1,\ldots,g_n\), the physical operator is
+\(U=g_n\cdots g_1\). Then
+
+\[
+U^{-*}=g_n^{-*}\cdots g_1^{-*}.
+\tag{3}
+\]
+
+Thus the chronological order does not change. For each scalar gate:
+
+- Replace `target += c * source` by `source -= c * target`.
+- Replace a real scale c by the scale \(c^{-1}\).
+
+All coefficients here are real. Every scale is a nonzero signed power
+of two. No CLEAR or noninvertible gate occurs.
+
+Each native child and each physical monomial map is unitary. Therefore
+its inverse-adjoint is the same physical operator, with the same global
+phase. The emitter retains every native event, phase recipe, input
+adapter, output adapter, DATA map, and late map at its original position.
+It checks all nine-dimensional monomial matrices for invertibility and
+all stored quadratic phases for unit modulus. The exact native recipe
+identities are inherited from the pinned independent phase review.
+No new native phase recipe is inferred from a binary rank alone.
+
+At every scalar event, the source and target have the same physical
+frame. Transposing that event therefore remains legal. The new replay
+checks this equality at every event, with the exact live frame ledger.
+It checks all 640 input columns. The native prefix gives
+
+\[
+x\longmapsto x-(A_t)_R^{*}w_R,\qquad w\longmapsto w.
+\tag{4}
+\]
+
+The late word then subtracts \((L_sA_t)^*w_P\) from X. Its maps touch
+only X and selected Y fields, which are FULL at that cut. Ordinary Y
+fields keep their hole frames and do not enter the late query.
+Equations (4) and this final subtraction give (2).
+
+The complete physical order remains:
+
+```text
+DATA entry
+128 native input adapters
+complete native carrier cover sweep
+96 ordinary output adapters
+DATA exit
+complete-cover barrier
+late inverse-adjoint reader query
+```
+
+The late map source fields are not relabelled. A former query target
+becomes a scalar source, while its physical map stays at the same place
+in the word. This distinction is checked in the serialized program.
+
+The same construction applies to any finite word of unitary field maps
+and invertible linear scalar gates. It requires the physical frame and
+field at each event, not an inverse of its response matrix. If the
+forward endpoint is a lower shear with reader D and is the identity
+on arbitrary borrowed fields, the new endpoint is the upper shear with
+reader \(-D^*\) and is also the identity on those fields. D can be
+rectangular or singular. For composition, apply the rule to the complete
+physical gate list in its existing chronological order. A new boundary
+conversion is needed only when the original words did not already have
+compatible physical types.
+
+## Actual D25 source and phase binding
+
+Each field uses the exact regular-cover route
+\(h=d\rho_{t,p}\). The route is orthogonal, fixes the port's intrinsic
+line, and has the pinned DATA translation. The emitter repeats all
+448 entry and 448 exit Z4 identities in the dispatcher. It also checks
+the complete Z4 identity and inverse translation of each late FULL map.
+
+The native input and output types in the current body are
+
+\[
+\operatorname{diag}(Q,Z),\qquad
+\operatorname{diag}(F_9,F_9G_R),
+\quad Z=\operatorname{diag}(Q_P,I_R).
+\]
+
+The DATA identities identify these types with the two global boundaries
+in (2), with the same common exterior. They apply to the new word
+because all its physical frame operators are unchanged.
+
+For a unitary input frame I and output frame O, a content map C has
+physical action \(OCI^{-1}\). Its inverse-adjoint is
+\(OC^{-*}I^{-1}\). This proves the direction of the retained physical
+boundaries. It does not reverse the stage progression or exchange the
+two DATA views.
+
+The regular-cover replay retains both the input field and the complete
+25-axis owner matrix in every coefficient. It lifts the replayed native
+prefix through the actual DATA arrays, then executes the literal late
+word. For all six provider/pair cases, it equals the direct operator in
+(2). Both products with the forward adjoint are the identity on all
+640 fields. The actual source-view order is part of this calculation.
+
+## Full invoice and bounds
+
+| Part | Real scalar primitives | Map calls |
+| --- | ---: | ---: |
+| Native carrier prefix | 6,456 | 224 endpoint adapters |
+| Late inverse-adjoint query | 8,440 | 672 |
+| DATA entry and exit | 0 | 448 |
+| Native child side maps | 0 | at most 3,040 |
+| Complete word | 14,896 | at most 4,384 |
+
+The native profile is
+
+```text
+1392 H1 + 64 H2 + 48 H3 + 16 H8.
+```
+
+There are 1,520 native children and total native rank 1,792. Scalar
+transposition and inversion of signed power-of-two scales preserve
+the frozen tariff. Native child sizes and physical side maps do not
+change.
+
+The exact coefficient row-sum peak of the native prefix is 12, with
+binary denominator height one. The late dual on independent inputs
+has peak 30 and height two. After the actual native prefix, the complete
+emitted-boundary peak is 40 and height two in all six cases.
+These are content bounds at the emitted gate boundaries. They exclude
+internal arithmetic in a lowered ADD, a recursive child, or a caller.
+
+The original helper owner contract is retained. The same helper fields
+and native events occur at the same times, and the new 640-column replay
+restores every arbitrary helper value. This does not prove a new
+recursive parking construction or change the inherited helper count.
+
+## Verification, scope, and credit
+
+Run `emit_dual.py --output <new-directory>` with normal Python and with
+`python3 -O`. The payloads and receipts must be byte equal. The emitter
+rejects an existing output directory.
+
+The checks include the complete physical frame ledgers, all 640 native
+and routed columns, all 416 helper identities, both inverse product
+orders, the 896 DATA phase equations, and all late map phases.
+Changing a dual ADD sign fails in both native prefixes and in all three
+late queries. The serialized complete words are replayed again.
+
+The packet uses the controller lane's row involution, the native lane's
+carrier prefix, the reviewed fixed-reader forward query, and the
+independent native, DATA, and late-dual reviews. Their exact paths and
+hashes are in the program and freeze manifest. This work was produced
+with AI assistance and exact rational computation.
+
+This result supplies a complete backward service with the types in
+(2). It does not assert that \(D_{s,t}\) is reciprocal, that it is the
+same at different stages, or that a complete caller closes. The original
+raw-output phases, recursive hosting, finite map costs, and final
+supplier calculation remain separate obligations.
+
+No PR or publication is authorized. Before any future PR description,
+read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json
new file mode 100644
index 0000000000..a4a2556a48
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json
@@ -0,0 +1,19 @@
+{
+  "PR_description_prerequisite": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md",
+  "all_416_other_fields_untouched_by_emitted_top_level_events": true,
+  "explicit_top_level_fields_used": 224,
+  "files": {
+    "COMPLETE-DUAL.md": "37a3a187acf93cad2048f9147457bf8925cf53ce61836b5e899dd13bc4239c5e",
+    "emit_dual.py": "4c10ca91f788052bc3e1da43f63d6dde0a84d4b8b1c34e8f64f3912e47a86a32",
+    "final-normal/CHECKS.json": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84",
+    "final-normal/COMPLETE-DUAL.json.gz": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1",
+    "final-optimized/CHECKS.json": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84",
+    "final-optimized/COMPLETE-DUAL.json.gz": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1"
+  },
+  "independent_review": "Requested separately; not claimed by this freeze.",
+  "normal_optimized_byte_equal": true,
+  "payload_decompressed_sha256": "f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be",
+  "publication": "No PR or publication authorized.",
+  "schema": "complete-inverse-adjoint-reader-freeze-v1",
+  "status": "PASS_PRODUCER_EXACT_NORMAL_AND_OPTIMIZED"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py
new file mode 100644
index 0000000000..3e7c798f7e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py
@@ -0,0 +1,433 @@
+"""Emit the complete inverse-adjoint routed reader service."""
+
+import argparse
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+PINS = {
+    "forward": (
+        "bridge-access-20261017/involution-reader-20261020/"
+        "final-normal/INVOLUTION-READER.json.gz",
+        "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091",
+    ),
+    "forward_freeze": (
+        "bridge-access-20261017/involution-reader-20261020/FREEZE.json",
+        "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6",
+    ),
+    "forward_review": (
+        "bridge-review-20261017/involution-reader-review-20261020/FREEZE.json",
+        "b4770cbd56bc8b115728529ab218d60ca2bd1a385896ba78cfdf374f04370c97",
+    ),
+    "native_phase_review": (
+        "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json",
+        "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c",
+    ),
+    "dispatcher_freeze": (
+        "bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json",
+        "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331",
+    ),
+    "engine": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "fixed-reader-reuse-20261020/emit_routed_query.py",
+        "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900",
+    ),
+    "views": (
+        "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json",
+        "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473",
+    ),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = (LANES / path).read_bytes()
+    if path.endswith(".gz"):
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source: " + name)
+    return raw
+
+
+def load_engine():
+    read("engine")
+    spec = importlib.util.spec_from_file_location(
+        "complete_reader_dual_engine", LANES / PINS["engine"][0])
+    result = importlib.util.module_from_spec(spec)
+    sys.modules[spec.name] = result
+    spec.loader.exec_module(result)
+    return result
+
+
+def scalar_dual(gate):
+    op, target, source, raw = gate
+    value = F(raw)
+    if op == "add":
+        return [op, source, target, str(-value)]
+    need(op == "scale" and value, "Every scalar gate is invertible")
+    return [op, target, None, str(1 / value)]
+
+
+def dual_prefix(original):
+    word = deepcopy(original)
+    for old, new in zip(original["events"], word["events"]):
+        if old[0] == "scalar":
+            new[1] = scalar_dual(old[1])
+        else:
+            need(old[0] == "native" and new == old, "Native events do not change")
+    for key in original:
+        if key != "events":
+            need(word[key] == original[key], "All native records and adapters stay fixed")
+    return word
+
+
+def dual_query(original):
+    word = deepcopy(original)
+    for index, event in enumerate(original["events"]):
+        if event[0] == "scalar":
+            word["events"][index] = ["scalar"] + scalar_dual(event[1:])
+        else:
+            need(event[0] == "map" and word["events"][index] == event,
+                 "Every physical field map stays in the same position")
+    need(word["maps"] == original["maps"], "All map phases and inverse records stay fixed")
+    return word
+
+
+def unitary_records(engine, word):
+    records = []
+    for recipe in word["native_recipes"].values():
+        need(1 <= recipe["rank"] <= 9, "A normalized native child has positive rank")
+        records.extend(recipe[key] for key in ("left", "right") if recipe[key] is not None)
+    for view in word["input_views"]:
+        need(view["rank"] == 0 and view["right"] is None, "A monomial input adapter")
+        records.append(view["left"])
+    for view in word["output_views"]:
+        recipe = view["recipe"]
+        need(recipe["rank"] == 0 and recipe["right"] is None, "A monomial output adapter")
+        records.append(recipe["left"])
+    for record in records:
+        need(len(record["matrix_rows"]) == 9
+             and len(engine.base.n.basis(record["matrix_rows"])) == 9,
+             "A physical monomial side map is a bijection")
+        need(0 <= record["offset"] < 512 and 0 <= record["phase"] < 4,
+             "A physical offset and unit-modulus global phase")
+        need(len(record["linear_Z4"]) == len(record["quadratic_rows"]) == 9
+             and all(0 <= x < 4 for x in record["linear_Z4"])
+             and all(0 <= x < 512 for x in record["quadratic_rows"]),
+             "The complete unit-modulus quadratic phase record")
+    return len(records)
+
+
+def replay_prefix(engine, word):
+    current = list(word["start"])
+    state = engine.base.n.r.identity(640)
+    profile = Counter()
+    maximum, height, price = F(1), 0, 0
+    for event in word["events"]:
+        if event[0] == "native":
+            _, target, old, new, rank, key = event
+            need(current[target] == old, "The physical native input frame")
+            a, b = word["frames"][old], word["frames"][new]
+            need(len(engine.base.n.basis(a + b)) == len(b), "Nested native frames")
+            need(len(b) - len(a) == rank == word["native_recipes"][key]["rank"],
+                 "The physical native rank and recipe")
+            current[target] = new
+            profile[rank] += 1
+            continue
+        need(event[0] == "scalar", "The complete native event grammar")
+        gate, frame = event[1:]
+        op, target, source, raw = gate
+        value = F(raw)
+        need(current[target] == frame, "The dual scalar target frame")
+        if op == "add":
+            need(source != target and current[source] == frame,
+                 "The dual scalar source has the same physical frame")
+            engine.base.n.r.add(state[target], state[source], value)
+        else:
+            need(op == "scale", "Only ADD and SCALE")
+            state[target] = {j: value * x for j, x in state[target].items()}
+        price += engine.base.n.r.price([gate])
+        maximum = max(maximum, sum(abs(x) for x in state[target].values()))
+        for x in state[target].values():
+            d = x.denominator
+            need(d & (d - 1) == 0, "All scalar coefficients are dyadic")
+            height = max(height, d.bit_length() - 1)
+    need(current == word["final"], "All 640 final physical frames")
+    need(state[224:] == engine.base.n.r.identity(640)[224:],
+         "All 416 arbitrary helper fields are restored")
+    return state, {
+        "input_fields": 640, "restored_helper_fields": 416,
+        "native_profile": dict(sorted(profile.items())),
+        "native_children": sum(profile.values()),
+        "native_mass": sum(k * v for k, v in profile.items()),
+        "scalar_primitives": price,
+        "coefficient_prefix_row_sum": str(maximum),
+        "coefficient_binary_height": height,
+        "input_adapter_maps": len(word["input_views"]),
+        "output_adapter_maps": len(word["output_views"]),
+    }
+
+
+def phase_bindings(engine, bundle, views):
+    records = {(v["stage"], v["port"]): v for v in views["entries"]}
+    counts = Counter()
+    for stage in bundle["stage_views"]:
+        t = stage["service_stage"]
+        need(stage["physical_input_level"] == t - 1
+             and stage["physical_output_level"] == t, "The adjacent physical levels")
+        before = [(v, 1) for v in engine.UNIT[:9 + 8 * (t - 1)]]
+        after = [(v, 1) for v in engine.UNIT[:9 + 8 * t]]
+        exterior = [(v, 1) for v in engine.UNIT[9:9 + 8 * t]]
+        for key in ("DATA_entry", "DATA_exit"):
+            need(len(stage[key]) == 224 and {v["field"] for v in stage[key]} == set(range(224)),
+                 "The DATA maps cover every field exactly once")
+            for view in stage[key]:
+                p = view["port"]
+                side = view["side"]
+                need(view["field"] == p + (112 if side == "Y" else 0),
+                     "The physical field and bank are unchanged")
+                literal = records[t, p]
+                rho = literal["route_columns"]
+                q = literal["q"]
+                align = literal["literal_stage_alignment"]
+                need(view["route_columns"] == rho and view["owner_from_body"] == "h=d*rho",
+                     "The exact regular-cover owner view")
+                need(engine.compose(tuple(rho), engine.transpose(rho)) == engine.UNIT
+                     and engine.act(rho, q) == q, "Orthogonal own-line DATA route")
+                full = side == "X" or p in bundle["pivots"]
+                if key == "DATA_entry":
+                    delta = engine.act(rho, align["entry_" + side])
+                    need(view["translation_before_route"] == align["entry_" + side]
+                         and view["translation_after_route"] == delta, "The literal entry phase")
+                    source = before + ([] if full else [(q, -1)])
+                    wanted = exterior + ([(q, 1)] if full else [])
+                else:
+                    exit_key = "exit_X" if full else "exit_Y"
+                    delta = align[exit_key]
+                    need(view["translation_after_route"] == delta
+                         and view["literal_translation_key"] == exit_key, "The literal exit phase")
+                    source = after + ([] if full else [(q, -1)])
+                    wanted = source
+                actual = engine.phase.add_phase(
+                    engine.phase.product([(engine.act(rho, v), n) for v, n in source]),
+                    engine.phase.line(delta, 2))
+                need(actual == engine.phase.product(wanted), "The complete DATA Z4 identity")
+                counts[key] += 1
+    return dict(counts)
+
+
+def identity(engine):
+    return [{(i, engine.UNIT): F(1)} for i in range(640)]
+
+
+def adjoint(engine, rows):
+    result = [{} for _ in rows]
+    for target, row in enumerate(rows):
+        for (source, route), value in row.items():
+            engine.add(result[source], {(target, engine.transpose(route)): value})
+    return result
+
+
+def lift_prefix(engine, local, stage):
+    rho = {v["field"]: tuple(v["route_columns"]) for v in stage["DATA_exit"]}
+    result = []
+    for target, row in enumerate(local):
+        if target >= 224:
+            need(row == {target: F(1)}, "The helper endpoint is the actual identity")
+            result.append({(target, engine.UNIT): F(1)})
+            continue
+        need(all(source < 224 for source in row), "No borrowed helper enters a data output")
+        result.append({
+            (source, engine.compose(engine.transpose(rho[target]), rho[source])): value
+            for source, value in row.items()
+        })
+    return result
+
+
+def check_query_maps(engine, word):
+    t = word["service_stage"]
+    full_axes = engine.UNIT[:9 + 8 * t]
+    full = engine.phase.product([(v, 1) for v in full_axes])
+    for record in word["maps"]:
+        route, inverse = tuple(record["columns"]), tuple(record["inverse_columns"])
+        need(engine.compose(route, inverse) == engine.compose(inverse, route) == engine.UNIT,
+             "The late map and its inverse are exact")
+        need(inverse == engine.transpose(route), "The late route is orthogonal")
+        need(route[9 + 8 * t:] == engine.UNIT[9 + 8 * t:], "Future axes stay fixed")
+        need(record["inverse_translation"] == engine.act(inverse, record["translation"]),
+             "The inverse translation is exact")
+        actual = engine.phase.add_phase(
+            engine.phase.product([(engine.act(route, v), 1) for v in full_axes]),
+            engine.phase.line(record["translation"], 2))
+        need(actual == full, "The complete late FULL phase identity")
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    sources = {name: read(name) for name in PINS}
+    forward = json.loads(sources["forward"])
+    views = json.loads(sources["views"])
+    engine = load_engine()
+    selected = set(forward["pivots"])
+    response = engine.base.n.rows(forward["response"])
+    phase_report = phase_bindings(engine, forward, views)
+    prefixes, prefix_states, prefix_reports = {}, {}, {}
+    expected_local = engine.base.n.r.identity(640)
+    for target, row in enumerate(response):
+        if target not in selected:
+            for source, value in row.items():
+                engine.base.n.r.add(expected_local[source], {112 + target: -value})
+    for provider, original in forward["native_prefixes"].items():
+        word = dual_prefix(original)
+        unitary_count = unitary_records(engine, word)
+        state, report = replay_prefix(engine, word)
+        need(state == expected_local, "All 640 local inverse-adjoint columns")
+        need(report["native_mass"] == 1792 and report["native_children"] == 1520
+             and report["scalar_primitives"] == 6456, "The complete native dual invoice")
+        need(dual_prefix(word) == original, "The gatewise operation is an involution")
+        bad = deepcopy(word)
+        index = next(i for i, event in enumerate(bad["events"])
+                     if event[0] == "scalar" and event[1][0] == "add")
+        bad["events"][index][1][3] = str(-F(bad["events"][index][1][3]))
+        altered, _ = replay_prefix(engine, bad)
+        need(altered != expected_local, "A wrong native-prefix dual sign fails")
+        report["unitary_monomial_records_checked"] = unitary_count
+        report["negative_control_wrong_native_prefix_sign"] = True
+        prefixes[provider], prefix_states[provider], prefix_reports[provider] = word, state, report
+    query_words, reports, complete_states = {}, {}, {}
+    unit = identity(engine)
+    for key, original in forward["queries"].items():
+        word = dual_query(original)
+        need(dual_query(word) == original, "The late gatewise operation is an involution")
+        check_query_maps(engine, word)
+        query_forward, _ = engine.replay(original["events"], original["maps"], unit, selected)
+        query_expected = adjoint(engine, [
+            {term: (2 * value if term == (i, engine.UNIT) else F(0)) - value
+             for term, value in row.items()}
+            for i, row in enumerate(query_forward)
+        ])
+        actual_query, query_report = engine.replay(word["events"], word["maps"], unit, selected)
+        need(actual_query == query_expected, "All 640 independent late dual columns")
+        need(query_report["scalar_primitives"] == 8440 and query_report["monomial_maps"] == 672,
+             "The exact late dual invoice")
+        t = word["service_stage"]
+        stage = forward["stage_views"][t - 1]
+        per_provider = {}
+        for provider, local in prefix_states.items():
+            initial = lift_prefix(engine, local, stage)
+            actual, report = engine.replay(word["events"], word["maps"], initial, selected)
+            local_forward = engine.base.n.r.identity(640)
+            for p in range(112):
+                if p not in selected:
+                    engine.base.n.r.add(local_forward[112 + p], response[p])
+            forward_initial = lift_prefix(engine, local_forward, stage)
+            forward_complete, _ = engine.replay(
+                original["events"], original["maps"], forward_initial, selected)
+            inverse_forward = [dict(row) for row in unit]
+            for target in range(112, 224):
+                for term, value in forward_complete[target].items():
+                    if term != (target, engine.UNIT):
+                        engine.add(inverse_forward[target], {term: -value})
+            expected = adjoint(engine, inverse_forward)
+            need(actual == expected, "All 640 complete routed inverse-adjoint columns")
+            complete_states[key, provider] = actual
+            need(actual[112:] == unit[112:], "All target records and 416 helper fields are restored")
+            forward_star = adjoint(engine, forward_complete)
+            need(engine.product(actual, forward_star) == engine.product(forward_star, actual) == unit,
+                 "Both complete content inverse-adjoint products")
+            need(engine.product(forward_complete, inverse_forward)
+                 == engine.product(inverse_forward, forward_complete) == unit,
+                 "Both complete forward inverse products")
+            per_provider[provider] = report
+        bad = deepcopy(word)
+        index = next(i for i, e in enumerate(bad["events"])
+                     if e[0] == "scalar" and e[1] == "add" and e[3] >= 112)
+        bad["events"][index][4] = str(-F(bad["events"][index][4]))
+        altered, _ = engine.replay(bad["events"], bad["maps"], unit, selected)
+        need(altered != actual_query, "A wrong transferred source sign fails")
+        query_words[key] = word
+        reports[key] = {"late_query": query_report, "complete_word": per_provider,
+                        "all_640_columns": True, "both_inverse_products": True,
+                        "negative_control_wrong_transferred_source_sign": True}
+    invocations = deepcopy(forward["invocations"])
+    expected_order = ["DATA_entry", "native_input_adapters",
+                      "complete_native_carrier_cover_sweep", "ordinary_output_adapters",
+                      "DATA_exit", "complete_cover_barrier", "fixed_past_reader_query"]
+    for call in invocations:
+        need([b["op"] for b in call["ordered_blocks"]] == expected_order,
+             "The complete physical block order stays fixed")
+        need(call["physical_input_level"] == call["service_stage"] - 1,
+             "The physical entry level is separate from the old reader label")
+        need(call["query_key"] in query_words and call["provider"] in prefixes,
+             "Every invocation resolves to complete emitted words")
+        call["ordered_blocks"][-1]["op"] = "inverse_adjoint_fixed_past_reader_query"
+    payload = {
+        "schema": "complete-inverse-adjoint-involution-reader-v1",
+        "source_pins": PINS, "pivots": forward["pivots"], "response": forward["response"],
+        "native_prefixes": prefixes, "queries": query_words,
+        "stage_views": forward["stage_views"], "invocations": invocations,
+        "helper_hosting": forward["helper_hosting"],
+        "physical_contract": {
+            "input": "(Fprev*x, Fprev*diag(I_P,q_R)*w)",
+            "output": "(Fnew*(x-D_st^*w), Fnew*diag(I_P,q_R)*w)",
+            "D_st_rows_P": "L_s*A_t", "D_st_rows_R": "(A_t)_R",
+            "physical_input_level": "t-1, independent of reader stage s",
+            "arbitrary_inputs": "All 640 fields; no zero selected baseline.",
+        },
+        "scope": "Complete typed inverse-adjoint service for three D25 pairs and two providers. "
+                 "No complete caller, new helper host, finite map cost, or exponent claim.",
+    }
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    need(saved["stage_views"] == forward["stage_views"]
+         and saved["helper_hosting"] == forward["helper_hosting"],
+         "Serialized DATA phase records and helper contract are unchanged")
+    for provider, word in saved["native_prefixes"].items():
+        state, report = replay_prefix(engine, word)
+        need(state == prefix_states[provider]
+             and all(value == prefix_reports[provider][key] for key, value in report.items()),
+             "The serialized complete native dual passes")
+    for key, word in saved["queries"].items():
+        stage = saved["stage_views"][word["service_stage"] - 1]
+        for provider in prefixes:
+            actual, report = engine.replay(word["events"], word["maps"],
+                lift_prefix(engine, prefix_states[provider], stage), selected)
+            need(actual == complete_states[key, provider]
+                 and report == reports[key]["complete_word"][provider],
+                 "The serialized complete routed dual passes")
+    args.output.mkdir(parents=True, exist_ok=False)
+    (args.output / "COMPLETE-DUAL.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {
+        "status": "PASS_COMPLETE_TYPED_INVERSE_ADJOINT_READER",
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_decompressed_sha256": sha256(raw).hexdigest(),
+        "prefix_reports": prefix_reports, "query_reports": reports,
+        "DATA_phase_equations": phase_report,
+        "all_native_and_endpoint_phase_records_unchanged": True,
+        "all_late_map_fields_phases_and_positions_unchanged": True,
+        "all_640_columns_and_416_helpers_checked": True,
+        "complete_scalar_primitives": 14896, "complete_native_rank": 1792,
+        "complete_native_children": 1520, "own_word_map_call_bound": 4384,
+        "scope": payload["scope"],
+    }
+    (args.output / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json
new file mode 100644
index 0000000000..382247af36
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json
@@ -0,0 +1,134 @@
+{
+  "DATA_phase_equations": {
+    "DATA_entry": 448,
+    "DATA_exit": 448
+  },
+  "all_640_columns_and_416_helpers_checked": true,
+  "all_late_map_fields_phases_and_positions_unchanged": true,
+  "all_native_and_endpoint_phase_records_unchanged": true,
+  "complete_native_children": 1520,
+  "complete_native_rank": 1792,
+  "complete_scalar_primitives": 14896,
+  "own_word_map_call_bound": 4384,
+  "payload_decompressed_sha256": "f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be",
+  "prefix_reports": {
+    "base": {
+      "coefficient_binary_height": 1,
+      "coefficient_prefix_row_sum": "12",
+      "input_adapter_maps": 128,
+      "input_fields": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "negative_control_wrong_native_prefix_sign": true,
+      "output_adapter_maps": 96,
+      "restored_helper_fields": 416,
+      "scalar_primitives": 6456,
+      "unitary_monomial_records_checked": 3150
+    },
+    "extra": {
+      "coefficient_binary_height": 1,
+      "coefficient_prefix_row_sum": "12",
+      "input_adapter_maps": 128,
+      "input_fields": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "negative_control_wrong_native_prefix_sign": true,
+      "output_adapter_maps": 96,
+      "restored_helper_fields": 416,
+      "scalar_primitives": 6456,
+      "unitary_monomial_records_checked": 3150
+    }
+  },
+  "producer_sha256": "4c10ca91f788052bc3e1da43f63d6dde0a84d4b8b1c34e8f64f3912e47a86a32",
+  "query_reports": {
+    "0:1": {
+      "all_640_columns": true,
+      "both_inverse_products": true,
+      "complete_word": {
+        "base": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        },
+        "extra": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        }
+      },
+      "late_query": {
+        "additional_binary_height": 2,
+        "exact_prefix_content_one_norm": "30",
+        "monomial_maps": 672,
+        "scalar_primitives": 8440
+      },
+      "negative_control_wrong_transferred_source_sign": true
+    },
+    "0:2": {
+      "all_640_columns": true,
+      "both_inverse_products": true,
+      "complete_word": {
+        "base": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        },
+        "extra": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        }
+      },
+      "late_query": {
+        "additional_binary_height": 2,
+        "exact_prefix_content_one_norm": "30",
+        "monomial_maps": 672,
+        "scalar_primitives": 8440
+      },
+      "negative_control_wrong_transferred_source_sign": true
+    },
+    "1:2": {
+      "all_640_columns": true,
+      "both_inverse_products": true,
+      "complete_word": {
+        "base": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        },
+        "extra": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        }
+      },
+      "late_query": {
+        "additional_binary_height": 2,
+        "exact_prefix_content_one_norm": "30",
+        "monomial_maps": 672,
+        "scalar_primitives": 8440
+      },
+      "negative_control_wrong_transferred_source_sign": true
+    }
+  },
+  "scope": "Complete typed inverse-adjoint service for three D25 pairs and two providers. No complete caller, new helper host, finite map cost, or exponent claim.",
+  "status": "PASS_COMPLETE_TYPED_INVERSE_ADJOINT_READER"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/COMPLETE-DUAL.json.gz b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/COMPLETE-DUAL.json.gz
new file mode 100644
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-optimized/CHECKS.json
new file mode 100644
index 0000000000..382247af36
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-optimized/CHECKS.json
@@ -0,0 +1,134 @@
+{
+  "DATA_phase_equations": {
+    "DATA_entry": 448,
+    "DATA_exit": 448
+  },
+  "all_640_columns_and_416_helpers_checked": true,
+  "all_late_map_fields_phases_and_positions_unchanged": true,
+  "all_native_and_endpoint_phase_records_unchanged": true,
+  "complete_native_children": 1520,
+  "complete_native_rank": 1792,
+  "complete_scalar_primitives": 14896,
+  "own_word_map_call_bound": 4384,
+  "payload_decompressed_sha256": "f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be",
+  "prefix_reports": {
+    "base": {
+      "coefficient_binary_height": 1,
+      "coefficient_prefix_row_sum": "12",
+      "input_adapter_maps": 128,
+      "input_fields": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "negative_control_wrong_native_prefix_sign": true,
+      "output_adapter_maps": 96,
+      "restored_helper_fields": 416,
+      "scalar_primitives": 6456,
+      "unitary_monomial_records_checked": 3150
+    },
+    "extra": {
+      "coefficient_binary_height": 1,
+      "coefficient_prefix_row_sum": "12",
+      "input_adapter_maps": 128,
+      "input_fields": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "negative_control_wrong_native_prefix_sign": true,
+      "output_adapter_maps": 96,
+      "restored_helper_fields": 416,
+      "scalar_primitives": 6456,
+      "unitary_monomial_records_checked": 3150
+    }
+  },
+  "producer_sha256": "4c10ca91f788052bc3e1da43f63d6dde0a84d4b8b1c34e8f64f3912e47a86a32",
+  "query_reports": {
+    "0:1": {
+      "all_640_columns": true,
+      "both_inverse_products": true,
+      "complete_word": {
+        "base": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        },
+        "extra": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        }
+      },
+      "late_query": {
+        "additional_binary_height": 2,
+        "exact_prefix_content_one_norm": "30",
+        "monomial_maps": 672,
+        "scalar_primitives": 8440
+      },
+      "negative_control_wrong_transferred_source_sign": true
+    },
+    "0:2": {
+      "all_640_columns": true,
+      "both_inverse_products": true,
+      "complete_word": {
+        "base": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        },
+        "extra": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        }
+      },
+      "late_query": {
+        "additional_binary_height": 2,
+        "exact_prefix_content_one_norm": "30",
+        "monomial_maps": 672,
+        "scalar_primitives": 8440
+      },
+      "negative_control_wrong_transferred_source_sign": true
+    },
+    "1:2": {
+      "all_640_columns": true,
+      "both_inverse_products": true,
+      "complete_word": {
+        "base": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        },
+        "extra": {
+          "additional_binary_height": 2,
+          "exact_prefix_content_one_norm": "40",
+          "monomial_maps": 672,
+          "scalar_primitives": 8440
+        }
+      },
+      "late_query": {
+        "additional_binary_height": 2,
+        "exact_prefix_content_one_norm": "30",
+        "monomial_maps": 672,
+        "scalar_primitives": 8440
+      },
+      "negative_control_wrong_transferred_source_sign": true
+    }
+  },
+  "scope": "Complete typed inverse-adjoint service for three D25 pairs and two providers. No complete caller, new helper host, finite map cost, or exponent claim.",
+  "status": "PASS_COMPLETE_TYPED_INVERSE_ADJOINT_READER"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-optimized/COMPLETE-DUAL.json.gz b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-optimized/COMPLETE-DUAL.json.gz
new file mode 100644
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json
new file mode 100644
index 0000000000..df6d92de6f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json
@@ -0,0 +1,12810 @@
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py
new file mode 100644
index 0000000000..8ff43e525f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py
@@ -0,0 +1,237 @@
+"""Check the actual matching response in complete supplier stage views."""
+
+from collections import Counter, defaultdict
+import ast
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+PINS = {
+    "matching": ("controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json", "plain", "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902"),
+    "permutation64": ("history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz", "gzip", "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9"),
+    "views": ("bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", "compressed", "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f"),
+    "phase": ("bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py", "python", "cf39b15752fcb96cc22b9013dce38e13a4399d99b30dc9f53eef788d5ded2bf4"),
+    "scalar_price": ("new-core-transfer-20261017/emit_raw_selected.py", "source", "a07cf4894a2599993006c7b99e6cb62146ece82f2ae6df72a28100ccb3a689bc"),
+}
+
+
+def need(ok, label):
+    if not ok:
+        raise ValueError(label)
+
+
+def load():
+    data = {}
+    for name, (rel, kind, pin) in PINS.items():
+        raw = (LANES / rel).read_bytes()
+        if kind == "gzip":
+            raw = gzip.decompress(raw)
+        need(sha256(raw).hexdigest() == pin, name + " source pin")
+        if kind == "python":
+            spec = importlib.util.spec_from_file_location("matched_access_phase", LANES / rel)
+            module = importlib.util.module_from_spec(spec)
+            spec.loader.exec_module(module)
+            base, ports = module.load()
+        elif kind != "source":
+            data[name] = json.loads(gzip.decompress(raw) if kind == "compressed" else raw)
+    return base, ports, data
+
+
+def rows(matrix):
+    return [{int(j): F(c) for j, c in row.items() if F(c)} for row in matrix]
+
+
+def product(a, b):
+    result = []
+    for row in a:
+        out = defaultdict(F)
+        for j, c in row.items():
+            for k, d in b[j].items():
+                out[k] += c * d
+        result.append({j: c for j, c in out.items() if c})
+    return result
+
+
+def inverse_word(word):
+    return [[op, p, q, str(-F(c))] if op == "add" else [op, p, q, str(1 / F(c))]
+            for op, p, q, c in reversed(word)]
+
+
+def scale(word, p, c):
+    if c != 1:
+        word.append(["scale", p, p, str(c)])
+
+
+def swap(word, p, r, sign=1):
+    word += [["add", p, r, "1"], ["add", r, p, "-1"], ["add", p, r, "1"]]
+    scale(word, r, F(-1))
+    scale(word, p, F(sign))
+    scale(word, r, F(sign))
+
+
+def pair_word(source):
+    word = []
+    for pair in source["pair_codes"]:
+        p, r = pair["ports"]
+        a, b = map(F, pair["matrix"][0])
+        c, d = map(F, pair["matrix"][1])
+        need(d == -c * b / a and abs(a) == abs(b) == abs(c) == 1, "Signed pair code")
+        scale(word, p, a)
+        scale(word, r, b)
+        word += [["add", p, r, "1"], ["scale", r, r, "-2"], ["add", r, p, "1"]]
+        scale(word, r, c / a)
+        need([source["modes"][j]["carrier"] for j in pair["mode_ids"]] == [p, r], "Mode carrier order")
+    return word
+
+
+def scalar_word(source, permutation):
+    pre = pair_word(source)
+    word = list(pre)
+    for vertex in source["vertex_matchings"]:
+        for pair in vertex["matching_pairs"]:
+            p, r = [source["modes"][j]["carrier"] for j in pair["modes"]]
+            swap(word, p, r, pair["weight"])
+    word += inverse_word(pre)
+    for p, r in sorted((int(p), int(r)) for p, r in permutation["partner"].items() if int(p) < int(r)):
+        swap(word, p, r, -1)
+    return word
+
+
+def replay(word, target):
+    state = [{p: F(1)} for p in range(112)]
+    peak = F(1)
+    price = 0
+    census = Counter()
+    for op, p, r, raw in word:
+        c = F(raw)
+        a, b = abs(c.numerator), c.denominator
+        need(b & (b - 1) == 0, "Dyadic scalar")
+        if op == "add":
+            need(p != r, "Distinct scalar rows")
+            out = defaultdict(F, state[p])
+            for j, d in state[r].items():
+                out[j] += c * d
+            state[p] = {j: d for j, d in out.items() if d}
+            price += 2 * (3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1)
+        else:
+            need(op == "scale" and a & (a - 1) == 0, "Dyadic unit scale")
+            state[p] = {j: c * d for j, d in state[p].items()}
+            price += 2 * (abs(a.bit_length() - b.bit_length()) + int(c < 0))
+        census[op] += 1
+        peak = max(peak, sum(abs(c) for c in state[p].values()))
+    need(state == target, "All 112 scalar input columns")
+    return {"events": len(word), "census": dict(census), "real_scalar_primitives": price,
+            "peak_row_one_norm": str(peak), "native_children": 0, "owned_fields": 0}
+
+
+def compose(base, *maps):
+    out = list(base.UNIT)
+    for item in reversed(maps):
+        out = [base.act(item, v) for v in out]
+    return out
+
+
+def main():
+    base, ports, data = load()
+    q = [p["q"] for p in ports]
+    source = data["matching"]
+    identity = [{p: F(1)} for p in range(112)]
+    matched = rows(source["response"])
+    permuted = [dict(row) for row in matched]
+    for p in data["permutation64"]["active_ports"]:
+        permuted[p] = rows([data["permutation64"]["response"][p]])[0]
+    for response in (matched, permuted):
+        need(product(response, response) == identity, "Both full response involutions")
+        need(all(p not in row for p, row in enumerate(response)), "Every physical diagonal is zero")
+    word = scalar_word(source, data["permutation64"])
+    invoice = replay(word, permuted)
+    need(replay(inverse_word(word), permuted)["native_children"] == 0, "Exact inverse word")
+    syntax = ast.parse((LANES / PINS["scalar_price"][0]).read_text())
+    price_node = next(node for node in syntax.body if isinstance(node, ast.FunctionDef) and node.name == "core_price")
+    price_scope = {"Q": F, "need": need}
+    exec(compile(ast.Module(body=[price_node], type_ignores=[]), "pinned_core_price", "exec"), price_scope)
+    billed = []
+    for op, p, r, raw in word:
+        c = F(raw)
+        gate = [op, ["D", p]] + ([["D", r]] if op == "add" else []) + [c.numerator, c.denominator]
+        billed.append(["scalar", gate, 0])
+    need(price_scope["core_price"](billed) == invoice["real_scalar_primitives"], "Pinned source scalar invoice")
+    views = {(v["stage"], v["port"], v["side"]): v for v in data["views"]["views"]}
+    route = {(s, p): views[s, p, "X"]["route_columns"] for s in range(1, 9) for p in range(112)}
+    full = base.product([(e, 1) for e in base.UNIT])
+    past_checks = 0
+    for s in range(1, 9):
+        for p in range(112):
+            view = views[s, p, "X"]
+            rho, delta = route[s, p], view["translation_after_route"]
+            phase = base.product([(v, 1) for v in rho])
+            need(base.add_phase(phase, base.line(delta, 2)) == full, "Literal final-FULL stage view")
+            need(base.act(rho, q[p]) == q[p], "Own intrinsic line is fixed")
+            past_checks += 1
+    reports = {}
+    witness = None
+    for name, response in (("half_hadamard64", matched), ("permutation64", permuted)):
+        stage_rows = []
+        for s, t in ((1, 2), (3, 4), (5, 6), (7, 8)):
+            grouped = defaultdict(dict)
+            count = 0
+            for p, row in enumerate(response):
+                for j, c in row.items():
+                    for r, d in response[j].items():
+                        mapping = compose(base, route[s, p], route[s, j], route[t, j], route[t, r])
+                        key = tuple(mapping)
+                        need(key not in grouped[p, r], "Distinct intermediate ports have distinct owner maps")
+                        grouped[p, r][key] = c * d
+                        second = base.act(mapping, q[r])
+                        fresh = ((1 << 8) - 1) << (9 + 8 * (t - 1))
+                        need(second & fresh, "The second intrinsic line has a nonzero future component")
+                        need(q[p] != second, "Two distinct positive intrinsic lines")
+                        correction = base.add_phase(full, base.negative(base.product([(v, 1) for v in mapping])))
+                        need(correction[0] == correction[2] == 0, "FULL cover conjugation is a translation")
+                        phase = base.add_phase(base.product([(q[p], 1), (second, 1)]), correction)
+                        need(phase[0] == q[p] ^ second, "Full Z4 phase has the required odd mask")
+                        count += 1
+                        if witness is None:
+                            witness = {"stages": [s, t], "target": p, "middle": j, "source": r,
+                                       "coefficient": str(c * d), "route_columns": mapping,
+                                       "lines": [q[p], second], "FULL_translation": correction[1],
+                                       "phase": list(phase)}
+            stage_rows.append({"stages": [s, t], "nonzero_path_blocks": count,
+                               "output_port_rows": len({p for p, r in grouped}),
+                               "port_blocks": len(grouped), "rank_two_path_blocks": count})
+        reports[name] = {"local_nonzero_entries": sum(map(len, response)), "stage_pairs": stage_rows}
+    a, b = witness["lines"]
+    kernel = {0: 1, a: 0, b: 0, a ^ b: 3}
+    need(len(kernel) == 4, "Four nonzero one-copy entries")
+    expanded = {0: 0}
+    support = []
+    for width in range(1, 6):
+        expanded = {old ^ (v << (73 * (width - 1))): (phase + power) % 4
+                    for old, phase in expanded.items() for v, power in kernel.items()}
+        need(len(expanded) == 4**width, "Exact tensor support")
+        support.append(len(expanded))
+    program = {"schema": "matched-final-full-gauge-v1", "source_pins": PINS,
+               "response": [{str(j): str(c) for j, c in row.items()} for row in permuted],
+               "scalar_word": word, "inverse_scalar_word": inverse_word(word),
+               "stage_contract": {"stages": list(range(1, 9)), "completed_level": 8,
+                                  "view_source": PINS["views"][0], "view_side": "X",
+                                  "order": ["apply_all_literal_stage_views", "scalar_word", "invert_all_literal_stage_views"],
+                                  "monomial_view_calls": 224}, "invoice": invoice}
+    (HERE / "FULL-GAUGE-PROGRAM.json").write_text(json.dumps(program, sort_keys=True, indent=2) + "\n")
+    result = {"status": "PASS_MATCHED_RESPONSE_STAGE_ACCESS", "source_pins": PINS,
+              "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+              "literal_FULL_view_checks": past_checks, "terminal_upper_blocks": reports,
+              "witness": witness, "tensor_support": support, "FULL_gauge_invoice": invoice,
+              "scope": "Exact specified responses and raw phase operator. No full supplier or general native lower bound."}
+    (HERE / "CHECKS.json").write_text(json.dumps(result, sort_keys=True, indent=2) + "\n")
+    print(result["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/check_triple25.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/check_triple25.py
new file mode 100644
index 0000000000..1c7a73be54
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/matched-stage-access-20261018/check_triple25.py
@@ -0,0 +1,273 @@
+"""Check the five current cuts and the complete three-stage raw code."""
+
+from collections import defaultdict
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+GAUGE = "independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json"
+GAUGE_PIN = "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89"
+SOURCE_PIN = "d2954018666ea2c1b6557615fdf0e6eba7b651fc89e4fdac899b0ccc0f16b839"
+CONTROLLER = "encoded-controller/one-pair-current-codes-20261018/PROGRAM.json"
+CONTROLLER_PIN = "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7"
+
+
+def need(ok, label):
+    if not ok:
+        raise ValueError(label)
+
+
+def dot(a, b):
+    return (a & b).bit_count() & 1
+
+
+def binary_solution(equations):
+    pivots = {}
+    for row, rhs in equations:
+        while row:
+            lead = row.bit_length() - 1
+            if lead not in pivots:
+                pivots[lead] = (row, rhs)
+                break
+            old, value = pivots[lead]
+            row ^= old
+            rhs ^= value
+        need(row or not rhs, "Consistent basis extension")
+    value = 0
+    for lead, (row, rhs) in sorted(pivots.items()):
+        if dot(row, value) != rhs:
+            value ^= 1 << lead
+    need(all(dot(row, value) == rhs for row, rhs in equations), "Exact binary solution")
+    return value
+
+
+def child_basis(base, wanted):
+    unit = [1 << j for j in range(25)]
+    columns = list(unit)
+    transvections = []
+    for j, target in enumerate(wanted):
+        current = columns[j]
+        if current == target:
+            continue
+        if not dot(current, target):
+            changes = [current ^ target]
+        else:
+            middle = binary_solution([((1 << 25) - 1, 1), (current, 0), (target, 0)]
+                                     + [(v, 0) for v in wanted[:j]])
+            changes = [current ^ middle, middle ^ target]
+        for vector in changes:
+            need(vector and not dot(vector, vector), "An orthogonal transvection")
+            need(all(not dot(vector, v) for v in wanted[:j]), "The earlier child axes stay fixed")
+            columns = [v ^ (vector if dot(vector, v) else 0) for v in columns]
+            transvections.append(vector)
+        need(columns[j] == target, "The next child axis")
+    inverse = [sum(((columns[j] >> i) & 1) << j for j in range(25)) for i in range(25)]
+    need(columns[:len(wanted)] == wanted, "The stated native axes")
+    need([base.act(columns, v) for v in inverse] == unit, "The left basis inverse")
+    need([base.act(inverse, v) for v in columns] == unit, "The right basis inverse")
+    return columns, inverse, transvections
+
+
+def native_record(base, target, source, lines, translation, route, sign=1):
+    columns, inverse, steps = child_basis(base, lines)
+    need(all(dot(a, b) == int(i == j)
+             for i, a in enumerate(lines) for j, b in enumerate(lines)),
+         "The native line directions are orthonormal")
+    wanted = base.add_phase(base.product([(v, 1) for v in lines]), base.line(translation, 2))
+    characters = [0] + [1 << j for j in range(25)]
+    characters += [(1 << i) ^ (1 << j) for i in range(25) for j in range(i)]
+    for eta in characters:
+        transformed = base.act(inverse, eta)
+        expected = sum(dot(v, eta) for v in lines) + 2 * dot(translation, eta)
+        actual = (transformed & ((1 << len(lines)) - 1)).bit_count() + 2 * dot(translation, eta)
+        need((actual - expected) % 4 == 0, "The complete child phase polynomial")
+    return {
+        "target": target, "source": source, "rank": len(lines), "sign": sign,
+        "cover_route_columns": route,
+        "child_basis_columns": columns, "child_basis_inverse_columns": inverse,
+        "basis_transvections_in_time_order": steps,
+        "output_translation": translation,
+        "factor_in_output_coordinates": "sign * X_translation * P_G * H_rank * P_G^-1 * P_route",
+        "phase": list(wanted), "phase_coefficient_checks": len(characters),
+    }
+
+
+def main():
+    path = HERE / "check_matched_access.py"
+    need(sha256(path.read_bytes()).hexdigest() == SOURCE_PIN, "Frozen stage checker")
+    spec = importlib.util.spec_from_file_location("triple25_source", path)
+    source = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(source)
+    base, ports, data = source.load()
+    need(sha256((source.LANES / CONTROLLER).read_bytes()).hexdigest() == CONTROLLER_PIN,
+         "The actual three-call controller pin")
+    q = [p["q"] for p in ports]
+    unit = [1 << j for j in range(25)]
+    mask = (1 << 25) - 1
+    views = {(v["stage"], v["port"], v["side"]): v for v in data["views"]["views"]}
+    rho = {(s, p): unit if s == 0 else views[s, p, "X"]["route_columns"][:25]
+           for s in range(3) for p in range(112)}
+    full = base.product([(v, 1) for v in unit])
+    matched = source.rows(data["matching"]["response"])
+    preferred = [dict(row) for row in matched]
+    for p in data["permutation64"]["active_ports"]:
+        preferred[p] = source.rows([data["permutation64"]["response"][p]])[0]
+    raw = (source.LANES / GAUGE).read_bytes()
+    need(sha256(raw).hexdigest() == GAUGE_PIN, "Improved scalar gauge pin")
+    gauge = json.loads(raw)
+    need(source.rows(gauge["response"]) == preferred, "Improved gauge uses this actual response")
+    word = []
+    for event in gauge["events"]:
+        if event[0] == "add":
+            op, p, r, a, b = event
+        else:
+            op, p, a, b = event
+            r = p
+        word.append([op, p, r, str(F(a, b))])
+    invoice = source.replay(word, preferred)
+    need(invoice["real_scalar_primitives"] == 2396 and invoice["peak_row_one_norm"] == "4",
+         "Improved scalar invoice and guard")
+    source.replay(source.inverse_word(word), preferred)
+    small = set(data["permutation64"]["active_ports"])
+    dense = set(range(112)) - small
+    dense_word = [event for event in word if event[1] in dense]
+    need(all(event[2] in dense for event in dense_word), "The dense code has no small-port read")
+    dense_target = [preferred[p] if p in dense else {p: F(1)} for p in range(112)]
+    dense_invoice = source.replay(dense_word, dense_target)
+    source.replay(source.inverse_word(dense_word), dense_target)
+    need(dense_invoice["real_scalar_primitives"] == 1564, "The restricted dense scalar invoice")
+    cuts = []
+    for label, stage, side, level in (("after_F0", 0, "X", 0), ("before_B1", 1, "Y", 0),
+                                      ("after_B1", 1, "X", 1), ("before_F2", 2, "Y", 1),
+                                      ("after_F2", 1, "X", 2)):
+        records = []
+        for p in range(112):
+            route = rho[stage, p]
+            delta = 0 if stage == 0 else views[stage, p, side]["translation_after_route"]
+            need(delta <= mask, "The cut translation is in D25")
+            terms = [(base.act(route, v), 1) for v in unit[:9 + 8 * level]]
+            if side == "Y":
+                terms.append((q[p], -1))
+            actual = base.add_phase(base.product(terms), base.line(delta, 2))
+            axes = unit[:9 + 8 * level] if side == "X" else unit[9:9 + 8 * level] + unit[9 + 8 * (stage - 1):9 + 8 * stage]
+            expected = base.product([(v, 1) for v in axes])
+            need(actual == expected, "Exact five-cut common frame")
+            records.append({"port": p, "route_columns": route, "translation_after_route": delta,
+                            "inverse_translation_after_route": base.act(route, delta)})
+        cuts.append({"cut": label, "stage_code": stage, "side": side, "global_level": level,
+                     "views": records, "scalar_gauge": GAUGE, "scalar_gauge_sha256": GAUGE_PIN,
+                     "monomial_view_calls_bound": 224, "real_scalar_primitives": 2396})
+    path_records = {}
+    reports = {}
+    for name, matrix in (("half_hadamard64", matched), ("permutation64", preferred)):
+        reports[name] = {}
+        for direction, stages in (("T", (2, 1, 0)), ("T_inverse", (0, 1, 2))):
+            grouped = defaultdict(set)
+            records = []
+            orthogonal = 0
+            for p, row in enumerate(matrix):
+                for j, a in row.items():
+                    for k, b in matrix[j].items():
+                        for r, c in matrix[k].items():
+                            factors = [rho[stages[0], p], rho[stages[0], j], rho[stages[1], j],
+                                       rho[stages[1], k], rho[stages[2], k], rho[stages[2], r]]
+                            route = list(unit)
+                            for factor in reversed(factors):
+                                route = [base.act(factor, v) for v in route]
+                            key = tuple(route)
+                            need(key not in grouped[p, r], "Distinct complete triple owner paths")
+                            grouped[p, r].add(key)
+                            second = base.act(route, q[r])
+                            need(q[p] != second, "The two raw terminal line factors do not cancel")
+                            correction = base.add_phase(full, base.negative(base.product([(v, 1) for v in route])))
+                            need(correction[0] == correction[2] == 0, "Triple FULL conjugation is a translation")
+                            phase = base.add_phase(base.product([(q[p], 1), (second, -1)]), correction)
+                            need(phase[0] == q[p] ^ second, "Complete raw triple odd phase")
+                            coefficient = a * b * c
+                            record = {"target": p, "middle": [j, k], "source": r,
+                                      "coefficient": str(coefficient), "route_columns": route,
+                                      "lines": [q[p], second], "line_powers": [1, -1],
+                                      "FULL_translation": correction[1], "phase": list(phase)}
+                            records.append(record)
+                            orthogonal += (q[p] & second).bit_count() % 2 == 0
+            reports[name][direction] = {"stages": stages, "path_blocks": len(records),
+                                        "rank_two_path_blocks": len(records), "orthogonal_line_pairs": orthogonal,
+                                        "port_blocks": len(grouped), "first_witness": records[0]}
+            if name == "permutation64":
+                path_records[direction] = records
+    need(reports["permutation64"]["T"]["path_blocks"] == 3136, "Preferred complete triple count")
+    need(reports["half_hadamard64"]["T"]["path_blocks"] == 7168, "Alternative complete triple count")
+    fused = []
+    source_ports = set()
+    for record in path_records["T_inverse"]:
+        if record["target"] not in small:
+            continue
+        need(record["coefficient"] == "-1", "The exact small-path scalar sign")
+        a, b = record["lines"]
+        translation = record["FULL_translation"] ^ b
+        child = native_record(base, record["target"], record["source"], [a, b],
+                              translation, record["route_columns"], -1)
+        need(child["phase"] == record["phase"], "Absorb the inverse line as a translation")
+        need(base.add_phase(base.product([(a, 1), (b, 1)]), base.line(translation, 2))
+             == tuple(record["phase"]), "The full signed-line identity")
+        fused.append(child)
+        source_ports.add(record["source"])
+    need(len(fused) == 64 and source_ports == small, "The complete small-port bijection")
+    dense_lines = []
+    for power in (-1, 1):
+        for p in sorted(dense):
+            dense_lines.append(native_record(base, p, p, [q[p]], q[p] if power == -1 else 0,
+                                             unit))
+    need(len(dense_lines) == 96, "The two complete dense line passes")
+    mixed = {
+        "chronology": ["dense48 inverse lines", "dense48 E2 inverse code",
+                       "dense48 E1 inverse code", "dense48 E0 inverse code",
+                       "dense48 positive lines", "small64 direct rank-two paths"],
+        "dense48_line_children": dense_lines, "small64_children": fused,
+        "dense48_scalar_inverse_events": source.inverse_word(dense_word),
+        "dense48_scalar_code_stages_in_time_order": [2, 1, 0],
+        "dense48_code_real_scalar_primitives": 3 * dense_invoice["real_scalar_primitives"],
+        "small64_complex_signs": 64, "small64_sign_real_scalar_primitives": 128,
+        "profile": {"1": 96, "2": 64}, "native_rank_mass": 224,
+        "owned_fields": 0, "private_fields": 0,
+        "map_inventory": {"dense48_code_views": 288, "dense48_child_wrappers": 192,
+                          "small64_child_wrappers": 128},
+        "scope": "Exact operators and native recipes. Recursive hosting and finite map cost are separate.",
+    }
+    program = {"schema": "matched-triple25-v1", "source_pins": source.PINS,
+               "controller_path": CONTROLLER, "controller_sha256": CONTROLLER_PIN,
+               "stage_checker_sha256": SOURCE_PIN, "dimension": 25, "five_scalar_codes": cuts,
+               "preferred_response": [{str(j): str(c) for j, c in row.items()} for row in preferred],
+               "raw_code": "Q (E2 E1 E0) Q^-1", "raw_inverse": "Q (E0 E1 E2) Q^-1",
+               "path_records": path_records,
+               "safe_native_line_word": ["Q^-1 on112 fields", "three admitted final-FULL scalar E gauges", "Q on112 fields"],
+               "safe_native_profile": {"1": 224}, "mixed_native_decoder": mixed,
+               "dense_H2_fusion_claimed": False}
+    encoded = (json.dumps(program, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    (HERE / "TRIPLE25-PROGRAMS.json.gz").write_bytes(gzip.compress(encoded, mtime=0))
+    receipt = {"status": "PASS_MATCHED_TRIPLE25_AND_FIVE_CUTS", "source_pins": source.PINS,
+               "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "program_decompressed_sha256": sha256(encoded).hexdigest(),
+               "five_cut_phase_checks": 560, "scalar_gauge_pin": GAUGE_PIN,
+               "controller_sha256": CONTROLLER_PIN,
+               "independent_scalar_gauge_replay": invoice, "terminal_path_checks": reports,
+               "dense48_scalar_gauge_replay": dense_invoice,
+               "safe_profile": {"1": 224}, "mixed_profile": mixed["profile"],
+               "mixed_native_rank_mass": mixed["native_rank_mass"],
+               "mixed_child_phase_coefficient_checks": sum(c["phase_coefficient_checks"]
+                                                          for c in fused + dense_lines),
+               "mixed_scalar_real_primitives": 3 * dense_invoice["real_scalar_primitives"] + 128,
+               "mixed_map_inventory": mixed["map_inventory"],
+               "dense_H2_fusion_claimed": False,
+               "scope": "Exact current cuts and triple raw operator. No coupled native lower bound or supplier improvement."}
+    (HERE / "TRIPLE25-CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n")
+    print(receipt["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/CHECKS.json
new file mode 100644
index 0000000000..f9b7c93564
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/CHECKS.json
@@ -0,0 +1,70 @@
+{
+  "checker_sha256": "175abdb7d0ceda381ab7dab568d6a6cf5eae4853ddba0fa74d3e11d53e02af96",
+  "child_count_reduction": 64,
+  "complete_finite_map_price_claimed": false,
+  "complete_native_profile_after": {
+    "1": 576,
+    "2": 144,
+    "5": 144,
+    "7": 272,
+    "8": 192,
+    "9": 64
+  },
+  "complete_native_profile_before": {
+    "1": 576,
+    "2": 208,
+    "5": 144,
+    "7": 336,
+    "8": 192
+  },
+  "complete_native_rank": 5600,
+  "kappa_improvement_claimed": false,
+  "program_decompressed_sha256": "9a8e4f1e34b23f97435ea7d953f1a6e1a1059f88920f314712fa592be52ddaac",
+  "providers": {
+    "base": {
+      "complete_Gaussian_state_checks": 64,
+      "local_phase_checks": 128,
+      "native_phase_coefficient_checks": 20864,
+      "rank9_children": 64,
+      "signed_Pauli_columns": 3200,
+      "source_and_output_bijection": true,
+      "wrong_translation_controls": 64
+    },
+    "extra": {
+      "complete_Gaussian_state_checks": 64,
+      "local_phase_checks": 128,
+      "native_phase_coefficient_checks": 20864,
+      "rank9_children": 64,
+      "signed_Pauli_columns": 3200,
+      "source_and_output_bijection": true,
+      "wrong_translation_controls": 64
+    }
+  },
+  "source_pins": {
+    "native": [
+      "oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz",
+      "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025"
+    ],
+    "permutation": [
+      "history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz",
+      "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9"
+    ],
+    "phase": [
+      "interface-proof/verify_native_lift.py",
+      "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b"
+    ],
+    "stage": [
+      "bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py",
+      "d2954018666ea2c1b6557615fdf0e6eba7b651fc89e4fdac899b0ccc0f16b839"
+    ],
+    "triple": [
+      "bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-PROGRAMS.json.gz",
+      "b65a2b14a1e61c566063195d0ef363c7dae0d06bb2232e4c872275479f327419"
+    ],
+    "triple_checker": [
+      "bridge-access-20261017/matched-stage-access-20261018/check_triple25.py",
+      "847d0dd8cfaf869b2a425fbd3b05c309d4d5859e8eab7dd1f0cb77dd761d4b57"
+    ]
+  },
+  "status": "PASS_MATCHED_LAST_COMPLETION_RANK9"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/FREEZE.json
new file mode 100644
index 0000000000..35e5eda37d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/FREEZE.json
@@ -0,0 +1,13 @@
+{
+  "files": {
+    "CHECKS.json": "c4b92b37441c095ff3c4d51ea920dd918edd54113764d76ce721a30ec435a2b0",
+    "RANK9-PROGRAMS.json.gz": "4d0f400e4c560de13b2ced393721d3b051c81ce9357591fec74fe6b39552da40",
+    "RANK9.md": "a9271f13f08a25d48906051216200ed4424c52de2dabde4e7227eceffb49ef99",
+    "check_rank9.py": "175abdb7d0ceda381ab7dab568d6a6cf5eae4853ddba0fa74d3e11d53e02af96"
+  },
+  "independent_review": "pending",
+  "normal_optimized_outputs_identical": true,
+  "program_decompressed_sha256": "9a8e4f1e34b23f97435ea7d953f1a6e1a1059f88920f314712fa592be52ddaac",
+  "publication_authorized": false,
+  "schema": "matched-rank9-completion-freeze-v1"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/RANK9-PROGRAMS.json.gz b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/RANK9-PROGRAMS.json.gz
new file mode 100644
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/RANK9.md b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/RANK9.md
new file mode 100644
index 0000000000..e89edb293a
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/RANK9.md
@@ -0,0 +1,206 @@
+# Combine the last completion with the terminal decoder
+
+This packet replaces 64 final rank-seven target completions and their
+64 rank-two terminal calls with 64 rank-nine calls. It applies to the
+one-pair controller in dimension 25, with the preferred permutation on
+the complementary 64 ports. The total native rank stays at 5,600.
+The number of children decreases by 64.
+
+This is an exact contraction of adjacent operations on each target.
+It does not save native rank. It does not give a kappa improvement.
+The exact full-cost budget remains a separate obligation.
+
+## Pinned inputs
+
+The checker uses the complete matched native word and the literal
+permutation64 component. It checks that the latter is the unchanged
+event suffix of the former. It also uses the full inverse triple from
+[TRIPLE25.md](../matched-stage-access-20261018/TRIPLE25.md), including
+its owner maps and full Fourier translations. All hashes are in the
+program and receipt.
+
+The controller has five scalar code cuts. After the final forward
+call, its last scalar code acts only on the X bank. Each of the 64
+target Y fields has no further local read after its last scalar
+transfer. Thus its final rank-seven completion can be deferred.
+
+## Local canonical adapter
+
+Let p be the source of the last scalar transfer and let r be its
+permutation partner. The source frame at this transfer is the
+canonical line frame T_p. It is not the pure line C_(q_p).
+Let M_p be the pinned source endpoint adapter. Its exact convention is
+
+```text
+T_p = M_p C_(q_p).
+```
+
+The rank-seven target completion, followed by the inverse target
+endpoint adapter, has operator
+
+```text
+R_r = F9 C_(q_r)^-1 T_p^-1
+    = F9 C_(q_r)^-1 C_(q_p)^-1 M_p^-1.             (1)
+```
+
+The checker reads both endpoint adapters and the actual rank-seven
+recipe. It verifies (1) by signed Pauli conjugation and an exact
+Gaussian state calculation.
+
+The two labels q_r and q_p are orthogonal unit vectors. Extend them
+to an orthonormal root basis
+
+```text
+(q_r, q_p, u_1,...,u_7).
+```
+
+The difference between the full Fourier phase in this basis and the
+standard root basis is an even linear phase. The checker computes its
+translation Delta from the complete Z4 phase polynomial. Hence
+
+```text
+R_r = X_Delta (product_j C_(u_j)) M_p^-1.          (2)
+```
+
+Both providers pass this full phase equation on all 64 targets.
+
+## The exact final product
+
+Write rho for the literal stage-two route of target r. Its current
+exit map is X_exit P_rho, where exit is the pinned DATA translation.
+The retained raw terminal applies C_(q_r)^2=X_(q_r) to this output.
+
+Let A be the complete inverse-triple owner map from source r to
+output p. The exact terminal correction is
+
+```text
+-X_delta C_a C_b^-1 P_A,
+a=q_p,       b=A q_r.                              (3)
+```
+
+The full Fourier translation delta comes from the frozen triple
+packet. Equations (2) and (3), in the required order, give
+
+```text
+-X_tau C_a C_b (product_j C_(A rho u_j)) P_(A rho) M_p^-1,
+tau = delta + A(exit + rho Delta).                 (4)
+```
+
+All vector sums are binary. The inverse-line translation from
+C_b^-1=X_b C_b cancels the transported old terminal map
+A q_r=b. This cancellation is why (4) has two positive lines.
+It does not remove either native direction.
+
+For every literal path, the nine directions
+
+```text
+a, b, A rho u_1,...,A rho u_7
+```
+
+are orthonormal. The two terminal directions are orthogonal to the
+transported seven-dimensional completion space. The complete product
+therefore has Fourier rank nine.
+
+The program extends these nine directions to an orthonormal basis G
+of the 25-dimensional space. It emits two full affine monomial
+records, with their quadratic phases, so that (4) is
+
+```text
+- L H9 R,
+R = P_G^-1 P_(A rho) M_p^-1,
+L = X_tau P_G.                                    (5)
+```
+
+The right record includes the canonical source adapter. The left
+record includes the exact translation. The negative complex sign is
+kept separate in the invoice. Each record contains its full binary
+matrix, offset, quadratic phase, linear Z4 coefficients, and constant
+phase. No endpoint adapter is implicit.
+
+## In-place order and cover assignment
+
+After the last scalar transfer to each of these 64 Y fields, omit
+its rank-seven completion, target endpoint adapter, and stage exit
+map. Complete the other native work and the final X-only scalar
+code. The deferred fields are arbitrary; no zero-state assumption
+is used.
+
+Next apply the retained signed bank exchange. On these 64 ports,
+omit its Q-squared map, since that map is already in (4). The old
+Y values now occupy the first bank and the old X values, with a
+negative sign, occupy the second bank. This exchange is valid on
+arbitrary arrays. It does not require the deferred Y values to be
+in a completed frame.
+
+Apply the 64 recipes (5) to the first bank. A record for output p
+reads source port r in the current body chart with owner map
+A rho. The port assignment is a permutation and each owner map is
+invertible. Thus the complete source assignment is a bijection.
+It can be implemented as a field and address permutation before
+the fieldwise children. It does not need a second copy of the bank.
+
+The regular cover is the same O(25,2) cover as in the source access
+packet. The local word uses complete cover sweeps. The contraction
+does not assume that a source and target have the same invocation
+body. The map A rho states which source body is read.
+
+## Invoice and verification
+
+The original complete native profile, with the mixed terminal, is
+
+```text
+{1:576, 2:208, 5:144, 7:336, 8:192}.
+```
+
+The contracted profile is
+
+```text
+{1:576, 2:144, 5:144, 7:272, 8:192, 9:64}.
+```
+
+Both have rank mass 5,600. The 64 new recipes use 128 monomial
+wrappers and the same 64 complex negative signs as the replaced
+terminal paths. These signs cost 128 real scalar primitives.
+The old signed bank exchange remains. No owned or private field
+is added. The change does not alter the scalar response or its
+peak row norm.
+
+For equal field volume and exponent sigma in (0,1), the change in
+the native child moment is
+
+```text
+64 * (9^sigma - 7^sigma - 2^sigma) < 0.
+```
+
+This is a cost reduction at fixed rank mass. It does not by itself
+make the complete supplier moment less than one. The inherited
+full-cover correction, map cost, precision bound, and recursive row
+hosting still belong in a complete supplier certificate.
+
+Run with one process:
+
+```text
+python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/rank9-completion-20261020/check_rank9.py
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/rank9-completion-20261020/check_rank9.py
+```
+
+Both runs must end with `PASS_MATCHED_LAST_COMPLETION_RANK9`. The
+program and receipt must agree byte for byte.
+
+For each provider, the checker verifies 64 complete signed Pauli
+maps, 64 exact Gaussian state phases, 128 local phase identities,
+and 20,864 native phase coefficients. It also checks the complete
+source bijection, the literal event suffix, the absence of a later
+target read, and 64 incorrect-translation controls. The full signed
+Pauli map plus one exact state image proves operator equality on
+arbitrary inputs. Tensor products preserve that equality at every
+width.
+
+The history lane supplied the native permutation word. The controller
+lane supplied the five-cut one-pair identity. The bridge review lane
+independently checked the preceding triple terminal. OpenAI Codex
+assisted this work.
+
+No PR, push, or publication commit is authorized. Before any future
+PR description, read
+/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/check_rank9.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/check_rank9.py
new file mode 100644
index 0000000000..0a65005c48
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/rank9-completion-20261020/check_rank9.py
@@ -0,0 +1,313 @@
+"""Combine the last 64 completions with their exact terminal paths."""
+
+from collections import Counter
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+PINS = {
+    "stage": ("bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py",
+              "d2954018666ea2c1b6557615fdf0e6eba7b651fc89e4fdac899b0ccc0f16b839"),
+    "triple_checker": ("bridge-access-20261017/matched-stage-access-20261018/check_triple25.py",
+                       "847d0dd8cfaf869b2a425fbd3b05c309d4d5859e8eab7dd1f0cb77dd761d4b57"),
+    "triple": ("bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-PROGRAMS.json.gz",
+               "b65a2b14a1e61c566063195d0ef363c7dae0d06bb2232e4c872275479f327419"),
+    "native": ("oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz",
+               "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025"),
+    "permutation": ("history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz",
+                    "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9"),
+    "phase": ("interface-proof/verify_native_lift.py",
+              "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b"),
+}
+
+
+def need(condition, label):
+    if not condition:
+        raise ValueError(label)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = (LANES / path).read_bytes()
+    if path.endswith(".gz"):
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, name + " source pin")
+    return raw
+
+
+def module(name):
+    read(name)
+    spec = importlib.util.spec_from_file_location("rank9_" + name, LANES / PINS[name][0])
+    value = importlib.util.module_from_spec(spec)
+    sys.modules[spec.name] = value
+    spec.loader.exec_module(value)
+    return value
+
+
+def rank(vectors):
+    pivots = {}
+    for value in vectors:
+        while value:
+            lead = value.bit_length() - 1
+            if lead not in pivots:
+                pivots[lead] = value
+                break
+            value ^= pivots[lead]
+    return len(pivots)
+
+
+def root_basis(helper, wanted):
+    columns = [1 << j for j in range(9)]
+    for j, target in enumerate(wanted):
+        current = columns[j]
+        if current == target:
+            continue
+        if helper.dot(current, target):
+            middle = helper.binary_solution([(511, 1), (current, 0), (target, 0)]
+                                            + [(v, 0) for v in wanted[:j]])
+            changes = [current ^ middle, middle ^ target]
+        else:
+            changes = [current ^ target]
+        for vector in changes:
+            need(vector < 512 and not helper.dot(vector, vector), "A root orthogonal transvection")
+            columns = [v ^ (vector if helper.dot(v, vector) else 0) for v in columns]
+        need(columns[:j + 1] == wanted[:j + 1], "The root basis has the required first axes")
+    need(all(helper.dot(a, b) == int(i == j) for i, a in enumerate(columns)
+             for j, b in enumerate(columns)), "The full root basis is orthonormal")
+    return columns
+
+
+def embed(circuit):
+    out = []
+    for gate in circuit:
+        if gate[0] == "P":
+            out.append(("P", tuple(gate[1]) + tuple(1 << j for j in range(9, 25))))
+        elif gate[0] == "D":
+            out.append(("D", tuple(gate[1]) + (0,) * 16, tuple(gate[2]) + (0,) * 16))
+        else:
+            out.append(gate)
+    return tuple(out)
+
+
+def scalar_phase(phase, gate, x):
+    return (sum(gate[2][i] for i in range(25) if x >> i & 1)
+            + 2 * sum(phase.parity((gate[1][i] >> (i + 1)) & (x >> (i + 1)))
+                      for i in range(25) if x >> i & 1)) % 4
+
+
+def monomial_action(phase, circuit, x):
+    power = 0
+    for gate in circuit:
+        if gate[0] == "P":
+            x = phase.mul(gate[1], x)
+        elif gate[0] == "X":
+            x ^= gate[1]
+        elif gate[0] == "D":
+            power += scalar_phase(phase, gate, x)
+        else:
+            need(gate[0] == "phase", "A monomial wrapper")
+            power += gate[1]
+    return x, power % 4
+
+
+def mono_circuit(record):
+    return (("D", tuple(record["quadratic_rows"]), tuple(record["linear_Z4"])),
+            ("P", tuple(record["matrix_rows"])), ("X", record["offset"]),
+            ("phase", record["phase"]))
+
+
+def fold_monomial(phase, circuit):
+    offset, constant = monomial_action(phase, circuit, 0)
+    singles = [monomial_action(phase, circuit, 1 << j) for j in range(25)]
+    columns = [x ^ offset for x, _ in singles]
+    linear = [(power - constant) % 4 for _, power in singles]
+    quadratic = [(linear[j] % 2) << j for j in range(25)]
+    for i in range(25):
+        for j in range(i):
+            x, power = monomial_action(phase, circuit, (1 << i) ^ (1 << j))
+            need(x == offset ^ columns[i] ^ columns[j], "The affine wrapper map")
+            cross = (power - constant - linear[i] - linear[j]) % 4
+            need(cross in (0, 2), "The quadratic wrapper phase")
+            if cross:
+                quadratic[i] ^= 1 << j
+                quadratic[j] ^= 1 << i
+    record = {"matrix_rows": list(phase.transpose(columns)), "offset": offset,
+              "quadratic_rows": quadratic, "linear_Z4": linear, "phase": constant}
+    folded = mono_circuit(record)
+    need(phase.tableau(folded, 25) == phase.tableau(circuit, 25),
+         "The wrapper has the complete signed Pauli action")
+    need(monomial_action(phase, folded, 0) == monomial_action(phase, circuit, 0),
+         "The wrapper has the exact constant phase")
+    return record
+
+
+def sparse_state(phase, circuit, basis=0):
+    value, denominator = {basis: (1, 0)}, 0
+    for gate in circuit:
+        tag = gate[0]
+        if tag == "C":
+            moved = {}
+            direction, sign = gate[1:]
+            for x, (a, b) in value.items():
+                for target, term in ((x, (a - sign * b, b + sign * a)),
+                                     (x ^ direction, (a + sign * b, b - sign * a))):
+                    old = moved.get(target, (0, 0))
+                    moved[target] = (old[0] + term[0], old[1] + term[1])
+            value = {x: pair for x, pair in moved.items() if pair != (0, 0)}
+            denominator += 1
+        elif tag == "P":
+            value = {phase.mul(gate[1], x): pair for x, pair in value.items()}
+        elif tag == "X":
+            value = {x ^ gate[1]: pair for x, pair in value.items()}
+        elif tag == "D":
+            value = {x: phase.rotate(pair, scalar_phase(phase, gate, x))
+                     for x, pair in value.items()}
+        else:
+            need(tag == "phase", "An exact state gate")
+            value = {x: phase.rotate(pair, gate[1]) for x, pair in value.items()}
+        while denominator and all((a | b) % 2 == 0 for a, b in value.values()):
+            value = {x: (a // 2, b // 2) for x, (a, b) in value.items()}
+            denominator -= 1
+    return value, denominator
+
+
+def main():
+    source, helper, phase = module("stage"), module("triple_checker"), module("phase")
+    base, ports, data = source.load()
+    triple = json.loads(read("triple"))
+    native = json.loads(read("native"))
+    permutation = json.loads(read("permutation"))
+    small = set(permutation["active_ports"])
+    paths = {r["target"]: r for r in triple["path_records"]["T_inverse"]
+             if r["target"] in small}
+    views = {(v["stage"], v["port"], v["side"]): v for v in data["views"]["views"]}
+    unit = [1 << j for j in range(25)]
+    records, reports = {}, {}
+    for provider, words in permutation["providers"].items():
+        word = words["forward"]
+        whole = native["providers"][provider]["forward"]
+        need(whole["events"][whole["inherited_64_first_event"]:] == word["events"],
+             "The complete core retains the literal 64-port event suffix")
+        adapters = {(r["port"], r["role"]): r for r in word["endpoint_adapters"]}
+        endpoint_records, total_checks = [], 0
+        for p, path in sorted(paths.items()):
+            r = path["source"]
+            transfer = next(x for x in word["transfers"] if x["source_port"] == p)
+            need(transfer["target_port"] == r, "The final transfer and terminal pair agree")
+            event = word["events"][transfer["event"] + 2]
+            need(event[:2] == ["native", 112 + r] and event[4] == 7,
+                 "The last target completion is the required H7")
+            for later in word["events"][transfer["event"] + 3:]:
+                touched = [later[1]] if later[0] == "native" else later[1][1:3]
+                need(112 + r not in touched, "No later local event reads the deferred target")
+            completion = word["native_recipes"][event[5]]
+            need(completion == whole["native_recipes"][event[5]],
+                 "The complete core uses the same rank-seven recipe")
+            source_adapter = phase.recipe(adapters[p, "source"])
+            target_adapter = phase.recipe(adapters[r, "target"])
+            qp, qr = ports[p]["q"], ports[r]["q"]
+            local_actual = phase.recipe(completion) + phase.adjoint(target_adapter)
+            local_expected = phase.adjoint(source_adapter) + (("C", qp, -1), ("C", qr, -1)) + phase.fourier(9)
+            phase.equal(local_actual, local_expected, "The conventional target completion")
+            local_basis = root_basis(helper, [qr, qp])
+            complement = local_basis[2:9]
+            local_phase = base.add_phase(base.product([(v, 1) for v in unit[:9]]),
+                                         base.negative(base.product([(v, 1) for v in local_basis[:9]])))
+            need(local_phase[0] == local_phase[2] == 0, "The local full-frame correction is a translation")
+            local_delta = local_phase[1]
+            local_factored = phase.adjoint(source_adapter) + tuple(("C", v, 1) for v in complement) + (("X", local_delta),)
+            phase.equal(local_actual, local_factored, "The exact seven-axis completion")
+            route = path["route_columns"]
+            rho = views[2, r, "X"]["route_columns"][:25]
+            composed = [base.act(route, v) for v in rho]
+            exit_delta = ports[r]["stage_alignment"][2]["exit_Y"]
+            a, b = path["lines"]
+            need(a == qp and b == base.act(route, qr), "The terminal line order")
+            lines = [a, b] + [base.act(composed, v) for v in complement]
+            translation = path["FULL_translation"] ^ base.act(route, exit_delta ^ base.act(rho, local_delta))
+            child = helper.native_record(base, p, r, lines, translation, composed, -1)
+            right_circuit = embed(phase.adjoint(source_adapter)) + (
+                ("P", phase.transpose(composed)), ("P", phase.transpose(child["child_basis_inverse_columns"])))
+            left_circuit = (("P", phase.transpose(child["child_basis_columns"])), ("X", translation))
+            right, left = fold_monomial(phase, right_circuit), fold_monomial(phase, left_circuit)
+            actual = embed(local_actual) + (
+                ("P", phase.transpose(rho)), ("X", exit_delta), ("X", qr),
+                ("P", phase.transpose(route)), ("C", b, -1), ("C", a, 1),
+                ("X", path["FULL_translation"]), ("phase", 2))
+            compiled = mono_circuit(right) + tuple(("C", 1 << j, 1) for j in range(9)) + mono_circuit(left) + (("phase", 2),)
+            expected_tableau = phase.tableau(actual, 25)
+            need(phase.tableau(compiled, 25) == expected_tableau,
+                 "The full native completion and terminal have the same signed Pauli action")
+            need(sparse_state(phase, compiled) == sparse_state(phase, actual),
+                 "The full native completion and terminal have the same exact Gaussian phase")
+            need(rank([x for x, _, _ in expected_tableau[25:]]) == 9,
+                 "The complete product has Fourier rank nine")
+            wrong = dict(left, offset=left["offset"] ^ 1)
+            bad = mono_circuit(right) + tuple(("C", 1 << j, 1) for j in range(9)) + mono_circuit(wrong)
+            need(phase.tableau(bad, 25) != expected_tableau, "An incorrect output translation is rejected")
+            total_checks += child["phase_coefficient_checks"]
+            endpoint_records.append({
+                "source_field_before_signed_exchange": 112 + r,
+                "source_field_after_signed_exchange": r,
+                "output_field": p, "source_port": r, "output_port": p,
+                "last_transfer_source_port": p, "removed_native_event": transfer["event"] + 2,
+                "old_completion_recipe_key": event[5], "rank": 9, "sign": -1,
+                "right": right, "left": left, "native_axes": lines,
+                "cover_route_columns": composed, "terminal_route_columns": route,
+                "stage2_route_columns": rho, "source_canonical_adapter": adapters[p, "source"],
+                "local_seven_axes": complement, "local_full_translation": local_delta,
+                "output_translation": translation,
+                "basis_transvections_in_time_order": child["basis_transvections_in_time_order"],
+            })
+        need(len(endpoint_records) == 64 and {r["source_port"] for r in endpoint_records} == small,
+             "The complete output assignment is a bijection")
+        records[provider] = endpoint_records
+        reports[provider] = {
+            "rank9_children": 64, "signed_Pauli_columns": 64 * 50,
+            "complete_Gaussian_state_checks": 64, "local_phase_checks": 128,
+            "native_phase_coefficient_checks": total_checks,
+            "wrong_translation_controls": 64, "source_and_output_bijection": True,
+        }
+        print(provider, "PASS_RANK9_COMPLETION", flush=True)
+    old = Counter({1: 480, 2: 144, 5: 144, 7: 336, 8: 192})
+    old.update({1: 96, 2: 64})
+    new = old.copy()
+    new.subtract({7: 64, 2: 64})
+    new.update({9: 64})
+    need(sum(r * c for r, c in old.items()) == sum(r * c for r, c in new.items()) == 5600,
+         "The complete native rank is unchanged")
+    program = {"schema": "matched-last-completion-rank9-v1", "dimension": 25,
+               "source_pins": PINS, "providers": records,
+               "complete_native_profile_before": dict(sorted(old.items())),
+               "complete_native_profile_after": dict(sorted(new.items())),
+               "replaced_children": {"rank7": 64, "rank2": 64}, "new_children": {"rank9": 64},
+               "new_wrapper_calls": 128, "complex_signs": 64, "real_sign_primitives": 128,
+               "owned_fields": 0, "private_fields": 0,
+               "chronology": ["Complete the final 64 scalar transfers at their canonical line cuts.",
+                              "Omit their last H7 target completions, target exit adapters, and stage exit maps.",
+                              "Complete all remaining disjoint work and the final X-only scalar code.",
+                              "Apply the retained signed bank exchange, without its Q^2 map on these 64 ports.",
+                              "Apply the emitted H9 recipes to the 64 fields now in the first bank.",
+                              "Assign the 64 results to their specified output fields and cover owners."],
+               "scope": "Exact adjacent native contraction. No rank saving or complete finite supplier price."}
+    raw = (json.dumps(program, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    (HERE / "RANK9-PROGRAMS.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {"status": "PASS_MATCHED_LAST_COMPLETION_RANK9", "source_pins": PINS,
+               "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "program_decompressed_sha256": sha256(raw).hexdigest(), "providers": reports,
+               "complete_native_profile_before": program["complete_native_profile_before"],
+               "complete_native_profile_after": program["complete_native_profile_after"],
+               "complete_native_rank": 5600, "child_count_reduction": 64,
+               "complete_finite_map_price_claimed": False, "kappa_improvement_claimed": False}
+    (HERE / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(receipt["status"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/ACCESS.md b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/ACCESS.md
new file mode 100644
index 0000000000..154e7404b7
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/ACCESS.md
@@ -0,0 +1,163 @@
+# Access for sixteen centre rows in FULL frames
+
+The actual forward word permits a new output type. Sixteen target rows
+can contain a normalized centre reader in the FULL frame. The other
+ninety-six target rows keep their original hole frames. The source
+fields keep their original progress.
+
+This packet checks the path isolation, the late source cut, and the
+literal D25 owner views. The separate native emitter must supply the
+new rank-nine child recipes and replay the complete word. This packet
+does not establish a complete supplier or a recursive cost.
+
+## Exact row code
+
+Use the actual response \(E=I+UV\) from the pinned odd16 native word.
+Use the pivot order
+
+```text
+0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23.
+```
+
+Write \(P\) for this set, \(R\) for its complement, and put
+\(L=V_P^{-1}V\). The separate row-capture packet proves that \(V_P\)
+is a unit and supplies the exact normalized reader. Define C by
+
+\[
+(Cy)_P=Ly,\qquad (Cy)_R=y_R.
+\]
+
+In the order P,R, the code has the form
+
+\[
+C=\begin{bmatrix}I&B\\0&I\end{bmatrix},\qquad
+C^{-1}=\begin{bmatrix}I&-B\\0&I\end{bmatrix}.
+\]
+
+In particular, the precode changes only P and reads only R. The centre
+action is
+
+\[
+LE=HL,\qquad H=\operatorname{diag}(-5I_8,-7I_8).
+\]
+
+Here H denotes the centre action, not the physical pair code in the
+native word. The precode and the late query use only dyadic scalar
+operations. No division by five or seven is needed.
+
+## Native path isolation
+
+The selected large ports form four complete physical pair blocks:
+
+```text
+(0,27), (36,111), (20,46), (7,57).
+```
+
+The other eight selected ports belong to the small component. For both
+native providers, remove each event whose target is one of the sixteen
+selected Y fields. Exactly 250 events are removed: 128 rank-one native
+calls and 122 scalar operations.
+
+The checker inspects every retained event. None reads a selected Y
+field. No forward event reads any Y field into X. Thus the removal
+cannot change a retained source, a retained target, or an outside field.
+The complete-pair condition is essential: it removes both directions of
+each selected target pair code.
+
+The last source event is event 2638. It completes X102 to FULL. Event
+2639 is the last original event. After the complete retained sweep,
+all 112 X fields are FULL, all selected Y fields still have frame I,
+and all other fields have their original final frames.
+
+Use this order:
+
+1. Apply C to Y in its current I frame.
+2. Execute the retained native sweep.
+3. Apply the exact full nine-axis transform to each selected Y.
+4. At the common FULL cut, add \((CE)_{P,*}X=HLX\) to selected Y.
+5. Apply the declared output views.
+
+The result in the local body chart is
+
+\[
+X_{\rm out}=F_9x,\qquad
+Y_{P,\rm out}=F_9L(y+Ex),\qquad
+Y_{R,\rm out}=F_9q_R(y+Ex)_R.
+\]
+
+These equations hold for arbitrary x and y. The new precode is
+invertible. It does not assume a zero centre baseline. The late query
+adds to the existing target value. It does not replace that value.
+The 416 fields outside the two data banks are unchanged.
+
+The native profile is
+
+```text
+1392 H1 + 64 H2 + 48 H3 + 16 H9.
+```
+
+It has 1,520 children and native rank 1,808. Relative to the old word,
+the sixteen new H9 calls replace 128 H1 calls. This count does not
+include scalar work, view costs, precision, or recursive hosting.
+
+## Literal D25 views
+
+Use the regular \(O(25,2)\) cover and the exact stage routes
+\(\rho_{s,p}\) for \(s=0,1,2\). Each route is an orthogonal involution
+that fixes its own \(q_p\). Right multiplication by a route permutes
+the cover. The owner views therefore give a bijection between each
+field's global owners and its native body invocations.
+
+At a current local entry, the literal entry-Y route and translation
+put every old Y field in the same exterior frame. Its local frame is
+I. Thus the row precode is a legal scalar operation at that entry.
+
+At the late query, every source X and every selected target Y has
+the same exterior frame times \(F_9\). Their scalar query is legal.
+No old-stage read from a hole field is used.
+
+A selected Y output now uses the FULL exit identity. The checker uses
+the serialized `exit_X` translation for that identity. In this actual
+source, `exit_X` and `exit_Y` are equal in every record, so this change
+does not add a translation. The proof uses the FULL identity; it does
+not infer the identity from equality of translation labels.
+
+The checker verifies all 48 selected current-entry equations and all
+48 selected FULL-exit equations as exact Z4 phase polynomials.
+Complete the whole local cover sweep before the next stage. No helper
+owner is shared by this word.
+
+## The next entry is a new type
+
+Let a selected output at completed level s have physical frame
+\(F_{9+8s}\), and apply a later current-Y view at stage \(t>s\).
+The exact view gives
+
+\[
+\left(\prod_{j=9}^{9+8s-1}C_{e_j}\right)
+\left(\prod_{j=9+8(t-1)}^{9+8t-1}C_{e_j}\right)Q_p.
+\]
+
+For an ordinary hole output, the same formula has no final \(Q_p\).
+Thus the local incoming types are \(Q_P\) on the centre carriers and
+I on their complement. They are not the old all-I target type.
+The checker verifies all 48 such selected future-entry equations.
+It also checks that omission of the intrinsic Q factor fails.
+
+This is a concrete interface for a later construction. A caller must
+consume the Q-type carriers or pay for their conversion. The present
+packet does not count that conversion as free.
+
+## Reproduction and scope
+
+Run `check_access.py` once normally and once with `python3 -O`, with
+different output directories. The two program files and the two check
+files must be byte equal. The checker pins the native word, the exact
+row code, the D25 views, and the Z4 phase functions.
+
+The new local emitter, its independent phase review, and the complete
+caller are separate obligations. In particular, this proof does not
+identify the new mixed output type with a raw supplier endpoint.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/FREEZE.json
new file mode 100644
index 0000000000..71412147d1
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/FREEZE.json
@@ -0,0 +1,13 @@
+{
+  "files": {
+    "ACCESS.md": "b28785e70fd700a4ed564f4cfc9d154c1b154939541053dc8fb802911c1448b1",
+    "check_access.py": "48baba6e09b787924c496c8d4ce89c9dd3f77585946516f90ff8803d45adb5cd",
+    "run-normal/ACCESS-PROGRAM.json": "c2d6a3300f759c4052236fec5ca8ef446f35b444f78369eaa9aed9ab9625f139",
+    "run-normal/CHECKS.json": "fc30fa5c4923633ff2aac86881656a086416193a90511bf06754fc9f7c17174b",
+    "run-optimized/ACCESS-PROGRAM.json": "c2d6a3300f759c4052236fec5ca8ef446f35b444f78369eaa9aed9ab9625f139",
+    "run-optimized/CHECKS.json": "fc30fa5c4923633ff2aac86881656a086416193a90511bf06754fc9f7c17174b"
+  },
+  "normal_optimized_byte_equal": true,
+  "schema": "row-capture-access-freeze-v1",
+  "scope": "Actual forward path isolation, common FULL query, and D25 hybrid endpoint views. Separate emitter and caller obligations remain."
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json
new file mode 100644
index 0000000000..b022f3636e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json
@@ -0,0 +1,12 @@
+{
+  "files": {
+    "INTEGRATION.md": "7fce1ef14e08963b84bb43f839db280e83879261fc8af950dad072998edcb8a2",
+    "check_integration.py": "c178c339b0398d7e6f0232d68d681527dfaed70da10941f09bd9db3f141887fb",
+    "integration-v2-normal/CHECKS.json": "ee6add0c9f4a6330d5180190f29a052f491b1adefef7d9aabb6bc389f4ed057c",
+    "integration-v2-normal/DISPATCHER.json": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24",
+    "integration-v2-optimized/CHECKS.json": "ee6add0c9f4a6330d5180190f29a052f491b1adefef7d9aabb6bc389f4ed057c",
+    "integration-v2-optimized/DISPATCHER.json": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Exact native-prefix/data-view/query splice; inherited helper hosting and complete supplier remain separate."
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION.md b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION.md
new file mode 100644
index 0000000000..ed2c9ee398
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION.md
@@ -0,0 +1,218 @@
+# The native prefix and the fixed-reader dispatcher
+
+This packet joins the emitted carrier prefix to the fixed past-reader
+query. It gives the exact data interface at the D25 stages 1 and 2.
+It preserves the native helper contract as an explicit premise.
+It does not give a complete supplier or a multiplication exponent.
+
+The inputs are the frozen `CARRIER-PREFIX.json.gz`,
+`REUSE-PROGRAM.json`, `ROUTED-QUERY.json.gz`, and
+`DIMENSION25-VIEWS.json`. The dispatcher records their paths and hashes.
+It does not change those files.
+
+## The physical level and the reader label
+
+Let P be the fixed sixteen selected ports. Let R be the other 96 ports.
+Let \(F_\ell\) be the full transform on the first \(9+8\ell\) axes.
+Put
+
+\[
+G_R=\operatorname{diag}(I_P,q_R).
+\]
+
+Here q is the portwise inverse intrinsic line. Fix a reader stage s
+and a service stage t, with \(s<t\). The physical input must have
+completed level \(t-1\), even when \(s<t-1\). For example, the pair
+\((s,t)=(0,2)\) uses a reader from stage 0 that has already been carried
+to level 1. It is not a direct physical jump from level 0 to level 2.
+
+The selected records can be arbitrary independent values. Write w for
+the complete bank of selected records and ordinary values. The exact
+global input is
+
+\[
+(F_{t-1}x,\ F_{t-1}G_Rw).
+\tag{1}
+\]
+
+If \(w=C_sy\), then its selected entries are \(L_sy\), and its other
+entries are \(y_R\). The unit row code makes this interpretation valid
+for every w.
+
+## The current native prefix
+
+The current DATA entry views take (1) to a common exterior frame,
+with local input types
+
+\[
+X=Qx_{\rm body},\qquad
+Y_P=Q_Pw_{P,\rm body},\qquad
+Y_R=w_{R,\rm body}.
+\tag{2}
+\]
+
+For each field, the body owner d reads the global owner
+\(h=d\rho_{t,p}\). The map is a bijection on the regular \(O(25,2)\)
+cover. The program retains both the literal route and the entry
+translation. It checks the full Z4 phase equation. In particular,
+the selected target input in (2) is a positive intrinsic line,
+not an I frame.
+
+The pinned prefix then executes 2,406 events. The first 2,390 events
+are the retained core. The last sixteen events carry the selected
+records from their intrinsic line to FULL with H8 calls. There is
+no selected query in this prefix.
+
+The exact local output is
+
+\[
+X'=F_9x_{\rm body},\quad
+Y'_P=F_9w_{P,\rm body},\quad
+Y'_R=F_9q_R
+   \bigl(w_{\rm body}+E x_{\rm body}\bigr)_R.
+\tag{3}
+\]
+
+All 112 source fields and all 416 helper fields retain their contents.
+This statement holds for arbitrary values in those fields. The
+checker replays all 640 input columns and the full frame ledger.
+The native phase recipes and the local endpoint adapters are bound
+to the pinned independent line-entry review.
+
+There are 128 local input adapters: 112 source adapters and sixteen
+copies on the selected target fields. There are 96 ordinary target
+output adapters. There is no output adapter on a selected target.
+
+After the ordinary output adapters, use the current DATA exit views.
+For selected targets, use the FULL exit translation, the same
+translation used for X. The actual source records also have equal
+X and Y exit translations, but the required FULL phase equation is
+checked directly.
+
+Let \(E_t\) include the current owner routes. After the complete
+native cover sweep, (3) becomes
+
+\[
+X'=F_tx,\quad
+Y'_P=F_tw_P,\quad
+Y'_R=F_tq_R(w+E_tx)_R.
+\tag{4}
+\]
+
+The checker verifies all 448 data entry phase equations and all 448
+data exit phase equations for stages 1 and 2. These checks include
+the common exterior factors.
+
+## The query after the cover barrier
+
+Finish the native prefix and its DATA exits for the complete cover
+before the late query. At this cut, every X field and every selected
+Y field has the global FULL frame \(F_t\). The ordinary Y fields
+remain in their hole frames and are not read by the query.
+
+Use the six-step word in `REUSE-PROGRAM.json` for the selected pair
+\((s,t)\), with its literal map and scalar expansion in
+`ROUTED-QUERY.json.gz`. It adds \(L_sE_tx\) to the sixteen selected records. It
+restores every X field. The past reader, current code, complete
+middle owner paths, and their translations remain in the exact order
+given in that program.
+
+Define \(A_{s,t}\) by
+
+\[
+(A_{s,t})_P=L_sE_t,\qquad
+(A_{s,t})_R=(E_t)_R.
+\]
+
+Equations (1)--(4) and the late query give the complete data interface
+
+\[
+(F_{t-1}x,\ F_{t-1}G_Rw)
+\longmapsto
+(F_tx,\ F_tG_R(w+A_{s,t}x)).
+\tag{5}
+\]
+
+If the input records represent \(L_sy\), the output records represent
+\(L_s(y+E_tx)\). Thus the same past reader is carried through the new
+service. No old-stage ordinary target read is used.
+
+Equation (5) includes the actual stage routes. The two stage responses
+are not replaced by a common scalar matrix. The reader label s does
+not change any native entry frame.
+
+## The schedule and the helper premise
+
+Each dispatcher record has this order:
+
+1. Apply the current DATA entry views.
+2. Apply the local input adapters.
+3. Execute the complete carrier prefix.
+4. Apply the ordinary target output adapters.
+5. Apply the current DATA exit views.
+6. Complete the cover barrier.
+7. Execute the fixed past-reader query at global FULL.
+
+For each data field, the owner map \(d\mapsto d\rho_{t,p}\) is a
+bijection. Thus two body invocations do not write the same data
+record of that field. Complete body invocations can use the inherited
+helper host and restore it before the next invocation. Moving the
+query to the cover barrier needs no additional helper.
+
+This packet does not construct a new helper host. The prefix retains
+416 arbitrary helper fields and their typed input contract. A complete
+supplier must still provide those fields through a valid host, and
+must price any helper access and recursive parking that the host
+requires. The data route bijection alone does not prove that contract.
+
+The same-chronology inverse-adjoint in `DUAL.md` applies to (5).
+Its central upper response is \(-A_{s,t}^*\), with the same unitary
+input and output frames. It is not an inverse response unless a
+separate identity proves that fact.
+
+## The invoice
+
+The prefix has
+
+```text
+1392 H1 + 64 H2 + 48 H3 + 16 H8
+```
+
+Its native rank is 1,792. It has 1,520 native children and 6,456 real
+scalar primitives. The late query has no native child and has 11,168
+real scalar primitives. The complete word therefore has 17,624 real
+scalar primitives. The smaller 9,880 price belongs to the separate
+same-reader local word and does not price this past-reader service.
+
+The conservative monomial call bound is:
+
+| Part | Calls |
+| --- | ---: |
+| DATA entry and exit | 448 |
+| Local endpoint adapters | 224 |
+| Native side maps | 3,040 |
+| Fixed past-reader query | 2,064 |
+| Total | 5,776 |
+
+The native side-map bound allows two maps for each child. The bound
+does not include helper acquisition, recursive parking, or an outer
+caller. A map call is not a finite real-operation price. That price
+and recursive precision remain separate obligations.
+
+## Validation and scope
+
+Run `check_integration.py --output <new-directory>` with normal Python
+and with `python3 -O`. The two dispatcher files and the two receipts
+must be byte equal. The checker rejects an existing output directory.
+
+The checks bind both providers and the three pairs
+\((0,1),(0,2),(1,2)\). They replay the carrier prefix, check every
+adjacent data boundary phase, and bind the complete late-query
+program. The pinned native integration lane replay covers the 2,064
+literal query maps and its scalar word after this exact prefix.
+
+This work extends the controller lane's normalized row capture, the
+native lane's line-entry carrier, and the earlier D25 view proof.
+OpenAI Codex assisted the work. No publication is authorized. Before
+any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json
new file mode 100644
index 0000000000..f58eb9a9f7
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "REUSE.md": "5038811fc5097ed0e86df6c7d4e5ea147c8b0e977e7ba633499b72528dc28d5d",
+    "check_reuse.py": "5728ceb5877e3e59ce4d8d4ae21672bb22029944051e6193f9a36b4996b66279",
+    "reuse-normal/REUSE-CHECKS.json": "1ae1c147f99cf31c7fa6886516e3417417767a08888923bea09afa73dac43729",
+    "reuse-normal/REUSE-PROGRAM.json": "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b",
+    "reuse-optimized/REUSE-CHECKS.json": "1ae1c147f99cf31c7fa6886516e3417417767a08888923bea09afa73dac43729",
+    "reuse-optimized/REUSE-PROGRAM.json": "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b"
+  },
+  "formation_freeze_sha256": "9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11",
+  "normal_optimized_byte_equal": true,
+  "schema": "fixed-reader-reuse-freeze-v1",
+  "scope": "Exact forward fixed-reader query, carrier phases and actual D25 owner views. Complete native integration, backward companion and supplier remain separate."
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE.md b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE.md
new file mode 100644
index 0000000000..f2684a085b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE.md
@@ -0,0 +1,197 @@
+# A fixed centre reader can be carried through forward services
+
+The sixteen FULL centre rows need not be converted back to plain target
+rows before the next forward service. Their exact next-entry type is
+the required intrinsic line. A rank-eight path can carry each row to
+the next FULL cut. A dyadic query at that cut updates the same past
+reader and restores all source fields.
+
+This result gives a typed forward-service extension. It does not give
+a backward companion or a complete caller. The separate local formation
+word has been emitted. The complete reuse native word still needs its
+own integration and replay.
+
+## The carried reader
+
+Keep the pivot set P and the normalized row readers from `ACCESS.md`.
+Let J insert sixteen values at P, and let \(J^{\mathsf T}\) select P.
+At stage s, write
+
+\[
+L_s=J^{\mathsf T}+B_s,\qquad B_sJ=0,\qquad
+C_s=I+JB_s.
+\]
+
+Each symbol includes its actual stage routes. In particular, \(B_s\)
+and \(B_t\) are different operators when \(s\ne t\).
+
+Suppose the target bank contains \(L_sy\) on its selected FULL rows
+and \(y_R\) on its other hole rows. This is a unit encoding of arbitrary
+y. Equivalently, its selected and ordinary input values can be chosen
+independently.
+
+At a later current entry t, the literal views give local target types
+\(Q_p\) on P and I on R. Keep the original ordinary target paths. On
+each selected carrier, replace the removed path by
+
+\[
+Q_p\longrightarrow F_9.
+\]
+
+This is the operator \(F_9q_p\), of native rank eight. The program gives
+an exact positive H8 recipe for every selected port. It uses the actual
+orthogonal port chart, with its eight complementary axes first, and an
+explicit output translation. The full Z4 phase polynomial is checked.
+
+After the retained sweep and these carrier paths, all X fields and
+all selected Y fields are FULL. Add \(L_sE_tx\) to the selected target
+bank at that cut. The outputs are
+
+\[
+X_{\rm out}=F_9x,\qquad
+Y_{P,\rm out}=F_9L_s(y+E_tx),\qquad
+Y_{R,\rm out}=F_9q_R(y+E_tx)_R.
+\]
+
+The same reader \(L_s\) has been retained. No old-stage target read was
+used. The input reader was not replaced by \(L_t\).
+
+## A query through sixteen existing source carriers
+
+The actual response has \(E_t[P,P]=0\). It also has
+
+\[
+E_t=I+A_tL_t,\qquad
+L_t=J^{\mathsf T}+B_t,\qquad C_t=I+JB_t,
+\]
+
+where \(A_t=(E_t-I)J\). These are routed operator identities. Since
+\(L_sJ=I\), direct multiplication gives
+
+\[
+L_sE_tC_t^{-1}
+  = B_s-B_t + (L_sE_tJ)J^{\mathsf T}.
+\]
+
+No factor at stage s is commuted through a factor at stage t. Put
+\(M_{s,t}=L_sE_tJ\). Use this complete order at the FULL cut:
+
+1. Add \(B_sX_R\) to \(Y_P\).
+2. Add the current \(X_P\) to \(Y_P\).
+3. Apply \(C_t\) to X.
+4. Subtract the new \(X_P\) from \(Y_P\).
+5. Add \(M_{s,t}X_P\) to \(Y_P\).
+6. Apply \(C_t^{-1}\) to X.
+
+Steps 2 and 4 contribute \(-B_tX_R\). The query in step 5 reads the
+current centres \(L_tX\) from the existing sixteen X fields. Thus the
+complete increment is \(L_sE_tX_{\rm original}\).
+Step 6 restores every X field. Every target baseline is retained.
+No scratch field or zero input is used.
+
+This factorization avoids an inverse of E. In particular, it needs no
+division by five or seven. Both C words are the emitted dyadic shears
+from the normalized row-capture packet.
+
+## Actual owner paths and phases
+
+The checker binds the three D25 pairs \((s,t)=(0,1),(0,2),(1,2)\).
+For a term with intermediate port j and final source port r, the
+complete owner multiplier is
+
+\[
+A=\rho_{s,p}\rho_{s,j}\rho_{t,j}\rho_{t,r}.
+\]
+
+The coefficient is \(L_{p,j}E_{j,r}\). The full query \(L_sE_t\) has
+3,808 such terms. Its selected-source part \(M_{s,t}\) has 696 terms.
+Each of the latter reads one of the sixteen selected X fields.
+Different owner paths are kept as different terms.
+
+All factors of A act within the completed prefix at level t. They fix
+every uncompleted axis. A is orthogonal. Therefore
+
+\[
+F_{9+8t}P_AF_{9+8t}^{-1}=X_{\delta_A}P_A.
+\]
+
+The program computes the entire Z4 difference polynomial to obtain
+\(\delta_A\). It verifies that its odd and quadratic parts vanish.
+It also checks the inverse map, whose route is \(A^{-1}\) and whose
+translation is \(A^{-1}\delta_A\).
+
+The owner read is \(h\mapsto hA\). The payload map \(P_A\) expresses the
+source chart in the target chart. Together with the translation, these
+are one field/address map. They are not two independent uses of the
+source data.
+
+For each middle-query term, apply that map to its source field, add
+the required scalar multiple to the selected Y field, and apply the
+inverse map to the source. This restores the full arbitrary source
+array before the next term. Right multiplication by A is a cover
+bijection, so this procedure is legal on the regular orthogonal cover.
+
+Step 1 uses the literal past-stage FULL views on 96 source fields and
+16 target fields. Steps 3 and 6 use the current-stage FULL views on
+all 112 source fields. The checker verifies these full phase equations.
+Steps 2 and 4 are same-port copies between FULL fields.
+
+The checker also expands both sides of the query identity as exact
+sums of owner paths. It compares coefficients only after the complete
+route matrices agree. This prevents a false cancellation between
+different body owners.
+
+## Invoice and bounds
+
+The conservative query invoice for each checked pair is:
+
+| Part | Real scalar primitives | Monomial map calls |
+| --- | ---: | ---: |
+| Past-reader complement query | 1,760 | 224 |
+| Two same-port copies | 256 | 0 |
+| Current C and its inverse | 3,520 | 448 |
+| Selected-source middle query | 5,632 | 1,392 |
+| Total | 11,168 | 2,064 |
+
+The middle query scales each large target by four, executes its
+integer-coefficient additions, then divides that target by four.
+The small targets need no such scale. This uses only dyadic units.
+The two copies use all sixteen selected ports.
+
+The query uses no native child and no extra field. A conservative
+triangle-inequality bound for every scalar prefix is 972, relative to
+unit one-norm inputs at the query entrance. The checker derives this
+bound from the literal scalar order. It also bounds the new binary
+denominator height by three. These are bounds for one query. They are
+not a recursive precision certificate.
+
+The retained native word has scalar price 6,456. Replacing its selected
+paths by sixteen H8 calls gives the prospective local profile
+
+```text
+1392 H1 + 64 H2 + 48 H3 + 16 H8.
+```
+
+Its native rank is 1,792, equal to the old rank. The retained word plus
+the new query has scalar price 17,624. The 2,064 query maps are additional
+to native wrappers and ordinary boundary maps. Their finite cost and
+the child hosting must still be included in a complete supplier.
+
+## Reuse scope
+
+The operator proof applies whenever the later FULL cut admits both
+stage routes, the pivot normalization \(L_sJ=I\) holds, and the ordinary
+target paths do not read a selected target. These are concrete
+conditions. They do not require a common response across stages.
+
+This packet verifies those conditions for the actual D25 forward
+services and all three possible past/current stage pairs. It does not
+assert the same input type for a backward service. That service needs
+its own dual code and native proof.
+
+Run `check_reuse.py` normally and with `python3 -O`, with separate output
+directories. The two program files and the two receipts must be byte
+equal. The immutable formation packet remains unchanged.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_access.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_access.py
new file mode 100644
index 0000000000..b4187b33ac
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_access.py
@@ -0,0 +1,249 @@
+"""Check native path isolation and exact row-capture boundary views."""
+
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import argparse
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+PINS = {
+    "native": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+        "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    ),
+    "capture": (
+        "controller-followthrough-20261017/row-capture-20261020/"
+        "run-normal/ROW-CAPTURE.json",
+        "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7",
+    ),
+    "views": (
+        "bridge-access-20261017/matched-stage-access-20261018/"
+        "DIMENSION25-VIEWS.json",
+        "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473",
+    ),
+    "phase": (
+        "bridge-access-20261017/check_bridge_access.py",
+        "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111",
+    ),
+}
+PIVOTS = [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23]
+PAIRS = [(0, 27), (36, 111), (20, 46), (7, 57)]
+
+
+def need(value, message):
+    if not value:
+        raise ValueError(message)
+
+
+def raw_source(name):
+    path, pin = PINS[name]
+    raw = (LANES / path).read_bytes()
+    if path.endswith(".gz"):
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Source pin: " + name)
+    return raw
+
+
+def matrix(rows):
+    return [{int(j): F(v) for j, v in row.items() if F(v)} for row in rows]
+
+
+def multiply(a, b):
+    result = []
+    for row in a:
+        acc = {}
+        for j, v in row.items():
+            for k, w in b[j].items():
+                acc[k] = acc.get(k, F(0)) + v * w
+        result.append({j: v for j, v in acc.items() if v})
+    return result
+
+
+def dump(rows):
+    return [{str(j): str(v) for j, v in sorted(row.items())} for row in rows]
+
+
+def native_isolation(word):
+    selected = {112 + p for p in PIVOTS}
+    live = list(word["start"])
+    kept = []
+    removed = []
+    old_profile = Counter()
+    removed_profile = Counter()
+    scalar_removed = Counter()
+    last_source = -1
+    for i, event in enumerate(word["events"]):
+        if event[0] == "native":
+            _, target, old, new, rank, _ = event
+            old_profile[rank] += 1
+            omit = target in selected
+            if omit:
+                removed_profile[rank] += 1
+            else:
+                need(live[target] == old, "Retained native input frame")
+                live[target] = new
+        else:
+            need(event[0] == "scalar", "Native event type")
+            _, (op, target, source, coefficient), frame = event
+            omit = target in selected
+            if omit:
+                scalar_removed[op + ":" + coefficient] += 1
+            else:
+                need(source not in selected, "Removed target is not read")
+                need(live[target] == frame, "Retained scalar target frame")
+                if source is not None:
+                    need(live[source] == frame, "Retained scalar source frame")
+            need(not (target < 112 and source is not None and source >= 112),
+                 "Forward word has no target-to-source feedback")
+        if target < 112:
+            last_source = i
+        (removed if omit else kept).append(i)
+    need(len(removed) == 250 and removed_profile == {1: 128},
+         "Exact selected path census")
+    need(sum(scalar_removed.values()) == 122, "Exact scalar deletion census")
+    need(last_source == 2638, "Last complete source cut")
+    need(all(live[p] == 1 for p in range(112)), "All sources are FULL")
+    need(all(live[t] == 0 for t in selected), "Selected targets stay at I")
+    need(all(live[t] == word["final"][t] for t in range(len(live))
+             if t not in selected), "Other endpoint frames are retained")
+    need(len(word["frames"][1]) == 9, "FULL is the nine-axis frame")
+    need(all(word["start"][i] == word["final"][i] for i in range(224, 640)),
+         "The 416 outside fields are retained")
+    for t in selected:
+        live[t] = 1
+    profile = old_profile - removed_profile
+    profile[9] += 16
+    need(profile == {1: 1392, 2: 64, 3: 48, 9: 16}, "Hybrid native profile")
+    need(sum(k * v for k, v in profile.items()) == 1808, "Hybrid native rank")
+    return {
+        "removed_event_indices": removed,
+        "retained_event_indices": kept,
+        "removed_native_profile": dict(sorted(removed_profile.items())),
+        "removed_scalar_census": dict(sorted(scalar_removed.items())),
+        "last_source_event": last_source,
+        "query_cut_after_original_event": len(word["events"]) - 1,
+        "hybrid_final_frames": live,
+        "native_profile": dict(sorted(profile.items())),
+        "native_rank": 1808,
+        "native_children": sum(profile.values()),
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "run-normal")
+    args = parser.parse_args()
+    source = json.loads(raw_source("native"))
+    capture = json.loads(raw_source("capture"))
+    views = json.loads(raw_source("views"))
+    raw_source("phase")
+    spec = importlib.util.spec_from_file_location(
+        "row_capture_phase", LANES / PINS["phase"][0])
+    phase = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(phase)
+    need(capture["pivots"] == PIVOTS, "Capture pivot order")
+    c, ci, e = (matrix(capture[k]) for k in ("code", "code_inverse", "response"))
+    ident = [{i: F(1)} for i in range(112)]
+    need(multiply(c, ci) == multiply(ci, c) == ident, "Capture is a unit")
+    need(e == matrix(source["model"]["response"]), "Same actual response")
+    ce = multiply(c, e)
+    for p in range(112):
+        if p in PIVOTS:
+            need(c[p].get(p) == 1 and set(c[p]) & set(PIVOTS) == {p},
+                 "Capture reads only unchanged complement rows")
+        else:
+            need(c[p] == ident[p] and ce[p] == e[p],
+                 "Capture leaves every complement row unchanged")
+    providers = {
+        name: native_isolation(words["forward"])
+        for name, words in source["providers"].items()
+    }
+    unit = [1 << j for j in range(25)]
+    entries = []
+    counts = Counter()
+    for record in views["entries"]:
+        p, s, q = record["port"], record["stage"], record["q"]
+        rho = record["route_columns"]
+        align = record["literal_stage_alignment"]
+        if p not in PIVOTS:
+            continue
+        exterior = [(v, 1) for v in unit[9:9 + 8 * s]]
+        before = [] if not s else (
+            [(v, 1) for v in unit[:9 + 8 * (s - 1)]] + [(q, -1)])
+        entry = phase.add_phase(
+            phase.product([(phase.act(rho, v), k) for v, k in before]),
+            phase.line(phase.act(rho, align["entry_Y"]), 2))
+        need(entry == phase.product(exterior), "Current-I selected Y entry")
+        counts["current_I_entries"] += 1
+        full = [(v, 1) for v in unit[:9 + 8 * s]]
+        exit_phase = phase.add_phase(
+            phase.product([(phase.act(rho, v), k) for v, k in full]),
+            phase.line(align["exit_X"], 2))
+        need(exit_phase == phase.product(full), "Selected FULL output phase")
+        need(align["exit_X"] == align["exit_Y"],
+             "Actual FULL and hole exit translations agree")
+        counts["selected_FULL_exits"] += 1
+        item = dict(record)
+        item["hybrid_exit_translation"] = align["exit_X"]
+        item["next_current_entries"] = []
+        for nxt in views["entries"]:
+            if nxt["port"] != p or nxt["stage"] <= s:
+                continue
+            t = nxt["stage"]
+            rho_t = nxt["route_columns"]
+            delta = phase.act(rho_t, nxt["literal_stage_alignment"]["entry_Y"])
+            actual = phase.add_phase(
+                phase.product([(phase.act(rho_t, v), k) for v, k in full]),
+                phase.line(delta, 2))
+            common_axes = unit[9:9 + 8 * s] + unit[9 + 8 * (t - 1):9 + 8 * t]
+            expected = phase.product([(v, 1) for v in common_axes] + [(q, 1)])
+            need(actual == expected, "Carried FULL centre has intrinsic Q")
+            need(actual != phase.product([(v, 1) for v in common_axes]),
+                 "Carried FULL centre is not an I input")
+            counts["future_intrinsic_Q_entries"] += 1
+            item["next_current_entries"].append({
+                "stage": t, "common_exterior_axes": common_axes,
+                "intrinsic_line": q, "intrinsic_exponent": 1,
+                "translation_after_route": delta,
+            })
+        entries.append(item)
+    need(counts == {"current_I_entries": 48, "selected_FULL_exits": 48,
+                    "future_intrinsic_Q_entries": 48}, "All selected D25 cuts")
+    program = {
+        "schema": "row-capture-access-v1", "source_pins": PINS,
+        "pivots": PIVOTS, "complete_large_pairs": PAIRS,
+        "providers": providers, "selected_views": entries,
+        "selected_output_rows": dump([ce[p] for p in PIVOTS]),
+        "selected_input_rows": dump([c[p] for p in PIVOTS]),
+        "owner_cover": "Regular O(25,2); use a complete cover sweep per stage.",
+        "new_native_recipes_emitted_here": False,
+        "recursive_hosting_proved_here": False,
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(program, sort_keys=True, indent=2) + "\n").encode()
+    (args.output / "ACCESS-PROGRAM.json").write_bytes(raw)
+    receipt = {
+        "status": "PASS_ROW_CAPTURE_NATIVE_ISOLATION_AND_D25_ACCESS",
+        "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "source_pins": PINS, "program_sha256": sha256(raw).hexdigest(),
+        "phase_checks": dict(counts),
+        "native_profile": {"1": 1392, "2": 64, "3": 48, "9": 16},
+        "native_rank": 1808, "native_children": 1520,
+        "outside_arbitrary_fields": 416,
+        "next_interface": "FULL centre rows become Q at a future current-Y entry.",
+        "complete_supplier_claimed": False,
+    }
+    (args.output / "CHECKS.json").write_text(
+        json.dumps(receipt, sort_keys=True, indent=2) + "\n")
+    print(receipt["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_integration.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_integration.py
new file mode 100644
index 0000000000..3f95ba2894
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_integration.py
@@ -0,0 +1,341 @@
+"""Bind the native carrier prefix to the actual D25 reuse dispatcher."""
+
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import argparse
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+PINS = {
+    "prefix": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz",
+        "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e",
+    ),
+    "prefix_freeze": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "fixed-reader-reuse-20261020/PREFIX-FREEZE.json",
+        "fc3cef0e499e5bc85c25bb0fc88f5ecd12e44b66799e3d793dac37de8d88d26e",
+    ),
+    "native_phase_review": (
+        "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json",
+        "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c",
+    ),
+    "query": (
+        "bridge-access-20261017/row-capture-access-20261020/"
+        "reuse-normal/REUSE-PROGRAM.json",
+        "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b",
+    ),
+    "query_freeze": (
+        "bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json",
+        "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf",
+    ),
+    "literal_query": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz",
+        "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a",
+    ),
+    "literal_query_freeze": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "fixed-reader-reuse-20261020/QUERY-FREEZE.json",
+        "f111a90f7403f93494e9d1f83ae35dbf7dd72eddc8c9f8bf730d677b4a31402d",
+    ),
+    "views": (
+        "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json",
+        "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473",
+    ),
+    "phase": (
+        "bridge-access-20261017/check_bridge_access.py",
+        "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111",
+    ),
+}
+UNIT = [1 << j for j in range(25)]
+
+
+def need(test, label):
+    if not test:
+        raise ValueError(label)
+
+
+def raw_source(name):
+    path, pin = PINS[name]
+    raw = (LANES / path).read_bytes()
+    if path.endswith(".gz"):
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source: " + name)
+    return raw
+
+
+def rank(vectors):
+    pivots = {}
+    for value in vectors:
+        while value:
+            bit = value.bit_length() - 1
+            if bit not in pivots:
+                pivots[bit] = value
+                break
+            value ^= pivots[bit]
+    return len(pivots)
+
+
+def add(target, source, coefficient):
+    for column, value in source.items():
+        target[column] = target.get(column, F(0)) + coefficient * value
+        if not target[column]:
+            del target[column]
+
+
+def price(op, value):
+    n, d = abs(value.numerator), value.denominator
+    need(n and d & (d - 1) == 0, "Nonzero dyadic coefficient")
+    if op == "scale":
+        need(n & (n - 1) == 0, "The scale is a dyadic unit")
+        return 2 * (abs(n.bit_length() - d.bit_length()) + (value < 0))
+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)
+
+
+def check_prefix(word, response, selected):
+    live = list(word["start"])
+    state = [{p: F(1)} for p in range(640)]
+    profile = Counter()
+    scalar_price = 0
+    for index, event in enumerate(word["events"]):
+        if event[0] == "native":
+            _, target, old, new, mass, key = event
+            need(live[target] == old, "Native input frame")
+            left, right = word["frames"][old], word["frames"][new]
+            need(rank(left + right) == len(right), "Nested native frame")
+            need(len(right) - len(left) == mass
+                 == word["native_recipes"][key]["rank"], "Native rank")
+            live[target] = new
+            profile[mass] += 1
+        else:
+            need(event[0] == "scalar", "Prefix event grammar")
+            (_, (op, target, source, coefficient), frame) = event
+            value = F(coefficient)
+            need(live[target] == frame, "Scalar target frame")
+            if op == "add":
+                need(source != target and live[source] == frame,
+                     "Scalar source frame")
+                need(source not in {112 + p for p in selected},
+                     "The prefix does not read a selected target")
+                add(state[target], state[source], value)
+            else:
+                need(op == "scale", "Prefix scalar grammar")
+                state[target] = {j: value * v for j, v in state[target].items()}
+            scalar_price += price(op, value)
+        if index == 2389:
+            need(all(live[p] == 1 for p in range(112)),
+                 "All sources are FULL after the complete retained core")
+    expected = [{p: F(1)} for p in range(640)]
+    for p in range(112):
+        if p not in selected:
+            add(expected[112 + p], response[p], F(1))
+    need(state == expected, "The full 640-column carrier prefix")
+    need(live == word["final"], "The full prefix frame ledger")
+    need(all(live[p] == live[112 + p] == 1 for p in selected),
+         "Every selected query source and target is FULL")
+    need(all(state[p] == {p: F(1)} for p in range(224, 640)),
+         "All 416 arbitrary helper fields are restored")
+    need(len(word["events"]) == 2406
+         and word["stage_ranges"]["retained_core"] == [0, 2390]
+         and word["stage_ranges"]["selected_line_progress"] == [2390, 2406]
+         and "late_query" not in word["stage_ranges"], "The exact prefix cut")
+    need(profile == {1: 1392, 2: 64, 3: 48, 8: 16}
+         and scalar_price == 6456, "The complete prefix invoice")
+    source_views = {v["port"]: v for v in word["input_views"] if v["role"] == "source"}
+    selected_views = [v for v in word["input_views"] if v["role"] == "selected_target"]
+    need(set(source_views) == set(range(112)) and len(selected_views) == 16,
+         "The complete input adapter stock")
+    for view in selected_views:
+        source = source_views[view["port"]]
+        need(view["field"] == 112 + view["port"] and view["port"] in selected
+             and view["source_entry_port"] == view["port"], "Selected input adapter field")
+        need(all(view[key] == source[key] for key in ("frame", "rank", "left", "right")),
+             "The selected input adapter equals the source adapter")
+    need({v["port"] for v in word["output_views"]} == set(range(112)) - selected,
+         "Only ordinary target output adapters remain")
+    need(len(word["input_views"]) == 128 and len(word["output_views"]) == 96,
+         "The exact adapter count")
+    return {
+        "native_profile": dict(sorted(profile.items())),
+        "native_rank": sum(k * v for k, v in profile.items()),
+        "native_children": sum(profile.values()),
+        "scalar_primitives": scalar_price,
+        "arbitrary_input_columns": 640,
+        "restored_arbitrary_helper_fields": 416,
+        "input_adapters": 128, "ordinary_output_adapters": 96,
+        "native_phase_review_is_pinned_dependency": True,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, required=True)
+    args = parser.parse_args()
+    sources = {key: raw_source(key) for key in PINS}
+    prefix, query, views = (json.loads(sources[key]) for key in ("prefix", "query", "views"))
+    literal_query = json.loads(sources["literal_query"])
+    need(literal_query["native_prefixes"] == prefix["providers"],
+         "The literal query uses this exact complete native prefix")
+    need(literal_query["source_pins"]["query"]["sha256"] == PINS["query"][1],
+         "The literal query uses this exact path program")
+    spec = importlib.util.spec_from_file_location("reuse_dispatcher_phase", LANES / PINS["phase"][0])
+    phase = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(phase)
+    selected = set(prefix["selected_ports"])
+    need(prefix["selected_ports"] == query["pivots"], "The exact carried pivot set")
+    response = [{int(j): F(v) for j, v in row.items()} for row in prefix["response"]]
+    reports = {name: check_prefix(word, response, selected)
+               for name, word in prefix["providers"].items()}
+    records = {(v["stage"], v["port"]): v for v in views["entries"]}
+    stage_programs, counts = [], Counter()
+    for t in (1, 2):
+        full_before = [(v, 1) for v in UNIT[:9 + 8 * (t - 1)]]
+        full_after = [(v, 1) for v in UNIT[:9 + 8 * t]]
+        exterior = [(v, 1) for v in UNIT[9:9 + 8 * t]]
+        data_entries, data_exits = [], []
+        for side, offset in (("X", 0), ("Y", 112)):
+            for p in range(112):
+                record = records[t, p]
+                rho, q, align = (record[key] for key in
+                                 ("route_columns", "q", "literal_stage_alignment"))
+                need(all((a & b).bit_count() % 2 == int(i == j)
+                         for i, a in enumerate(rho) for j, b in enumerate(rho)),
+                     "Regular-cover orthogonal route")
+                need([phase.act(rho, v) for v in rho] == UNIT
+                     and phase.act(rho, q) == q, "The route fixes its intrinsic line")
+                need(rho[9 + 8 * t:] == UNIT[9 + 8 * t:], "No future coordinate is changed")
+                full_input = side == "X" or p in selected
+                before = full_before + ([] if full_input else [(q, -1)])
+                entry_delta = phase.act(rho, align["entry_" + side])
+                actual = phase.add_phase(
+                    phase.product([(phase.act(rho, v), n) for v, n in before]),
+                    phase.line(entry_delta, 2))
+                expected = phase.product(exterior + ([(q, 1)] if full_input else []))
+                need(actual == expected, "Exact adjacent current entry phase")
+                counts["entry_phase_equations"] += 1
+                after = full_after + ([] if full_input else [(q, -1)])
+                exit_key = "exit_X" if full_input else "exit_Y"
+                exit_delta = align[exit_key]
+                actual = phase.add_phase(
+                    phase.product([(phase.act(rho, v), n) for v, n in after]),
+                    phase.line(exit_delta, 2))
+                need(actual == phase.product(after), "Exact global output phase")
+                counts["exit_phase_equations"] += 1
+                data_entries.append({
+                    "field": offset + p, "port": p, "side": side,
+                    "owner_from_body": "h=d*rho",
+                    "route_columns": rho,
+                    "translation_before_route": align["entry_" + side],
+                    "translation_after_route": entry_delta,
+                    "intrinsic_input": "Q_p" if full_input else "I",
+                })
+                data_exits.append({
+                    "field": offset + p, "port": p, "side": side,
+                    "owner_from_body": "h=d*rho",
+                    "route_columns": rho,
+                    "translation_after_route": exit_delta,
+                    "global_output": "FULL" if full_input else "FULL*q_p",
+                    "literal_translation_key": exit_key,
+                })
+        stage_programs.append({
+            "service_stage": t, "physical_input_level": t - 1,
+            "physical_output_level": t,
+            "common_exterior_axes": [v for v, _ in exterior],
+            "DATA_entry": data_entries, "DATA_exit": data_exits,
+        })
+    invocations = []
+    for number, pair in enumerate(query["pairs"]):
+        s, t = pair["reader_stage"], pair["service_stage"]
+        need((s, t) in ((0, 1), (0, 2), (1, 2)) and s < t,
+             "The checked past/current pair")
+        need(pair["real_scalar_primitives"] == 11168
+             and pair["monomial_map_calls"] == 2064
+             and pair["native_children_in_query"] == 0, "The complete routed query invoice")
+        literal = literal_query["queries"][f"{s}:{t}"]
+        need(literal["reader_stage"] == s and literal["service_stage"] == t,
+             "The exact literal query stage labels")
+        need(sum(event[0] == "map" for event in literal["events"]) == 2064,
+             "All literal query maps are retained")
+        need(sum(price(event[1], F(event[4])) for event in literal["events"]
+                 if event[0] == "scalar") == 11168, "The literal scalar query price")
+        need(all(record["port"] in selected for record in query["carrier_recipes"]),
+             "Only selected carrier paths are added")
+        for provider in prefix["providers"]:
+            invocations.append({
+                "provider": provider, "reader_stage": s, "service_stage": t,
+                "physical_input_level": t - 1,
+                "physical_output_level": t,
+                "stage_view_record": t - 1, "query_pair_record": number,
+                "ordered_blocks": [
+                    {"op": "DATA_entry", "record": t - 1, "map_calls": 224},
+                    {"op": "native_input_adapters", "source": "prefix",
+                     "provider": provider, "map_calls": 128},
+                    {"op": "complete_native_carrier_cover_sweep", "source": "prefix",
+                     "provider": provider, "event_range": [0, 2406]},
+                    {"op": "ordinary_output_adapters", "source": "prefix",
+                     "provider": provider, "map_calls": 96},
+                    {"op": "DATA_exit", "record": t - 1, "map_calls": 224},
+                    {"op": "complete_cover_barrier"},
+                    {"op": "fixed_past_reader_query", "source": "query",
+                     "pair_record": number, "literal_source": "literal_query",
+                     "literal_key": f"{s}:{t}", "map_calls": 2064},
+                ],
+                "scalar_primitives": 17624,
+                "map_call_bound": {
+                    "DATA": 448, "local_endpoint_adapters": 224,
+                    "native_side_maps": 3040, "late_query": 2064,
+                    "total": 5776,
+                },
+            })
+    need(counts == {"entry_phase_equations": 448, "exit_phase_equations": 448},
+         "The complete adjacent D25 boundary census")
+    payload = {
+        "schema": "fixed-reader-global-dispatcher-v1", "source_pins": PINS,
+        "dimension": 25, "selected_ports": prefix["selected_ports"],
+        "stage_views": stage_programs, "invocations": invocations,
+        "contract": {
+            "input": "(Fprev*x, Fprev*diag(I_P,q_R)*w)",
+            "output": "(Fnew*x, Fnew*diag(I_P,q_R)*(w+A_st*x))",
+            "response_rows_P": "L_s*E_t",
+            "response_rows_R": "(E_t)_R",
+            "reader_label_is_not_physical_level": True,
+            "arbitrary_independent_selected_records": True,
+            "full_native_sweep_before_global_query": True,
+        },
+        "owner_contract": {
+            "cover": "Regular O(25,2)",
+            "data_partition": "For each field, d -> d*rho_(t,p) is a bijection.",
+            "native_helpers": "Use the inherited 416-field helper contract; restore it per body.",
+            "helper_hosting_reproved_here": False,
+        },
+        "native_phase_validation": "Use the pinned independent line-entry review.",
+        "complete_supplier_claimed": False,
+    }
+    args.output.mkdir(parents=True, exist_ok=False)
+    raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode()
+    (args.output / "DISPATCHER.json").write_bytes(raw)
+    receipt = {
+        "status": "PASS_FIXED_READER_NATIVE_D25_DISPATCHER",
+        "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "program_sha256": sha256(raw).hexdigest(), "source_pins": PINS,
+        "providers": reports, "boundary_checks": dict(counts),
+        "reader_service_pairs": [[0, 1], [0, 2], [1, 2]],
+        "scalar_primitives": 17624, "query_map_calls": 2064,
+        "total_monomial_call_bound": 5776,
+        "inherited_helper_hosting_still_required": True,
+        "complete_supplier_claimed": False,
+    }
+    (args.output / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(receipt["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_reuse.py b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_reuse.py
new file mode 100644
index 0000000000..641266ee7f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/check_reuse.py
@@ -0,0 +1,321 @@
+"""Check the fixed-reader query at actual completed D25 cuts."""
+
+from collections import defaultdict
+from fractions import Fraction as F
+from functools import cache
+from hashlib import sha256
+import argparse
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+ACCESS_PIN = "48baba6e09b787924c496c8d4ce89c9dd3f77585946516f90ff8803d45adb5cd"
+UNIT = tuple(1 << j for j in range(25))
+IDENTITY = UNIT
+
+
+def need(value, message):
+    if not value:
+        raise ValueError(message)
+
+
+def module(path, name):
+    spec = importlib.util.spec_from_file_location(name, path)
+    out = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(out)
+    return out
+
+
+def act(a, value):
+    out = 0
+    while value:
+        bit = value & -value
+        out ^= a[bit.bit_length() - 1]
+        value ^= bit
+    return out
+
+
+@cache
+def compose(a, b):
+    return tuple(act(a, value) for value in b)
+
+
+def transpose(a):
+    return tuple(sum(((a[j] >> i) & 1) << j for j in range(25))
+                 for i in range(25))
+
+
+def accumulate(row, key, value):
+    row[key] += value
+    if not row[key]:
+        del row[key]
+
+
+def compose_rows(left, right):
+    out = []
+    for row in left:
+        acc = defaultdict(F)
+        for (j, a), value in row.items():
+            for (r, b), other in right[j].items():
+                accumulate(acc, (r, compose(a, b)), value * other)
+        out.append(dict(acc))
+    return out
+
+
+def price(op, value):
+    n, d = abs(value.numerator), value.denominator
+    need(n and d & (d - 1) == 0, "Nonzero dyadic coefficient")
+    if op == "scale":
+        need(n & (n - 1) == 0, "Scale is a dyadic unit")
+        return 2 * (abs(n.bit_length() - d.bit_length()) + (value < 0))
+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "reuse-normal")
+    args = parser.parse_args()
+    access_path = HERE / "check_access.py"
+    need(sha256(access_path.read_bytes()).hexdigest() == ACCESS_PIN,
+         "Frozen formation checker")
+    source = module(access_path, "fixed_reader_source")
+    capture = json.loads(source.raw_source("capture"))
+    native = json.loads(source.raw_source("native"))
+    views = json.loads(source.raw_source("views"))
+    source.raw_source("phase")
+    phase = module(LANES / source.PINS["phase"][0], "fixed_reader_phase")
+    pset = set(source.PIVOTS)
+    pindex = {p: i for i, p in enumerate(source.PIVOTS)}
+    e = source.matrix(capture["response"])
+    l = source.matrix(capture["centre_reader"])
+    need(all(not (set(e[p]) & pset) for p in pset), "Actual E[P,P] is zero")
+    rho = {(v["stage"], v["port"]): tuple(v["route_columns"])
+           for v in views["entries"]}
+    records = {(v["stage"], v["port"]): v for v in views["entries"]}
+    code = capture["scalar_word"]
+    inverse = capture["inverse_scalar_word"]
+    need(sum(price(g[0], F(g[3])) for g in code) == 1760,
+         "Current capture scalar price")
+    need(sum(price(g[0], F(g[3])) for g in inverse) == 1760,
+         "Current capture inverse scalar price")
+    need(all(g[2] not in pset for g in code if g[0] == "add"),
+         "Current capture reads only complement")
+    for provider in native["providers"].values():
+        retained_price = sum(
+            price(event[1][0], F(event[1][3]))
+            for event in provider["forward"]["events"]
+            if event[0] == "scalar" and event[1][1] not in {112 + p for p in pset})
+        need(retained_price == 6456, "Retained scalar word invoice")
+    carrier_recipes = []
+    for p in source.PIVOTS:
+        q = records[0, p]["q"]
+        chart = phase.chart(q)[:9]
+        basis = tuple(chart[1:] + chart[:1]) + UNIT[9:]
+        need(compose(transpose(basis), basis) == IDENTITY,
+             "Rank-eight carrier basis")
+        expected = phase.product([(x, 1) for x in UNIT[:9]] + [(q, -1)])
+        head = phase.product([(x, 1) for x in basis[:8]])
+        delta = phase.add_phase(expected, phase.negative(head))
+        need(delta[0] == delta[2] == 0, "Carrier remainder is a translation")
+        need(phase.add_phase(head, phase.line(delta[1], 2)) == expected,
+             "Exact F9 q carrier recipe")
+        carrier_recipes.append({
+            "port": p, "q": q, "rank": 8, "basis_columns": basis,
+            "inverse_columns": transpose(basis),
+            "output_translation": delta[1],
+            "input_frame": "Q_p", "output_frame": "F9",
+        })
+
+    def routed(rows, targets, stage):
+        return [{
+            (r, compose(rho[stage, p], rho[stage, r])): value
+            for r, value in row.items()
+        } for p, row in zip(targets, rows)]
+
+    def full_view(stage, port, level):
+        record = records[stage, port]
+        a = rho[stage, port]
+        delta = record["literal_stage_alignment"]["exit_X"]
+        full = [(x, 1) for x in UNIT[:9 + 8 * level]]
+        actual = phase.add_phase(
+            phase.product([(act(a, x), n) for x, n in full]),
+            phase.line(delta, 2))
+        need(actual == phase.product(full), "Literal past/current FULL view")
+        return {"port": port, "route_columns": a, "translation": delta}
+
+    all_pairs = []
+    for s, t in ((0, 1), (0, 2), (1, 2)):
+        ls = routed(l, source.PIVOTS, s)
+        lt = routed(l, source.PIVOTS, t)
+        et = routed(e, range(112), t)
+        direct = compose_rows(ls, et)
+        middle = [
+            {(r, a): v for (r, a), v in row.items() if r in pset}
+            for row in direct
+        ]
+        need(sum(map(len, direct)) == 3808, "Complete direct query census")
+        need(sum(map(len, middle)) == 696, "Selected-source query census")
+        lifted_lt = [{} for _ in range(112)]
+        for p, row in zip(source.PIVOTS, lt):
+            lifted_lt[p] = row
+        factored = compose_rows(middle, lifted_lt)
+        for i, p in enumerate(source.PIVOTS):
+            row = defaultdict(F, factored[i])
+            for key, value in ls[i].items():
+                if key[0] not in pset:
+                    accumulate(row, key, value)
+            for key, value in lt[i].items():
+                if key[0] not in pset:
+                    accumulate(row, key, -value)
+            need(dict(row) == direct[i],
+                 "Full noncommutative owner-path query identity")
+        full = [(x, 1) for x in UNIT[:9 + 8 * t]]
+        full_phase = phase.product(full)
+        routes = {}
+        route_table = []
+        query = []
+        scalar_bill = 0
+        map_count = 0
+        for p, row in zip(source.PIVOTS, middle):
+            denominator = max(v.denominator for v in row.values())
+            if denominator != 1:
+                query.append(["scale", p, None, str(denominator), None])
+                scalar_bill += price("scale", F(denominator))
+            for (r, a), value in sorted(row.items()):
+                need(r in pset and a != IDENTITY, "Selected source, actual route")
+                need(a[9 + 8 * t:] == UNIT[9 + 8 * t:],
+                     "Route fixes every uncompleted axis")
+                ai = transpose(a)
+                need(compose(ai, a) == compose(a, ai) == IDENTITY,
+                     "Composed query route is orthogonal")
+                if a not in routes:
+                    transformed = phase.product([(act(a, x), n) for x, n in full])
+                    difference = phase.add_phase(full_phase, phase.negative(transformed))
+                    need(difference[0] == difference[2] == 0,
+                         "FULL conjugate is a pure translation and address map")
+                    delta = difference[1]
+                    reverse = phase.add_phase(
+                        full_phase,
+                        phase.negative(phase.product([(act(ai, x), n) for x, n in full])))
+                    need(reverse == phase.line(act(ai, delta), 2),
+                         "Exact inverse source map")
+                    routes[a] = len(route_table)
+                    route_table.append({
+                        "columns": a, "inverse_columns": ai,
+                        "FULL_translation": delta,
+                        "inverse_FULL_translation": act(ai, delta),
+                    })
+                integer = denominator * value
+                need(integer.denominator == 1, "Normalized query integer")
+                query.append(["mapped_add_restore", p, r, str(integer), routes[a]])
+                scalar_bill += price("add", integer)
+                map_count += 2
+            if denominator != 1:
+                query.append(["scale", p, None, str(F(1, denominator)), None])
+                scalar_bill += price("scale", F(1, denominator))
+        need(scalar_bill == 5632 and map_count == 1392, "Middle query invoice")
+        old_reader_views = [full_view(s, p, t) for p in range(112)]
+        current_code_views = [full_view(t, p, t) for p in range(112)]
+        # All view maps preserve row one-norm. Use the triangle inequality
+        # at each scalar step to obtain a conservative prefix bound.
+        bounds = [F(1) for _ in range(224)]
+        grid = [0 for _ in range(224)]
+        peak = F(1)
+        peak_grid = 0
+
+        def apply_bound(op, target, origin, value):
+            nonlocal peak, peak_grid
+            if op == "scale":
+                bounds[target] *= abs(value)
+                grid[target] = max(
+                    0, grid[target] + value.denominator.bit_length()
+                    - abs(value.numerator).bit_length())
+            else:
+                bounds[target] += abs(value) * bounds[origin]
+                grid[target] = max(grid[target], grid[origin]
+                                   + value.denominator.bit_length() - 1)
+            peak = max(peak, bounds[target])
+            peak_grid = max(peak_grid, grid[target])
+
+        for op, p, r, value in code:
+            apply_bound(op, 112 + p, r, F(value))
+        for p in source.PIVOTS:
+            apply_bound("add", 112 + p, p, F(1))
+        for op, p, r, value in code:
+            apply_bound(op, p, r, F(value))
+        for p in source.PIVOTS:
+            apply_bound("add", 112 + p, p, F(-1))
+        for op, p, r, value, _ in query:
+            apply_bound("add" if op == "mapped_add_restore" else op,
+                        112 + p, r, F(value))
+        for op, p, r, value in inverse:
+            apply_bound(op, p, r, F(value))
+        need(peak_grid == 3, "Additional binary grid bound")
+        all_pairs.append({
+            "reader_stage": s, "service_stage": t,
+            "chronology": [
+                "Y_P += B_s X_R through old_reader_views",
+                "Y_P += X_P",
+                "X <- C_t X through current_code_views",
+                "Y_P -= X_P",
+                "Y_P += (L_s E_t selector_P) X_P through middle_query",
+                "X <- C_t^-1 X through current_code_views",
+            ],
+            "old_reader_views": old_reader_views,
+            "old_reader_view_ports": {
+                "X": sorted(set(range(112)) - pset), "Y": source.PIVOTS},
+            "current_code_views": current_code_views,
+            "middle_routes": route_table,
+            "middle_query": query,
+            "direct_owner_paths_checked": 3808,
+            "selected_source_paths": 696,
+            "real_scalar_primitives": 11168,
+            "monomial_map_calls": 2064,
+            "native_children_in_query": 0, "extra_fields": 0,
+            "conservative_prefix_one_norm": str(peak),
+            "additional_binary_grid_levels_at_most": 3,
+            "odd_divisions": 0,
+        })
+    payload = {
+        "schema": "fixed-row-reader-reuse-v1",
+        "formation_checker_sha256": ACCESS_PIN, "source_pins": source.PINS,
+        "pivots": source.PIVOTS, "carrier_recipes": carrier_recipes,
+        "pairs": all_pairs,
+        "input_Y": "Selected Q_p L_s y; complement y_R, in the current body.",
+        "output_Y": "Selected F9 L_s(y+E_t x); complement F9 q_R(y+E_t x)_R.",
+        "restored_source_fields": 112, "unchanged_outside_fields": 416,
+        "reuse_native_profile": {"1": 1392, "2": 64, "3": 48, "8": 16},
+        "reuse_native_rank": 1792,
+        "retained_scalar_primitives": 6456,
+        "retained_word_plus_query_scalar_primitives": 17624,
+        "complete_local_emitter_bound_here": False,
+        "recursive_hosting_bound_here": False,
+        "backward_companion_bound_here": False,
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(payload, sort_keys=True, indent=2) + "\n").encode()
+    (args.output / "REUSE-PROGRAM.json").write_bytes(raw)
+    receipt = {
+        "status": "PASS_FIXED_READER_D25_REUSE_QUERY",
+        "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "program_sha256": sha256(raw).hexdigest(),
+        "source_pins": source.PINS,
+        "stage_pairs": [[0, 1], [0, 2], [1, 2]],
+        "direct_owner_paths_per_pair": 3808,
+        "selected_source_paths_per_pair": 696,
+        "query_scalar_primitives": 11168, "query_monomial_maps": 2064,
+        "carrier_rank8_phase_recipes": 16,
+        "additional_binary_grid_levels_at_most": 3,
+        "prefix_one_norm_bounds": [p["conservative_prefix_one_norm"] for p in all_pairs],
+        "complete_supplier_claimed": False,
+    }
+    (args.output / "REUSE-CHECKS.json").write_text(
+        json.dumps(receipt, sort_keys=True, indent=2) + "\n")
+    print(receipt["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/CHECKS.json
new file mode 100644
index 0000000000..27d453f43b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/CHECKS.json
@@ -0,0 +1,100 @@
+{
+  "boundary_checks": {
+    "entry_phase_equations": 448,
+    "exit_phase_equations": 448
+  },
+  "checker_sha256": "c178c339b0398d7e6f0232d68d681527dfaed70da10941f09bd9db3f141887fb",
+  "complete_supplier_claimed": false,
+  "inherited_helper_hosting_still_required": true,
+  "program_sha256": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24",
+  "providers": {
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+      "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b"
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+    ]
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+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json
new file mode 100644
index 0000000000..83e7eed134
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json
@@ -0,0 +1,32749 @@
+{
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+    "reader_label_is_not_physical_level": true,
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+    "response_rows_R": "(E_t)_R"
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/CHECKS.json
new file mode 100644
index 0000000000..27d453f43b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/CHECKS.json
@@ -0,0 +1,100 @@
+{
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+      "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a"
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+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/DISPATCHER.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/DISPATCHER.json
new file mode 100644
index 0000000000..83e7eed134
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-optimized/DISPATCHER.json
@@ -0,0 +1,32749 @@
+{
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-CHECKS.json
new file mode 100644
index 0000000000..8883f7953d
--- /dev/null
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-PROGRAM.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-PROGRAM.json
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-optimized/REUSE-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-optimized/REUSE-CHECKS.json
new file mode 100644
index 0000000000..8883f7953d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-optimized/REUSE-CHECKS.json
@@ -0,0 +1,49 @@
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+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-optimized/REUSE-PROGRAM.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-optimized/REUSE-PROGRAM.json
new file mode 100644
index 0000000000..42b9b9dc2b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/reuse-optimized/REUSE-PROGRAM.json
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+        "X <- C_t X through current_code_views",
+        "Y_P -= X_P",
+        "Y_P += (L_s E_t selector_P) X_P through middle_query",
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/ACCESS-PROGRAM.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/ACCESS-PROGRAM.json
new file mode 100644
index 0000000000..2b3247f981
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/ACCESS-PROGRAM.json
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/CHECKS.json
new file mode 100644
index 0000000000..370d3432d3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-normal/CHECKS.json
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+{
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+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-optimized/ACCESS-PROGRAM.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-optimized/ACCESS-PROGRAM.json
new file mode 100644
index 0000000000..2b3247f981
--- /dev/null
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-optimized/CHECKS.json
new file mode 100644
index 0000000000..370d3432d3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-access-20261017/row-capture-access-20261020/run-optimized/CHECKS.json
@@ -0,0 +1,39 @@
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+    "1": 1392,
+    "2": 64,
+    "3": 48,
+    "9": 16
+  },
+  "native_rank": 1808,
+  "next_interface": "FULL centre rows become Q at a future current-Y entry.",
+  "outside_arbitrary_fields": 416,
+  "phase_checks": {
+    "current_I_entries": 48,
+    "future_intrinsic_Q_entries": 48,
+    "selected_FULL_exits": 48
+  },
+  "program_sha256": "c2d6a3300f759c4052236fec5ca8ef446f35b444f78369eaa9aed9ab9625f139",
+  "source_pins": {
+    "capture": [
+      "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json",
+      "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+    ],
+    "native": [
+      "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+      "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+    ],
+    "phase": [
+      "bridge-access-20261017/check_bridge_access.py",
+      "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111"
+    ],
+    "views": [
+      "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json",
+      "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"
+    ]
+  },
+  "status": "PASS_ROW_CAPTURE_NATIVE_ISOLATION_AND_D25_ACCESS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..63f8379a5f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "PEER-REVIEW.md": "a71c3cf4f5f0587b476ae21ed17f9a41d5cba36c707db08f3978b1f2a6640da1",
+    "REPRODUCTION.json": "e286eb25985980cd5e8e7789898827403197625b2a82d86ba0d55b209f350927",
+    "REVIEW.md": "fabb4fec8bf52fef4fc3c873c00dad2f0b7ee5dc6804be3426062d6c262d759c",
+    "check_review.py": "1908fe146d5dd006e84bf3c067509ba1b51e7d95af815f0fa84247939bc39264",
+    "normal/REVIEW-CHECKS.json": "b76233f91b441dc680db0df7bb2d889364d269222b3f0a711be31f96c461d0b2",
+    "optimized/REVIEW-CHECKS.json": "b76233f91b441dc680db0df7bb2d889364d269222b3f0a711be31f96c461d0b2"
+  },
+  "producer_freeze_sha256": "c2ee7b116d5b177c06b94fffb167354c3e6b49d759f2df16a4599eefded121d5",
+  "schema": "independent-clean-exchange-budget-review-v1",
+  "scope": "All eight literal invoices and sharp conditional extra-rank budgets. No routed caller or cleanup admission.",
+  "third_engine_freeze_sha256": "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/PEER-REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/PEER-REVIEW.md
new file mode 100644
index 0000000000..457926212f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/PEER-REVIEW.md
@@ -0,0 +1,29 @@
+# Peer check of the sharp mixed-rank bounds
+
+On 2026-10-20, the budget-geometry producer independently checked
+the final section of `REVIEW.md`. It found no material defect.
+It checked these points:
+
+- \(c_1<c_2<2c_1\). Thus the maximum and minimum H1/H2 bills
+  have the stated forms. The minimum increases at both
+  parity transitions.
+- The concavity transfer is valid with \(f(0)=0\). It sends
+  rank from one partial child to another until one is full
+  or the other is empty.
+- The four packed profiles have total ranks 197, 198, 181,
+  and 182. Rank 17 is the correct size cap.
+- Both of the producer's pinned exact engines give the
+  claimed strict sign for all eight extremal witnesses.
+
+The peer requested one clarification: the packed minimum
+must be stated to increase with total rank, including at
+a multiple of 17. That sentence was added before this
+review was frozen. It makes the exclusion of all larger
+total ranks explicit.
+
+The peer check concerns the new mixed-rank consequence.
+It does not independently admit the proposed routed
+caller or cleanup.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..a7656c1dcd
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/REPRODUCTION.json
@@ -0,0 +1,11 @@
+{
+  "commands": [
+    "python3 -I -B check_review.py --output normal",
+    "python3 -I -B -O check_review.py --output optimized"
+  ],
+  "normal_optimized_byte_identical": true,
+  "one_cpu": true,
+  "producer_files_changed": false,
+  "receipt_sha256": "b76233f91b441dc680db0df7bb2d889364d269222b3f0a711be31f96c461d0b2",
+  "status": "PASS_INDEPENDENT_CLEAN_EXCHANGE_BUDGET"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..98323dac30
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/REVIEW.md
@@ -0,0 +1,236 @@
+# Independent review of the clean-exchange native budget
+
+All eight serialized local words have the stated native and scalar
+counts. A third independently written rational engine confirms
+every strict budget threshold. No material defect was found.
+
+The result is a conditional three-call native budget. It does not
+provide a routed three-call composition, an initial Q entry, a
+cleanup word, a recursive host, or a complete supplier. It does
+not change the selected exponent.
+
+## Sources and coverage
+
+The budget producer freeze has SHA-256
+`c2ee7b116d5b177c06b94fffb167354c3e6b49d759f2df16a4599eefded121d5`.
+Its receipt has SHA-256
+`30a59c5cda0ff3c6f9e6ad7f9f38ec98fbfe71d34c58ddf768964cda304ba30d`.
+
+The clean local-word freeze has SHA-256
+`96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc`.
+The separate dual-word freeze has SHA-256
+`fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43`.
+The independent clean local review has SHA-256
+`6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d`.
+
+This review reads and checks those frozen bytes. It counts both
+clean variants and both dual variants for each of the two native
+providers. Every serialized event is counted. It does not rerun
+the native phase or 640-column local map proofs. In particular,
+its invoice check is not a new independent phase review of the
+separate dual words.
+
+The numerical engine comes from this lane's earlier independent
+review, freeze
+`953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87`.
+No budget-producer code or either of its two numerical engines
+is imported.
+
+## Literal invoices
+
+Each Q, inverse-adjoint, or selected-swap word has the profile
+
+\[
+1392H_1+64H_2+48H_3+16H_8.
+\]
+
+Its native rank is 1,792. Each I-entry word replaces the sixteen
+H8 children by H9 children, for rank 1,808. Each word has
+1,520 children.
+
+The checker verifies the rank of every recipe. All native data
+roles are between 0 and 223. In each Q or dual word, every
+productive field has total native rank eight. In an I word,
+sixteen fields have rank nine and the other 208 have rank eight.
+Every individual child satisfies \(2r^2<25^2\).
+
+Every scalar event uses a productive data role. The exact tariff
+census for each word is:
+
+| Operation tariff | Count | Subtotal |
+| --- | ---: | ---: |
+| Unit complex ADD, price 8 | 1,032 | 8,256 |
+| SCALE, price 2 | 96 | 192 |
+| SCALE, price 4 | 38 | 152 |
+| Total | 1,166 | 8,600 |
+
+The Q and dual words have 128 input views, 96 output views, and
+at most 3,040 native side maps. Their total map bound is 3,264.
+The I word has 112 input views, 96 output views, and at most
+3,008 native side maps. Both side records of each direct H9
+are literal identities, which the checker verifies. The I map
+bound is 3,216.
+
+Three Q calls therefore have 25,800 scalar primitives and a
+map bound of 9,792. One I call and two Q calls have the same
+scalar count and a map bound of 9,744. These are component
+subtotals. They do not price a caller or map lowering.
+
+## Historical exponent and exact arithmetic
+
+The exponent is read directly from the selected certificate
+and its bound assembly at commit
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`:
+
+\[
+b=\frac{67018507072324140917}{40000000000000000000000}.
+\]
+
+Both source hashes are checked. This is a historical pin,
+not a statement about the current frontier.
+
+For dimension 25, productive width 224, and no idle jobs,
+the moment of a histogram H is
+
+\[
+M_H(b)=\sum_r H_r\frac{r}{5600}
+          \left(\frac{25}{r}\right)^b.
+\]
+
+The third engine uses exact fractions. It reduces each
+logarithm to the series
+
+\[
+\log x=2\sum_{j\geq0}\frac{z^{2j+1}}{2j+1},
+\qquad z=\frac{x-1}{x+1},
+\]
+
+with \(0\leq z\leq1/3\). After 64 terms, its upper tail bound is
+\(2z^{129}/(129(1-z^2))\). It bounds the exponential through
+degree 20. For \(0\leq x<1/100\), its upper tail is
+\(x^{21}/(21!(1-x/22))\). Outward rational rounding preserves
+both bounds. No floating-point result determines a claim.
+
+The new intervals lie inside the producer's displayed
+intervals. The checker separately proves a strict upper
+bound below one at every accepted count and a strict lower
+bound above one at the next count.
+
+## Confirmed limits
+
+| Three-call profile | Native rank | Extra H1 limit | Extra H2 limit |
+| --- | ---: | ---: | ---: |
+| Three Q | 5,376 | 196 | 98 |
+| One I and two Q | 5,392 | 180 | 90 |
+
+After a hypothetical H1 cleanup, the limits are:
+
+| Profile | Cleanup H1 | Further H1 limit | Further H2 limit |
+| --- | ---: | ---: | ---: |
+| Three Q | 112 | 84 | 42 |
+| Three Q | 128 | 68 | 34 |
+| Three Q | 144 | 52 | 26 |
+| One I and two Q | 112 | 68 | 34 |
+| One I and two Q | 128 | 52 | 26 |
+| One I and two Q | 144 | 36 | 18 |
+
+The cleanup rows are budget hypotheses. Their required queries,
+scatter, views, phase correction, and restoration are not
+constructed by these numbers.
+
+A full 224-H1 terminal fails. With three Q calls its total
+native rank is 5,600. Since each rank is less than 25, every
+factor \((25/r)^b\) is greater than one for \(b>0\). Its moment
+is therefore greater than one. The one-I case has rank 5,616
+and fails already at \(b=0\). At the pinned positive exponent,
+the terminal must save at least 28 or 44 H1 children,
+respectively, before any other native cost is added.
+
+## Sharp bounds for mixed extra ranks
+
+Let \(c_r=r(25/r)^b/5600\). Since \(0<b<1\), the function
+\(r^{1-b}\) is increasing and strictly concave.
+
+For any mixture of H1 and H2 with total added rank m,
+the largest possible moment increment is \(mc_1\).
+The smallest is
+
+\[
+\left\lfloor\frac m2\right\rfloor c_2
+ +(m\bmod2)c_1.
+\]
+
+The checker proves that the all-H1 bill at m=196 passes
+for three Q calls, while the cheapest H1/H2 bill at m=197
+fails. These minimum and maximum bills increase with m.
+Thus every H1/H2 mixture is classified exactly:
+
+\[
+\boxed{n_1+2n_2\leq196.}
+\]
+
+For one I call and two Q calls the corresponding necessary
+and sufficient condition is
+
+\[
+\boxed{n_1+2n_2\leq180.}
+\]
+
+These conditions concern only the stated conditional moment.
+They do not admit a physical mixture of children.
+
+The largest legal individual child rank is 17. For any fixed
+total added rank m, strict concavity shows that the cheapest
+histogram consists of \(\lfloor m/17\rfloor\) rank-17 children
+and one child of rank \(m\bmod17\), if that remainder is nonzero.
+To prove this, take two nonzero ranks below 17. Move rank from
+the smaller to the larger until one becomes zero or the larger
+becomes 17. Concavity cannot increase the cost. Repeat until
+only one partial rank remains.
+
+This packed minimum strictly increases with total rank.
+Within a partial child, its increment is \(c_{r+1}-c_r>0\).
+At a multiple-of-17 boundary, the increment is
+\(c_{17}-c_{16}>0\); the next increment is \(c_1>0\).
+Thus failure at the next total rank also excludes every
+larger total rank in this fixed histogram.
+
+The exact certificates give:
+
+| Profile | Largest possible added rank | Passing best profile | Failing next best profile |
+| --- | ---: | --- | --- |
+| Three Q | 197 | \(11H_{17}+H_{10}\) | \(11H_{17}+H_{11}\) |
+| One I and two Q | 181 | \(10H_{17}+H_{11}\) | \(10H_{17}+H_{12}\) |
+
+Thus rank fusion in this fixed base histogram can buy at most
+one rank beyond the H1/H2 budget. This does not exclude a new
+base construction, a different productive width, or a changed
+caller. It is not a general lower bound on centre encoding.
+
+## Reproduction and credit
+
+Run from this directory:
+
+```text
+python3 -I -B check_review.py --output normal
+python3 -I -B -O check_review.py --output optimized
+```
+
+Both runs print `PASS_INDEPENDENT_CLEAN_EXCHANGE_BUDGET`.
+Their `REVIEW-CHECKS.json` files must be byte equal.
+
+The budget-geometry lane supplied the two-engine budget.
+The root and controller lanes supplied the coupled interface.
+The native lanes supplied the literal words and clean-word
+review. The cover-algebra lane supplied the dual formulation.
+This review adds the independent invoice, a third exact engine,
+and the sharp mixed-rank consequences. AI agents prepared
+these local records.
+
+The budget producer independently checked the mixed-rank
+proof and reran all eight extremal witnesses with both of
+its exact engines. All strict signs agree. The review
+record is in `PEER-REVIEW.md`.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/check_review.py b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/check_review.py
new file mode 100644
index 0000000000..c0f51866b2
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/check_review.py
@@ -0,0 +1,258 @@
+"""Check the clean words and bound their conditional native budgets."""
+
+import argparse
+from collections import Counter
+from fractions import Fraction as Q
+import gzip
+from hashlib import sha256
+import importlib.util
+import json
+from pathlib import Path
+import subprocess
+
+
+HERE = Path(__file__).resolve().parent
+CAMPAIGN = HERE.parents[2]
+REPO = CAMPAIGN.parents[1]
+PRODUCER = CAMPAIGN / "lanes/budget-geometry-20261017/clean-exchange-budget-20261020"
+ENGINE = HERE.parent / "low-displacement-budget-review-20261020"
+ENGINE_PIN = "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87"
+FREEZE_PIN = "c2ee7b116d5b177c06b94fffb167354c3e6b49d759f2df16a4599eefded121d5"
+RECEIPT_PIN = "30a59c5cda0ff3c6f9e6ad7f9f38ec98fbfe71d34c58ddf768964cda304ba30d"
+COMMIT = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f"
+LOCAL = "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/"
+B = Q(67018507072324140917, 40000000000000000000000)
+
+
+def need(test, reason):
+    if not test:
+        raise ValueError(reason)
+
+
+def digest(raw):
+    return sha256(raw).hexdigest()
+
+
+def read(path, pin, compressed=False):
+    raw = path.read_bytes()
+    if compressed:
+        raw = gzip.decompress(raw)
+    need(digest(raw) == pin, "Source pin: " + str(path))
+    return json.loads(raw)
+
+
+def freeze(path, pin):
+    result = read(path, pin)
+    for name, expected in result["files"].items():
+        need(digest((path.parent / name).read_bytes()) == expected, "Frozen file: " + name)
+    return result
+
+
+freeze(ENGINE / "FREEZE.json", ENGINE_PIN)
+spec = importlib.util.spec_from_file_location("third_exact_budget_engine", ENGINE / "check_review.py")
+math = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(math)
+
+
+def encode(interval):
+    return [str(value) for value in interval]
+
+
+def enclosure(interval, outer, label):
+    a, b = map(Q, outer)
+    need(a <= interval[0] <= interval[1] <= b, "Independent interval: " + label)
+
+
+def census(word, initial):
+    profile = Counter()
+    field_ranks = Counter()
+    tariffs = Counter()
+    recipe_identity = {
+        "matrix_rows": [1 << i for i in range(9)],
+        "linear_Z4": [0] * 9,
+        "quadratic_rows": [0] * 9,
+        "offset": 0,
+        "phase": 0,
+    }
+    direct = 0
+    for event in word["events"]:
+        if event[0] == "native":
+            _, field, _, _, rank, key = event
+            need(0 <= field < 224 and 0 < rank <= 17 and 2 * rank * rank < 25 * 25,
+                 "Native data role and size")
+            recipe = word["native_recipes"][key]
+            need(recipe["rank"] == rank and recipe["left"] is not None
+                 and recipe["right"] is not None, "Complete native recipe")
+            profile[rank] += 1
+            field_ranks[field] += rank
+            if initial and rank == 9:
+                need(recipe["left"] == recipe_identity == recipe["right"], "Direct H9 has identity sides")
+                direct += 1
+        else:
+            need(event[0] == "scalar" and len(event[1]) == 4, "Every event is counted")
+            op, target, source, value = event[1]
+            value = Q(value)
+            need(0 <= target < 224 and op in ("add", "scale"), "Scalar data role")
+            if op == "add":
+                need(0 <= source < 224 and abs(value) == 1, "Unit complex data ADD")
+                price = 8
+            else:
+                need(source is None and value in (-1, 2, Q(1, 2), -2, Q(-1, 2)),
+                     "Power-of-two SCALE")
+                price = 2 * ((abs(value) != 1) + (value < 0))
+            tariffs[price] += 1
+    expected = Counter({1: 1392, 2: 64, 3: 48, 9 if initial else 8: 16})
+    need(profile == expected, "Native histogram")
+    need(set(field_ranks) == set(range(224)), "Every productive field is counted")
+    need(Counter(field_ranks.values()) == (Counter({8: 208, 9: 16}) if initial else Counter({8: 224})),
+         "Per-field rank sum")
+    need(tariffs == Counter({8: 1032, 2: 96, 4: 38}), "Complete scalar tariff census")
+    need(len(word["input_views"]) == (112 if initial else 128)
+         and len(word["output_views"]) == 96 and direct == (16 if initial else 0),
+         "All external and direct views are counted")
+    side_maps = 2 * sum(profile.values()) - 2 * direct
+    return {
+        "profile": dict(sorted(profile.items())),
+        "children": sum(profile.values()),
+        "native_mass": sum(rank * n for rank, n in profile.items()),
+        "scalar_primitives": sum(price * n for price, n in tariffs.items()),
+        "scalar_tariff_census": dict(sorted(tariffs.items())),
+        "input_maps": len(word["input_views"]),
+        "output_maps": len(word["output_views"]),
+        "native_side_map_bound": side_maps,
+        "total_map_bound": len(word["input_views"]) + len(word["output_views"]) + side_maps,
+        "field_rank_census": dict(sorted(Counter(field_ranks.values()).items())),
+    }
+
+
+def check_threshold(profile, row):
+    expected = Counter({int(r): n for r, n in row["profile"].items()})
+    need(profile == expected, "Complete histogram binding")
+    need(sum(r * n for r, n in profile.items()) == row["mass"], "Complete native mass")
+    value = math.moment(profile)
+    enclosure(value, row["moment"], "base")
+    need(value[1] < 1, "Positive conditional allowance")
+    result = {"profile": dict(sorted(profile.items())), "moment": encode(value), "limits": {}}
+    for rank in (1, 2):
+        old = row["limits"][str(rank)]
+        n = old["children"]
+        yes = math.moment(profile + Counter({rank: n}))
+        no = math.moment(profile + Counter({rank: n + 1}))
+        enclosure(yes, old["accepted"], "accepted H" + str(rank))
+        enclosure(no, old["next"], "next H" + str(rank))
+        need(yes[1] < 1 < no[0] and old["rank_mass"] == rank * n, "Strict threshold")
+        result["limits"][str(rank)] = {"children": n, "accepted": encode(yes), "next": encode(no)}
+    return result
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "normal")
+    args = parser.parse_args()
+    freeze(PRODUCER / "FREEZE.json", FREEZE_PIN)
+    receipt = read(PRODUCER / "BUDGET.json", RECEIPT_PIN)
+    need(receipt["dimension"] == 25 and receipt["productive_width"] == 224
+         and receipt["calls"] == 3 and receipt["idle_profile"] == {}, "Exact conditional model")
+    need(Q(receipt["historical_selected_b"]) == B == math.B and 0 < B < 1,
+         "Exact positive historical exponent")
+    need(receipt["engine_commit"] == COMMIT, "Historical certificate commit")
+    selected_raw = subprocess.check_output(
+        ["git", "-C", str(REPO), "show", COMMIT + ":certificates/selected-result.json"])
+    need(digest(selected_raw) == receipt["selected_result_sha256"] == math.PINS["selected"],
+         "Selected certificate source")
+    selected = json.loads(selected_raw)
+    assembly_raw = subprocess.check_output(
+        ["git", "-C", str(REPO), "show", COMMIT + ":" + selected["certificate"]])
+    need(digest(assembly_raw) == selected["certificate_sha256"]
+         == receipt["assembly_sha256"] == math.PINS["assembly"], "Selected assembly source")
+    need(Q(json.loads(assembly_raw)["complex_lower"]) == B, "Selected exponent from assembly")
+    source = {}
+    for path, pin in receipt["source_pins"].items():
+        source[path] = read(CAMPAIGN / path, pin, path.endswith(".gz"))
+        if path.endswith("FREEZE.json"):
+            freeze(CAMPAIGN / path, pin)
+    invoices = {}
+    for name, suffix in (("clean", "run-normal/CLEAN-LATE-EXCHANGE.json.gz"),
+                         ("dual", "dual-normal/CLEAN-DUAL.json.gz")):
+        payload = source[LOCAL + suffix]
+        need(set(payload["providers"]) == {"base", "extra"}, "Both native providers")
+        for provider, variants in payload["providers"].items():
+            need(set(variants) == ({"I", "Q"} if name == "clean"
+                                   else {"inverse_adjoint", "selected_swap_conjugate"}),
+                 "All clean and dual variants")
+            for variant, word in variants.items():
+                key = name + "/" + provider + "/" + variant
+                bill = census(word, name == "clean" and variant == "I")
+                old = receipt["literal"][name][provider + "/" + variant]
+                need(bill["profile"] == {int(k): n for k, n in old["profile"].items()}
+                     and bill["children"] == old["children"]
+                     and bill["native_mass"] == old["mass"]
+                     and bill["scalar_primitives"] == old["scalar"]
+                     and bill["native_side_map_bound"] == old["native_side_map_bound"]
+                     and bill["total_map_bound"] == old["total_map_bound"], "Independent literal invoice")
+                invoices[key] = bill
+    need(len(invoices) == 8, "All eight literal words")
+    results = {}
+    for name, initial in (("three_Q", 0), ("one_I_two_Q", 1)):
+        local_q = Counter(invoices["clean/base/Q"]["profile"])
+        local_i = Counter(invoices["clean/base/I"]["profile"])
+        profile = Counter({r: (3 - initial) * n for r, n in local_q.items()})
+        profile.update({r: initial * n for r, n in local_i.items()})
+        profile = +profile
+        old = receipt["results"][name]
+        result = check_threshold(profile, old)
+        result["cleanup"] = {}
+        for size in (112, 128, 144):
+            result["cleanup"][str(size)] = check_threshold(
+                profile + Counter({1: size}), old["hypothetical_H1_cleanup"][str(size)])
+        need(old["three_call_scalar_subtotal"] == 3 * 8600 == 25800, "Three scalar calls")
+        maps = (3 - initial) * invoices["clean/base/Q"]["total_map_bound"]
+        maps += initial * invoices["clean/base/I"]["total_map_bound"]
+        need(maps == old["three_call_map_bound"] == 9792 - 48 * initial, "Three map counts")
+        narrow = 196 - 16 * initial
+        yes = math.moment(profile + Counter({1: narrow}))
+        next_two = Counter({2: (narrow + 1) // 2, 1: (narrow + 1) % 2})
+        no = math.moment(profile + next_two)
+        need(yes[1] < 1 < no[0], "All mixtures of H1 and H2 have the stated sharp rank budget")
+        result["all_H1_H2_mixtures"] = {
+            "total_rank_limit": narrow, "all_H1_at_limit": encode(yes),
+            "cheapest_next_profile": dict(sorted(next_two.items())),
+            "cheapest_next_moment": encode(no),
+        }
+        broad = narrow + 1
+        need(2 * 17**2 < 25**2 < 2 * 18**2, "Largest legal child rank")
+        yes = math.moment(profile + math.packed(broad))
+        no = math.moment(profile + math.packed(broad + 1))
+        need(yes[1] < 1 < no[0], "Sharp total-rank budget over all legal child ranks")
+        result["all_legal_ranks"] = {
+            "largest_child_rank": 17, "total_rank_limit": broad,
+            "best_profile": dict(sorted(math.packed(broad).items())),
+            "accepted": encode(yes),
+            "next_best_profile": dict(sorted(math.packed(broad + 1).items())),
+            "next": encode(no),
+        }
+        terminal = math.moment(profile + Counter({1: 224}))
+        need(terminal[0] > 1, "The complete 224-H1 terminal fails")
+        result["full_terminal"] = {"moment": encode(terminal), "minimum_H1_removal": 224 - narrow}
+        results[name] = result
+    result = {
+        "status": "PASS_INDEPENDENT_CLEAN_EXCHANGE_BUDGET",
+        "checker_sha256": digest(Path(__file__).read_bytes()),
+        "producer_freeze_sha256": FREEZE_PIN,
+        "third_engine_review_sha256": ENGINE_PIN,
+        "third_engine_imported_from_producer": False,
+        "historical_certificate_commit": COMMIT,
+        "historical_b": str(B),
+        "invoices": invoices,
+        "results": results,
+        "scope": "Literal invoice and strict conditional native arithmetic only. No new phase review or routed caller.",
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(result, sort_keys=True, indent=2) + "\n").encode()
+    (args.output / "REVIEW-CHECKS.json").write_bytes(raw)
+    print(result["status"])
+    print(digest(raw))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/normal/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/normal/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..574b30f698
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/normal/REVIEW-CHECKS.json
@@ -0,0 +1,580 @@
+{
+  "checker_sha256": "1908fe146d5dd006e84bf3c067509ba1b51e7d95af815f0fa84247939bc39264",
+  "historical_b": "67018507072324140917/40000000000000000000000",
+  "historical_certificate_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "invoices": {
+    "clean/base/I": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 208,
+        "9": 16
+      },
+      "input_maps": 112,
+      "native_mass": 1808,
+      "native_side_map_bound": 3008,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "9": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3216
+    },
+    "clean/base/Q": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "clean/extra/I": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 208,
+        "9": 16
+      },
+      "input_maps": 112,
+      "native_mass": 1808,
+      "native_side_map_bound": 3008,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "9": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3216
+    },
+    "clean/extra/Q": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "dual/base/inverse_adjoint": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "dual/base/selected_swap_conjugate": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "dual/extra/inverse_adjoint": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "dual/extra/selected_swap_conjugate": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    }
+  },
+  "producer_freeze_sha256": "c2ee7b116d5b177c06b94fffb167354c3e6b49d759f2df16a4599eefded121d5",
+  "results": {
+    "one_I_two_Q": {
+      "all_H1_H2_mixtures": {
+        "all_H1_at_limit": [
+          "1399864385571008710465479939076979813571884516118259584814114319/1400000000000000000000000000000000000000000000000000000000000000",
+          "10936440512273505550511562024038904793530347782173903006360279/10937500000000000000000000000000000000000000000000000000000000"
+        ],
+        "cheapest_next_moment": [
+          "5600252899922312010247686405247210817822710122363403911710522451/5600000000000000000000000000000000000000000000000000000000000000",
+          "700031612490289001280960800655901352227838765295425488963816003/700000000000000000000000000000000000000000000000000000000000000"
+        ],
+        "cheapest_next_profile": {
+          "1": 1,
+          "2": 90
+        },
+        "total_rank_limit": 180
+      },
+      "all_legal_ranks": {
+        "accepted": [
+          "799944169301775128581928503960747910727149655826973559381106611/800000000000000000000000000000000000000000000000000000000000000",
+          "111992183702248518001469990554504707501800951815776298313355037/112000000000000000000000000000000000000000000000000000000000000"
+        ],
+        "best_profile": {
+          "11": 1,
+          "17": 10
+        },
+        "largest_child_rank": 17,
+        "next": [
+          "400043486420647557579103411833350452624146833243865747702471237/400000000000000000000000000000000000000000000000000000000000000",
+          "1400152202472266451526861941416726584184513916353530116958650723/1400000000000000000000000000000000000000000000000000000000000000"
+        ],
+        "next_best_profile": {
+          "12": 1,
+          "17": 10
+        },
+        "total_rank_limit": 181
+      },
+      "cleanup": {
+        "112": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "1399864385571008710465479939076979813571884516118259584814114319/1400000000000000000000000000000000000000000000000000000000000000",
+                "10936440512273505550511562024038904793530347782173903006360279/10937500000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 68,
+              "next": [
+                "5600462949959317406589963058771300339249166509451553879762468951/5600000000000000000000000000000000000000000000000000000000000000",
+                "1400115737489829351647490764692825084812291627362888469940618631/1400000000000000000000000000000000000000000000000000000000000000"
+              ]
+            },
+            "2": {
+              "accepted": [
+                "699922273755979100405465794233185679385248484224411599471270797/700000000000000000000000000000000000000000000000000000000000000",
+                "1399844547511958200810931588466371358770496968448823198942542987/1400000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 34,
+              "next": [
+                "1400346667877274468185113582327161652580682145418391663728736469/1400000000000000000000000000000000000000000000000000000000000000",
+                "112027733430181957454809086586172932206454571633471333098299029/112000000000000000000000000000000000000000000000000000000000000"
+              ]
+            }
+          },
+          "moment": [
+            "345693113772801277522185949299875342306050237870873849052978961/350000000000000000000000000000000000000000000000000000000000000",
+            "69138622754560255504437189859975068461210047574174769810595861/70000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "profile": {
+            "1": 4288,
+            "2": 192,
+            "3": 144,
+            "8": 32,
+            "9": 16
+          }
+        },
+        "128": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "1399864385571008710465479939076979813571884516118259584814114319/1400000000000000000000000000000000000000000000000000000000000000",
+                "10936440512273505550511562024038904793530347782173903006360279/10937500000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 52,
+              "next": [
+                "5600462949959317406589963058771300339249166509451553879762468951/5600000000000000000000000000000000000000000000000000000000000000",
+                "1400115737489829351647490764692825084812291627362888469940618631/1400000000000000000000000000000000000000000000000000000000000000"
+              ]
+            },
+            "2": {
+              "accepted": [
+                "699924607645279160364824423716786674067764666303168821338514647/700000000000000000000000000000000000000000000000000000000000000",
+                "1399849215290558320729648847433573348135529332606337642677030687/1400000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 26,
+              "next": [
+                "1400351335655874588103830841294363641945714509575906107463224169/1400000000000000000000000000000000000000000000000000000000000000",
+                "22405621370493993409661293460709818271131432153214497719411609/22400000000000000000000000000000000000000000000000000000000000"
+              ]
+            }
+          },
+          "moment": [
+            "86674630362020960562557312940814106816919670712347347389747659/87500000000000000000000000000000000000000000000000000000000000",
+            "49528360206869120321461321680465203895382668978484198508427283/50000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "profile": {
+            "1": 4304,
+            "2": 192,
+            "3": 144,
+            "8": 32,
+            "9": 16
+          }
+        },
+        "144": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "1399864385571008710465479939076979813571884516118259584814114319/1400000000000000000000000000000000000000000000000000000000000000",
+                "10936440512273505550511562024038904793530347782173903006360279/10937500000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 36,
+              "next": [
+                "5600462949959317406589963058771300339249166509451553879762468951/5600000000000000000000000000000000000000000000000000000000000000",
+                "1400115737489829351647490764692825084812291627362888469940618631/1400000000000000000000000000000000000000000000000000000000000000"
+              ]
+            },
+            "2": {
+              "accepted": [
+                "99989563076368460046311864742912524107182978340275149029394071/100000000000000000000000000000000000000000000000000000000000000",
+                "199979126152736920092623729485825048214365956680550298058788341/200000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 18,
+              "next": [
+                "1400356003434474708022548100261565631310746873733420551197711869/1400000000000000000000000000000000000000000000000000000000000000",
+                "112028480274757976641803848020925250504859749898673644095817061/112000000000000000000000000000000000000000000000000000000000000"
+              ]
+            }
+          },
+          "moment": [
+            "347703929123366406978272554226637512229307127827904930065002311/350000000000000000000000000000000000000000000000000000000000000",
+            "347703929123366406978272554226637512229307127827904930065002657/350000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "profile": {
+            "1": 4320,
+            "2": 192,
+            "3": 144,
+            "8": 32,
+            "9": 16
+          }
+        }
+      },
+      "full_terminal": {
+        "minimum_H1_removal": 44,
+        "moment": [
+          "176365483749889615309244533271771468518724676360241316297530343/175000000000000000000000000000000000000000000000000000000000000",
+          "352730967499779230618489066543542937037449352720482632595061037/350000000000000000000000000000000000000000000000000000000000000"
+        ]
+      },
+      "limits": {
+        "1": {
+          "accepted": [
+            "1399864385571008710465479939076979813571884516118259584814114319/1400000000000000000000000000000000000000000000000000000000000000",
+            "10936440512273505550511562024038904793530347782173903006360279/10937500000000000000000000000000000000000000000000000000000000"
+          ],
+          "children": 180,
+          "next": [
+            "5600462949959317406589963058771300339249166509451553879762468951/5600000000000000000000000000000000000000000000000000000000000000",
+            "1400115737489829351647490764692825084812291627362888469940618631/1400000000000000000000000000000000000000000000000000000000000000"
+          ]
+        },
+        "2": {
+          "accepted": [
+            "699905936530878680689955387847978716607635209673111046400563847/700000000000000000000000000000000000000000000000000000000000000",
+            "1399811873061757361379910775695957433215270419346222092801129087/1400000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "children": 90,
+          "next": [
+            "1400313993427073628754092769556747727025455596315790557587322569/1400000000000000000000000000000000000000000000000000000000000000",
+            "112025119474165890300327421564539818162036447705263244606985917/112000000000000000000000000000000000000000000000000000000000000"
+          ]
+        }
+      },
+      "moment": [
+        "84663815011455831106470708014051936893662780755316266377724309/87500000000000000000000000000000000000000000000000000000000000",
+        "338655260045823324425882832056207747574651123021265065510897573/350000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "profile": {
+        "1": 4176,
+        "2": 192,
+        "3": 144,
+        "8": 32,
+        "9": 16
+      }
+    },
+    "three_Q": {
+      "all_H1_H2_mixtures": {
+        "all_H1_at_limit": [
+          "1399885489812070930378428274732974175916721377934147480013025683/1400000000000000000000000000000000000000000000000000000000000000",
+          "349971372453017732594607068683243543979180344483536870003256769/350000000000000000000000000000000000000000000000000000000000000"
+        ],
+        "cheapest_next_moment": [
+          "5600318645772160410224610712002380309741928112996897717568217107/5600000000000000000000000000000000000000000000000000000000000000",
+          "140007966144304010255615267800059507743548202824922442939205567/140000000000000000000000000000000000000000000000000000000000000"
+        ],
+        "cheapest_next_profile": {
+          "1": 1,
+          "2": 98
+        },
+        "total_rank_limit": 196
+      },
+      "all_legal_ranks": {
+        "accepted": [
+          "5599618290337967880109727288567065604452827121852291658725933101/5600000000000000000000000000000000000000000000000000000000000000",
+          "2799809145168983940054863644283532802226413560926145829362969337/2800000000000000000000000000000000000000000000000000000000000000"
+        ],
+        "best_profile": {
+          "10": 1,
+          "17": 11
+        },
+        "largest_child_rank": 17,
+        "next": [
+          "700077258449308394735776084231957297141845526577727552342814729/700000000000000000000000000000000000000000000000000000000000000",
+          "400044147685319082706157762418261312652483158044415744195894529/400000000000000000000000000000000000000000000000000000000000000"
+        ],
+        "next_best_profile": {
+          "11": 1,
+          "17": 11
+        },
+        "total_rank_limit": 197
+      },
+      "cleanup": {
+        "112": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "1399885489812070930378428274732974175916721377934147480013025683/1400000000000000000000000000000000000000000000000000000000000000",
+                "349971372453017732594607068683243543979180344483536870003256769/350000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 84,
+              "next": [
+                "5600547366923566286241756401395277788628513956715105460558114407/5600000000000000000000000000000000000000000000000000000000000000",
+                "280027368346178314312087820069763889431425697835755273027905999/280000000000000000000000000000000000000000000000000000000000000"
+              ]
+            },
+            "2": {
+              "accepted": [
+                "699930491987210150402581332577581865875150733053598325203482629/700000000000000000000000000000000000000000000000000000000000000",
+                "1399860983974420300805162665155163731750301466107196650406966651/1400000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 42,
+              "next": [
+                "1400363104339736568179344659015954025560486643076765115193160133/1400000000000000000000000000000000000000000000000000000000000000",
+                "2800726208679473136358689318031908051120973286153530230386323053/2800000000000000000000000000000000000000000000000000000000000000"
+              ]
+            }
+          },
+          "moment": [
+            "344692982157784267772379730750492847930631008346330282346695127/350000000000000000000000000000000000000000000000000000000000000",
+            "34469298215778426777237973075049284793063100834633028234669547/35000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "profile": {
+            "1": 4288,
+            "2": 192,
+            "3": 144,
+            "8": 48
+          }
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diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/optimized/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/optimized/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..574b30f698
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/clean-exchange-budget-review-20261020/optimized/REVIEW-CHECKS.json
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+                "1400363104339736568179344659015954025560486643076765115193160133/1400000000000000000000000000000000000000000000000000000000000000",
+                "2800726208679473136358689318031908051120973286153530230386323053/2800000000000000000000000000000000000000000000000000000000000000"
+              ]
+            }
+          },
+          "moment": [
+            "344692982157784267772379730750492847930631008346330282346695127/350000000000000000000000000000000000000000000000000000000000000",
+            "34469298215778426777237973075049284793063100834633028234669547/35000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "profile": {
+            "1": 4288,
+            "2": 192,
+            "3": 144,
+            "8": 48
+          }
+        },
+        "128": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "1399885489812070930378428274732974175916721377934147480013025683/1400000000000000000000000000000000000000000000000000000000000000",
+                "349971372453017732594607068683243543979180344483536870003256769/350000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 68,
+              "next": [
+                "5600547366923566286241756401395277788628513956715105460558114407/5600000000000000000000000000000000000000000000000000000000000000",
+                "280027368346178314312087820069763889431425697835755273027905999/280000000000000000000000000000000000000000000000000000000000000"
+              ]
+            },
+            "2": {
+              "accepted": [
+                "699932825876510210361939962061182860557666915132355547070726479/700000000000000000000000000000000000000000000000000000000000000",
+                "1399865651753020420723879924122365721115333830264711094141454351/1400000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 34,
+              "next": [
+                "1400367772118336688098061917983156014925519007234279558927647833/1400000000000000000000000000000000000000000000000000000000000000",
+                "2800735544236673376196123835966312029851038014468559117855298453/2800000000000000000000000000000000000000000000000000000000000000"
+              ]
+            }
+          },
+          "moment": [
+            "172849194916533416250211516606936966446129726662422911426353401/175000000000000000000000000000000000000000000000000000000000000",
+            "172849194916533416250211516606936966446129726662422911426353573/175000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "profile": {
+            "1": 4304,
+            "2": 192,
+            "3": 144,
+            "8": 48
+          }
+        },
+        "144": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "1399885489812070930378428274732974175916721377934147480013025683/1400000000000000000000000000000000000000000000000000000000000000",
+                "349971372453017732594607068683243543979180344483536870003256769/350000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 52,
+              "next": [
+                "5600547366923566286241756401395277788628513956715105460558114407/5600000000000000000000000000000000000000000000000000000000000000",
+                "280027368346178314312087820069763889431425697835755273027905999/280000000000000000000000000000000000000000000000000000000000000"
+              ]
+            },
+            "2": {
+              "accepted": [
+                "99990737109401467188756941649254836462883299601587538419710047/100000000000000000000000000000000000000000000000000000000000000",
+                "199981474218802934377513883298509672925766599203175076839420293/200000000000000000000000000000000000000000000000000000000000000"
+              ],
+              "children": 26,
+              "next": [
+                "1400372439896936808016779176950358004290551371391794002662135533/1400000000000000000000000000000000000000000000000000000000000000",
+                "2800744879793873616033558353900716008581102742783588005324273853/2800000000000000000000000000000000000000000000000000000000000000"
+              ]
+            }
+          },
+          "moment": [
+            "346703797508349397228466335677255017853887898303361363358718477/350000000000000000000000000000000000000000000000000000000000000",
+            "173351898754174698614233167838627508926943949151680681679359411/175000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "profile": {
+            "1": 4320,
+            "2": 192,
+            "3": 144,
+            "8": 48
+          }
+        }
+      },
+      "full_terminal": {
+        "minimum_H1_removal": 28,
+        "moment": [
+          "87932708971190555217170711998540110665507530798984766472194213/87500000000000000000000000000000000000000000000000000000000000",
+          "175865417942381110434341423997080221331015061597969532944388601/175000000000000000000000000000000000000000000000000000000000000"
+        ]
+      },
+      "limits": {
+        "1": {
+          "accepted": [
+            "1399885489812070930378428274732974175916721377934147480013025683/1400000000000000000000000000000000000000000000000000000000000000",
+            "349971372453017732594607068683243543979180344483536870003256769/350000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "children": 196,
+          "next": [
+            "5600547366923566286241756401395277788628513956715105460558114407/5600000000000000000000000000000000000000000000000000000000000000",
+            "280027368346178314312087820069763889431425697835755273027905999/280000000000000000000000000000000000000000000000000000000000000"
+          ]
+        },
+        "2": {
+          "accepted": [
+            "699914154762109730687070926192374903097537458502297772132775679/700000000000000000000000000000000000000000000000000000000000000",
+            "1399828309524219461374141852384749806195074917004595544265552751/1400000000000000000000000000000000000000000000000000000000000000"
+          ],
+          "children": 98,
+          "next": [
+            "1400330429889535728748323846245540100005260093974164009051746233/1400000000000000000000000000000000000000000000000000000000000000",
+            "2800660859779071457496647692491080200010520187948328018103495253/2800000000000000000000000000000000000000000000000000000000000000"
+          ]
+        }
+      },
+      "moment": [
+        "168827564215403157338038306753412626599615946748360749402306701/175000000000000000000000000000000000000000000000000000000000000",
+        "168827564215403157338038306753412626599615946748360749402306869/175000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "profile": {
+        "1": 4176,
+        "2": 192,
+        "3": 144,
+        "8": 48
+      }
+    }
+  },
+  "scope": "Literal invoice and strict conditional native arithmetic only. No new phase review or routed caller.",
+  "status": "PASS_INDEPENDENT_CLEAN_EXCHANGE_BUDGET",
+  "third_engine_imported_from_producer": false,
+  "third_engine_review_sha256": "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..7171cfa615
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/FREEZE.json
@@ -0,0 +1,11 @@
+{
+  "files": {
+    "REVIEW.md": "f398499be52193a8c7f0f7a44a306086873cf6adddc3d7d6b5d398a0d2dfda2f",
+    "check_budget.py": "fb356e824d0f5581ddda6f0e99f606f3b81d06b6205067308105d149543c3c1e",
+    "normal.json": "13335f11799d34af003fbb7dc76eddc27423ee1d1ff54d473b49dd0030da4db6",
+    "optimized.json": "13335f11799d34af003fbb7dc76eddc27423ee1d1ff54d473b49dd0030da4db6"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Four fixed-profile budget thresholds; no native or caller claim.",
+  "status": "FROZEN_THIRD_ENGINE_NUMERIC_REVIEW"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..6b1ccee1ed
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/REVIEW.md
@@ -0,0 +1,44 @@
+# Third-engine check of the coalesced reciprocal budget
+
+The four fixed-profile numerical limits pass an independent rational
+interval calculation. With the three-call profile
+
+```text
+{1:2913, 2:711, 3:138, 4:36, 5:15, 6:33, 7:30},
+```
+
+the extra allowance is 198 rank-one children or 99 rank-two children.
+After a stipulated 64 rank-one cleanup, it is 134 rank-one children
+or 67 rank-two children. Each maximum has moment strictly below one,
+and its next integer count has moment strictly above one.
+
+The check uses dimension 25, 224 productive fields, and the exact
+historical saving exponent
+`67018507072324140917/40000000000000000000000`. The source commit is
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. This is a historical
+comparison, not a refreshed selected frontier.
+
+The consumed [budget receipt](../../budget-geometry-20261017/coalesced-reciprocal-budget-20261020/BUDGET.json)
+has SHA256
+`a24f6b95c5f341817b4f49ce845fa58b83060dc991c9f7772691c0edfcb9ad77`.
+The checker imports the independent engine from this lane's freeze
+`953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87`.
+It checks all engine files, the historical source pins, and exact
+containment within the producer's stated intervals.
+
+This check does not repeat the twelve native-word counts or their
+phase review. It takes the stated frozen profile as input. The
+64-line cleanup is a separate construction premise. No complete
+caller, terminal, host, finite-precision bound, supplier, or kappa
+improvement is certified here.
+
+Run `python3 -I -B check_budget.py normal.json` and
+`python3 -I -O -B check_budget.py optimized.json`. The expected
+status is `PASS_THIRD_ENGINE_COALESCED_BUDGET`. Both receipts must
+match.
+
+The budget-geometry lane supplied the profile budget and two exact
+evaluators. This lane supplies a third evaluator for the four stated
+thresholds. The work used AI assistance. Publication is coordinated
+by the parent. Before a PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/check_budget.py b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/check_budget.py
new file mode 100644
index 0000000000..b24a97240f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/check_budget.py
@@ -0,0 +1,72 @@
+"""Check the four stated coalesced budget limits with the third engine."""
+
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+ENGINE = HERE.parent / "low-displacement-budget-review-20261020"
+SOURCE = HERE.parent.parent / "budget-geometry-20261017/coalesced-reciprocal-budget-20261020/BUDGET.json"
+ENGINE_PIN = "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87"
+SOURCE_PIN = "a24f6b95c5f341817b4f49ce845fa58b83060dc991c9f7772691c0edfcb9ad77"
+
+
+def need(test, reason):
+    if not test:
+        raise ValueError(reason)
+
+
+def main():
+    raw = (ENGINE / "FREEZE.json").read_bytes()
+    need(sha256(raw).hexdigest() == ENGINE_PIN, "Exact engine freeze")
+    for name, pin in json.loads(raw)["files"].items():
+        need(sha256((ENGINE / name).read_bytes()).hexdigest() == pin, "Exact engine file")
+    spec = importlib.util.spec_from_file_location("third_budget_engine", ENGINE / "check_review.py")
+    engine = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(engine)
+    raw = SOURCE.read_bytes()
+    need(sha256(raw).hexdigest() == SOURCE_PIN, "Budget receipt pin")
+    source = json.loads(raw)
+    need(F(source["saving_exponent"]) == engine.B and source["ambient_dimension"] == engine.D
+         and source["productive_fields"] == engine.W and source["selected_commit"] == engine.BASE,
+         "Historical exponent and dimensions")
+    need(source["selected_certificate_sha256"] == engine.PINS["selected"]
+         and source["assembly_sha256"] == engine.PINS["assembly"], "Historical source pins")
+    base = Counter({1: 2913, 2: 711, 3: 138, 4: 36, 5: 15, 6: 33, 7: 30})
+    need(base == engine.counts(source["three_call_profile"]) and engine.mass(base) == 5376,
+         "Stated three-call profile")
+    moment = engine.moment(base)
+    engine.enclosure(moment, source["base_moment"], "Base")
+    results = {}
+    expected = {(0, 1): 198, (0, 2): 99, (64, 1): 134, (64, 2): 67}
+    for (cleanup, rank), count in expected.items():
+        key = f"cleanup_{cleanup}_rank_{rank}"
+        profile = base.copy()
+        profile[1] += cleanup
+        profile[rank] += count
+        low = engine.moment(profile)
+        profile[rank] += 1
+        high = engine.moment(profile)
+        need(low[1] < 1 < high[0], "Both strict signs")
+        original = source["limits"][key]
+        need(original["maximum_count"] == count, "Exact threshold")
+        engine.enclosure(low, original["accepted_moment"], key + " accepted")
+        engine.enclosure(high, original["next_rejected_moment"], key + " rejected")
+        results[key] = dict(maximum_count=count, accepted=list(map(str, low)), rejected=list(map(str, high)))
+    output = dict(status="PASS_THIRD_ENGINE_COALESCED_BUDGET", checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(),
+                  engine_freeze_sha256=ENGINE_PIN, source_receipt_sha256=SOURCE_PIN,
+                  base_moment=list(map(str, moment)), limits=results,
+                  scope="Four fixed-profile numerical limits. No fresh native census, phase, caller, host or supplier review.")
+    data = (json.dumps(output, sort_keys=True, indent=2) + "\n").encode()
+    (HERE / (sys.argv[1] if len(sys.argv) > 1 else "normal.json")).write_bytes(data)
+    print(output["status"])
+    print(sha256(data).hexdigest())
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/normal.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/normal.json
new file mode 100644
index 0000000000..d8b62b8e26
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/normal.json
@@ -0,0 +1,57 @@
+{
+  "base_moment": [
+    "540082389761279261885562158965593029143222346118264663212454729/560000000000000000000000000000000000000000000000000000000000000",
+    "2700411948806396309427810794827965145716111730591323316062276333/2800000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "checker_sha256": "fb356e824d0f5581ddda6f0e99f606f3b81d06b6205067308105d149543c3c1e",
+  "engine_freeze_sha256": "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87",
+  "limits": {
+    "cleanup_0_rank_1": {
+      "accepted": [
+        "279994730865937021750409773870269255691732778346436182615742947/280000000000000000000000000000000000000000000000000000000000000",
+        "2799947308659370217504097738702692556917327783464361826157432257/2800000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 198,
+      "rejected": [
+        "1120180004998804599947247755973753239759256802381447838564174123/1120000000000000000000000000000000000000000000000000000000000000",
+        "560090002499402299973623877986876619879628401190723919282087619/560000000000000000000000000000000000000000000000000000000000000"
+      ]
+    },
+    "cleanup_0_rank_2": {
+      "accepted": [
+        "559966356227803449903169115852888664026555354113175868745771779/560000000000000000000000000000000000000000000000000000000000000",
+        "1399915890569508624757922789632221660066388385282939671864430841/1400000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 99,
+      "rejected": [
+        "560167204373929956852841913397204781550629424901003254660249729/560000000000000000000000000000000000000000000000000000000000000",
+        "2800836021869649784264209566986023907753147124505016273301251433/2800000000000000000000000000000000000000000000000000000000000000"
+      ]
+    },
+    "cleanup_64_rank_1": {
+      "accepted": [
+        "279994730865937021750409773870269255691732778346436182615742947/280000000000000000000000000000000000000000000000000000000000000",
+        "2799947308659370217504097738702692556917327783464361826157432257/2800000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 134,
+      "rejected": [
+        "1120180004998804599947247755973753239759256802381447838564174123/1120000000000000000000000000000000000000000000000000000000000000",
+        "560090002499402299973623877986876619879628401190723919282087619/560000000000000000000000000000000000000000000000000000000000000"
+      ]
+    },
+    "cleanup_64_rank_2": {
+      "accepted": [
+        "79996260667651948824730961457201692430086733823599854102993157/80000000000000000000000000000000000000000000000000000000000000",
+        "1399934561683909104432791825501029617526517841912997446802381641/1400000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 67,
+      "rejected": [
+        "560174672819690148722789527744727964534681207553026364635430049/560000000000000000000000000000000000000000000000000000000000000",
+        "2800873364098450743613947638723639822673406037765131823177153033/2800000000000000000000000000000000000000000000000000000000000000"
+      ]
+    }
+  },
+  "scope": "Four fixed-profile numerical limits. No fresh native census, phase, caller, host or supplier review.",
+  "source_receipt_sha256": "a24f6b95c5f341817b4f49ce845fa58b83060dc991c9f7772691c0edfcb9ad77",
+  "status": "PASS_THIRD_ENGINE_COALESCED_BUDGET"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/optimized.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/optimized.json
new file mode 100644
index 0000000000..d8b62b8e26
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/coalesced-budget-review-20261020/optimized.json
@@ -0,0 +1,57 @@
+{
+  "base_moment": [
+    "540082389761279261885562158965593029143222346118264663212454729/560000000000000000000000000000000000000000000000000000000000000",
+    "2700411948806396309427810794827965145716111730591323316062276333/2800000000000000000000000000000000000000000000000000000000000000"
+  ],
+  "checker_sha256": "fb356e824d0f5581ddda6f0e99f606f3b81d06b6205067308105d149543c3c1e",
+  "engine_freeze_sha256": "953690464698b38801b4f2ddf0f56035203a9337214595a557c7d3950e2e6f87",
+  "limits": {
+    "cleanup_0_rank_1": {
+      "accepted": [
+        "279994730865937021750409773870269255691732778346436182615742947/280000000000000000000000000000000000000000000000000000000000000",
+        "2799947308659370217504097738702692556917327783464361826157432257/2800000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 198,
+      "rejected": [
+        "1120180004998804599947247755973753239759256802381447838564174123/1120000000000000000000000000000000000000000000000000000000000000",
+        "560090002499402299973623877986876619879628401190723919282087619/560000000000000000000000000000000000000000000000000000000000000"
+      ]
+    },
+    "cleanup_0_rank_2": {
+      "accepted": [
+        "559966356227803449903169115852888664026555354113175868745771779/560000000000000000000000000000000000000000000000000000000000000",
+        "1399915890569508624757922789632221660066388385282939671864430841/1400000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 99,
+      "rejected": [
+        "560167204373929956852841913397204781550629424901003254660249729/560000000000000000000000000000000000000000000000000000000000000",
+        "2800836021869649784264209566986023907753147124505016273301251433/2800000000000000000000000000000000000000000000000000000000000000"
+      ]
+    },
+    "cleanup_64_rank_1": {
+      "accepted": [
+        "279994730865937021750409773870269255691732778346436182615742947/280000000000000000000000000000000000000000000000000000000000000",
+        "2799947308659370217504097738702692556917327783464361826157432257/2800000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 134,
+      "rejected": [
+        "1120180004998804599947247755973753239759256802381447838564174123/1120000000000000000000000000000000000000000000000000000000000000",
+        "560090002499402299973623877986876619879628401190723919282087619/560000000000000000000000000000000000000000000000000000000000000"
+      ]
+    },
+    "cleanup_64_rank_2": {
+      "accepted": [
+        "79996260667651948824730961457201692430086733823599854102993157/80000000000000000000000000000000000000000000000000000000000000",
+        "1399934561683909104432791825501029617526517841912997446802381641/1400000000000000000000000000000000000000000000000000000000000000"
+      ],
+      "maximum_count": 67,
+      "rejected": [
+        "560174672819690148722789527744727964534681207553026364635430049/560000000000000000000000000000000000000000000000000000000000000",
+        "2800873364098450743613947638723639822673406037765131823177153033/2800000000000000000000000000000000000000000000000000000000000000"
+      ]
+    }
+  },
+  "scope": "Four fixed-profile numerical limits. No fresh native census, phase, caller, host or supplier review.",
+  "source_receipt_sha256": "a24f6b95c5f341817b4f49ce845fa58b83060dc991c9f7772691c0edfcb9ad77",
+  "status": "PASS_THIRD_ENGINE_COALESCED_BUDGET"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..30776ef158
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json
@@ -0,0 +1,15 @@
+{
+  "files": {
+    "GENERAL-READER.md": "b8fb7892bc351fb3f872b81526e3f6b3c311525942a1283413e3e14b86313e9a",
+    "PEER-REVIEW.md": "428f1085e7c4cba5f178c09309b23b16f7a8569cbc58cc2ea1ad62cb0fbfa977",
+    "REPRODUCTION.json": "798531c4347439aca79fcf4f52f1209eabc8982f154ce1ee7aa5fbd53fd35cce",
+    "REVIEW.md": "da80ad6a9ad957fa4de2f7a81d5d6e3a573947b1d8a32057ae4d5300dee0f42c",
+    "check_review.py": "c1caa97a3929c3750e6e663c2d7429297a1e50e7a835264ee7ecde17c47f0b7e",
+    "normal/REVIEW-CHECKS.json": "18226da65a8eb6e07f716d328451107e97c8905c2c429edfe54608310e97e1a9",
+    "optimized/REVIEW-CHECKS.json": "18226da65a8eb6e07f716d328451107e97c8905c2c429edfe54608310e97e1a9"
+  },
+  "producer_dual_freeze_sha256": "92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455",
+  "producer_reuse_freeze_sha256": "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf",
+  "schema": "independent-fixed-reader-review-freeze-v1",
+  "scope": "Independent D25 query, carrier phase and typed dual review. Complete native integration and supplier admission are separate."
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/GENERAL-READER.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/GENERAL-READER.md
new file mode 100644
index 0000000000..841cd48bc5
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/GENERAL-READER.md
@@ -0,0 +1,111 @@
+# A reusable query for an arbitrary old reader
+
+This theorem extends the fixed-reader factorization from the
+bridge-access lane. It uses ordered operators. It does not assume
+that spatial maps commute.
+
+Let X and Z be modules over the coefficient ring. Let J insert a centre
+module into X, and let P select it, so \(PJ=I\). Suppose the current
+reader and response satisfy
+
+\[
+L_tJ=I,\qquad E_t=I+A_tL_t.
+\]
+
+Put \(B_t=L_t-P\) and \(C_t=I+JB_t\). Since \(B_tJ=0\), the code is a
+unit with \(C_t^{-1}=I-JB_t\). Let \(L_s:X\to Z\) be any old reader.
+Define
+
+\[
+W=L_sJ,\qquad B_s=L_s-WP,\qquad M=L_sE_tJ.
+\]
+
+Then \(B_sJ=0\), and
+
+\[
+\boxed{L_sE_tC_t^{-1}=B_s-WB_t+MP.}
+\]
+
+To prove the identity, keep the order of all factors:
+
+\[
+\begin{aligned}
+E_tC_t^{-1}
+  &=(I+A_tL_t)(I-JB_t)\\
+  &=I-JB_t+A_t(L_t-B_t)\\
+  &=I-JB_t+A_tP.
+\end{aligned}
+\]
+
+Multiplication by \(L_s\), followed by
+\(L_s=B_s+WP\) and \(M=W+L_sA_t\), gives the stated identity.
+
+The following six-step query therefore works for arbitrary independent
+X and Z inputs:
+
+1. Add \(B_sX\) to Z.
+2. Add \(WPX\) to Z.
+3. Apply \(C_t\) to X.
+4. Subtract the new \(WPX\) from Z.
+5. Add \(MPX\) to Z.
+6. Apply \(C_t^{-1}\) to X.
+
+The resulting map is
+
+\[
+(X,Z)\longmapsto(X,Z+L_sE_tX).
+\]
+
+In particular, steps 2 and 4 contribute \(-WB_tX_{\rm initial}\),
+and step 5 contributes \(ML_tX_{\rm initial}\). Each X field is
+restored. Z keeps its arbitrary baseline. An inverse of E is never
+used. Neither invertibility of E nor a zero selected block of E is
+required.
+
+The map W is a service obligation. It must act additively on Z, and its
+access and implementation must be priced. An in-place application of W
+to an existing centre value does not by itself give this additive
+service. No inverse of W is required by the theorem.
+
+The theorem is a query identity. It does not by itself make \(L_s\)
+a unit encoding of a complete target bank. Such an encoding requires
+a unit completion of \(L_s\). If the centre width and the ordinary
+coordinates R stay the same, this completion is
+\(\left[\begin{smallmatrix}W&B_s\\0&I\end{smallmatrix}\right]\).
+It is a unit exactly when W is a unit on the centre space. A completion
+with different ordinary coordinates changes the interface and needs
+its own implementation. The query identity itself also permits singular W.
+In the actual normalized case
+\(L_sJ=I\), W is I and \(C_s=I+J(L_s-P)\) gives that completion. The
+two W services are then plain same-port copies. Only this case has
+the actual 11,168-scalar and 2,064-map invoice in `REVIEW.md`.
+
+The independent checker includes a finite example with two-dimensional
+blocks
+
+\[
+T=\begin{bmatrix}0&1\\1&0\end{bmatrix},\quad
+W=\begin{bmatrix}1&1\\0&1\end{bmatrix},\quad
+S=\begin{bmatrix}2&1\\-1&0\end{bmatrix},\quad
+A=\begin{bmatrix}-1&0\\0&1\end{bmatrix}.
+\]
+
+Take \(L_t=[I,T]\), \(L_s=[W,S]\), and
+
+\[
+E_t=\begin{bmatrix}I+A&AT\\0&I\end{bmatrix}.
+\]
+
+Here E is singular, its selected block is nonzero, and \(WT\ne TW\).
+The six-step query passes all six independent input columns. The word
+with plain copies in place of W fails. This example tests the removed
+hypotheses. The ordered proof above applies to all modules and maps
+with the stated types.
+
+This theorem does not emit a new native response family. It does not
+provide a new complete supplier or a change to the selected frontier.
+The actual native frame and access conditions remain those in the
+separate D25 review.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/PEER-REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/PEER-REVIEW.md
new file mode 100644
index 0000000000..2859baa83a
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/PEER-REVIEW.md
@@ -0,0 +1,27 @@
+# Peer check of the added consequences
+
+The bridge-access producer checked the new consequences on 2026-10-20.
+This check concerns the new theorem and norm argument. It does not
+serve as independent approval of that producer's original query.
+
+The producer accepted the arbitrary-reader identity and the two
+additive W services. The producer requested one qualification:
+with the same ordinary coordinates, the completed bank code is
+\(\left[\begin{smallmatrix}W&B_s\\0&I\end{smallmatrix}\right]\), so it
+is a unit exactly when W is a unit. `GENERAL-READER.md` now states
+this condition. A different completion changes the interface.
+
+The producer also accepted the sharp norm argument on the regular
+cover. At a fixed owner h, different route matrices A give different
+owners \(hA\). The payload view for each route must also be retained.
+The checked maps use the unique FULL conjugate \(\Psi_t(A)\), so this
+condition holds. The claim concerns emitted scalar and map boundaries.
+It excludes quotient covers, internal scalar arithmetic, and native
+child interiors.
+
+The producer confirmed the chronology of pair \((0,2)\): reader zero
+has been carried through physical level one. It is not a skipped
+physical advance.
+
+All producer freezes remain unchanged. The later native dispatcher
+has a separate freeze and is outside this review.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..1ac718edf9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REPRODUCTION.json
@@ -0,0 +1,11 @@
+{
+  "commands": [
+    "python3 check_review.py --output normal",
+    "python3 -O check_review.py --output optimized"
+  ],
+  "normal_optimized_byte_equal": true,
+  "python": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
+  "receipt_sha256": "18226da65a8eb6e07f716d328451107e97c8905c2c429edfe54608310e97e1a9",
+  "schema": "independent-fixed-reader-reproduction-v1",
+  "status": "PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..e21b9062e8
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REVIEW.md
@@ -0,0 +1,283 @@
+# Independent review of the fixed-reader query
+
+The forward query is correct for all three declared D25 pairs. The
+literal query restores all 112 source fields. It preserves each arbitrary
+target baseline and all 416 outside fields. Its price is 11,168 real
+scalar primitives and 2,064 monomial map calls. It uses no native child
+and no extra field.
+
+The sixteen positive H8 carrier phase identities and the retained path
+conditions pass independent checks. These results do not verify an
+integrated native reuse word. The complete supplier, map price, child
+hosting, and recursive precision remain separate.
+
+The separate typed inverse-adjoint lemma is correct. This review also
+emits its late query in memory and checks its exact map on all 640
+arbitrary input columns. This is a check of the late query, not a complete
+native backward service.
+
+## Frozen inputs and method
+
+The forward source is
+`../../bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json`,
+SHA-256
+`41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf`.
+The separate dual source is `DUAL-FREEZE.json` in that directory,
+SHA-256
+`92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455`.
+The checker validates both freezes and their files before it starts.
+It also validates the earlier formation freeze.
+
+`check_review.py` imports no producer code. It uses exact rational
+arithmetic and a separate Z4 polynomial representation. It reads the
+actual rank-sixteen native response, row-capture word, and D25 views.
+The receipt records their full hashes.
+
+The review derives \(L=V_P^{-1}V\) from the actual factorization
+\(E=I+UV\). The selected minor has determinant 16. The resulting L equals
+the emitted reader. The review checks \(LJ=I\), \(E[P,P]=0\),
+\(E=I+AL\), and both orders of the code inverse. Here J inserts the
+sixteen selected fields and \(A=(E-I)J\).
+
+Both native providers have the same retained path count. The review
+removes 128 H1 events and 122 scalar events that write selected Y.
+No retained event reads these selected Y fields. No forward scalar
+event feeds Y into X. The last source event is 2638. After the retained
+sweep, all source fields are FULL, and the selected Y fields retain
+their input type.
+
+## The algebra needs no inverse response
+
+Let P select the coordinates that J inserts, so \(PJ=I\). This P is
+an operator; in the actual coordinate notation it is \(J^{\mathsf T}\).
+Let
+
+\[
+L_tJ=I,\quad B_t=L_t-P,\quad
+C_t=I+JB_t,\quad E_t=I+A_tL_t.
+\]
+
+Then \(B_tJ=0\), so \(C_t^{-1}=I-JB_t\). Direct ordered
+multiplication gives
+
+\[
+E_tC_t^{-1}=I-JB_t+A_tP.
+\]
+
+For a normalized old reader \(L_sJ=I\), put \(B_s=L_s-P\) and
+\(M=L_sE_tJ\). It follows that
+
+\[
+L_sE_tC_t^{-1}=B_s-B_t+MP.
+\]
+
+The six steps in the producer follow:
+
+1. Add \(B_sX\) to the selected target bank.
+2. Add \(PX\) to that bank.
+3. Apply \(C_t\) to X.
+4. Subtract the new \(PX\) from that bank.
+5. Add \(MPX\) to that bank.
+6. Apply \(C_t^{-1}\) to X.
+
+Steps 2 and 4 add \(-B_tX_{\rm initial}\). Step 5 adds
+\(ML_tX_{\rm initial}\). Their sum with step 1 is
+\(L_sE_tX_{\rm initial}\). The target baseline has coefficient I at
+the endpoint. This argument does not commute operators at two stages.
+
+Neither \(E_t[P,P]=0\) nor invertibility of \(E_t\) is needed for this
+identity. The former is a property of the actual inexpensive middle
+query. It is not a hypothesis of the general factorization.
+
+`GENERAL-READER.md` records a separate extension to an arbitrary old
+reader. It replaces the two copies by a paid map \(W=L_sJ\).
+The actual invoice in this review applies only to \(W=I\).
+
+## Actual owner paths and source chronology
+
+The checker reconstructs all 336 D25 routes from the native q values
+and the actual orthogonal chart rule. It checks the canonical Z4
+phase identities with a separate coefficient representation. The
+canonical operator model itself is inherited from the source supplier
+and the earlier formation and D25 reviews.
+
+The checked reader/service pairs are \((0,1),(0,2),(1,2)\). In each
+case the physical level before service t is \(t-1\). The label s
+identifies a retained reader. Thus \((0,2)\) assumes that reader \(L_0\)
+was carried through stage one. It does not mean a physical jump from
+level zero to stage two.
+
+At the adjacent entry, a selected FULL target becomes its positive
+intrinsic line \(Q_p\), with the common exterior retained. An ordinary
+hole target becomes I with the same exterior. The checker verifies
+448 source/target FULL-to-Q identities and 224 hole-to-I identities
+over all ports. It also verifies 672 past/current FULL view identities.
+Omission of the positive intrinsic line gives a different phase.
+
+Each carrier uses eight orthogonal axes perpendicular to its actual
+q, plus an explicit output translation. The full phase polynomial is
+that of \(F_9Q_p^{-1}\), with no constant phase. All sixteen carriers
+pass. The opposite intrinsic sign fails.
+
+For a term of \(L_sE_t\), the route is
+
+\[
+\rho_{s,p}\rho_{s,j}\rho_{t,j}\rho_{t,r}.
+\]
+
+The independent multiplication retains this exact order. It combines
+terms only if both the input field and the complete route agree.
+There are 3,808 terms per pair. Restriction to the selected source
+fields gives 696 terms. The first two pairs use 216 distinct middle
+routes; the last pair uses 696.
+
+Every route A is orthogonal and fixes all uncompleted axes. At the
+completed level t, its actual view is
+
+\[
+\Psi_t(A)=F_{9+8t}P_AF_{9+8t}^{-1}
+         =X_{\delta_A}P_A.
+\]
+
+The checker verifies the entire Z4 difference polynomial and the
+inverse translation \(A^{-1}\delta_A\). The map is a single owner and
+payload map: the owner read is \(h\mapsto hA\), and the payload map
+expresses that source chart in the target chart.
+
+The review expands the complete literal query. It applies each old
+view, code view, temporary source map, scalar gate, and restoration map
+in order. Its matrix is compared with the direct \(L_sE_t\) product on
+all 640 arbitrary input columns. There is no zero baseline assumption.
+The retained X rows are available only after the complete cover sweep.
+
+Two negative controls test route order. Commuting the middle stage
+factors fails for \((1,2)\). Replacing an inverse source map by a second
+copy of its forward map also fails. Stage zero is the identity, so it
+cannot supply the first negative control.
+
+## Price and sharper local bounds
+
+The literal query gives:
+
+| Part | Real scalar primitives | Monomial maps |
+| --- | ---: | ---: |
+| Old complement query | 1,760 | 224 |
+| Two copies | 256 | 0 |
+| Current code and inverse | 3,520 | 448 |
+| Middle query | 5,632 | 1,392 |
+| Total | 11,168 | 2,064 |
+
+The middle uses 456 additions with coefficient -1 and 240 with
+coefficient +1. It uses eight pairs of scales by 4 and 1/4.
+The retained native word has scalar price 6,456. With sixteen H8
+carriers, its prospective profile is
+
+\[
+1392H_1+64H_2+48H_3+16H_8,
+\]
+
+of total native rank 1,792. The prospective retained-word-plus-query
+scalar price is 17,624. These counts do not include a finite price for
+the 2,064 query maps, native wrappers, ordinary boundary maps, or
+recursive hosting.
+
+The producer's conservative forward bounds, 972 and binary height 3,
+are valid. Exact coefficient cancellation gives stronger bounds at
+each emitted scalar or map boundary:
+
+| Late query | Maximum coefficient row sum | Maximum binary denominator height |
+| --- | ---: | ---: |
+| Forward | 448 | 2 |
+| Inverse-adjoint | \(43/2\) | 3 |
+
+These values hold for all three pairs. The receipt gives the first
+maximal row and exact denominator witnesses. For example, a forward
+prefix contains a coefficient -1/4, and a dual prefix contains 1/8.
+Thus the indicated coefficient heights cannot be reduced.
+
+Here the row sum also gives the sharp physical sup norm on the
+regular cover. Each coefficient is attached to an input field and a
+route A. At a fixed output owner h, distinct A give distinct source
+owners \(hA\). The payload view for a given A is uniquely \(\Psi_t(A)\)
+and is monomial. Therefore equal field/route terms can be combined
+exactly, and the remaining independent source locations can take the
+signs that attain the row sum. This statement uses the regular cover.
+It does not assert sharpness on a quotient cover.
+
+The bounds concern complete emitted gates. They do not bound the
+internal arithmetic states of a lowered scalar instruction, a native
+child, or a recursive caller. They do not supply a complete precision
+certificate.
+
+## The typed inverse-adjoint
+
+Let \(Q_P\) be the positive intrinsic line on the selected target
+fields, with I on the other target fields. Let \(H_R\) be the inverse
+intrinsic line on the ordinary target fields, with I on the selected
+fields. Put
+
+\[
+F_{\rm in}=\operatorname{diag}(Q,Q_P),\qquad
+F_{\rm out}=\operatorname{diag}(F,FH_R),\qquad A=C_sE_t.
+\]
+
+The exterior factors and cover views belong to these unitary frames.
+For an integrated forward word, the physical operator is
+
+\[
+U=F_{\rm out}
+\begin{bmatrix}I&0\\A&I\end{bmatrix}F_{\rm in}^{-1}.
+\]
+
+For a chronological word \(U=G_n\cdots G_1\), its inverse-adjoint is
+\(G_n^{-*}\cdots G_1^{-*}\). Thus the chronological gate order stays
+the same. Unitary native and monomial gates stay the same. An ADD
+\(b\leftarrow b+ca\) becomes \(a\leftarrow a-\overline c b\), and a
+real unit SCALE becomes its reciprocal. Therefore
+
+\[
+U^{-*}=F_{\rm out}
+\begin{bmatrix}I&-E_t^*C_s^*\\0&I\end{bmatrix}
+F_{\rm in}^{-1}.
+\]
+
+This is an adjoint response, not a reciprocal response. It retains
+the selected \(Q_P\) input type.
+
+The late dual query is checked independently by this gate transform.
+It implements \(X\leftarrow X-E_t^*L_s^*Y_P\), retains every selected
+Y baseline at its endpoint, and leaves ordinary Y and outside fields
+unchanged. Its maps have the same order, and it reads only the FULL
+selected Y fields. The complete route in each adjoint coefficient is
+the inverse of the forward route. The price is unchanged. The
+different prefix bounds are computed separately.
+
+This proves the conditional circuit lemma and the emitted late query.
+It does not replace the missing integrated native forward and backward
+replays. It also does not provide a controller that accepts these
+boundary types.
+
+## Reproduction and credit
+
+Run from this directory:
+
+```text
+python3 check_review.py --output normal
+python3 -O check_review.py --output optimized
+```
+
+Both commands must print
+`PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL`.
+The two `REVIEW-CHECKS.json` files must be byte equal.
+
+The bridge-access lane supplied the fixed-reader factorization, literal
+D25 query, and typed dual lemma. The controller lane supplied the
+normalized row capture. The new-core-transfer lane supplied the
+rank-sixteen native response. This review supplies independent route,
+phase, map-order, and arbitrary-input checks. It adds the arbitrary-reader
+form and the sharper local prefix bounds. The bridge-access author
+separately checked the regular-cover norm argument and the weaker
+algebraic hypotheses. AI research agents produced these local records.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/check_review.py b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/check_review.py
new file mode 100644
index 0000000000..d06084e8c0
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/check_review.py
@@ -0,0 +1,680 @@
+"""Check the fixed-reader query without producer code imports."""
+
+import argparse
+from collections import Counter
+from fractions import Fraction as F
+from functools import cache
+import gzip
+from hashlib import sha256
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+PRODUCER = LANES / "bridge-access-20261017/row-capture-access-20261020"
+UNIT = tuple(1 << i for i in range(25))
+PIVOTS = (0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23)
+PSET = set(PIVOTS)
+REUSE_PIN = "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf"
+DUAL_PIN = "92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455"
+PINS = {
+    "capture": (
+        "controller-followthrough-20261017/row-capture-20261020/"
+        "run-normal/ROW-CAPTURE.json",
+        "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7",
+    ),
+    "native": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+        "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    ),
+    "views": (
+        "bridge-access-20261017/matched-stage-access-20261018/"
+        "DIMENSION25-VIEWS.json",
+        "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473",
+    ),
+}
+
+
+def require(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def digest(raw):
+    return sha256(raw).hexdigest()
+
+
+def pinned_json(path, pin, compressed=False):
+    raw = path.read_bytes()
+    if compressed:
+        raw = gzip.decompress(raw)
+    require(digest(raw) == pin, "Pin: " + str(path))
+    return json.loads(raw)
+
+
+def put(row, key, value):
+    value += row.get(key, F(0))
+    if value:
+        row[key] = value
+    else:
+        row.pop(key, None)
+
+
+def sparse(raw):
+    return [{int(j): F(v) for j, v in row.items() if F(v)} for row in raw]
+
+
+def eye(n):
+    return [{i: F(1)} for i in range(n)]
+
+
+def matmul(a, b):
+    result = []
+    for row in a:
+        out = {}
+        for j, value in row.items():
+            for k, other in b[j].items():
+                put(out, k, value * other)
+        result.append(out)
+    return result
+
+
+def invert(a):
+    n = len(a)
+    rows = [[a[i].get(j, F(0)) for j in range(n)]
+            + [F(i == j) for j in range(n)] for i in range(n)]
+    determinant = F(1)
+    for j in range(n):
+        p = next((i for i in range(j, n) if rows[i][j]), None)
+        require(p is not None, "The pivot minor is a unit over Q")
+        if p != j:
+            rows[j], rows[p] = rows[p], rows[j]
+            determinant = -determinant
+        value = rows[j][j]
+        determinant *= value
+        rows[j] = [v / value for v in rows[j]]
+        for i in range(n):
+            if i != j and rows[i][j]:
+                value = rows[i][j]
+                rows[i] = [x - value * y for x, y in zip(rows[i], rows[j])]
+    return [{j: v for j, v in enumerate(row[n:]) if v} for row in rows], determinant
+
+
+def scalar_word(rows, word):
+    result = [dict(row) for row in rows]
+    for op, dst, src, value in word:
+        value = F(value)
+        if op == "scale":
+            result[dst] = {j: value * v for j, v in result[dst].items()}
+        else:
+            require(op == "add" and src != dst, "Scalar ADD")
+            for j, v in result[src].items():
+                put(result[dst], j, value * v)
+    return result
+
+
+def apply(a, vector):
+    result = 0
+    while vector:
+        bit = vector & -vector
+        result ^= a[bit.bit_length() - 1]
+        vector ^= bit
+    return result
+
+
+@cache
+def product(a, b):
+    return tuple(apply(a, x) for x in b)
+
+
+def transpose(a):
+    return tuple(sum(((a[j] >> i) & 1) << j for j in range(25))
+                 for i in range(25))
+
+
+def route_product(*args):
+    result = UNIT
+    for a in args:
+        result = product(result, a)
+    return result
+
+
+def dot(a, b):
+    return (a & b).bit_count() & 1
+
+
+def chart(q):
+    hole = next(i for i in range(9) if not (q >> i) & 1)
+    vector = q ^ (1 << hole)
+    order = list(range(9))
+    order[0], order[hole] = order[hole], order[0]
+    basis = tuple((1 << i) ^ (vector if (vector >> i) & 1 else 0)
+                  for i in order) + UNIT[9:]
+    require(basis[0] == q and product(transpose(basis), basis) == UNIT,
+            "Independent port chart")
+    return basis
+
+
+def route(q, stage):
+    if not stage:
+        return UNIT
+    basis = chart(q)
+    swaps = [basis[j + 1] ^ UNIT[9 + 8 * (stage - 1) + j] for j in range(8)]
+    return tuple(x ^ xor(v for v in swaps if dot(v, x)) for x in UNIT)
+
+
+def xor(values):
+    result = 0
+    for value in values:
+        result ^= value
+    return result
+
+
+@cache
+def line_phase(vector, exponent):
+    exponent %= 4
+    linear = tuple(exponent if (vector >> i) & 1 else 0 for i in range(25))
+    quadratic = 0
+    if exponent & 1:
+        for i in range(25):
+            if (vector >> i) & 1:
+                for j in range(i + 1, 25):
+                    if (vector >> j) & 1:
+                        quadratic ^= 1 << (25 * i + j)
+    return linear, quadratic
+
+
+ZERO_PHASE = ((0,) * 25, 0)
+
+
+def add_phase(a, b):
+    return tuple((x + y) % 4 for x, y in zip(a[0], b[0])), a[1] ^ b[1]
+
+
+def minus_phase(a):
+    return tuple(-x % 4 for x in a[0]), a[1]
+
+
+def sum_phase(terms):
+    result = ZERO_PHASE
+    for vector, exponent in terms:
+        result = add_phase(result, line_phase(vector, exponent))
+    return result
+
+
+@cache
+def full_phase(level, a=UNIT):
+    return sum_phase((a[j], 1) for j in range(9 + 8 * level))
+
+
+def phase_translation(phase):
+    require(phase[1] == 0 and all(x % 2 == 0 for x in phase[0]),
+            "The phase difference is a translation")
+    return sum((x // 2) << i for i, x in enumerate(phase[0]))
+
+
+def routed_matrix(rows, targets, stage, routes):
+    return [{(r, product(routes[stage, p], routes[stage, r])): value
+             for r, value in row.items()}
+            for p, row in zip(targets, rows)]
+
+
+def multiply_routed(a, b):
+    result = []
+    for row in a:
+        out = {}
+        for (j, ra), value in row.items():
+            for (k, rb), other in b[j].items():
+                put(out, (k, product(ra, rb)), value * other)
+        result.append(out)
+    return result
+
+
+def real_price(op, value):
+    value = F(value)
+    numerator, denominator = abs(value.numerator), value.denominator
+    require(numerator and denominator & (denominator - 1) == 0, "Dyadic coefficient")
+    if op == "scale":
+        require(numerator & (numerator - 1) == 0, "Dyadic unit scale")
+        return 2 * (abs(numerator.bit_length() - denominator.bit_length()) + (value < 0))
+    return 2 * (3 + numerator.bit_length() - 1 + numerator.bit_count()
+                + denominator.bit_length() - 1)
+
+
+def replay(operations, dual=False):
+    rows = [{(i, UNIT): F(1)} for i in range(640)]
+    bounds = [F(1)] * 640
+    grid = [0] * 640
+    peak, height = F(1), 0
+    exact_peak, exact_height = F(1), 0
+    norm_witness = None
+    height_witness = None
+    bill = Counter()
+    for index, (op, dst, src, value) in enumerate(operations):
+        if op == "map":
+            rows[dst] = {(j, product(value, a)): c for (j, a), c in rows[dst].items()}
+            bill["maps"] += 1
+            continue
+        if dual and op == "add":
+            dst, src, value = src, dst, -value
+        elif dual and op == "scale":
+            value = 1 / value
+        bill["real_scalar"] += real_price(op, value)
+        if op == "scale":
+            rows[dst] = {j: value * v for j, v in rows[dst].items()}
+            bounds[dst] *= abs(value)
+            grid[dst] = max(0, grid[dst] + value.denominator.bit_length()
+                            - abs(value.numerator).bit_length())
+        else:
+            for j, v in rows[src].items():
+                put(rows[dst], j, value * v)
+            bounds[dst] += abs(value) * bounds[src]
+            grid[dst] = max(grid[dst], grid[src] + value.denominator.bit_length() - 1)
+        peak, height = max(peak, bounds[dst]), max(height, grid[dst])
+        current_norm = sum(abs(v) for v in rows[dst].values())
+        current_height = max((v.denominator.bit_length() - 1 for v in rows[dst].values()),
+                             default=0)
+        if current_norm > exact_peak:
+            exact_peak = current_norm
+            norm_witness = {"event_index": index, "target": dst,
+                            "coefficient_terms": len(rows[dst]),
+                            "coefficient_census": dict(Counter(str(c) for c in rows[dst].values()))}
+        if current_height > exact_height:
+            exact_height = current_height
+            (origin, a), coefficient = next(
+                (key, c) for key, c in rows[dst].items()
+                if c.denominator.bit_length() - 1 == current_height)
+            height_witness = {"event_index": index, "target": dst,
+                              "origin": origin, "route": a, "coefficient": str(coefficient)}
+    return rows, dict(bill), peak, height, {
+        "coefficient_row_sum_peak": str(exact_peak),
+        "coefficient_binary_height": exact_height,
+        "norm_witness": norm_witness, "height_witness": height_witness}
+
+
+def isolation(word, ports):
+    selected = {112 + p for p in PIVOTS}
+    frames = list(word["start"])
+    require(len(frames) == len(word["final"]) == 640, "All literal input fields")
+    require(set(word["frames"][1]) == set(UNIT[:9]), "Literal local FULL frame")
+    require(all(word["frames"][frames[p]] == [ports[p]] for p in range(112)),
+            "The literal source lines are the actual model ports")
+    for p in PIVOTS:
+        frames[112 + p] = frames[p]
+    initial = list(frames)
+    count = Counter()
+    native = Counter()
+    last_x = None
+    for i, event in enumerate(word["events"]):
+        op = event[0]
+        dst = event[1] if op == "native" else event[1][1]
+        if dst < 112:
+            last_x = i
+        if dst in selected:
+            count["removed_" + op] += 1
+            if op == "native":
+                require(event[4] == 1, "Removed selected children have rank one")
+            continue
+        if op == "native":
+            _, dst, old, new, rank, _ = event
+            require(frames[dst] == old, "Retained native frame")
+            frames[dst] = new
+            native[rank] += 1
+        else:
+            require(op == "scalar", "Retained event kind")
+            _, (kind, dst, src, coefficient), frame = event
+            require(src not in selected, "The retained word does not read selected Y")
+            require(frames[dst] == frame and (src is None or frames[src] == frame),
+                    "Retained scalar frames")
+            require(not (dst < 112 and src is not None and src >= 112),
+                    "The source word does not read target fields")
+            count["retained_scalar"] += real_price(kind, F(coefficient))
+    require(count == {"removed_native": 128, "removed_scalar": 122,
+                      "retained_scalar": 6456}, "Native deletion and scalar invoice")
+    require(last_x == 2638 and len(word["events"]) == 2640, "The complete source cut")
+    require(all(frames[p] == 1 for p in range(112)), "All source fields are FULL")
+    require(all(frames[t] == initial[t] for t in selected), "Selected Q fields are retained")
+    require(all(frames[i] == word["final"][i] for i in range(640) if i not in selected),
+            "Other final frames")
+    require(all(word["start"][i] == word["final"][i] for i in range(224, 640)),
+            "Outside frame endpoints")
+    require(native == {1: 1392, 2: 64, 3: 48}, "Retained child census")
+    native[8] += 16
+    require(sum(k * n for k, n in native.items()) == 1792, "Prospective native mass")
+    return {"deletion": dict(count), "last_source_event": last_x,
+            "prospective_native_profile": dict(native), "prospective_native_mass": 1792}
+
+
+def general_reader_example():
+    t = [{1: F(1)}, {0: F(1)}]
+    w = [{0: F(1), 1: F(1)}, {1: F(1)}]
+    b = [{0: F(2), 1: F(1)}, {0: F(-1)}]
+    a = [{0: F(-1)}, {1: F(1)}]
+    selected_e = [{}, {1: F(2)}]
+    m = matmul(w, selected_e)
+    computed_selected = eye(2)
+    for row, correction in zip(computed_selected, a):
+        for j, value in correction.items():
+            put(row, j, value)
+    require(computed_selected == selected_e and not selected_e[0] and bool(selected_e[1]),
+            "The selected response is nonzero and singular")
+    require(matmul(w, t) != matmul(t, w), "The general reader example does not commute")
+
+    def mv(matrix, vector):
+        return [sum(value * vector[j] for j, value in row.items()) for row in matrix]
+
+    def add(left, right, sign=1):
+        return [x + sign * y for x, y in zip(left, right)]
+
+    wrong_copy = False
+    for column in range(6):
+        initial = [F(i == column) for i in range(6)]
+        xp, xr, z = initial[:2], initial[2:4], initial[4:]
+        ex_p = add(mv(selected_e, xp), mv(matmul(a, t), xr))
+        desired = add(z, add(mv(w, ex_p), mv(b, xr)))
+        z = add(z, mv(b, xr))
+        z = add(z, mv(w, xp))
+        changed = add(xp, mv(t, xr))
+        z = add(z, mv(w, changed), -1)
+        z = add(z, mv(m, changed))
+        restored = add(changed, mv(t, xr), -1)
+        require(restored == xp and z == desired, "The arbitrary-reader six-step identity")
+        wrong = add(initial[4:], mv(b, xr))
+        wrong = add(wrong, xp)
+        wrong = add(wrong, changed, -1)
+        wrong = add(wrong, mv(m, changed))
+        wrong_copy |= wrong != desired
+    require(wrong_copy, "A nonidentity W cannot be replaced by two plain copies")
+    return {"arbitrary_input_columns": 6, "E_is_singular": True,
+            "E_selected_block_is_nonzero": True, "W_and_B_t_do_not_commute": True,
+            "plain_copy_negative_control": "fails"}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "normal")
+    args = parser.parse_args()
+    frozen = pinned_json(PRODUCER / "REUSE-FREEZE.json", REUSE_PIN)
+    for name, pin in frozen["files"].items():
+        require(digest((PRODUCER / name).read_bytes()) == pin, "Producer file: " + name)
+    formation = pinned_json(PRODUCER / "FREEZE.json", frozen["formation_freeze_sha256"])
+    for name, pin in formation["files"].items():
+        require(digest((PRODUCER / name).read_bytes()) == pin, "Formation file: " + name)
+    dual = pinned_json(PRODUCER / "DUAL-FREEZE.json", DUAL_PIN)
+    require(digest((PRODUCER / "DUAL.md").read_bytes()) == dual["proof_sha256"],
+            "The dual proof pin")
+    require(dual["reuse_freeze_sha256"] == REUSE_PIN, "The dual dependency pin")
+    sources = {name: pinned_json(LANES / path, pin, path.endswith(".gz"))
+               for name, (path, pin) in PINS.items()}
+    capture, native, views = (sources[k] for k in ("capture", "native", "views"))
+    emitted = json.loads((PRODUCER / "reuse-normal/REUSE-PROGRAM.json").read_bytes())
+    require(tuple(capture["pivots"]) == tuple(emitted["pivots"]) == PIVOTS, "Pivots")
+    model = native["model"]
+    e, u, v = (sparse(model[k]) for k in ("response", "correction_U", "correction_V"))
+    expected_e = eye(112)
+    for row, correction in zip(expected_e, matmul(u, v)):
+        for j, value in correction.items():
+            put(row, j, value)
+    require(e == expected_e == sparse(capture["response"]), "The actual E = I + UV")
+    vp = [{j: row[p] for j, p in enumerate(PIVOTS) if p in row} for row in v]
+    vpi, vp_det = invert(vp)
+    reader = matmul(vpi, v)
+    require(reader == sparse(capture["centre_reader"]), "Independent reader derivation")
+    require(all({j: value for j, value in row.items() if j in PSET} == {p: F(1)}
+                for row, p in zip(reader, PIVOTS)), "LJ = I")
+    require(all(not (set(e[p]) & PSET) for p in PIVOTS), "E[P,P] = 0")
+    a = [{j: e[i].get(p, F(0)) - F(i == p)
+          for j, p in enumerate(PIVOTS) if e[i].get(p, F(0)) != F(i == p)}
+         for i in range(112)]
+    reconstructed_e = eye(112)
+    for row, correction in zip(reconstructed_e, matmul(a, reader)):
+        for j, value in correction.items():
+            put(row, j, value)
+    require(reconstructed_e == e, "E = I + A L")
+    code = eye(112)
+    inverse = eye(112)
+    for p, row in zip(PIVOTS, reader):
+        code[p] = dict(row)
+        for r, value in row.items():
+            if r != p:
+                inverse[p][r] = -value
+    require(code == sparse(capture["code"]) and inverse == sparse(capture["code_inverse"]),
+            "Independent capture maps")
+    require(matmul(code, inverse) == matmul(inverse, code) == eye(112), "Both inverse orders")
+    for key, target in (("scalar_word", code), ("inverse_scalar_word", inverse)):
+        require(scalar_word(eye(112), capture[key]) == target, "Literal capture word: " + key)
+        require(sum(real_price(op, F(c)) for op, _, _, c in capture[key]) == 1760,
+                "Capture price: " + key)
+        require(all(dst in PSET and (src is None or src not in PSET)
+                    for _, dst, src, _ in capture[key]), "Complement-only capture word")
+    provider_checks = {name: isolation(value["forward"], model["ports"])
+                       for name, value in native["providers"].items()}
+    records = {(r["stage"], r["port"]): r for r in views["entries"]}
+    require(set(records) == {(s, p) for s in range(3) for p in range(112)},
+            "All actual D25 views")
+    routes = {}
+    phase_checks = Counter()
+    for (stage, p), record in records.items():
+        q = model["ports"][p]
+        require(record["q"] == q, "Actual native q")
+        rho = route(q, stage)
+        routes[stage, p] = rho
+        require(rho == tuple(record["route_columns"]), "Independent D25 route")
+        require(product(rho, rho) == UNIT and transpose(rho) == rho
+                and apply(rho, q) == q, "Route properties")
+        align = record["literal_stage_alignment"]
+        for level in range(stage, 3):
+            actual = add_phase(full_phase(level, rho), line_phase(align["exit_X"], 2))
+            require(actual == full_phase(level), "Past-reader FULL view")
+            phase_checks["full_views"] += 1
+        require(align["exit_X"] == align["exit_Y"], "Equal physical output translations")
+        if stage:
+            exterior = sum_phase((UNIT[j], 1) for j in range(9, 9 + 8 * stage))
+            for name in ("entry_X", "entry_Y"):
+                actual = add_phase(full_phase(stage - 1, rho),
+                                   line_phase(apply(rho, align[name]), 2))
+                expected = add_phase(exterior, line_phase(q, 1))
+                require(actual == expected and actual != exterior,
+                        "An adjacent physical FULL entry has the positive intrinsic line")
+                phase_checks["adjacent_full_to_Q"] += 1
+            ordinary = add_phase(actual, line_phase(q, -1))
+            require(ordinary == exterior, "An adjacent hole entry has the identity type")
+            phase_checks["adjacent_hole_to_I"] += 1
+    carrier_checks = []
+    for rec in emitted["carrier_recipes"]:
+        p, q = rec["port"], model["ports"][rec["port"]]
+        basis = tuple(rec["basis_columns"])
+        expected_basis = chart(q)[1:9] + chart(q)[:1] + UNIT[9:]
+        require(basis == expected_basis and rec["q"] == q and rec["rank"] == 8,
+                "Actual H8 carrier basis")
+        require(tuple(rec["inverse_columns"]) == transpose(basis)
+                and product(transpose(basis), basis) == UNIT, "Carrier orthogonality")
+        desired = add_phase(full_phase(0), line_phase(q, -1))
+        implemented = add_phase(sum_phase((b, 1) for b in basis[:8]),
+                                line_phase(rec["output_translation"], 2))
+        require(implemented == desired, "Exact H8 carrier phase")
+        require(implemented != add_phase(full_phase(0), line_phase(q, 1)),
+                "Negative control: the opposite intrinsic sign fails")
+        carrier_checks.append({"port": p, "q": q, "translation": rec["output_translation"]})
+    require({c["port"] for c in carrier_checks} == PSET, "All sixteen carriers")
+    pair_checks = []
+    for pair in emitted["pairs"]:
+        s, t = pair["reader_stage"], pair["service_stage"]
+        ls = routed_matrix(reader, PIVOTS, s, routes)
+        lt = routed_matrix(reader, PIVOTS, t, routes)
+        et = routed_matrix(e, range(112), t, routes)
+        direct = multiply_routed(ls, et)
+        middle = [{key: value for key, value in row.items() if key[0] in PSET}
+                  for row in direct]
+        require(sum(map(len, direct)) == 3808 and sum(map(len, middle)) == 696,
+                "Independent owner-path counts")
+        prefix = 9 + 8 * t
+        route_table = pair["middle_routes"]
+        for record in route_table:
+            a, ai = tuple(record["columns"]), tuple(record["inverse_columns"])
+            require(ai == transpose(a) and product(a, ai) == product(ai, a) == UNIT,
+                    "The source map inverse")
+            require(a[prefix:] == UNIT[prefix:], "Every uncompleted axis is fixed")
+            delta = phase_translation(add_phase(full_phase(t), minus_phase(full_phase(t, a))))
+            reverse_delta = phase_translation(
+                add_phase(full_phase(t), minus_phase(full_phase(t, ai))))
+            require(record["FULL_translation"] == delta
+                    and record["inverse_FULL_translation"] == reverse_delta
+                    and reverse_delta == apply(ai, delta), "Complete map and inverse phases")
+        for label, stage in (("old_reader_views", s), ("current_code_views", t)):
+            require({rec["port"] for rec in pair[label]} == set(range(112)), "All FULL views")
+            for rec in pair[label]:
+                require(tuple(rec["route_columns"]) == routes[stage, rec["port"]]
+                        and rec["translation"] ==
+                        records[stage, rec["port"]]["literal_stage_alignment"]["exit_X"],
+                        "Emitted FULL view")
+        require(pair["old_reader_view_ports"] ==
+                {"X": sorted(set(range(112)) - PSET), "Y": list(PIVOTS)}, "Old reader fields")
+        operations = []
+        part_invoices = []
+
+        def scalar(op, dst, src, coefficient):
+            operations.append((op, dst, src, F(coefficient)))
+
+        def maps(stage, ports, offset):
+            for p in ports:
+                operations.append(("map", offset + p, None, routes[stage, p]))
+
+        def mark(name, begin):
+            part = operations[begin:]
+            part_invoices.append({
+                "part": name,
+                "maps": sum(op == "map" for op, _, _, _ in part),
+                "real_scalar": sum(real_price(op, value) for op, _, _, value in part
+                                   if op != "map"),
+            })
+
+        begin = len(operations)
+        ordinary = sorted(set(range(112)) - PSET)
+        maps(s, ordinary, 0)
+        maps(s, PIVOTS, 112)
+        for op, p, r, value in capture["scalar_word"]:
+            scalar(op, 112 + p, r, value)
+        maps(s, ordinary, 0)
+        maps(s, PIVOTS, 112)
+        mark("old_complement", begin)
+        begin = len(operations)
+        for p in PIVOTS:
+            scalar("add", 112 + p, p, 1)
+        mark("first_copy", begin)
+        begin = len(operations)
+        maps(t, range(112), 0)
+        for op, p, r, value in capture["scalar_word"]:
+            scalar(op, p, r, value)
+        maps(t, range(112), 0)
+        mark("current_code", begin)
+        begin = len(operations)
+        for p in PIVOTS:
+            scalar("add", 112 + p, p, -1)
+        mark("second_copy", begin)
+        begin = len(operations)
+        middle_rows = [{} for _ in PIVOTS]
+        pindex = {p: i for i, p in enumerate(PIVOTS)}
+        integer_census = Counter()
+        for op, p, r, value, route_id in pair["middle_query"]:
+            value = F(value)
+            if op == "scale":
+                require(r is None and route_id is None, "Middle scale format")
+                middle_rows[pindex[p]] = {
+                    key: value * v for key, v in middle_rows[pindex[p]].items()}
+                scalar(op, 112 + p, None, value)
+            else:
+                require(op == "mapped_add_restore" and p in PSET and r in PSET,
+                        "The middle query reads existing centres")
+                require(value.denominator == 1, "The middle ADD is integral")
+                integer_census[str(value)] += 1
+                a = tuple(route_table[route_id]["columns"])
+                ai = tuple(route_table[route_id]["inverse_columns"])
+                put(middle_rows[pindex[p]], (r, a), value)
+                operations.append(("map", r, None, a))
+                scalar("add", 112 + p, r, value)
+                operations.append(("map", r, None, ai))
+        require(middle_rows == middle, "The emitted middle query equals the independent product")
+        mark("middle", begin)
+        begin = len(operations)
+        maps(t, range(112), 0)
+        for op, p, r, value in capture["inverse_scalar_word"]:
+            scalar(op, p, r, value)
+        maps(t, range(112), 0)
+        mark("current_inverse", begin)
+        actual, bill, peak, height, exact_prefix = replay(operations)
+        expected = [{(i, UNIT): F(1)} for i in range(640)]
+        for p, row in zip(PIVOTS, direct):
+            for key, value in row.items():
+                put(expected[112 + p], key, value)
+        require(actual == expected, "All 640 arbitrary input columns of the complete query")
+        require(bill == {"maps": 2064, "real_scalar": 11168}
+                and peak == 972 and height == 3, "Independent complete query invoice and bounds")
+        require(exact_prefix["coefficient_row_sum_peak"] == "448"
+                and exact_prefix["coefficient_binary_height"] == 2,
+                "Sharper forward bounds at emitted gate boundaries")
+        actual_dual, dual_bill, dual_peak, dual_height, exact_dual_prefix = replay(
+            operations, dual=True)
+        expected_dual = [{(i, UNIT): F(1)} for i in range(640)]
+        for p, row in zip(PIVOTS, direct):
+            for (r, a), value in row.items():
+                put(expected_dual[r], (112 + p, transpose(a)), -value)
+        require(actual_dual == expected_dual, "All 640 input columns of the literal late dual query")
+        require(dual_bill == bill, "The dual query keeps the invoice")
+        require(exact_dual_prefix["coefficient_row_sum_peak"] == "43/2"
+                and exact_dual_prefix["coefficient_binary_height"] == 3,
+                "Sharper dual bounds at emitted gate boundaries")
+        unordered = [{} for _ in PIVOTS]
+        for row_index, (p, row) in enumerate(zip(PIVOTS, reader)):
+            for j, value in row.items():
+                for r, other in e[j].items():
+                    wrong = route_product(routes[s, p], routes[t, j],
+                                          routes[s, j], routes[t, r])
+                    put(unordered[row_index], (r, wrong), value * other)
+        if s:
+            require(unordered != direct, "Negative control: inner stage factors cannot commute")
+        first_map = next((record for record in route_table
+                          if tuple(record["columns"]) != tuple(record["inverse_columns"])), None)
+        require(first_map is not None, "Negative control has a noninvolutive map")
+        require(product(tuple(first_map["columns"]), tuple(first_map["columns"])) != UNIT,
+                "Negative control: repeat of the forward source map does not restore")
+        pair_checks.append({
+            "reader_stage": s, "physical_level_before_service": t - 1, "service_stage": t,
+            "direct_paths": sum(map(len, direct)), "selected_paths": sum(map(len, middle)),
+            "distinct_middle_maps": len(route_table),
+            "middle_integer_census": dict(integer_census), "parts": part_invoices,
+            "query_invoice": bill, "triangle_prefix_bound": str(peak), "binary_height_bound": height,
+            "exact_prefix": exact_prefix,
+            "all_input_columns": 640, "unchanged_outside_fields": 416,
+            "dual_query_all_input_columns": 640,
+            "dual_triangle_prefix_bound": str(dual_peak), "dual_binary_height_bound": dual_height,
+            "dual_exact_prefix": exact_dual_prefix,
+            "ordered_factor_negative_control": "fails" if s else "stage zero is identity",
+            "wrong_inverse_map_negative_control": "fails",
+        })
+    require({(r["reader_stage"], r["service_stage"]) for r in pair_checks} ==
+            {(0, 1), (0, 2), (1, 2)}, "All three pairs")
+    output = {
+        "status": "PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL",
+        "checker_sha256": digest(Path(__file__).read_bytes()),
+        "producer_reuse_freeze_sha256": REUSE_PIN,
+        "producer_dual_freeze_sha256": DUAL_PIN,
+        "source_pins": PINS, "pivot_minor_determinant": str(vp_det),
+        "providers": provider_checks, "phase_checks": dict(phase_checks),
+        "H8_carriers": carrier_checks, "pairs": pair_checks,
+        "general_reader_example": general_reader_example(),
+        "producer_code_imported": False,
+        "complete_native_integration_checked": False,
+        "complete_supplier_claimed": False,
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(output, indent=2, sort_keys=True) + "\n").encode()
+    (args.output / "REVIEW-CHECKS.json").write_bytes(raw)
+    print(output["status"])
+    print(digest(raw))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/normal/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/normal/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..00610f175c
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/normal/REVIEW-CHECKS.json
@@ -0,0 +1,635 @@
+{
+  "H8_carriers": [
+    {
+      "port": 0,
+      "q": 11,
+      "translation": 15
+    },
+    {
+      "port": 27,
+      "q": 38,
+      "translation": 39
+    },
+    {
+      "port": 36,
+      "q": 146,
+      "translation": 147
+    },
+    {
+      "port": 111,
+      "q": 191,
+      "translation": 255
+    },
+    {
+      "port": 20,
+      "q": 161,
+      "translation": 163
+    },
+    {
+      "port": 7,
+      "q": 21,
+      "translation": 23
+    },
+    {
+      "port": 57,
+      "q": 56,
+      "translation": 57
+    },
+    {
+      "port": 46,
+      "q": 140,
+      "translation": 141
+    },
+    {
+      "port": 1,
+      "q": 19,
+      "translation": 23
+    },
+    {
+      "port": 3,
+      "q": 67,
+      "translation": 71
+    },
+    {
+      "port": 6,
+      "q": 13,
+      "translation": 15
+    },
+    {
+      "port": 8,
+      "q": 37,
+      "translation": 39
+    },
+    {
+      "port": 17,
+      "q": 81,
+      "translation": 83
+    },
+    {
+      "port": 18,
+      "q": 145,
+      "translation": 147
+    },
+    {
+      "port": 24,
+      "q": 385,
+      "translation": 387
+    },
+    {
+      "port": 23,
+      "q": 321,
+      "translation": 323
+    }
+  ],
+  "checker_sha256": "c1caa97a3929c3750e6e663c2d7429297a1e50e7a835264ee7ecde17c47f0b7e",
+  "complete_native_integration_checked": false,
+  "complete_supplier_claimed": false,
+  "general_reader_example": {
+    "E_is_singular": true,
+    "E_selected_block_is_nonzero": true,
+    "W_and_B_t_do_not_commute": true,
+    "arbitrary_input_columns": 6,
+    "plain_copy_negative_control": "fails"
+  },
+  "pairs": [
+    {
+      "all_input_columns": 640,
+      "binary_height_bound": 3,
+      "direct_paths": 3808,
+      "distinct_middle_maps": 216,
+      "dual_binary_height_bound": 3,
+      "dual_exact_prefix": {
+        "coefficient_binary_height": 3,
+        "coefficient_row_sum_peak": "43/2",
+        "height_witness": {
+          "coefficient": "1/8",
+          "event_index": 3160,
+          "origin": 112,
+          "route": [
+            3584,
+            3086,
+            2574,
+            1550,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256,
+            131072,
+            262144,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 0
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 1,
+            "-1/4": 8,
+            "-1/8": 30,
+            "1": 1,
+            "1/2": 4,
+            "1/4": 24,
+            "1/8": 50
+          },
+          "coefficient_terms": 118,
+          "event_index": 3253,
+          "target": 21
+        }
+      },
+      "dual_query_all_input_columns": 640,
+      "dual_triangle_prefix_bound": "53",
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "448",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 1185,
+          "origin": 0,
+          "route": [
+            1034,
+            1036,
+            1,
+            1030,
+            16,
+            32,
+            64,
+            128,
+            256,
+            512,
+            14,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            131072,
+            262144,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 148,
+            "-1/2": 198,
+            "-2": 17,
+            "-3/2": 14,
+            "1": 40,
+            "1/2": 186,
+            "2": 3,
+            "3/2": 2,
+            "4": 1
+          },
+          "coefficient_terms": 609,
+          "event_index": 1123,
+          "target": 112
+        }
+      },
+      "middle_integer_census": {
+        "-1": 456,
+        "1": 240
+      },
+      "ordered_factor_negative_control": "stage zero is identity",
+      "parts": [
+        {
+          "maps": 224,
+          "part": "old_complement",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "first_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 224,
+          "part": "current_code",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "second_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 1392,
+          "part": "middle",
+          "real_scalar": 5632
+        },
+        {
+          "maps": 224,
+          "part": "current_inverse",
+          "real_scalar": 1760
+        }
+      ],
+      "physical_level_before_service": 0,
+      "query_invoice": {
+        "maps": 2064,
+        "real_scalar": 11168
+      },
+      "reader_stage": 0,
+      "selected_paths": 696,
+      "service_stage": 1,
+      "triangle_prefix_bound": "972",
+      "unchanged_outside_fields": 416,
+      "wrong_inverse_map_negative_control": "fails"
+    },
+    {
+      "all_input_columns": 640,
+      "binary_height_bound": 3,
+      "direct_paths": 3808,
+      "distinct_middle_maps": 216,
+      "dual_binary_height_bound": 3,
+      "dual_exact_prefix": {
+        "coefficient_binary_height": 3,
+        "coefficient_row_sum_peak": "43/2",
+        "height_witness": {
+          "coefficient": "1/8",
+          "event_index": 3160,
+          "origin": 112,
+          "route": [
+            917504,
+            786446,
+            655374,
+            393230,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216,
+            512,
+            1024,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ],
+          "target": 0
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 1,
+            "-1/4": 8,
+            "-1/8": 30,
+            "1": 1,
+            "1/2": 4,
+            "1/4": 24,
+            "1/8": 50
+          },
+          "coefficient_terms": 118,
+          "event_index": 3253,
+          "target": 21
+        }
+      },
+      "dual_query_all_input_columns": 640,
+      "dual_triangle_prefix_bound": "53",
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "448",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 1185,
+          "origin": 0,
+          "route": [
+            262154,
+            262156,
+            1,
+            262150,
+            16,
+            32,
+            64,
+            128,
+            256,
+            512,
+            1024,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            131072,
+            14,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 148,
+            "-1/2": 198,
+            "-2": 17,
+            "-3/2": 14,
+            "1": 40,
+            "1/2": 186,
+            "2": 3,
+            "3/2": 2,
+            "4": 1
+          },
+          "coefficient_terms": 609,
+          "event_index": 1123,
+          "target": 112
+        }
+      },
+      "middle_integer_census": {
+        "-1": 456,
+        "1": 240
+      },
+      "ordered_factor_negative_control": "stage zero is identity",
+      "parts": [
+        {
+          "maps": 224,
+          "part": "old_complement",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "first_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 224,
+          "part": "current_code",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "second_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 1392,
+          "part": "middle",
+          "real_scalar": 5632
+        },
+        {
+          "maps": 224,
+          "part": "current_inverse",
+          "real_scalar": 1760
+        }
+      ],
+      "physical_level_before_service": 1,
+      "query_invoice": {
+        "maps": 2064,
+        "real_scalar": 11168
+      },
+      "reader_stage": 0,
+      "selected_paths": 696,
+      "service_stage": 2,
+      "triangle_prefix_bound": "972",
+      "unchanged_outside_fields": 416,
+      "wrong_inverse_map_negative_control": "fails"
+    },
+    {
+      "all_input_columns": 640,
+      "binary_height_bound": 3,
+      "direct_paths": 3808,
+      "distinct_middle_maps": 696,
+      "dual_binary_height_bound": 3,
+      "dual_exact_prefix": {
+        "coefficient_binary_height": 3,
+        "coefficient_row_sum_peak": "43/2",
+        "height_witness": {
+          "coefficient": "1/8",
+          "event_index": 3160,
+          "origin": 112,
+          "route": [
+            656384,
+            787456,
+            917504,
+            394240,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216,
+            512,
+            14,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ],
+          "target": 0
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 1,
+            "-1/4": 8,
+            "-1/8": 30,
+            "1": 1,
+            "1/2": 4,
+            "1/4": 24,
+            "1/8": 50
+          },
+          "coefficient_terms": 118,
+          "event_index": 3253,
+          "target": 21
+        }
+      },
+      "dual_query_all_input_columns": 640,
+      "dual_triangle_prefix_bound": "53",
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "448",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 1185,
+          "origin": 0,
+          "route": [
+            262154,
+            262153,
+            4,
+            262147,
+            16,
+            32,
+            64,
+            128,
+            256,
+            512,
+            11,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            131072,
+            1024,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 148,
+            "-1/2": 198,
+            "-2": 17,
+            "-3/2": 14,
+            "1": 40,
+            "1/2": 186,
+            "2": 3,
+            "3/2": 2,
+            "4": 1
+          },
+          "coefficient_terms": 609,
+          "event_index": 1123,
+          "target": 112
+        }
+      },
+      "middle_integer_census": {
+        "-1": 456,
+        "1": 240
+      },
+      "ordered_factor_negative_control": "fails",
+      "parts": [
+        {
+          "maps": 224,
+          "part": "old_complement",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "first_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 224,
+          "part": "current_code",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "second_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 1392,
+          "part": "middle",
+          "real_scalar": 5632
+        },
+        {
+          "maps": 224,
+          "part": "current_inverse",
+          "real_scalar": 1760
+        }
+      ],
+      "physical_level_before_service": 1,
+      "query_invoice": {
+        "maps": 2064,
+        "real_scalar": 11168
+      },
+      "reader_stage": 1,
+      "selected_paths": 696,
+      "service_stage": 2,
+      "triangle_prefix_bound": "972",
+      "unchanged_outside_fields": 416,
+      "wrong_inverse_map_negative_control": "fails"
+    }
+  ],
+  "phase_checks": {
+    "adjacent_full_to_Q": 448,
+    "adjacent_hole_to_I": 224,
+    "full_views": 672
+  },
+  "pivot_minor_determinant": "16",
+  "producer_code_imported": false,
+  "producer_dual_freeze_sha256": "92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455",
+  "producer_reuse_freeze_sha256": "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf",
+  "providers": {
+    "base": {
+      "deletion": {
+        "removed_native": 128,
+        "removed_scalar": 122,
+        "retained_scalar": 6456
+      },
+      "last_source_event": 2638,
+      "prospective_native_mass": 1792,
+      "prospective_native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      }
+    },
+    "extra": {
+      "deletion": {
+        "removed_native": 128,
+        "removed_scalar": 122,
+        "retained_scalar": 6456
+      },
+      "last_source_event": 2638,
+      "prospective_native_mass": 1792,
+      "prospective_native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      }
+    }
+  },
+  "source_pins": {
+    "capture": [
+      "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json",
+      "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+    ],
+    "native": [
+      "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+      "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+    ],
+    "views": [
+      "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json",
+      "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"
+    ]
+  },
+  "status": "PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/optimized/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/optimized/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..00610f175c
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/optimized/REVIEW-CHECKS.json
@@ -0,0 +1,635 @@
+{
+  "H8_carriers": [
+    {
+      "port": 0,
+      "q": 11,
+      "translation": 15
+    },
+    {
+      "port": 27,
+      "q": 38,
+      "translation": 39
+    },
+    {
+      "port": 36,
+      "q": 146,
+      "translation": 147
+    },
+    {
+      "port": 111,
+      "q": 191,
+      "translation": 255
+    },
+    {
+      "port": 20,
+      "q": 161,
+      "translation": 163
+    },
+    {
+      "port": 7,
+      "q": 21,
+      "translation": 23
+    },
+    {
+      "port": 57,
+      "q": 56,
+      "translation": 57
+    },
+    {
+      "port": 46,
+      "q": 140,
+      "translation": 141
+    },
+    {
+      "port": 1,
+      "q": 19,
+      "translation": 23
+    },
+    {
+      "port": 3,
+      "q": 67,
+      "translation": 71
+    },
+    {
+      "port": 6,
+      "q": 13,
+      "translation": 15
+    },
+    {
+      "port": 8,
+      "q": 37,
+      "translation": 39
+    },
+    {
+      "port": 17,
+      "q": 81,
+      "translation": 83
+    },
+    {
+      "port": 18,
+      "q": 145,
+      "translation": 147
+    },
+    {
+      "port": 24,
+      "q": 385,
+      "translation": 387
+    },
+    {
+      "port": 23,
+      "q": 321,
+      "translation": 323
+    }
+  ],
+  "checker_sha256": "c1caa97a3929c3750e6e663c2d7429297a1e50e7a835264ee7ecde17c47f0b7e",
+  "complete_native_integration_checked": false,
+  "complete_supplier_claimed": false,
+  "general_reader_example": {
+    "E_is_singular": true,
+    "E_selected_block_is_nonzero": true,
+    "W_and_B_t_do_not_commute": true,
+    "arbitrary_input_columns": 6,
+    "plain_copy_negative_control": "fails"
+  },
+  "pairs": [
+    {
+      "all_input_columns": 640,
+      "binary_height_bound": 3,
+      "direct_paths": 3808,
+      "distinct_middle_maps": 216,
+      "dual_binary_height_bound": 3,
+      "dual_exact_prefix": {
+        "coefficient_binary_height": 3,
+        "coefficient_row_sum_peak": "43/2",
+        "height_witness": {
+          "coefficient": "1/8",
+          "event_index": 3160,
+          "origin": 112,
+          "route": [
+            3584,
+            3086,
+            2574,
+            1550,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256,
+            131072,
+            262144,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 0
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 1,
+            "-1/4": 8,
+            "-1/8": 30,
+            "1": 1,
+            "1/2": 4,
+            "1/4": 24,
+            "1/8": 50
+          },
+          "coefficient_terms": 118,
+          "event_index": 3253,
+          "target": 21
+        }
+      },
+      "dual_query_all_input_columns": 640,
+      "dual_triangle_prefix_bound": "53",
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "448",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 1185,
+          "origin": 0,
+          "route": [
+            1034,
+            1036,
+            1,
+            1030,
+            16,
+            32,
+            64,
+            128,
+            256,
+            512,
+            14,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            131072,
+            262144,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 148,
+            "-1/2": 198,
+            "-2": 17,
+            "-3/2": 14,
+            "1": 40,
+            "1/2": 186,
+            "2": 3,
+            "3/2": 2,
+            "4": 1
+          },
+          "coefficient_terms": 609,
+          "event_index": 1123,
+          "target": 112
+        }
+      },
+      "middle_integer_census": {
+        "-1": 456,
+        "1": 240
+      },
+      "ordered_factor_negative_control": "stage zero is identity",
+      "parts": [
+        {
+          "maps": 224,
+          "part": "old_complement",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "first_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 224,
+          "part": "current_code",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "second_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 1392,
+          "part": "middle",
+          "real_scalar": 5632
+        },
+        {
+          "maps": 224,
+          "part": "current_inverse",
+          "real_scalar": 1760
+        }
+      ],
+      "physical_level_before_service": 0,
+      "query_invoice": {
+        "maps": 2064,
+        "real_scalar": 11168
+      },
+      "reader_stage": 0,
+      "selected_paths": 696,
+      "service_stage": 1,
+      "triangle_prefix_bound": "972",
+      "unchanged_outside_fields": 416,
+      "wrong_inverse_map_negative_control": "fails"
+    },
+    {
+      "all_input_columns": 640,
+      "binary_height_bound": 3,
+      "direct_paths": 3808,
+      "distinct_middle_maps": 216,
+      "dual_binary_height_bound": 3,
+      "dual_exact_prefix": {
+        "coefficient_binary_height": 3,
+        "coefficient_row_sum_peak": "43/2",
+        "height_witness": {
+          "coefficient": "1/8",
+          "event_index": 3160,
+          "origin": 112,
+          "route": [
+            917504,
+            786446,
+            655374,
+            393230,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216,
+            512,
+            1024,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ],
+          "target": 0
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 1,
+            "-1/4": 8,
+            "-1/8": 30,
+            "1": 1,
+            "1/2": 4,
+            "1/4": 24,
+            "1/8": 50
+          },
+          "coefficient_terms": 118,
+          "event_index": 3253,
+          "target": 21
+        }
+      },
+      "dual_query_all_input_columns": 640,
+      "dual_triangle_prefix_bound": "53",
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "448",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 1185,
+          "origin": 0,
+          "route": [
+            262154,
+            262156,
+            1,
+            262150,
+            16,
+            32,
+            64,
+            128,
+            256,
+            512,
+            1024,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            131072,
+            14,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 148,
+            "-1/2": 198,
+            "-2": 17,
+            "-3/2": 14,
+            "1": 40,
+            "1/2": 186,
+            "2": 3,
+            "3/2": 2,
+            "4": 1
+          },
+          "coefficient_terms": 609,
+          "event_index": 1123,
+          "target": 112
+        }
+      },
+      "middle_integer_census": {
+        "-1": 456,
+        "1": 240
+      },
+      "ordered_factor_negative_control": "stage zero is identity",
+      "parts": [
+        {
+          "maps": 224,
+          "part": "old_complement",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "first_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 224,
+          "part": "current_code",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "second_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 1392,
+          "part": "middle",
+          "real_scalar": 5632
+        },
+        {
+          "maps": 224,
+          "part": "current_inverse",
+          "real_scalar": 1760
+        }
+      ],
+      "physical_level_before_service": 1,
+      "query_invoice": {
+        "maps": 2064,
+        "real_scalar": 11168
+      },
+      "reader_stage": 0,
+      "selected_paths": 696,
+      "service_stage": 2,
+      "triangle_prefix_bound": "972",
+      "unchanged_outside_fields": 416,
+      "wrong_inverse_map_negative_control": "fails"
+    },
+    {
+      "all_input_columns": 640,
+      "binary_height_bound": 3,
+      "direct_paths": 3808,
+      "distinct_middle_maps": 696,
+      "dual_binary_height_bound": 3,
+      "dual_exact_prefix": {
+        "coefficient_binary_height": 3,
+        "coefficient_row_sum_peak": "43/2",
+        "height_witness": {
+          "coefficient": "1/8",
+          "event_index": 3160,
+          "origin": 112,
+          "route": [
+            656384,
+            787456,
+            917504,
+            394240,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216,
+            512,
+            14,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ],
+          "target": 0
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 1,
+            "-1/4": 8,
+            "-1/8": 30,
+            "1": 1,
+            "1/2": 4,
+            "1/4": 24,
+            "1/8": 50
+          },
+          "coefficient_terms": 118,
+          "event_index": 3253,
+          "target": 21
+        }
+      },
+      "dual_query_all_input_columns": 640,
+      "dual_triangle_prefix_bound": "53",
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "448",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 1185,
+          "origin": 0,
+          "route": [
+            262154,
+            262153,
+            4,
+            262147,
+            16,
+            32,
+            64,
+            128,
+            256,
+            512,
+            11,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            131072,
+            1024,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 148,
+            "-1/2": 198,
+            "-2": 17,
+            "-3/2": 14,
+            "1": 40,
+            "1/2": 186,
+            "2": 3,
+            "3/2": 2,
+            "4": 1
+          },
+          "coefficient_terms": 609,
+          "event_index": 1123,
+          "target": 112
+        }
+      },
+      "middle_integer_census": {
+        "-1": 456,
+        "1": 240
+      },
+      "ordered_factor_negative_control": "fails",
+      "parts": [
+        {
+          "maps": 224,
+          "part": "old_complement",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "first_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 224,
+          "part": "current_code",
+          "real_scalar": 1760
+        },
+        {
+          "maps": 0,
+          "part": "second_copy",
+          "real_scalar": 128
+        },
+        {
+          "maps": 1392,
+          "part": "middle",
+          "real_scalar": 5632
+        },
+        {
+          "maps": 224,
+          "part": "current_inverse",
+          "real_scalar": 1760
+        }
+      ],
+      "physical_level_before_service": 1,
+      "query_invoice": {
+        "maps": 2064,
+        "real_scalar": 11168
+      },
+      "reader_stage": 1,
+      "selected_paths": 696,
+      "service_stage": 2,
+      "triangle_prefix_bound": "972",
+      "unchanged_outside_fields": 416,
+      "wrong_inverse_map_negative_control": "fails"
+    }
+  ],
+  "phase_checks": {
+    "adjacent_full_to_Q": 448,
+    "adjacent_hole_to_I": 224,
+    "full_views": 672
+  },
+  "pivot_minor_determinant": "16",
+  "producer_code_imported": false,
+  "producer_dual_freeze_sha256": "92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455",
+  "producer_reuse_freeze_sha256": "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf",
+  "providers": {
+    "base": {
+      "deletion": {
+        "removed_native": 128,
+        "removed_scalar": 122,
+        "retained_scalar": 6456
+      },
+      "last_source_event": 2638,
+      "prospective_native_mass": 1792,
+      "prospective_native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      }
+    },
+    "extra": {
+      "deletion": {
+        "removed_native": 128,
+        "removed_scalar": 122,
+        "retained_scalar": 6456
+      },
+      "last_source_event": 2638,
+      "prospective_native_mass": 1792,
+      "prospective_native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      }
+    }
+  },
+  "source_pins": {
+    "capture": [
+      "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json",
+      "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+    ],
+    "native": [
+      "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+      "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+    ],
+    "views": [
+      "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json",
+      "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"
+    ]
+  },
+  "status": "PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..467114e5d1
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/FREEZE.json
@@ -0,0 +1,13 @@
+{
+  "dispatcher_freeze_sha256": "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331",
+  "files": {
+    "REPRODUCTION.json": "939a9fcd92e0d14f7a5aac18c32a514451535ecfb4ab05b5f84f14d104fe2f3d",
+    "REVIEW.md": "4246f5c4b6113dbf045e4f6ef2b8b874551447ce1653eeb4f34e261facf1fc94",
+    "check_service.py": "0f34e7a3cebebdf4d43226104079cf0d4038fcdeac9ae3ab5165276b9df61974",
+    "normal/REVIEW-CHECKS.json": "11219ad28c4fb0d9eb5f485998bd219da228554ee9c78be153911de19873ab42",
+    "optimized/REVIEW-CHECKS.json": "11219ad28c4fb0d9eb5f485998bd219da228554ee9c78be153911de19873ab42"
+  },
+  "schema": "independent-six-fixed-reader-service-review-v1",
+  "scope": "Six exact forward data services under the inherited helper contract. No complete supplier claim.",
+  "service_freeze_sha256": "177d6ae2f3971deac98e3385dda32e82ddabf0c8176e88ac1255323aed8d688f"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..bfa544dedf
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/REPRODUCTION.json
@@ -0,0 +1,11 @@
+{
+  "commands": [
+    "python3 check_service.py --output normal",
+    "python3 -O check_service.py --output optimized"
+  ],
+  "normal_optimized_byte_equal": true,
+  "python": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
+  "receipt_sha256": "11219ad28c4fb0d9eb5f485998bd219da228554ee9c78be153911de19873ab42",
+  "schema": "independent-fixed-reader-service-reproduction-v1",
+  "status": "PASS_INDEPENDENT_SIX_FIXED_READER_D25_SERVICES"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..61a8f56ef1
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/REVIEW.md
@@ -0,0 +1,199 @@
+# Independent review of the six joined D25 services
+
+Both providers pass for all three reader/service pairs
+\((s,t)=(0,1),(0,2),(1,2)\). The joined word has the claimed complete
+data map on the regular D25 cover. No material defect was found.
+
+Each service has 17,624 real scalar primitives, native rank 1,792,
+and a bound of 5,776 monomial map calls. These are component counts.
+The inherited helper host, finite map cost, recursive precision, and
+complete supplier remain separate obligations.
+
+## Inputs and independent method
+
+The dispatcher freeze has SHA-256
+`bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331`.
+The joined-service freeze has SHA-256
+`177d6ae2f3971deac98e3385dda32e82ddabf0c8176e88ac1255323aed8d688f`.
+The decompressed joined payload has SHA-256
+`88d25925705e6657656afb727430ce0d541c5e657426166363694d8b66180d13`.
+
+The separate independent query review has freeze
+`d8d782ecc13fdd2d26380fc4b047fc6d6781417ec694fdd3dea910dce04c2e2a`.
+This review imports only that pinned independent mathematical helper.
+It imports no producer code.
+
+The local native phase review has freeze
+`cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c`.
+That review checks the exact line-entry native recipes and endpoint
+adapters, including global phase. This review reads its proof and
+receipt, rechecks all 35 consumed file hashes, and compares every
+inherited component with the new prefix. It does not rerun the
+4,194,304 spatial coefficients from that earlier phase check.
+
+The new checker validates all source freezes and source payloads. It
+replays the native prefix with exact fractions and a complete frame
+ledger. It checks the DATA phase equations with a separate Z4
+representation, reconstructs the actual owner routes, and then replays
+the bundled query on the routed prefix outputs.
+
+## The native prefix is an exact reviewed component
+
+For each provider, the new prefix has exactly the first 2,406 events
+of the independently reviewed line-entry word. Its frame table, native
+recipe table, start and final frames, endpoint adapters, and retained
+original indices are unchanged.
+
+There are 2,390 retained core events, followed by sixteen positive H8
+carrier events. There is no old same-reader query in this prefix.
+The selected input records have the same positive intrinsic line and
+input adapter as their source port. The 128 input adapters consist of
+112 source adapters and sixteen selected target adapters. The 96
+output adapters act only on ordinary targets.
+
+The independent replay gives the exact local content map:
+
+\[
+x'=x,\qquad z'_P=z_P,\qquad
+y'_R=(y+Ex)_R.
+\]
+
+All 640 input columns are independent. The 416 outside fields remain
+fixed. The frame ledger ends with FULL source and selected target
+fields; ordinary targets retain their hole frames. The native phase
+dependency converts this content statement into the stated physical
+local map.
+
+All scalar additions have equal source and target frames. Every
+native transition is a positive nested-frame transition of the
+declared rank. The native profile is
+
+\[
+1392H_1+64H_2+48H_3+16H_8.
+\]
+
+It has 1,520 children, native rank 1,792, and scalar price 6,456.
+The exact content coefficient row-sum peak is 22, with binary
+denominator height one.
+
+## Physical stage progress and the complete cover barrier
+
+The physical input before service t has completed level \(t-1\).
+The reader label s does not alter that level. Pair \((0,2)\) therefore
+uses a stage-zero reader that has already reached physical level one.
+
+For each stage t in \(\{1,2\}\), the checker binds all 224 input and
+224 output DATA maps to the actual D25 records. It reconstructs each
+route \(\rho_{t,p}\) from the native q and port chart. The route is
+an orthogonal involution and fixes q and all future axes.
+
+All 448 input and 448 output Z4 phase equations pass. The equations
+include the common exterior, the selected positive intrinsic line,
+the ordinary hole, and the exact translation order. Using the entry
+translation on the wrong side of its route fails all 448 input checks.
+
+At the global output of the native prefix, X and selected Y are FULL.
+The ordinary Y fields are in their hole frames. The query's current
+views are exactly the actual DATA exit views. Every literal query
+map also passes its own FULL conjugation and inverse-phase checks.
+
+For each field, right multiplication by \(\rho_{t,p}\) permutes the
+regular cover. Thus distinct body invocations have disjoint data
+records for that field. The body computations can be completed under
+the inherited helper contract. The complete cover barrier is required
+before the global query; a per-body query cannot replace that barrier
+without a separate source-availability proof.
+
+This data partition does not construct a helper host. Each native
+body still requires the inherited typed helper supply and restoration
+contract. The review does not infer that contract from the data
+permutation.
+
+## Exact global map
+
+Let \(G=\operatorname{diag}(I_P,q_R)\). Let \(F_\ell\) be FULL on the
+first \(9+8\ell\) axes. Let \(E_t\) include the actual current owner
+routes and let \(L_s\) be the retained old reader. Define
+
+\[
+(A_{s,t})_P=L_sE_t,\qquad
+(A_{s,t})_R=(E_t)_R.
+\]
+
+The complete service is
+
+\[
+(F_{t-1}x,\ F_{t-1}Gw)
+\longmapsto
+(F_tx,\ F_tG(w+A_{s,t}x)).
+\]
+
+The bank w is arbitrary. In particular, its selected records do not
+have to be zero or depend on x. If \(w=C_sy\), then the selected
+outputs are \(L_s(y+E_tx)\) and the ordinary outputs are
+\((y+E_tx)_R\). The normalized row code is a unit, so this
+interpretation imposes no restriction on w.
+
+The checker replays the literal query from the complete routed prefix
+state. It keeps a coefficient for each full input-field/owner-route
+pair. It checks every one of the 640 independent input columns and
+all six provider/stage records. It does not replace different routed
+responses with one scalar response.
+
+The query restores the X array at its FULL cut and does not change
+ordinary Y. Across the complete service, the intended X content is
+preserved while its physical frame advances from \(F_{t-1}\) to \(F_t\).
+All 416 outside fields keep their arbitrary input contents.
+
+## Price and limits
+
+The separate late query costs 11,168 scalar primitives and 2,064
+monomial map calls. Its exact content coefficient bound is 448 with
+binary denominator height two. This agrees with the independent
+query review.
+
+The complete monomial call bound is:
+
+| Part | Calls |
+| --- | ---: |
+| DATA entry and exit | 448 |
+| Local endpoint adapters | 224 |
+| Two side maps per native child | 3,040 |
+| Literal late query | 2,064 |
+| Total | 5,776 |
+
+The complete scalar count is \(6456+11168=17624\). No extra field or
+odd division is introduced by this join. Identity maps remain counted
+when they occur in the literal instruction stock.
+
+These bounds concern the emitted content maps. They do not give
+internal native-child bounds, primitive arithmetic guards, recursive
+parking costs, a finite price for each address map, or a complete
+supplier. The review does not claim an improvement to the complete
+kappa calculation.
+
+The earlier typed inverse-adjoint theorem now has a verified forward
+data service to which it can apply. This review does not emit or
+verify a separately packaged full backward service.
+
+## Reproduction and credit
+
+Run from this directory:
+
+```text
+python3 check_service.py --output normal
+python3 -O check_service.py --output optimized
+```
+
+Both runs must print `PASS_INDEPENDENT_SIX_FIXED_READER_D25_SERVICES`,
+and the two `REVIEW-CHECKS.json` files must be byte equal.
+
+The bridge-access lane supplied the D25 dispatcher and reader query.
+The new-core-transfer lane supplied the native prefix and joined
+payload. The new-native-recipes lane supplied the independent native
+phase review. The controller lane supplied the row capture. This
+review supplies the independent join, phase, owner-route, arbitrary
+input, and invoice checks. AI agents prepared these local records.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/check_service.py b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/check_service.py
new file mode 100644
index 0000000000..08e67399dc
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/check_service.py
@@ -0,0 +1,378 @@
+"""Review the complete D25 service from pinned local components."""
+
+import argparse
+from collections import Counter
+from fractions import Fraction as F
+import gzip
+from hashlib import sha256
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+QUERY_REVIEW = HERE.parent / "fixed-reader-reuse-review-20261020"
+DISPATCH = LANES / "bridge-access-20261017/row-capture-access-20261020"
+CORE = LANES / "new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020"
+PHASE_REVIEW = LANES / "new-native-recipes-20261017/line-entry-reuse-review-20261020"
+FREEZES = {
+    "independent_query": (QUERY_REVIEW / "FREEZE.json",
+                          "d8d782ecc13fdd2d26380fc4b047fc6d6781417ec694fdd3dea910dce04c2e2a"),
+    "dispatcher": (DISPATCH / "INTEGRATION-FREEZE.json",
+                   "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331"),
+    "service": (CORE / "SERVICE-FREEZE.json",
+                "177d6ae2f3971deac98e3385dda32e82ddabf0c8176e88ac1255323aed8d688f"),
+    "native_phase": (PHASE_REVIEW / "FREEZE.json",
+                     "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"),
+    "prefix": (CORE / "PREFIX-FREEZE.json",
+               "fc3cef0e499e5bc85c25bb0fc88f5ecd12e44b66799e3d793dac37de8d88d26e"),
+    "query": (CORE / "QUERY-FREEZE.json",
+              "f111a90f7403f93494e9d1f83ae35dbf7dd72eddc8c9f8bf730d677b4a31402d"),
+}
+PAYLOADS = {
+    "dispatcher": (DISPATCH / "integration-v2-normal/DISPATCHER.json",
+                   "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24"),
+    "service": (CORE / "service-normal/FIXED-READER-SERVICES.json.gz",
+                "88d25925705e6657656afb727430ce0d541c5e657426166363694d8b66180d13"),
+    "prefix": (CORE / "prefix-normal/CARRIER-PREFIX.json.gz",
+               "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e"),
+    "query": (CORE / "query-normal/ROUTED-QUERY.json.gz",
+              "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a"),
+    "line_entry": (
+        CORE.parent / "row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz",
+        "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110"),
+}
+
+
+def need(test, label):
+    if not test:
+        raise ValueError(label)
+
+
+def digest(raw):
+    return sha256(raw).hexdigest()
+
+
+def read(path, pin, decode_gzip=False):
+    raw = path.read_bytes()
+    if decode_gzip:
+        raw = gzip.decompress(raw)
+    need(digest(raw) == pin, "Source pin: " + str(path))
+    return raw
+
+
+def validate_freeze(path, pin):
+    value = json.loads(read(path, pin))
+    for name, expected in value["files"].items():
+        read(path.parent / name, expected)
+    return value
+
+
+validate_freeze(*FREEZES["independent_query"])
+spec = importlib.util.spec_from_file_location("independent_reuse_math", QUERY_REVIEW / "check_review.py")
+r = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(r)
+
+
+def binary_rank(vectors):
+    pivots = {}
+    for vector in vectors:
+        while vector:
+            bit = vector.bit_length() - 1
+            if bit not in pivots:
+                pivots[bit] = vector
+                break
+            vector ^= pivots[bit]
+    return len(pivots)
+
+
+def prefix_replay(word, response):
+    state = r.eye(640)
+    live = list(word["start"])
+    profile = Counter()
+    price = 0
+    peak = F(1)
+    height = 0
+    for index, event in enumerate(word["events"]):
+        if event[0] == "native":
+            _, target, old, new, rank, key = event
+            need(live[target] == old, "Prefix native frame")
+            left, right = word["frames"][old], word["frames"][new]
+            need(binary_rank(left) == len(left) and binary_rank(right) == len(right)
+                 and binary_rank(left + right) == len(right)
+                 and len(right) - len(left) == rank, "Positive nested native rank")
+            need(word["native_recipes"][key]["rank"] == rank, "Bound native recipe")
+            live[target] = new
+            profile[rank] += 1
+        else:
+            need(event[0] == "scalar", "Prefix event grammar")
+            _, (op, target, origin, coefficient), frame = event
+            value = F(coefficient)
+            need(live[target] == frame, "Prefix scalar target frame")
+            if op == "scale":
+                state[target] = {j: value * v for j, v in state[target].items()}
+            else:
+                need(op == "add" and live[origin] == frame and origin != target,
+                     "Prefix scalar source frame")
+                for j, v in state[origin].items():
+                    r.put(state[target], j, value * v)
+            price += r.real_price(op, value)
+            peak = max(peak, sum(abs(v) for v in state[target].values()))
+            height = max(height, max((v.denominator.bit_length() - 1
+                                      for v in state[target].values()), default=0))
+        need(target < 224, "No event writes an outside helper")
+        if index == 2389:
+            need(all(live[p] == 1 for p in range(112)), "The complete source cut")
+    expected = r.eye(640)
+    for p in range(112):
+        if p not in r.PSET:
+            for j, value in response[p].items():
+                r.put(expected[112 + p], j, value)
+    need(state == expected, "Independent complete prefix map on 640 input columns")
+    need(live == word["final"], "Complete prefix frame ledger")
+    need(all(live[p] == 1 for p in range(112))
+         and all(live[112 + p] == 1 for p in r.PIVOTS), "All query fields are FULL")
+    need(price == 6456 and profile == {1: 1392, 2: 64, 3: 48, 8: 16}, "Prefix price")
+    need(peak == 22 and height == 1, "Prefix content bounds")
+    return {"input_columns": 640, "restored_outside_fields": 416,
+            "native_profile": dict(profile), "native_mass": sum(k * v for k, v in profile.items()),
+            "native_children": sum(profile.values()), "scalar_primitives": price,
+            "content_row_sum_peak": str(peak), "content_binary_height": height}
+
+
+def query_replay(word, initial):
+    state = [dict(row) for row in initial]
+    scalar, maps = 0, 0
+    peak = max(sum(abs(v) for v in row.values()) for row in state)
+    height = max(v.denominator.bit_length() - 1 for row in state for v in row.values())
+    for event in word["events"]:
+        if event[0] == "map":
+            _, target, map_index = event
+            a = tuple(word["maps"][map_index]["columns"])
+            state[target] = {(j, r.product(a, b)): v for (j, b), v in state[target].items()}
+            maps += 1
+        else:
+            need(event[0] == "scalar", "Query event grammar")
+            _, op, target, origin, coefficient = event
+            value = F(coefficient)
+            scalar += r.real_price(op, value)
+            if op == "scale":
+                state[target] = {j: value * v for j, v in state[target].items()}
+            else:
+                need(op == "add" and origin != target, "Query ADD")
+                need(origin < 112 or origin - 112 in r.PSET, "No ordinary Y source")
+                for key, v in state[origin].items():
+                    r.put(state[target], key, value * v)
+            peak = max(peak, sum(abs(v) for v in state[target].values()))
+            height = max(height, max((v.denominator.bit_length() - 1
+                                      for v in state[target].values()), default=0))
+        need(target < 112 or target - 112 in r.PSET, "Only FULL query fields are changed")
+    need(scalar == 11168 and maps == 2064, "Literal query price")
+    return state, {"scalar_primitives": scalar, "map_calls": maps,
+                   "content_row_sum_peak": str(peak), "content_binary_height": height}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "normal")
+    args = parser.parse_args()
+    for path, pin in FREEZES.values():
+        validate_freeze(path, pin)
+    data = {key: json.loads(read(path, pin, path.suffix == ".gz"))
+            for key, (path, pin) in PAYLOADS.items()}
+    dispatcher, service, prefix, query, old = (data[key] for key in
+                                              ("dispatcher", "service", "prefix", "query", "line_entry"))
+    for path, pin in dispatcher["source_pins"].values():
+        read(LANES / path, pin, path.endswith(".gz"))
+    phase_inputs = json.loads((PHASE_REVIEW / "normal/INPUTS.json").read_bytes())
+    for path, pins in phase_inputs.items():
+        raw = read(LANES / path, pins["sha256"])
+        if "decompressed_sha256" in pins:
+            need(digest(gzip.decompress(raw)) == pins["decompressed_sha256"], "Phase input payload")
+    old_path = str(PAYLOADS["line_entry"][0].relative_to(LANES))
+    need(phase_inputs[old_path]["decompressed_sha256"] == PAYLOADS["line_entry"][1],
+         "The inherited phase review binds this exact line-entry word")
+    need(service["native_prefixes"] == prefix["providers"] == query["native_prefixes"],
+         "Exact native bundle")
+    need(service["queries"] == query["queries"], "Exact query bundle")
+    need(service["services"] == dispatcher["invocations"]
+         and service["stage_views"] == dispatcher["stage_views"]
+         and service["contract"] == dispatcher["contract"]
+         and service["owner_contract"] == dispatcher["owner_contract"], "Exact dispatcher bundle")
+    need(tuple(service["selected_ports"]) == tuple(prefix["selected_ports"]) == r.PIVOTS,
+         "Unchanged selected fields")
+    source = {key: json.loads(read(LANES / path, pin))
+              for key, (path, pin) in r.PINS.items() if key in ("capture", "views")}
+    capture, views = source["capture"], source["views"]
+    response = r.sparse(prefix["response"])
+    need(response == r.sparse(capture["response"]) and prefix["ports"] == old["ports"],
+         "The actual response and port order")
+    reader = r.sparse(capture["centre_reader"])
+    views_by_id = {(v["stage"], v["port"]): v for v in views["entries"]}
+    source_query = json.loads((DISPATCH / "reuse-normal/REUSE-PROGRAM.json").read_bytes())
+    prefix_reports = {}
+    for name, word in prefix["providers"].items():
+        inherited = old["providers"][name]
+        need(word["events"] == inherited["events"][:2406], "Exact reviewed native prefix")
+        need(word["stage_ranges"] == {
+            "precode": [0, 0], "retained_core": [0, 2390], "selected_line_progress": [2390, 2406]},
+            "The prefix has no local late query")
+        for key in ("start", "final", "frames", "native_recipes", "input_views",
+                    "output_views", "retained_original_event_indices"):
+            need(word[key] == inherited[key], "Inherited phase or frame bytes: " + key)
+        need(len(word["input_views"]) == 128 and len(word["output_views"]) == 96,
+             "Endpoint adapter counts")
+        need({v["field"] for v in word["input_views"]} ==
+             set(range(112)) | {112 + p for p in r.PIVOTS}, "Every input adapter field")
+        need({v["port"] for v in word["output_views"]} == set(range(112)) - r.PSET,
+             "Only ordinary output adapters")
+        prefix_reports[name] = prefix_replay(word, response)
+    routes = {(s, p): r.route(prefix["ports"][p], s) for s in range(3) for p in range(112)}
+    phase_count = Counter()
+    wrong_entry = 0
+    for stage in service["stage_views"]:
+        t = stage["service_stage"]
+        need(t in (1, 2) and stage["physical_input_level"] == t - 1
+             and stage["physical_output_level"] == t, "Adjacent physical stage")
+        need(stage["common_exterior_axes"] == list(r.UNIT[9:9 + 8 * t]), "Common exterior")
+        entries = {v["field"]: v for v in stage["DATA_entry"]}
+        exits = {v["field"]: v for v in stage["DATA_exit"]}
+        need(len(stage["DATA_entry"]) == len(stage["DATA_exit"]) == 224
+             and set(entries) == set(exits) == set(range(224)), "All DATA fields")
+        for field in range(224):
+            p = field % 112
+            side = "X" if field < 112 else "Y"
+            q = prefix["ports"][p]
+            rho = routes[t, p]
+            actual = views_by_id[t, p]
+            align = actual["literal_stage_alignment"]
+            entry, out = entries[field], exits[field]
+            full = side == "X" or p in r.PSET
+            need(tuple(entry["route_columns"]) == tuple(out["route_columns"]) ==
+                 tuple(actual["route_columns"]) == rho, "The literal DATA route")
+            need(entry["side"] == out["side"] == side
+                 and entry["port"] == out["port"] == p, "The boundary field binding")
+            need(entry["translation_before_route"] == align["entry_" + side]
+                 and entry["translation_after_route"] == r.apply(rho, align["entry_" + side]),
+                 "The literal input translation order")
+            exit_key = "exit_X" if full else "exit_Y"
+            need(out["literal_translation_key"] == exit_key
+                 and out["translation_after_route"] == align[exit_key], "The literal output translation")
+            before = r.full_phase(t - 1, rho)
+            if not full:
+                before = r.add_phase(before, r.line_phase(q, -1))
+            obtained = r.add_phase(before, r.line_phase(entry["translation_after_route"], 2))
+            expected = r.sum_phase((x, 1) for x in r.UNIT[9:9 + 8 * t])
+            if full:
+                expected = r.add_phase(expected, r.line_phase(q, 1))
+            need(obtained == expected and entry["intrinsic_input"] == ("Q_p" if full else "I"),
+                 "Exact input Z4 equation")
+            wrong_entry += r.add_phase(before, r.line_phase(entry["translation_before_route"], 2)) != expected
+            after = r.full_phase(t, rho)
+            expected_out = r.full_phase(t)
+            if not full:
+                after = r.add_phase(after, r.line_phase(q, -1))
+                expected_out = r.add_phase(expected_out, r.line_phase(q, -1))
+            need(r.add_phase(after, r.line_phase(out["translation_after_route"], 2)) == expected_out
+                 and out["global_output"] == ("FULL" if full else "FULL*q_p"), "Exact output Z4 equation")
+            phase_count["entry"] += 1
+            phase_count["exit"] += 1
+    need(phase_count == {"entry": 448, "exit": 448} and wrong_entry > 0, "Boundary completeness and control")
+    query_reports = {}
+    for key, word in service["queries"].items():
+        s, t = word["reader_stage"], word["service_stage"]
+        need(key == f"{s}:{t}", "Literal query labels")
+        for view in word["maps"]:
+            a, ai = tuple(view["columns"]), tuple(view["inverse_columns"])
+            need(r.product(a, ai) == r.product(ai, a) == r.UNIT
+                 and ai == r.transpose(a), "Literal query map inverse")
+            need(a[9 + 8 * t:] == r.UNIT[9 + 8 * t:], "No future query axis")
+            delta = r.phase_translation(r.add_phase(r.full_phase(t), r.minus_phase(r.full_phase(t, a))))
+            need(view["translation"] == delta and view["inverse_translation"] == r.apply(ai, delta),
+                 "Every literal query map phase")
+        pair = next(pair for pair in source_query["pairs"]
+                    if (pair["reader_stage"], pair["service_stage"]) == (s, t))
+        current = [{"port": p, "route_columns": list(routes[t, p]),
+                    "translation": views_by_id[t, p]["literal_stage_alignment"]["exit_X"]}
+                   for p in range(112)]
+        need(pair["current_code_views"] == current, "The query uses the actual DATA output chart")
+        et = r.routed_matrix(response, range(112), t, routes)
+        ls = r.routed_matrix(reader, r.PIVOTS, s, routes)
+        desired = r.multiply_routed(ls, et)
+        initial = [{(i, r.UNIT): F(1)} for i in range(640)]
+        for p in range(112):
+            if p not in r.PSET:
+                for term, value in et[p].items():
+                    r.put(initial[112 + p], term, value)
+        expected = [dict(row) for row in initial]
+        for p, row in zip(r.PIVOTS, desired):
+            for term, value in row.items():
+                r.put(expected[112 + p], term, value)
+        result, report = query_replay(word, initial)
+        need(result == expected, "The complete service map on all 640 input columns")
+        need(report["content_row_sum_peak"] == "448" and report["content_binary_height"] == 2,
+             "The complete literal query bounds")
+        query_reports[key] = report
+    reports = []
+    for record in service["services"]:
+        name, s, t = record["provider"], record["reader_stage"], record["service_stage"]
+        key = f"{s}:{t}"
+        blocks = record["ordered_blocks"]
+        need([b["op"] for b in blocks] == [
+            "DATA_entry", "native_input_adapters", "complete_native_carrier_cover_sweep",
+            "ordinary_output_adapters", "DATA_exit", "complete_cover_barrier", "fixed_past_reader_query"],
+            "The exact barrier order")
+        need(blocks[2]["event_range"] == [0, 2406] and blocks[6]["literal_key"] == key,
+             "The complete native and query blocks")
+        need(record["stage_view_record"] == blocks[0]["record"] == blocks[4]["record"] == t - 1
+             and service["stage_views"][t - 1]["service_stage"] == t,
+             "The service selects the actual stage views")
+        need(all(blocks[i]["provider"] == name and blocks[i]["source"] == "prefix"
+                 for i in (1, 2, 3)), "The service selects one complete native provider")
+        pair_index = record["query_pair_record"]
+        bound_pair = source_query["pairs"][pair_index]
+        need(blocks[6]["pair_record"] == pair_index
+             and blocks[6]["source"] == "query" and blocks[6]["literal_source"] == "literal_query"
+             and (bound_pair["reader_stage"], bound_pair["service_stage"]) == (s, t),
+             "The service selects the actual reader query")
+        need(record["physical_input_level"] == t - 1 and record["physical_output_level"] == t,
+             "The reader label is not the physical level")
+        prefix_report, query_report = prefix_reports[name], query_reports[key]
+        map_invoice = {
+            "DATA": 448, "local_endpoint_adapters": 128 + 96,
+            "native_side_maps": 2 * prefix_report["native_children"],
+            "late_query": query_report["map_calls"]}
+        map_invoice["total"] = sum(map_invoice.values())
+        scalar = prefix_report["scalar_primitives"] + query_report["scalar_primitives"]
+        need(scalar == record["scalar_primitives"] == 17624
+             and map_invoice == record["map_call_bound"] and map_invoice["total"] == 5776,
+             "The full service invoice")
+        reports.append({"provider": name, "reader_stage": s, "service_stage": t,
+                        "all_input_columns": 640, "native_mass": prefix_report["native_mass"],
+                        "scalar_primitives": scalar, "monomial_map_call_bound": map_invoice["total"]})
+    need(len(reports) == 6 and {(x["provider"], x["reader_stage"], x["service_stage"]) for x in reports}
+         == {(p, s, t) for p in prefix_reports for s, t in ((0, 1), (0, 2), (1, 2))},
+         "Both providers and all three pairs")
+    receipt = {
+        "status": "PASS_INDEPENDENT_SIX_FIXED_READER_D25_SERVICES",
+        "checker_sha256": digest(Path(__file__).read_bytes()),
+        "frozen_dependencies": {k: {"path": str(p), "sha256": h} for k, (p, h) in FREEZES.items()},
+        "payloads": {k: {"path": str(p), "decompressed_sha256": h} for k, (p, h) in PAYLOADS.items()},
+        "native_phase_files_rechecked": len(phase_inputs),
+        "prefix_reports": prefix_reports, "query_reports": query_reports,
+        "boundary_phase_checks": dict(phase_count), "wrong_entry_translation_control_failures": wrong_entry,
+        "services": reports, "producer_code_imported": False,
+        "native_phase_validation": "Exact bytes of the independently reviewed line-entry components.",
+        "helper_hosting_reproved": False, "finite_monomial_price_proved": False,
+        "recursive_precision_proved": False, "complete_supplier_claimed": False,
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode()
+    (args.output / "REVIEW-CHECKS.json").write_bytes(raw)
+    print(receipt["status"])
+    print(digest(raw))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/normal/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/normal/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..fedfda354b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/normal/REVIEW-CHECKS.json
@@ -0,0 +1,172 @@
+{
+  "boundary_phase_checks": {
+    "entry": 448,
+    "exit": 448
+  },
+  "checker_sha256": "0f34e7a3cebebdf4d43226104079cf0d4038fcdeac9ae3ab5165276b9df61974",
+  "complete_supplier_claimed": false,
+  "finite_monomial_price_proved": false,
+  "frozen_dependencies": {
+    "dispatcher": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json",
+      "sha256": "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331"
+    },
+    "independent_query": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json",
+      "sha256": "d8d782ecc13fdd2d26380fc4b047fc6d6781417ec694fdd3dea910dce04c2e2a"
+    },
+    "native_phase": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json",
+      "sha256": "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"
+    },
+    "prefix": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json",
+      "sha256": "fc3cef0e499e5bc85c25bb0fc88f5ecd12e44b66799e3d793dac37de8d88d26e"
+    },
+    "query": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json",
+      "sha256": "f111a90f7403f93494e9d1f83ae35dbf7dd72eddc8c9f8bf730d677b4a31402d"
+    },
+    "service": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICE-FREEZE.json",
+      "sha256": "177d6ae2f3971deac98e3385dda32e82ddabf0c8176e88ac1255323aed8d688f"
+    }
+  },
+  "helper_hosting_reproved": false,
+  "native_phase_files_rechecked": 35,
+  "native_phase_validation": "Exact bytes of the independently reviewed line-entry components.",
+  "payloads": {
+    "dispatcher": {
+      "decompressed_sha256": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json"
+    },
+    "line_entry": {
+      "decompressed_sha256": "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz"
+    },
+    "prefix": {
+      "decompressed_sha256": "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz"
+    },
+    "query": {
+      "decompressed_sha256": "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz"
+    },
+    "service": {
+      "decompressed_sha256": "88d25925705e6657656afb727430ce0d541c5e657426166363694d8b66180d13",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-normal/FIXED-READER-SERVICES.json.gz"
+    }
+  },
+  "prefix_reports": {
+    "base": {
+      "content_binary_height": 1,
+      "content_row_sum_peak": "22",
+      "input_columns": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_outside_fields": 416,
+      "scalar_primitives": 6456
+    },
+    "extra": {
+      "content_binary_height": 1,
+      "content_row_sum_peak": "22",
+      "input_columns": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_outside_fields": 416,
+      "scalar_primitives": 6456
+    }
+  },
+  "producer_code_imported": false,
+  "query_reports": {
+    "0:1": {
+      "content_binary_height": 2,
+      "content_row_sum_peak": "448",
+      "map_calls": 2064,
+      "scalar_primitives": 11168
+    },
+    "0:2": {
+      "content_binary_height": 2,
+      "content_row_sum_peak": "448",
+      "map_calls": 2064,
+      "scalar_primitives": 11168
+    },
+    "1:2": {
+      "content_binary_height": 2,
+      "content_row_sum_peak": "448",
+      "map_calls": 2064,
+      "scalar_primitives": 11168
+    }
+  },
+  "recursive_precision_proved": false,
+  "services": [
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 1
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 1
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 1,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 1,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    }
+  ],
+  "status": "PASS_INDEPENDENT_SIX_FIXED_READER_D25_SERVICES",
+  "wrong_entry_translation_control_failures": 448
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/optimized/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/optimized/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..fedfda354b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/fixed-reader-service-review-20261020/optimized/REVIEW-CHECKS.json
@@ -0,0 +1,172 @@
+{
+  "boundary_phase_checks": {
+    "entry": 448,
+    "exit": 448
+  },
+  "checker_sha256": "0f34e7a3cebebdf4d43226104079cf0d4038fcdeac9ae3ab5165276b9df61974",
+  "complete_supplier_claimed": false,
+  "finite_monomial_price_proved": false,
+  "frozen_dependencies": {
+    "dispatcher": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json",
+      "sha256": "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331"
+    },
+    "independent_query": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json",
+      "sha256": "d8d782ecc13fdd2d26380fc4b047fc6d6781417ec694fdd3dea910dce04c2e2a"
+    },
+    "native_phase": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json",
+      "sha256": "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"
+    },
+    "prefix": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json",
+      "sha256": "fc3cef0e499e5bc85c25bb0fc88f5ecd12e44b66799e3d793dac37de8d88d26e"
+    },
+    "query": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json",
+      "sha256": "f111a90f7403f93494e9d1f83ae35dbf7dd72eddc8c9f8bf730d677b4a31402d"
+    },
+    "service": {
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICE-FREEZE.json",
+      "sha256": "177d6ae2f3971deac98e3385dda32e82ddabf0c8176e88ac1255323aed8d688f"
+    }
+  },
+  "helper_hosting_reproved": false,
+  "native_phase_files_rechecked": 35,
+  "native_phase_validation": "Exact bytes of the independently reviewed line-entry components.",
+  "payloads": {
+    "dispatcher": {
+      "decompressed_sha256": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json"
+    },
+    "line_entry": {
+      "decompressed_sha256": "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz"
+    },
+    "prefix": {
+      "decompressed_sha256": "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz"
+    },
+    "query": {
+      "decompressed_sha256": "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz"
+    },
+    "service": {
+      "decompressed_sha256": "88d25925705e6657656afb727430ce0d541c5e657426166363694d8b66180d13",
+      "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-normal/FIXED-READER-SERVICES.json.gz"
+    }
+  },
+  "prefix_reports": {
+    "base": {
+      "content_binary_height": 1,
+      "content_row_sum_peak": "22",
+      "input_columns": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_outside_fields": 416,
+      "scalar_primitives": 6456
+    },
+    "extra": {
+      "content_binary_height": 1,
+      "content_row_sum_peak": "22",
+      "input_columns": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_outside_fields": 416,
+      "scalar_primitives": 6456
+    }
+  },
+  "producer_code_imported": false,
+  "query_reports": {
+    "0:1": {
+      "content_binary_height": 2,
+      "content_row_sum_peak": "448",
+      "map_calls": 2064,
+      "scalar_primitives": 11168
+    },
+    "0:2": {
+      "content_binary_height": 2,
+      "content_row_sum_peak": "448",
+      "map_calls": 2064,
+      "scalar_primitives": 11168
+    },
+    "1:2": {
+      "content_binary_height": 2,
+      "content_row_sum_peak": "448",
+      "map_calls": 2064,
+      "scalar_primitives": 11168
+    }
+  },
+  "recursive_precision_proved": false,
+  "services": [
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 1
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 1
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 0,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 1,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    },
+    {
+      "all_input_columns": 640,
+      "monomial_map_call_bound": 5776,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 1,
+      "scalar_primitives": 17624,
+      "service_stage": 2
+    }
+  ],
+  "status": "PASS_INDEPENDENT_SIX_FIXED_READER_D25_SERVICES",
+  "wrong_entry_translation_control_failures": 448
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..3808f618ad
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/FREEZE.json
@@ -0,0 +1,16 @@
+{
+  "files": {
+    "GENERAL-QUERY.md": "cc96ab14ce744b4acf30bc5e8088a35807611a497abc673b11eab225d9bf7993",
+    "PEER-REVIEW.md": "653372564d82ea8b7c8f7b2b1a76de4cf97f97879864dcd9479f09ca6ceaf86e",
+    "REPRODUCTION.json": "cbf5cf14b663c1c78f27f4f41ff18dc77eaa99619bf2d5f58373a574dc12a802",
+    "REVIEW.md": "e8862531740470b3bb4f45b421c0ab100c07f00bed71271b398ee7bdb89d834d",
+    "check_review.py": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7",
+    "normal/REVIEW-CHECKS.json": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830",
+    "optimized/REVIEW-CHECKS.json": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830"
+  },
+  "inherited_service_review_sha256": "ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7",
+  "payload_decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091",
+  "producer_freeze_sha256": "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6",
+  "schema": "independent-routed-involution-reader-review-v1",
+  "scope": "Six complete forward data services and three late inverse-adjoint queries. The helper host, complete backward caller, and supplier remain separate."
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md
new file mode 100644
index 0000000000..9eadd8701f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md
@@ -0,0 +1,105 @@
+# Sharing a restored source across target readers
+
+Let X be a source module. Let \(Y_1,\ldots,Y_k\) be distinct target
+modules. Let T be a unit on X. Assume that these operations are
+admitted at their actual physical views:
+
+1. T and \(T^{-1}\) act in place on X.
+2. Reader j adds \(L_jX\) to \(Y_j\). It preserves X and every
+   other target.
+3. Each operation restores its own borrowed fields.
+
+Then the word
+
+\[
+T;\quad
+(Y_1\mathrel{+}=L_1X);\quad\cdots\quad
+(Y_k\mathrel{+}=L_kX);\quad
+T^{-1}
+\]
+
+has the exact endpoint
+
+\[
+(x,y_1,\ldots,y_k)
+\longmapsto
+(x,y_1+L_1Tx,\ldots,y_k+L_kTx).
+\]
+
+The proof follows the actual order. After the first word the
+source is Tx. Each reader leaves that source unchanged and
+retains the independent baseline of its own target. The final
+word restores x. Thus the source transformations are paid once.
+No zero target, inverse reader, or commutation hypothesis is
+required.
+
+The price is
+
+\[
+a(T)+a(T^{-1})+\sum_{j=1}^k c(L_j),
+\]
+
+before any sharing of physical views. A reader that alters a
+source during its literal word is permitted only if that word
+restores the source before the next reader. The endpoint
+identity does not remove the cost of target storage or access.
+
+## Actual D25 schedule for one retained reader
+
+Use the reviewed current involution \(T=A_t\). Assume k distinct
+target banks are already available in the completed FULL frame,
+with the same retained reader \(L_s=P+B_s\). This is an explicit
+availability premise. It is not a new native host construction.
+
+Use this schedule:
+
+1. Apply the actual current A word to X, with its current views.
+2. Put the 96 ordinary X fields in the old s FULL views.
+3. For each target bank, add the sixteen selected X fields to
+   its selected target fields while those targets remain in
+   global FULL. Enter its sixteen old s target views, run the
+   1,760-scalar complement reader, and restore its target views.
+4. Restore the 96 old source views.
+5. Apply the actual current A word to X again.
+
+The selected X fields remain in global FULL throughout step 3.
+The complement reader does not need those selected X fields.
+Each target therefore receives both the selected copy and
+\(B_sA_tx\). Their sum is \(L_sA_tx\), with the full operator
+order retained.
+
+The two current A words cost 6,552 scalar primitives and
+448 maps. The k readers cost \(1888k\) scalar primitives.
+Their shared ordinary source views cost 192 maps. Their
+target views cost \(32k\) maps. Thus the complete query
+schedule has
+
+\[
+\boxed{6552+1888k\text{ scalar primitives},\qquad
+640+32k\text{ monomial calls}.}
+\]
+
+For k=1, these are the reviewed literal counts 8,440 and 672.
+For k=2, they are 10,328 and 704. The two-target schedule
+has not been joined to a native host or supplier in this
+packet. No extra fields are treated as free.
+
+If readers use g different old stages, the same source pair
+can still be shared. Group the targets by their old stage,
+and enter and restore the 96 ordinary source views for
+each group. The scalar count remains \(6552+1888k\); the
+map count becomes \(448+192g+32k\). This formula assumes
+that each stated old-stage view is admitted at the common
+completed cut.
+
+This theorem isolates a reusable source operation. It does
+not make a product \(C_sA_t\) reciprocal or stage independent.
+It does not construct a backward caller, a complete recursive
+host, or a terminal decoder.
+
+The bridge-access producer checked the actual one-reader
+view schedule and its multi-target count independently.
+Its response is recorded in `PEER-REVIEW.md`.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md
new file mode 100644
index 0000000000..cdee425048
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md
@@ -0,0 +1,26 @@
+# Peer check of the multi-target schedule
+
+On 2026-10-20, the bridge-access producer checked the proposed
+multi-target schedule independently. The producer confirmed
+the following points:
+
+- Keep the 96 ordinary source fields in the old s FULL views
+  between target queries. Enter and restore them once, for
+  192 map calls.
+- For each target bank, make the sixteen selected copies in
+  global FULL before entering its sixteen old target views.
+  Run the complement query, then restore those target views.
+  This costs 32 maps per target bank.
+- The selected X fields stay in global FULL. They remain
+  available for the same-port copies.
+- The complete query costs \(6552+1888k\) scalar primitives
+  and \(640+32k\) maps.
+- The target banks must be distinct and have paid FULL
+  hosting. This calculation does not provide that host.
+
+The peer check concerns the new schedule theorem. It does
+not replace the independent replay of the producer's actual
+one-target word in `REVIEW.md`.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..d93b1a0810
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json
@@ -0,0 +1,11 @@
+{
+  "commands": [
+    "python3 check_review.py --output normal",
+    "python3 -O check_review.py --output optimized"
+  ],
+  "no_producer_files_changed": true,
+  "normal_optimized_byte_identical": true,
+  "one_cpu": true,
+  "receipt_sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830",
+  "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..5493e5eb7c
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/REVIEW.md
@@ -0,0 +1,240 @@
+# Independent review of the routed involution reader
+
+The frozen forward service passes for both native providers and all
+three D25 reader/service pairs. The independent checks found no
+material defect. Each complete service has 14,896 real scalar
+primitives, native rank 1,792, and at most 4,384 monomial map calls.
+All 640 formal input columns are checked.
+
+This service computes the new involution response A. It changes the
+sixteen selected response rows. It is not a cheaper word for the old
+E response. The helper host, finite map price, recursive precision,
+backward caller, and complete supplier remain separate obligations.
+
+## Pinned input and independent method
+
+The producer freeze has SHA-256
+`3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6`.
+The decompressed query payload has SHA-256
+`35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091`.
+The controller involution payload has SHA-256
+`a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b`.
+
+This review uses the earlier independent joined-service review,
+whose freeze has SHA-256
+`ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7`.
+The new checker imports that pinned review's mathematical helpers.
+It imports no producer code.
+
+The earlier review binds the exact native prefix, all 896 DATA
+phase equations, all six cover schedules, and the independent
+native phase review. The new payload contains the same native
+prefixes and DATA records, byte for byte. This review checks that
+equality. It does not repeat the earlier large native spatial replay.
+It does replay the complete prefix on all 640 formal inputs.
+
+The new part reconstructs A from the original native U and V.
+It checks the full scalar word, the actual routed involutions,
+every late map phase, the ordered query, the complete data map,
+and each component of the invoice.
+
+## Independent matrix construction
+
+Write the original response as \(E=I+UV\). Let P be the actual
+sixteen selected ports, and let R be their 96-port complement.
+The selected column minor \(V_P\) has determinant 16. It is a
+dyadic unit. Keep \(U_R\), and set
+
+\[
+\widetilde U_P=V_P^{-1}(-2I-V_RU_R),
+\qquad
+A=I+\widetilde U V.
+\]
+
+The construction gives \(V\widetilde U=-2I\). Hence
+
+\[
+A^2=I+\widetilde U(2I+V\widetilde U)V=I.
+\]
+
+The checker constructs this matrix before it reads the emitted
+response for comparison. All 96 ordinary rows agree with E, and
+all sixteen selected rows differ from E. The actual normalized
+reader is \(L=V_P^{-1}V\), and \(LA=-L\).
+
+The full 3,276-scalar `common_frame_words.A` is replayed from the
+112-column identity matrix. Its result is exactly A. Its targets
+and sources are existing X fields. It uses no extra field and no
+odd division.
+
+The source identity \(A^2=I\) does not imply that A is symmetric
+or unitary. It does not make \(C_sA_t\) self-inverse, reciprocal,
+or independent of the stage.
+
+## Exact routed query and arbitrary inputs
+
+Let \(A_t\) include the actual current owner routes. Let \(L_s\)
+be the retained reader. At the completed FULL cut, use
+
+\[
+X\mathrel{\gets}A_tX,\qquad
+Y_P\mathrel{+}=L_sX,\qquad
+X\mathrel{\gets}A_tX.
+\]
+
+For arbitrary independent x and y, this word gives
+
+\[
+(x,y)\longmapsto(x,y+L_sA_tx).
+\]
+
+The second source transform restores X because the routed
+operator itself is an involution. No different owner routes
+are identified. No reader is commuted through a response.
+
+For each of \((s,t)=(0,1),(0,2),(1,2)\), the independent checker
+builds the actual D25 route matrices from the pinned q vectors.
+It checks that each map is orthogonal, that its inverse is exact,
+and that it fixes all future axes. Its FULL conjugation phase
+is checked as a complete Z4 polynomial, including translation.
+The current query views agree with the current DATA exits.
+
+The native cover sweep and all exits occur before the query.
+The physical input level is \(t-1\). In particular, reader pair
+\((0,2)\) uses a stage-zero reader carried to physical level one;
+it does not skip the stage-one physical advance.
+
+The literal late word has four parts:
+
+| Part | Scalar primitives | Monomial calls |
+| --- | ---: | ---: |
+| Current A on all X | 3,276 | 224 |
+| Old complement reader into selected Y | 1,760 | 224 |
+| Sixteen same-port selected copies | 128 | 0 |
+| Current A on all X | 3,276 | 224 |
+| Total | 8,440 | 672 |
+
+The old complement reader retains its arbitrary target baseline.
+The query neither reads nor changes the ordinary Y hole fields.
+All source fields return to their initial values at the FULL cut.
+The 416 outside fields keep their independent input values.
+
+Each direct \(L_sA_t\) product has 3,824 distinct field/owner-route
+terms. The independent replay keeps their order and compares all
+640 input columns. Omitting the second A word fails. Replacing
+the old reader by the current reader also fails, for all three pairs.
+
+## Complete forward map and cost
+
+The unchanged carrier prefix has the profile
+
+\[
+1392H_1+64H_2+48H_3+16H_8.
+\]
+
+It has 1,520 children, native rank 1,792, and 6,456 scalar
+primitives. Its ordinary output rows remain valid because
+\(A[R,*]=E[R,*]\). Its selected records are independent.
+All 416 helper values are restored under the inherited helper
+supply contract.
+
+Let \(G_R=\operatorname{diag}(I_P,q_R)\). Let \(F_\ell\) denote
+FULL on the first \(9+8\ell\) axes. Define
+
+\[
+(D_{s,t})_P=L_sA_t,\qquad
+(D_{s,t})_R=(A_t)_R.
+\]
+
+The complete forward data service is
+
+\[
+(F_{t-1}x,F_{t-1}G_Rw)
+\longmapsto
+(F_tx,F_tG_R(w+D_{s,t}x)).
+\]
+
+The target w is arbitrary. If \(w=C_sy\), the selected output
+records are \(L_s(y+A_tx)\). The same reader is retained.
+The checker composes the exact routed query with the full
+prefix and verifies all 640 input columns for all six
+provider/pair invocations.
+
+The complete scalar count is \(6456+8440=14896\).
+The monomial call bound is
+
+\[
+448+224+3040+672=4384.
+\]
+
+These terms count DATA entry/exit maps, local endpoint adapters,
+native side maps, and query maps. This is a map-call count. It
+does not price the finite implementation of a map. Identity
+maps remain counted where the literal word calls them.
+
+The native prefix's exact content coefficient bound is 22,
+with binary denominator height one. The late query's exact
+coefficient row-sum maximum is 202, with height two. These
+values hold for all three pairs.
+
+The query maximum is attained at an emitted boundary. Its
+witness has 266 coefficients of magnitude \(1/2\), another
+134 of magnitude \(1/2\), and one coefficient of magnitude 2.
+Their absolute sum is 202. The receipt also gives a coefficient
+of magnitude \(1/4\), so height two is attained.
+
+At these late boundaries the regular cover gives a sharp
+physical sup norm: different routes give different input
+owners, and the payload view for a route is its unique FULL
+conjugate. Terms with the same field and route have already
+been combined. The remaining source values can take the
+required signs independently. This argument does not assert
+sharpness for a quotient cover. It does not cover primitive
+arithmetic interiors, native-child interiors, or the full
+recursive caller.
+
+## Separate late inverse-adjoint check
+
+The checker also transforms each late scalar ADD to its negative
+transpose and each SCALE to its reciprocal. It keeps chronology.
+The map events remain unchanged because they are unitary.
+This is the gatewise inverse-adjoint word.
+
+The replay on all 640 inputs gives
+
+\[
+X\mathrel{-}=A_t^*L_s^*Y_P,\qquad Y_P\mathrel{\gets}Y_P.
+\]
+
+Its price is also 8,440 scalar primitives and 672 maps. Its
+exact emitted-boundary coefficient row-sum maximum is 30,
+and its binary denominator height is two, for each pair.
+
+This is a check of the late word. No separately packaged
+complete backward native service is emitted or approved
+by this review. The transpose of a query is not a reciprocal
+caller with the required physical input and output frames.
+
+## Reproduction, extension, and credit
+
+Run from this directory:
+
+```text
+python3 check_review.py --output normal
+python3 -O check_review.py --output optimized
+```
+
+Both runs print `PASS_INDEPENDENT_ROUTED_INVOLUTION_READER`.
+The two `REVIEW-CHECKS.json` files must be byte equal.
+`GENERAL-QUERY.md` gives a separate multi-target schedule theorem.
+It does not claim a new target host or native caller.
+
+The controller lane supplied the row involution. The bridge-access
+lane supplied the literal query and D25 binding. The native lanes
+supplied the unchanged carrier prefix and its independent phase
+review. This lane supplied the independent matrix, route, arbitrary
+input, full service, and late dual checks. AI agents prepared these
+local research records.
+
+No publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/check_review.py b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/check_review.py
new file mode 100644
index 0000000000..ec5ba02c71
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/check_review.py
@@ -0,0 +1,273 @@
+"""Check the routed involution reader with independent matrix algebra."""
+
+import argparse
+from fractions import Fraction as F
+import gzip
+from hashlib import sha256
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+OLD_REVIEW = HERE.parent / "fixed-reader-service-review-20261020"
+PRODUCER = LANES / "bridge-access-20261017/involution-reader-20261020"
+CONTROLLER = LANES / "controller-followthrough-20261017/row-involution-20261020"
+FREEZE_PIN = "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6"
+PAYLOAD_PIN = "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091"
+OLD_REVIEW_PIN = "ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7"
+A_PIN = "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def digest(raw):
+    return sha256(raw).hexdigest()
+
+
+def pinned(path, expected, compressed=False):
+    raw = path.read_bytes()
+    if compressed:
+        raw = gzip.decompress(raw)
+    need(digest(raw) == expected, "Pin: " + str(path))
+    return raw
+
+
+def freeze(path, expected):
+    result = json.loads(pinned(path, expected))
+    for name, pin in result["files"].items():
+        pinned(path.parent / name, pin)
+    return result
+
+
+freeze(OLD_REVIEW / "FREEZE.json", OLD_REVIEW_PIN)
+spec = importlib.util.spec_from_file_location("independent_service_math", OLD_REVIEW / "check_service.py")
+s = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(s)
+r = s.r
+
+
+def complete_matrix(u, v):
+    vp = [{j: row[p] for j, p in enumerate(r.PIVOTS) if p in row} for row in v]
+    vpi, determinant = r.invert(vp)
+    remaining_u = [{} if p in r.PSET else dict(row) for p, row in enumerate(u)]
+    residual = r.matmul(v, remaining_u)
+    requested = []
+    for i, row in enumerate(residual):
+        out = {j: -value for j, value in row.items()}
+        r.put(out, i, F(-2))
+        requested.append(out)
+    changed_rows = r.matmul(vpi, requested)
+    changed_u = [dict(row) for row in u]
+    for p, row in zip(r.PIVOTS, changed_rows):
+        changed_u[p] = row
+    need(r.matmul(v, changed_u) == [{i: F(-2)} for i in range(16)],
+         "Exact rank-sixteen involution certificate")
+    a = r.eye(112)
+    for row, correction in zip(a, r.matmul(changed_u, v)):
+        for j, value in correction.items():
+            r.put(row, j, value)
+    return a, changed_u, r.matmul(vpi, v), determinant
+
+
+def to_operations(word, level):
+    for record in word["maps"]:
+        a, ai = tuple(record["columns"]), tuple(record["inverse_columns"])
+        need(r.product(a, ai) == r.product(ai, a) == r.UNIT and ai == r.transpose(a),
+             "The literal map is orthogonal")
+        need(a[9 + 8 * level:] == r.UNIT[9 + 8 * level:], "Every future axis is fixed")
+        delta = r.phase_translation(r.add_phase(r.full_phase(level), r.minus_phase(r.full_phase(level, a))))
+        need(record["translation"] == delta
+             and record["inverse_translation"] == r.apply(ai, delta), "Literal FULL phase and inverse")
+    operations = []
+    for event in word["events"]:
+        if event[0] == "map":
+            _, field, index = event
+            operations.append(("map", field, None, tuple(word["maps"][index]["columns"])))
+        else:
+            need(event[0] == "scalar", "Literal query event grammar")
+            _, op, field, source, coefficient = event
+            need(op in ("add", "scale"), "Dyadic scalar grammar")
+            need(source is None or source < 112, "No target record is used as a source")
+            operations.append((op, field, source, F(coefficient)))
+        need(field < 112 or field - 112 in r.PSET, "Only FULL query fields are changed")
+    return operations
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "normal")
+    args = parser.parse_args()
+    producer_freeze = freeze(PRODUCER / "FREEZE.json", FREEZE_PIN)
+    need(producer_freeze["payload_decompressed_sha256"] == PAYLOAD_PIN, "Payload freeze")
+    bundle = json.loads(pinned(PRODUCER / "final-normal/INVOLUTION-READER.json.gz", PAYLOAD_PIN, True))
+    sources = {}
+    for name, (path, pin) in bundle["source_pins"].items():
+        raw = pinned(LANES / path, pin, path.endswith(".gz"))
+        if path.endswith(".json") or path.endswith(".json.gz"):
+            sources[name] = json.loads(raw)
+    inv = json.loads(pinned(CONTROLLER / "run-normal/ROW-INVOLUTION.json", A_PIN))
+    need(inv == sources["involution"], "Exact controller word source")
+    native_path, native_pin = r.PINS["native"]
+    native = json.loads(pinned(LANES / native_path, native_pin, True))
+    u, v, old_e = (r.sparse(native["model"][key])
+                   for key in ("correction_U", "correction_V", "response"))
+    a, changed_u, reader, vp_det = complete_matrix(u, v)
+    need(a == r.sparse(inv["response"]) == r.sparse(bundle["response"]),
+         "The emitted response equals the independently completed actual matrix")
+    need(changed_u == r.sparse(inv["correction_U"]), "The changed factor agrees")
+    need(r.matmul(a, a) == r.eye(112), "The complete 112-port involution")
+    need(all(a[p] == old_e[p] for p in range(112) if p not in r.PSET),
+         "Exactly the old ordinary rows are retained")
+    need(all(a[p] != old_e[p] for p in r.PIVOTS), "All sixteen selected rows change")
+    need(reader == r.sparse(sources["capture"]["centre_reader"]), "The retained old reader")
+    need(r.matmul(reader, a) == [{j: -x for j, x in row.items()} for row in reader],
+         "The current reader has eigenvalue minus one")
+    codeword = inv["common_frame_words"]["A"]
+    need(r.scalar_word(r.eye(112), codeword) == a, "Independent complete scalar A word")
+    need(sum(r.real_price(op, F(value)) for op, _, _, value in codeword) == 3276,
+         "Exact source unit price")
+    need(all(dst < 112 and (src is None or src < 112) for _, dst, src, _ in codeword),
+         "The source word uses existing X only")
+    old_payload = json.loads(s.read(*s.PAYLOADS["service"], True))
+    need(bundle["native_prefixes"] == old_payload["native_prefixes"]
+         and bundle["stage_views"] == old_payload["stage_views"]
+         and bundle["helper_hosting"] == old_payload["owner_contract"],
+         "The exact reviewed native and DATA components are retained")
+    need(tuple(bundle["pivots"]) == r.PIVOTS, "The exact selected field order")
+    prefix_reports = {name: s.prefix_replay(word, a)
+                      for name, word in bundle["native_prefixes"].items()}
+    ports = native["model"]["ports"]
+    routes = {(stage, p): r.route(ports[p], stage) for stage in range(3) for p in range(112)}
+    query_reports = {}
+    dual_reports = {}
+    query_parts = {
+        "apply_current_involution": (3276, 224),
+        "old_reader_complement": (1760, 224),
+        "selected_reader_copy": (128, 0),
+        "restore_current_involution": (3276, 224),
+    }
+    for key, word in bundle["queries"].items():
+        old_stage, level = word["reader_stage"], word["service_stage"]
+        need(key == f"{old_stage}:{level}", "Reader and service labels")
+        operations = to_operations(word, level)
+        at = r.routed_matrix(a, range(112), level, routes)
+        identity = [{(p, r.UNIT): F(1)} for p in range(112)]
+        need(r.multiply_routed(at, at) == identity, "The actual routed source involution")
+        ls = r.routed_matrix(reader, r.PIVOTS, old_stage, routes)
+        lt = r.routed_matrix(reader, r.PIVOTS, level, routes)
+        direct = r.multiply_routed(ls, at)
+        need(sum(map(len, direct)) == 3824, "Direct selected owner-path census")
+        end = 0
+        part_reports = {}
+        for label, (expected_scalar, expected_maps) in query_parts.items():
+            lo, hi = word["stage_ranges"][label]
+            need(lo == end and lo <= hi <= len(operations), "Complete ordered query intervals")
+            part = operations[lo:hi]
+            price = sum(r.real_price(op, value) for op, _, _, value in part if op != "map")
+            maps = sum(op == "map" for op, _, _, _ in part)
+            need((price, maps) == (expected_scalar, expected_maps), "Per-part exact invoice")
+            if label in ("apply_current_involution", "restore_current_involution"):
+                scalars = [[op, dst, src, str(value)] for op, dst, src, value in part if op != "map"]
+                need(scalars == codeword, "Both current words are the pinned A program")
+                expected_maps_list = (
+                    [("map", p, None, routes[level, p]) for p in range(112)]
+                    + [("map", p, None, routes[level, p]) for p in reversed(range(112))])
+                need([op for op in part if op[0] == "map"] == expected_maps_list,
+                     "The current A uses the exact DATA route views")
+            part_reports[label] = {"scalar_primitives": price, "maps": maps}
+            end = hi
+        need(end == len(operations), "No query event lies outside its complete schedule")
+        initial = [{(i, r.UNIT): F(1)} for i in range(640)]
+        expected = [dict(row) for row in initial]
+        for p, row in zip(r.PIVOTS, direct):
+            for term, value in row.items():
+                r.put(expected[112 + p], term, value)
+        actual, bill, triangle, grid, exact = r.replay(operations)
+        need(actual == expected, "All 640 arbitrary query input columns")
+        need(bill == {"real_scalar": 8440, "maps": 672}
+             and exact["coefficient_row_sum_peak"] == "202"
+             and exact["coefficient_binary_height"] == 2, "Query invoice and exact prefixes")
+        global_prefix = [dict(row) for row in initial]
+        for p in range(112):
+            if p not in r.PSET:
+                for term, value in at[p].items():
+                    r.put(global_prefix[112 + p], term, value)
+        complete = r.multiply_routed(actual, global_prefix)
+        complete_expected = [dict(row) for row in global_prefix]
+        for p, row in zip(r.PIVOTS, direct):
+            for term, value in row.items():
+                r.put(complete_expected[112 + p], term, value)
+        need(complete == complete_expected, "All 640 complete service input columns")
+        cutoff = word["stage_ranges"]["restore_current_involution"][0]
+        wrong, *_ = r.replay(operations[:cutoff])
+        need(wrong != expected and wrong[:112] != initial[:112], "No-restore control fails")
+        need(r.multiply_routed(lt, at) != direct, "The current reader cannot replace the old reader")
+        dual, dual_bill, dual_triangle, dual_grid, dual_exact = r.replay(operations, dual=True)
+        dual_expected = [dict(row) for row in initial]
+        for p, row in zip(r.PIVOTS, direct):
+            for (origin, path), value in row.items():
+                r.put(dual_expected[origin], (112 + p, r.transpose(path)), -value)
+        need(dual == dual_expected and dual_bill == bill,
+             "The literal inverse-adjoint late query on all 640 columns")
+        need(dual_exact["coefficient_row_sum_peak"] == "30"
+             and dual_exact["coefficient_binary_height"] == 2, "Exact late dual prefix bounds")
+        query_reports[key] = {
+            "input_columns": 640, "direct_paths": 3824, "parts": part_reports,
+            "invoice": bill, "exact_prefix": exact, "triangle_prefix": str(triangle),
+            "triangle_binary_height": grid,
+            "negative_controls": ["omitted_source_restore", "current_reader_substitution"],
+        }
+        dual_reports[key] = {"input_columns": 640, "invoice": dual_bill, "exact_prefix": dual_exact,
+                             "triangle_prefix": str(dual_triangle), "triangle_binary_height": dual_grid}
+    service_reports = []
+    for call in bundle["invocations"]:
+        provider, old_stage, level = call["provider"], call["reader_stage"], call["service_stage"]
+        old_call = next(c for c in old_payload["services"] if
+                        (c["provider"], c["reader_stage"], c["service_stage"]) ==
+                        (provider, old_stage, level))
+        need(call["ordered_blocks"][:-1] == old_call["ordered_blocks"][:-1],
+             "The complete native cover barrier is unchanged")
+        key = f"{old_stage}:{level}"
+        late = call["ordered_blocks"][-1]
+        need(late["op"] == "fixed_past_reader_query"
+             and late["source"] == late["literal_source"] == "queries"
+             and late["literal_key"] == call["query_key"] == key
+             and late["map_calls"] == 672, "The exact new query splice")
+        need(call["physical_input_level"] == level - 1 and call["physical_output_level"] == level
+             and call["stage_view_record"] == level - 1, "The adjacent physical stage")
+        prefix_report = prefix_reports[provider]
+        scalar = prefix_report["scalar_primitives"] + query_reports[key]["invoice"]["real_scalar"]
+        need(scalar == call["scalar_primitives"] == 14896
+             and call["map_call_bound"] == {
+                 "DATA": 448, "local_endpoint_adapters": 224, "native_side_maps": 3040,
+                 "late_query": 672, "total": 4384}, "The complete new response service invoice")
+        service_reports.append({"provider": provider, "reader_stage": old_stage, "service_stage": level,
+                                "scalar_primitives": scalar, "native_mass": prefix_report["native_mass"],
+                                "monomial_map_call_bound": 4384, "input_columns": 640})
+    need(len(service_reports) == 6 and len(query_reports) == 3, "All six actual services")
+    result = {
+        "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER",
+        "checker_sha256": digest(Path(__file__).read_bytes()),
+        "producer_freeze_sha256": FREEZE_PIN, "payload_decompressed_sha256": PAYLOAD_PIN,
+        "inherited_service_review_sha256": OLD_REVIEW_PIN, "actual_A_payload_sha256": A_PIN,
+        "pivot_minor_determinant": str(vp_det), "rank_certificate": "V U_tilde = -2 I16",
+        "actual_source_scalar_price": 3276, "changed_selected_rows": 16, "unchanged_ordinary_rows": 96,
+        "prefix_reports": prefix_reports, "queries": query_reports, "late_dual_queries": dual_reports,
+        "services": service_reports, "producer_code_imported": False,
+        "new_native_phase_checks": "The exact reviewed components are unchanged.",
+        "full_backward_service_emitted": False, "complete_supplier_claimed": False,
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(result, sort_keys=True, indent=2) + "\n").encode()
+    (args.output / "REVIEW-CHECKS.json").write_bytes(raw)
+    print(result["status"])
+    print(digest(raw))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..7aa6839fde
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json
@@ -0,0 +1,523 @@
+{
+  "actual_A_payload_sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+  "actual_source_scalar_price": 3276,
+  "changed_selected_rows": 16,
+  "checker_sha256": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7",
+  "complete_supplier_claimed": false,
+  "full_backward_service_emitted": false,
+  "inherited_service_review_sha256": "ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7",
+  "late_dual_queries": {
+    "0:1": {
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "30",
+        "height_witness": {
+          "coefficient": "1/4",
+          "event_index": 1276,
+          "origin": 112,
+          "route": [
+            3584,
+            3086,
+            2574,
+            1550,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256,
+            131072,
+            262144,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 25
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 1,
+            "-1/2": 20,
+            "-4": 1,
+            "1": 1,
+            "1/2": 20,
+            "4": 1
+          },
+          "coefficient_terms": 44,
+          "event_index": 1696,
+          "target": 111
+        }
+      },
+      "input_columns": 640,
+      "invoice": {
+        "maps": 672,
+        "real_scalar": 8440
+      },
+      "triangle_binary_height": 2,
+      "triangle_prefix": "4717"
+    },
+    "0:2": {
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "30",
+        "height_witness": {
+          "coefficient": "1/4",
+          "event_index": 1276,
+          "origin": 112,
+          "route": [
+            917504,
+            786446,
+            655374,
+            393230,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216,
+            512,
+            1024,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ],
+          "target": 25
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 1,
+            "-1/2": 20,
+            "-4": 1,
+            "1": 1,
+            "1/2": 20,
+            "4": 1
+          },
+          "coefficient_terms": 44,
+          "event_index": 1696,
+          "target": 111
+        }
+      },
+      "input_columns": 640,
+      "invoice": {
+        "maps": 672,
+        "real_scalar": 8440
+      },
+      "triangle_binary_height": 2,
+      "triangle_prefix": "4717"
+    },
+    "1:2": {
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "30",
+        "height_witness": {
+          "coefficient": "1/4",
+          "event_index": 1276,
+          "origin": 112,
+          "route": [
+            656384,
+            787456,
+            917504,
+            394240,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216,
+            512,
+            14,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ],
+          "target": 25
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 1,
+            "-1/2": 20,
+            "-4": 1,
+            "1": 1,
+            "1/2": 20,
+            "4": 1
+          },
+          "coefficient_terms": 44,
+          "event_index": 1696,
+          "target": 111
+        }
+      },
+      "input_columns": 640,
+      "invoice": {
+        "maps": 672,
+        "real_scalar": 8440
+      },
+      "triangle_binary_height": 2,
+      "triangle_prefix": "4717"
+    }
+  },
+  "new_native_phase_checks": "The exact reviewed components are unchanged.",
+  "payload_decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091",
+  "pivot_minor_determinant": "16",
+  "prefix_reports": {
+    "base": {
+      "content_binary_height": 1,
+      "content_row_sum_peak": "22",
+      "input_columns": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_outside_fields": 416,
+      "scalar_primitives": 6456
+    },
+    "extra": {
+      "content_binary_height": 1,
+      "content_row_sum_peak": "22",
+      "input_columns": 640,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_outside_fields": 416,
+      "scalar_primitives": 6456
+    }
+  },
+  "producer_code_imported": false,
+  "producer_freeze_sha256": "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6",
+  "queries": {
+    "0:1": {
+      "direct_paths": 3824,
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "202",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 821,
+          "origin": 0,
+          "route": [
+            3629,
+            3630,
+            11,
+            3587,
+            16,
+            7,
+            64,
+            128,
+            256,
+            3107,
+            2595,
+            8192,
+            4096,
+            1571,
+            16384,
+            32768,
+            65536,
+            131072,
+            262144,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 266,
+            "1/2": 134,
+            "2": 1
+          },
+          "coefficient_terms": 401,
+          "event_index": 820,
+          "target": 112
+        }
+      },
+      "input_columns": 640,
+      "invoice": {
+        "maps": 672,
+        "real_scalar": 8440
+      },
+      "negative_controls": [
+        "omitted_source_restore",
+        "current_reader_substitution"
+      ],
+      "parts": {
+        "apply_current_involution": {
+          "maps": 224,
+          "scalar_primitives": 3276
+        },
+        "old_reader_complement": {
+          "maps": 224,
+          "scalar_primitives": 1760
+        },
+        "restore_current_involution": {
+          "maps": 224,
+          "scalar_primitives": 3276
+        },
+        "selected_reader_copy": {
+          "maps": 0,
+          "scalar_primitives": 128
+        }
+      },
+      "triangle_binary_height": 2,
+      "triangle_prefix": "13742"
+    },
+    "0:2": {
+      "direct_paths": 3824,
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "202",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 821,
+          "origin": 0,
+          "route": [
+            917549,
+            917550,
+            11,
+            917507,
+            16,
+            7,
+            64,
+            128,
+            256,
+            512,
+            1024,
+            2048,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            786467,
+            655395,
+            2097152,
+            1048576,
+            393251,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 266,
+            "1/2": 134,
+            "2": 1
+          },
+          "coefficient_terms": 401,
+          "event_index": 820,
+          "target": 112
+        }
+      },
+      "input_columns": 640,
+      "invoice": {
+        "maps": 672,
+        "real_scalar": 8440
+      },
+      "negative_controls": [
+        "omitted_source_restore",
+        "current_reader_substitution"
+      ],
+      "parts": {
+        "apply_current_involution": {
+          "maps": 224,
+          "scalar_primitives": 3276
+        },
+        "old_reader_complement": {
+          "maps": 224,
+          "scalar_primitives": 1760
+        },
+        "restore_current_involution": {
+          "maps": 224,
+          "scalar_primitives": 3276
+        },
+        "selected_reader_copy": {
+          "maps": 0,
+          "scalar_primitives": 128
+        }
+      },
+      "triangle_binary_height": 2,
+      "triangle_prefix": "13742"
+    },
+    "1:2": {
+      "direct_paths": 3824,
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "202",
+        "height_witness": {
+          "coefficient": "-1/4",
+          "event_index": 821,
+          "origin": 0,
+          "route": [
+            920064,
+            920576,
+            3584,
+            919040,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            37,
+            38,
+            8,
+            16,
+            7,
+            64,
+            128,
+            256,
+            786467,
+            655395,
+            2097152,
+            1048576,
+            393251,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 112
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1/2": 266,
+            "1/2": 134,
+            "2": 1
+          },
+          "coefficient_terms": 401,
+          "event_index": 820,
+          "target": 112
+        }
+      },
+      "input_columns": 640,
+      "invoice": {
+        "maps": 672,
+        "real_scalar": 8440
+      },
+      "negative_controls": [
+        "omitted_source_restore",
+        "current_reader_substitution"
+      ],
+      "parts": {
+        "apply_current_involution": {
+          "maps": 224,
+          "scalar_primitives": 3276
+        },
+        "old_reader_complement": {
+          "maps": 224,
+          "scalar_primitives": 1760
+        },
+        "restore_current_involution": {
+          "maps": 224,
+          "scalar_primitives": 3276
+        },
+        "selected_reader_copy": {
+          "maps": 0,
+          "scalar_primitives": 128
+        }
+      },
+      "triangle_binary_height": 2,
+      "triangle_prefix": "13742"
+    }
+  },
+  "rank_certificate": "V U_tilde = -2 I16",
+  "services": [
+    {
+      "input_columns": 640,
+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 0,
+      "scalar_primitives": 14896,
+      "service_stage": 1
+    },
+    {
+      "input_columns": 640,
+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 0,
+      "scalar_primitives": 14896,
+      "service_stage": 1
+    },
+    {
+      "input_columns": 640,
+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 0,
+      "scalar_primitives": 14896,
+      "service_stage": 2
+    },
+    {
+      "input_columns": 640,
+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 0,
+      "scalar_primitives": 14896,
+      "service_stage": 2
+    },
+    {
+      "input_columns": 640,
+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 1,
+      "scalar_primitives": 14896,
+      "service_stage": 2
+    },
+    {
+      "input_columns": 640,
+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "extra",
+      "reader_stage": 1,
+      "scalar_primitives": 14896,
+      "service_stage": 2
+    }
+  ],
+  "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER",
+  "unchanged_ordinary_rows": 96
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/optimized/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/optimized/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..7aa6839fde
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/involution-reader-review-20261020/optimized/REVIEW-CHECKS.json
@@ -0,0 +1,523 @@
+{
+  "actual_A_payload_sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+  "actual_source_scalar_price": 3276,
+  "changed_selected_rows": 16,
+  "checker_sha256": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7",
+  "complete_supplier_claimed": false,
+  "full_backward_service_emitted": false,
+  "inherited_service_review_sha256": "ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7",
+  "late_dual_queries": {
+    "0:1": {
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "30",
+        "height_witness": {
+          "coefficient": "1/4",
+          "event_index": 1276,
+          "origin": 112,
+          "route": [
+            3584,
+            3086,
+            2574,
+            1550,
+            4096,
+            8192,
+            16384,
+            32768,
+            65536,
+            13,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256,
+            131072,
+            262144,
+            524288,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216
+          ],
+          "target": 25
+        },
+        "norm_witness": {
+          "coefficient_census": {
+            "-1": 1,
+            "-1/2": 20,
+            "-4": 1,
+            "1": 1,
+            "1/2": 20,
+            "4": 1
+          },
+          "coefficient_terms": 44,
+          "event_index": 1696,
+          "target": 111
+        }
+      },
+      "input_columns": 640,
+      "invoice": {
+        "maps": 672,
+        "real_scalar": 8440
+      },
+      "triangle_binary_height": 2,
+      "triangle_prefix": "4717"
+    },
+    "0:2": {
+      "exact_prefix": {
+        "coefficient_binary_height": 2,
+        "coefficient_row_sum_peak": "30",
+        "height_witness": {
+          "coefficient": "1/4",
+          "event_index": 1276,
+          "origin": 112,
+          "route": [
+            917504,
+            786446,
+            655374,
+            393230,
+            1048576,
+            2097152,
+            4194304,
+            8388608,
+            16777216,
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+        "coefficient_row_sum_peak": "30",
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+          "event_index": 1276,
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+        "norm_witness": {
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+            "-4": 1,
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+          "event_index": 1696,
+          "target": 111
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+      "invoice": {
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+        "real_scalar": 8440
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+      "triangle_binary_height": 2,
+      "triangle_prefix": "4717"
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+  "new_native_phase_checks": "The exact reviewed components are unchanged.",
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+      "scalar_primitives": 6456
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+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
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+        "3": 48,
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+  "producer_freeze_sha256": "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6",
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+      },
+      "triangle_binary_height": 2,
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+  },
+  "rank_certificate": "V U_tilde = -2 I16",
+  "services": [
+    {
+      "input_columns": 640,
+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "base",
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+    {
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+      "provider": "extra",
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+    },
+    {
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+      "monomial_map_call_bound": 4384,
+      "native_mass": 1792,
+      "provider": "base",
+      "reader_stage": 0,
+      "scalar_primitives": 14896,
+      "service_stage": 2
+    },
+    {
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+      "service_stage": 2
+    },
+    {
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+      "monomial_map_call_bound": 4384,
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+      "service_stage": 2
+    },
+    {
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+      "provider": "extra",
+      "reader_stage": 1,
+      "scalar_primitives": 14896,
+      "service_stage": 2
+    }
+  ],
+  "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER",
+  "unchanged_ordinary_rows": 96
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..147e0f6b2a
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/FREEZE.json
@@ -0,0 +1,13 @@
+{
+  "files": {
+    "REPRODUCTION.json": "316c97cbea92023a658952e49bcec070e3e46368078dd9e91dab6631a3943846",
+    "REVIEW.json": "e0047b4e85e3d93f765e9fb453a74b269a5cd5aeef03f88579998391b843bf52",
+    "REVIEW.md": "9b2c0661a9764fb9cbdb8b7218c0f0f929bd962f44b3a07555a1ef7f357f8e68",
+    "check_review.py": "1c0d4bd42ec556b0a2b866feb65d47ba864d2874963d2b43fd3ef276180de091"
+  },
+  "frozen_utc": "2026-10-20T16:29:47.732731+00:00",
+  "normal_optimized_byte_identical": true,
+  "publication_authorized": false,
+  "schema": "independent-low-displacement-budget-review-freeze-v1",
+  "scope": "Independent literal invoices and exact conditional native budgets; no global caller or admission."
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..1ae9befddb
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REPRODUCTION.json
@@ -0,0 +1,12 @@
+{
+  "checker_sha256": "1c0d4bd42ec556b0a2b866feb65d47ba864d2874963d2b43fd3ef276180de091",
+  "commands": [
+    "python3 -I -B check_review.py",
+    "python3 -I -B -O check_review.py"
+  ],
+  "producer_replay": false,
+  "receipt_sha256": "e0047b4e85e3d93f765e9fb453a74b269a5cd5aeef03f88579998391b843bf52",
+  "retained_engine_imports": false,
+  "status": "PASS_NORMAL_OPTIMIZED_BYTE_IDENTICAL",
+  "stdout": "PASS 176 exact profile intervals; 24 literal words; 16 unchanged scalar sequences\n"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.json
new file mode 100644
index 0000000000..1ea907b4bd
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.json
@@ -0,0 +1,3073 @@
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+        "profile": {
+          "1": 988,
+          "2": 48,
+          "5": 55,
+          "6": 55,
+          "7": 9,
+          "8": 9
+        },
+        "scalar_census": {
+          "add:-1": 156,
+          "add:-2": 4,
+          "add:-3": 8,
+          "add:1": 410,
+          "add:2": 28,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      },
+      "extra/forward": {
+        "children": 1164,
+        "endpoint_maps": 112,
+        "field_rank_census": {
+          "7": 96,
+          "9": 128
+        },
+        "inline_maps": 48,
+        "map_bound": 2488,
+        "native_mass": 1824,
+        "profile": {
+          "1": 988,
+          "2": 48,
+          "5": 55,
+          "6": 55,
+          "7": 9,
+          "8": 9
+        },
+        "scalar_census": {
+          "add:-1": 410,
+          "add:-2": 28,
+          "add:1": 156,
+          "add:2": 4,
+          "add:3": 8,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      }
+    },
+    "rank30_W48_I64": {
+      "base/backward": {
+        "children": 1164,
+        "endpoint_maps": 176,
+        "field_rank_census": {
+          "7": 96,
+          "8": 128
+        },
+        "inline_maps": 48,
+        "map_bound": 2552,
+        "native_mass": 1696,
+        "profile": {
+          "1": 988,
+          "2": 48,
+          "4": 55,
+          "5": 55,
+          "6": 9,
+          "7": 9
+        },
+        "scalar_census": {
+          "add:-1": 156,
+          "add:-2": 4,
+          "add:-3": 8,
+          "add:1": 410,
+          "add:2": 28,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      },
+      "base/forward": {
+        "children": 1164,
+        "endpoint_maps": 176,
+        "field_rank_census": {
+          "7": 96,
+          "8": 128
+        },
+        "inline_maps": 48,
+        "map_bound": 2552,
+        "native_mass": 1696,
+        "profile": {
+          "1": 988,
+          "2": 48,
+          "4": 55,
+          "5": 55,
+          "6": 9,
+          "7": 9
+        },
+        "scalar_census": {
+          "add:-1": 410,
+          "add:-2": 28,
+          "add:1": 156,
+          "add:2": 4,
+          "add:3": 8,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      },
+      "extra/backward": {
+        "children": 1164,
+        "endpoint_maps": 176,
+        "field_rank_census": {
+          "7": 96,
+          "8": 128
+        },
+        "inline_maps": 48,
+        "map_bound": 2552,
+        "native_mass": 1696,
+        "profile": {
+          "1": 988,
+          "2": 48,
+          "4": 55,
+          "5": 55,
+          "6": 9,
+          "7": 9
+        },
+        "scalar_census": {
+          "add:-1": 156,
+          "add:-2": 4,
+          "add:-3": 8,
+          "add:1": 410,
+          "add:2": 28,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      },
+      "extra/forward": {
+        "children": 1164,
+        "endpoint_maps": 176,
+        "field_rank_census": {
+          "7": 96,
+          "8": 128
+        },
+        "inline_maps": 48,
+        "map_bound": 2552,
+        "native_mass": 1696,
+        "profile": {
+          "1": 988,
+          "2": 48,
+          "4": 55,
+          "5": 55,
+          "6": 9,
+          "7": 9
+        },
+        "scalar_census": {
+          "add:-1": 410,
+          "add:-2": 28,
+          "add:1": 156,
+          "add:2": 4,
+          "add:3": 8,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      }
+    }
+  },
+  "literal_words_checked": 24,
+  "mixed_limits": {
+    "odd_rank16": {
+      "1": {
+        "1": 66,
+        "2": 33
+      },
+      "2": {
+        "1": 162,
+        "2": 81
+      },
+      "3": {
+        "1": 258,
+        "2": 129
+      }
+    },
+    "rank30": {
+      "1": {
+        "1": 71,
+        "2": 35
+      },
+      "2": {
+        "1": 167,
+        "2": 83
+      },
+      "3": {
+        "1": 263,
+        "2": 131
+      }
+    }
+  },
+  "profile_intervals_checked": 176,
+  "scope": "Literal event invoices and conditional D25 histograms. No native phase replay, routed caller, recursive admission, finite map cost, precision, or kappa claim.",
+  "selected_assembly": "research/community-frontier1094-audit/ASSEMBLY.json",
+  "selected_b_snapshot": "67018507072324140917/40000000000000000000000",
+  "selected_certificate": "certificates/selected-result.json",
+  "selected_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "source_pins": {
+    "assembly": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+    "low_freeze": "c730e61f7446b072c60411f9cb6af903e5b252b12ce9a4d9bce906990303fbef",
+    "low_receipt": "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2",
+    "mixed_freeze": "99f084410fcba6228d396d8c547dd4ed74835dc97de7fce004387b6de6ab92a5",
+    "mixed_receipt": "7359fbab24858a21ea9879fff0b61883134ee3bb754916085689136f6d833224",
+    "rank9_review": "50f2e168cdbf08e2bdad445bf2aa28f96d699cbc669a39892927bf94593e3b51",
+    "selected": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+  },
+  "status": "PASS_INDEPENDENT_LITERAL_AND_RATIONAL_BUDGET_REVIEW",
+  "unchanged_changed_scalar_sequences": 16,
+  "upstream_source_pins": {
+    "lanes/bridge-access-20261017/rank9-completion-20261020/CHECKS.json": "c4b92b37441c095ff3c4d51ea920dd918edd54113764d76ce721a30ec435a2b0",
+    "lanes/bridge-access-20261017/rank9-completion-20261020/FREEZE.json": "6177f89c88b503765a724e8c1baa934da582c490089dbe29e0f6ce2371f9904b",
+    "lanes/budget-geometry-20261017/matched-native-budget-20261018/MATCHED-NATIVE-BUDGET.json": "a1832aeb1d82498f423637ba8cab0ff11262383665ed440159759bc54fe5775e",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS-FREEZE.json": "f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json": "b36bee542add54bac48e409c6a4a054b3bca5fba9c98d5513a90a6a92628d576",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-PROGRAM.json.gz": "7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-CHECKS.json": "8acc084b5cd1d9513fdd3373eede998bd08e7f3fe1624f9fd41f758d4de7cb82",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..9a75789bee
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/REVIEW.md
@@ -0,0 +1,216 @@
+# Independent review of the low-displacement native budgets
+
+The two budget packets pass within their stated conditional scope. This
+review counts all 24 raw and changed words. It also checks 176 complete
+profile intervals with a separate exact rational evaluator. Each stated
+extra-child limit has a strict upper bound below one. The next count has
+a strict lower bound above one. No source file was changed.
+
+This is a native-budget result. It does not admit a changed output at a
+global stage. In particular, 224 H1 is a terminal cost comparator for the
+changed outputs. It is not an implemented decoder for those outputs.
+
+## Inputs and rate
+
+The reviewed freezes are:
+
+| Packet | Freeze SHA256 |
+| --- | --- |
+| `budget-geometry-20261017/low-displacement-budget-20261020` | `c730e61f7446b072c60411f9cb6af903e5b252b12ce9a4d9bce906990303fbef` |
+| `budget-geometry-20261017/mixed-exit-budget-20261020` | `99f084410fcba6228d396d8c547dd4ed74835dc97de7fce004387b6de6ab92a5` |
+
+Each path is relative to the campaign's `lanes` directory. The checker
+verifies every file in each freeze. It also verifies every upstream input
+pin in the first budget receipt.
+
+The exponent is read directly from the selected assembly at commit
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The selected record is
+[`certificates/selected-result.json`](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/certificates/selected-result.json).
+Its SHA256 is
+`10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32`.
+It binds
+[`research/community-frontier1094-audit/ASSEMBLY.json`](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1094-audit/ASSEMBLY.json)
+to SHA256
+`1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045`.
+The assembly's exact `complex_lower` is
+
+    b = 67018507072324140917 / 40000000000000000000000.
+
+Thus the rate is a verified historical selected snapshot. This review
+does not claim that it is the current selected rate. The calculation
+uses D=25, productive width W=224, three calls, and no idle jobs.
+
+## Literal invoices
+
+The checker imports no producer code. It reads each event from both
+providers in both orientations. It checks the native recipe reference
+and rank, counts the two side maps of each child, and counts each inline
+and endpoint monomial map. All scalar and native operands use the 224
+data roles.
+
+| Family and exit | Native histogram | Mass | Children | Scalar primitives | Map bound |
+| --- | --- | ---: | ---: | ---: | ---: |
+| Rank30 raw | 1036 H1, 48 H3, 55 H4, 55 H5, 9 H6, 9 H7 | 1792 | 1212 | 5288 | 2648 |
+| Rank16 raw | 1520 H1, 64 H2, 48 H3 | 1792 | 1632 | 7384 | 3488 |
+| Rank30 W48/I64 | 988 H1, 48 H2, 55 H4, 55 H5, 9 H6, 9 H7 | 1696 | 1164 | 5288 | 2552 |
+| Rank16 W48/I64 | 1472 H1, 112 H2 | 1696 | 1584 | 7384 | 3392 |
+| Rank30 W112 | 988 H1, 48 H2, 55 H5, 55 H6, 9 H7, 9 H8 | 1824 | 1164 | 5288 | 2488 |
+| Rank16 W112 | 1408 H1, 112 H2, 64 H3 | 1824 | 1584 | 7384 | 3328 |
+
+Every raw data field has total native rank eight. In W48/I64, 96 fields
+have rank seven and 128 have rank eight. In W112, those totals are seven
+and nine. These are sums along a field, not individual child ranks.
+
+The complete scalar sequence is equal before and after each changed
+exit. This was checked for all 16 changed words after exact coefficient
+schema conversion. The scalar prices use the stated model tariff:
+complex ADD coefficients of absolute value 1, 2, and 3 cost 8, 10, and
+12 real primitives. A sign costs two primitives; a double or half costs
+two more when present. All endpoint and inline maps remain separate.
+
+The resulting three-call raw subtotals are 15864 scalar primitives and
+7944 maps for rank30, or 22152 primitives and 10464 maps for rank16.
+The bound on a map count is not a finite implementation price.
+
+The source native phase proofs and the 640-column input checks remain
+pinned premises. This review does not repeat them. The source prefix
+norm bounds 46/30 for rank30 and 22/22 for rank16 also remain premises;
+the invoice check does not prove bounds on recursive child interiors.
+
+## Independent exact arithmetic
+
+For a histogram H, the calculation is
+
+    M(H) = sum_r H[r] r/(25*224) (25/r)^b.
+
+The new evaluator uses only Python integers and rational numbers. It
+imports neither retained moment engine. For x>=1, write x=2^k y with
+1<=y<2, and put z=(y-1)/(y+1). Then 0<=z<1/3 and
+
+    log(y) = 2 sum_(j>=0) z^(2j+1)/(2j+1).
+
+After 64 terms, the positive omitted tail is at most
+
+    2 z^129 / (129(1-z^2)).
+
+The same expression at z=1/3 bounds log(2). Combine the two bounds and
+round outwards to the rational grid 10^-60.
+
+For 0<=t<1/100, use the degree-20 exponential polynomial. Its omitted
+tail is at most
+
+    (t^20/20!) t/21 / (1-t/22).
+
+The argument condition is checked exactly for each rank. Monotonicity
+gives lower and upper exponential bounds from the logarithm interval.
+Each complete profile interval is contained in its retained budget
+interval. Floating-point numbers do not determine a result.
+
+The checked limits include ranks 1, 2, 4, 8, 9, and 17 for each of the
+nine allowance profiles. The checker also verifies every packed-rank
+limit and its successor, the hypothetical decoder comparators, and the
+six mixed-exit profiles and their H1/H2 limits.
+
+## Main thresholds and the packing theorem
+
+The raw three-call rank30 bill permits 199 H1 or 99 H2. The rank16 bill
+permits 195 H1 or 97 H2. Each pair gives alternatives, not joint
+allowances. A 224-H1 terminal must therefore lose at least 25 H1 or
+29 H1, respectively, if all other work is fixed.
+
+The strict child-size guard gives maximum rank 17. For 0<b<1, the
+function f(r)=r^(1-b) is increasing and strictly concave, with f(0)=0.
+For 1<=a<=c<17,
+
+    f(a-1) + f(c+1) < f(a) + f(c).
+
+Repeated use of this inequality puts all but at most one nonzero child
+at rank 17. Thus the minimum cost for a total of n ranks has
+floor(n/17) copies of H17 and one remainder. This minimum increases
+strictly with n, including each multiple of 17. The checker also checks
+all 136 discrete transfer inequalities at the stated b.
+
+The raw rank30 limit is 200 total ranks: 11 H17 + H13 passes, and
+11 H17 + H14 fails. The raw rank16 limit is 196: 11 H17 + H9 passes,
+and 11 H17 + H10 fails. After three W48/I64 calls and the 224-H1
+comparator, the corresponding limits are 264 and 259. These are
+favorable arithmetic bounds; they do not construct grouped children.
+
+For the mixed exits, the exact thresholds are:
+
+| Family | Changed calls | Extra H1 | Extra H2 |
+| --- | ---: | ---: | ---: |
+| Rank30 | 1 | 71 | 35 |
+| Rank30 | 2 | 167 | 83 |
+| Rank30 | 3 | 263 | 131 |
+| Rank16 | 1 | 66 | 33 |
+| Rank16 | 2 | 162 | 81 |
+| Rank16 | 3 | 258 | 129 |
+
+The next count fails in every column. Each allowance must pay for all
+added native work. The two columns cannot both be spent.
+
+The literal change is the same in both families:
+
+    H_changed - H_raw = 48(H2 - H1 - H3).
+
+Let u_r be the moment cost of one Hr. One changed call therefore saves
+48(u_1+u_3-u_2). In H1 units, this is exactly
+
+    48(1 + 3^(1-b) - 2^(1-b)).
+
+The independent rational enclosure is
+
+    95.846609456084463 < saving/u_1 < 95.846609456084464.
+
+This explains why a 96-rank mass reduction is not a 96-H1 moment
+allowance. Restoring all 96k ranks with H1 requires at least 25 H1 to
+be omitted for rank30, or 30 H1 for rank16, for k=1, 2, or 3. The
+rank16 value 30 is compatible with the raw value 29; the changed
+histogram saves fewer than 96 H1 units per call.
+
+For any positive b, a profile with mass DW and all child ranks below D
+has M(H)>1. This proves the stated conditional full-restoration
+obstruction. It does not prove that full restoration is necessary.
+Three W112 calls and terminal mass 224 have mass 5696>5600, so that
+combination also fails at b=0.
+
+## H9 comparison and remaining scope
+
+The H9 contraction has a separate independent native review at
+`bridge-review-20261017/rank9-completion-review-20261020/FREEZE.json`,
+SHA256
+`50f2e168cdbf08e2bdad445bf2aa28f96d699cbc669a39892927bf94593e3b51`.
+That review was completed after the two budget freezes. This new review
+pins it without changing the frozen budget text.
+
+Its complete profile is
+
+    {1:576, 2:144, 5:144, 7:272, 8:192, 9:64}.
+
+The complete mass is 5600. Its moment is inside
+[1.002547757087305755,1.002547757087305756]. With all other children
+fixed, at most 81 of the final 96 H1 can remain. A reduction of at least
+15 H1 is still required.
+
+No material error was found in either reviewed budget packet. The
+results do not prove a global caller, the placement of changed exits,
+a terminal decoder for their codes, map lowering, a recursive host,
+precision, an odd-grid interface, or a kappa improvement.
+
+## Reproduction and credit
+
+Run `python3 -I -B check_review.py`, then repeat with `-O`. Both runs
+produce the same receipt bytes. The checked output is:
+
+    PASS 176 exact profile intervals; 24 literal words; 16 unchanged scalar sequences
+
+The new-core-transfer lane supplied the local native words. The
+budget-geometry lane supplied the two budget packets. The bridge-access
+lane supplied the H9 contraction. This review uses a separate invoice
+reader and rational evaluator. It used AI assistance and is not an
+independent human review.
+
+No PR, commit, push, or publication is authorized. Before any future PR
+description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/check_review.py b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/check_review.py
new file mode 100644
index 0000000000..d9b374103b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/low-displacement-budget-review-20261020/check_review.py
@@ -0,0 +1,387 @@
+"""Check the literal invoices and the conditional native budgets."""
+
+from collections import Counter
+from fractions import Fraction as Q
+from functools import cache
+from hashlib import sha256
+from pathlib import Path
+import gzip
+import json
+import subprocess
+
+
+HERE = Path(__file__).resolve().parent
+CAMPAIGN = HERE.parents[2]
+REPO = CAMPAIGN.parents[1]
+BUDGET = CAMPAIGN / "lanes/budget-geometry-20261017"
+LOW = BUDGET / "low-displacement-budget-20261020"
+MIXED = BUDGET / "mixed-exit-budget-20261020"
+SOURCE = "lanes/new-core-transfer-20261017/low-displacement-20261020/"
+BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f"
+PINS = {
+    "low_freeze": "c730e61f7446b072c60411f9cb6af903e5b252b12ce9a4d9bce906990303fbef",
+    "low_receipt": "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2",
+    "mixed_freeze": "99f084410fcba6228d396d8c547dd4ed74835dc97de7fce004387b6de6ab92a5",
+    "mixed_receipt": "7359fbab24858a21ea9879fff0b61883134ee3bb754916085689136f6d833224",
+    "selected": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+    "assembly": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+    "rank9_review": "50f2e168cdbf08e2bdad445bf2aa28f96d699cbc669a39892927bf94593e3b51",
+}
+B = Q(67018507072324140917, 40000000000000000000000)
+D, W = 25, 224
+GRID = 10**60
+LOG_TERMS = 64
+EXP_DEGREE = 20
+
+
+def need(value, reason):
+    if not value:
+        raise ValueError(reason)
+
+
+def pinned(raw, digest, label):
+    need(sha256(raw).hexdigest() == digest, "Source pin: " + label)
+    return json.loads(raw)
+
+
+def read(path, digest):
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    return pinned(raw, digest, str(path.relative_to(CAMPAIGN)))
+
+
+def floor(value):
+    return Q((value * GRID).__floor__(), GRID)
+
+
+def ceil(value):
+    return -floor(-value)
+
+
+def log_series(z):
+    need(0 <= z <= Q(1, 3), "Reduced logarithm argument")
+    term, total = z, Q(0)
+    for j in range(LOG_TERMS):
+        total += 2 * term / (2 * j + 1)
+        term *= z * z
+    tail = 2 * term / ((2 * LOG_TERMS + 1) * (1 - z * z))
+    return total, total + tail
+
+
+@cache
+def logarithm(value):
+    need(value >= 1, "Positive logarithm")
+    k = 0
+    while value >= 2:
+        value /= 2
+        k += 1
+    a, b = log_series((value - 1) / (value + 1))
+    c, d = log_series(Q(1, 3))
+    return floor(a + k * c), ceil(b + k * d)
+
+
+def exponential(lo, hi):
+    need(0 <= lo <= hi < Q(1, 100), "Small positive exponential")
+
+    def partial(value):
+        total = term = Q(1)
+        for j in range(1, EXP_DEGREE + 1):
+            term *= value / j
+            total += term
+        return total, term
+
+    low, _ = partial(lo)
+    high, last = partial(hi)
+    tail = last * hi / (EXP_DEGREE + 1) / (1 - hi / (EXP_DEGREE + 2))
+    return floor(low), ceil(high + tail)
+
+
+@cache
+def unit(rank):
+    a, b = logarithm(Q(D, rank))
+    c, d = exponential(B * a, B * b)
+    return Q(rank, D * W) * c, Q(rank, D * W) * d
+
+
+def counts(value):
+    return Counter({int(r): n for r, n in value.items() if n})
+
+
+def mass(value):
+    return sum(r * n for r, n in value.items())
+
+
+def moment(profile):
+    answer = [Q(0), Q(0)]
+    for r, n in profile.items():
+        need(0 < r < D and n > 0, "Positive child multiplicity")
+        low, high = unit(r)
+        answer[0] += n * low
+        answer[1] += n * high
+    return tuple(answer)
+
+
+def encode(value):
+    return [str(x) for x in value]
+
+
+def enclosure(inner, outer, label):
+    a, b = map(Q, outer)
+    need(a <= inner[0] <= inner[1] <= b, "Independent interval is enclosed: " + label)
+
+
+def scalar_word(word):
+    answer = []
+    for event in word["events"]:
+        if event[0] != "scalar":
+            continue
+        gate = event[1]
+        if isinstance(gate[-1], str):
+            op, target, source, coefficient = gate
+            coefficient = Q(coefficient)
+        else:
+            op, target = gate[:2]
+            source = gate[2] if op == "add" else None
+            coefficient = Q(*gate[-2:])
+        need(op in ("add", "scale") and 0 <= target < W, "Data scalar target")
+        need(op != "add" or 0 <= source < W, "Data scalar source")
+        answer.append((op, target, source if op == "add" else None, coefficient))
+    return answer
+
+
+def scalar_price(gate):
+    op, _, _, coefficient = gate
+    if op == "add":
+        need(abs(coefficient) in (1, 2, 3), "Integer ADD tariff")
+        return {1: 8, 2: 10, 3: 12}[abs(coefficient)]
+    need(coefficient in (-1, 2, Q(1, 2), -2, Q(-1, 2)), "Dyadic scale tariff")
+    return 2 * ((abs(coefficient) != 1) + (coefficient < 0))
+
+
+def invoice(word):
+    profile, field_mass = Counter(), Counter()
+    inline = 0
+    for event in word["events"]:
+        kind = event[0]
+        need(kind in ("scalar", "native", "monomial"), "Known local event")
+        if kind == "scalar":
+            continue
+        need(0 <= event[1] < W, "Data native or map owner")
+        recipe = word["native_recipes"][event[-1]]
+        if kind == "native":
+            rank = event[4]
+            need(0 < rank <= 17 and recipe["rank"] == rank, "Native rank and recipe")
+            need(recipe["left"] is not None and recipe["right"] is not None, "Two native side maps")
+            profile[rank] += 1
+            field_mass[event[1]] += rank
+        else:
+            need(recipe["rank"] == 0 and recipe["left"] is not None
+                 and recipe["right"] is None, "One inline monomial map")
+            inline += 1
+    for endpoint in word["endpoint_adapters"]:
+        need(endpoint["rank"] == 0 and endpoint["left"] is not None
+             and endpoint["right"] is None, "One endpoint map")
+    need(set(field_mass) == set(range(W)), "All data fields occur")
+    scalars = scalar_word(word)
+    census = Counter((op, coefficient) for op, _, _, coefficient in scalars)
+    return {
+        "profile": dict(sorted(profile.items())),
+        "native_mass": mass(profile),
+        "children": sum(profile.values()),
+        "scalar_primitives": sum(map(scalar_price, scalars)),
+        "endpoint_maps": len(word["endpoint_adapters"]),
+        "inline_maps": inline,
+        "map_bound": 2 * sum(profile.values()) + len(word["endpoint_adapters"]) + inline,
+        "field_rank_census": dict(sorted(Counter(field_mass.values()).items())),
+        "scalar_census": {op + ":" + str(c): n for (op, c), n in sorted(census.items())},
+    }
+
+
+def packed(total):
+    q, r = divmod(total, 17)
+    return Counter({17: q}) + (Counter({r: 1}) if r else Counter())
+
+
+def main():
+    for directory, key in ((LOW, "low"), (MIXED, "mixed")):
+        freeze = read(directory / "FREEZE.json", PINS[key + "_freeze"])
+        for name, pin in freeze["files"].items():
+            need(sha256((directory / name).read_bytes()).hexdigest() == pin, "Frozen file: " + name)
+    low = read(LOW / "BUDGET.json", PINS["low_receipt"])
+    mixed = read(MIXED / "MIXED-BUDGET.json", PINS["mixed_receipt"])
+    read(HERE.parent / "rank9-completion-review-20261020/FREEZE.json", PINS["rank9_review"])
+    selected_path = "certificates/selected-result.json"
+    selected = pinned(subprocess.check_output(["git", "-C", str(REPO), "show", BASE + ":" + selected_path]),
+                      PINS["selected"], selected_path)
+    assembly = pinned(subprocess.check_output(["git", "-C", str(REPO), "show", BASE + ":" + selected["certificate"]]),
+                      PINS["assembly"], selected["certificate"])
+    need(selected["certificate_sha256"] == PINS["assembly"], "Selected certificate binding")
+    need(Q(assembly["complex_lower"]) == B == Q(low["selected_b_snapshot"])
+         == Q(mixed["selected_b_snapshot"]), "Historical selected exponent")
+    need(0 < B < 1 and (low["dimension"], low["productive_width"], low["calls"]) == (D, W, 3)
+         and low["idle_profile"] == {}, "Conditional schedule")
+
+    sources = {name: read(CAMPAIGN / name, digest) for name, digest in low["source_pins"].items()}
+    raw = {
+        "rank30": sources[SOURCE + "native-normal-v2/NATIVE-PROGRAM.json.gz"]["providers"],
+        "odd_rank16": sources[SOURCE + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz"]["providers"],
+    }
+    changed = sources[SOURCE + "coded-normal/CODED-EXITS-PROGRAM.json.gz"]["providers_by_response_and_code"]
+    words = dict(raw)
+    for family, local in (("rank30", "rank30"), ("odd_rank16", "rank16")):
+        for code in ("W48_I64", "W112"):
+            words[family + "_" + code] = changed[local][code]
+    invoices = {}
+    for name, providers in words.items():
+        need(set(providers) == {"base", "extra"}, "Both providers")
+        invoices[name] = {}
+        for provider, directions in providers.items():
+            need(set(directions) == {"forward", "backward"}, "Both orientations")
+            for direction, word in directions.items():
+                bill = invoice(word)
+                retained = low["literal_native_invoices"][name][provider + "/" + direction]
+                for key, value in bill.items():
+                    expected = retained[key]
+                    if key in ("profile", "field_rank_census"):
+                        expected = {int(k): v for k, v in expected.items()}
+                    need(value == expected, "Literal invoice: " + name + "/" + key)
+                if "_W" in name:
+                    family = name.split("_W")[0]
+                    need(scalar_word(word) == scalar_word(raw[family][provider][direction]),
+                         "The changed exit preserves the complete scalar sequence")
+                invoices[name][provider + "/" + direction] = bill
+    need(sum(len(x) for x in invoices.values()) == 24, "All raw and changed words")
+
+    certificates = {}
+
+    def check_profile(profile, retained, label):
+        interval = moment(profile)
+        enclosure(interval, retained, label)
+        certificates[label] = {"profile": dict(sorted(profile.items())), "moment": encode(interval)}
+        return interval
+
+    def allowance(row, label):
+        profile = counts(row["profile"])
+        need(mass(profile) == row["native_mass"], "Native mass")
+        need(check_profile(profile, row["moment"], label)[1] < 1, "Base passes")
+        for rank, entry in row["limits"].items():
+            rank, n = int(rank), entry["children"]
+            yes = check_profile(profile + Counter({rank: n}), entry["accepted"], label + "/H" + str(rank))
+            no = check_profile(profile + Counter({rank: n + 1}), entry["next"], label + "/H" + str(rank) + "+1")
+            need(yes[1] < 1 < no[0], "Strict threshold")
+            need(entry["rank_mass"] == rank * n, "Threshold rank mass")
+        entry = row["all_legal_ranks"]
+        n = entry["total_rank_limit"]
+        need(entry["maximum_child_rank"] == 17 and 2 * 17**2 < D**2 < 2 * 18**2, "Strict size guard")
+        need(counts(entry["best_profile"]) == packed(n)
+             and counts(entry["next_best_profile"]) == packed(n + 1), "Packed rank optimum")
+        yes = check_profile(profile + packed(n), entry["accepted"], label + "/packed")
+        no = check_profile(profile + packed(n + 1), entry["next"], label + "/packed+1")
+        need(yes[1] < 1 < no[0], "Strict total-rank threshold")
+
+    for family in ("rank30", "odd_rank16"):
+        row = low["results"][family]
+        profile = counts(invoices[family]["base/forward"]["profile"])
+        need(counts(row["profile"]) == Counter({r: 3 * n for r, n in profile.items()}), "Three raw calls")
+        allowance(row, family)
+        full = counts(row["profile"]) + Counter({1: 224})
+        need(mass(full) == D * W and check_profile(full, row["unfused_terminal_moment"], family + "/full")[0] > 1,
+             "Raw terminal comparator fails")
+        need(row["H1_removal_from_unfused_terminal"] == 224 - row["limits"]["1"]["children"], "Raw terminal saving")
+        for n, target in row["hypothetical_H1_terminal_targets"].items():
+            check_profile(counts(row["profile"]) + Counter({1: int(n)}), target["moment"], family + "/target" + n)
+            need(target["remaining_H1"] == row["limits"]["1"]["children"] - int(n), "Hypothetical remainder")
+        for code in ("W48_I64", "W112"):
+            name = family + "_" + code
+            row = low["results"][name]
+            local = counts(invoices[name]["base/forward"]["profile"])
+            three = Counter({r: 3 * n for r, n in local.items()})
+            need(counts(row["local_profile"]) == local
+                 and counts(row["preterminal"]["profile"]) == three, "Three changed calls")
+            allowance(row["preterminal"], name + "/preterminal")
+            full = three + Counter({1: 224})
+            check_profile(full, row["with_terminal_comparator_moment"], name + "/full")
+            need(mass(full) == row["with_terminal_comparator_rank_mass"], "Changed complete mass")
+            if code == "W48_I64":
+                need(counts(row["all_other_debt_after_terminal"]["profile"]) == full, "Changed debt profile")
+                allowance(row["all_other_debt_after_terminal"], name + "/debt")
+                need(mass(full) + row["full_per_call_restoration_rank"] == D * W, "Full restoration mass")
+            else:
+                need(mass(full) == D * W + 96, "Uniform exit excess")
+
+    fusion = low["results"]["matched_H7_H2_fusion"]
+    allowance(fusion, "matched_H9")
+    full = counts(fusion["profile"]) + Counter({1: 96})
+    check_profile(full, fusion["complete_moment"], "matched_H9/full")
+    need(full == Counter({1: 576, 2: 144, 5: 144, 7: 272, 8: 192, 9: 64})
+         and mass(full) == 5600 and fusion["minimum_H1_saving"] == 15, "Reviewed H9 profile")
+
+    mixed_limits = {}
+    for family, rows in mixed["rows"].items():
+        old = counts(invoices[family]["base/forward"]["profile"])
+        new = counts(invoices[family + "_W48_I64"]["base/forward"]["profile"])
+        difference = {r: new[r] - old[r] for r in old.keys() | new.keys() if new[r] != old[r]}
+        need(difference == {1: -48, 2: 48, 3: -48}, "The common changed-exit histogram")
+        mixed_limits[family] = {}
+        for k, row in rows.items():
+            k = int(k)
+            profile = Counter({r: (3 - k) * n for r, n in old.items()})
+            profile.update({r: k * n for r, n in new.items()})
+            profile[1] += 224
+            profile += Counter()
+            need(profile == counts(row["profile"]) and mass(profile) == 5600 - 96 * k, "Mixed word histogram")
+            label = family + "/mixed" + str(k)
+            need(check_profile(profile, row["moment"], label)[1] < 1, "Mixed base passes")
+            for rank, entry in row["limits"].items():
+                rank, n = int(rank), entry["children"]
+                yes = check_profile(profile + Counter({rank: n}), entry["accepted"], label + "/H" + str(rank))
+                no = check_profile(profile + Counter({rank: n + 1}), entry["next"], label + "/H" + str(rank) + "+1")
+                need(yes[1] < 1 < no[0], "Mixed strict threshold")
+            saving = 96 * k - row["limits"]["1"]["children"]
+            need(row["H1_saving_from_full_restoration"] == saving == (25 if family == "rank30" else 30),
+                 "Full all-H1 restoration saving")
+            mixed_limits[family][str(k)] = {rank: entry["children"] for rank, entry in row["limits"].items()}
+
+    u1, u2, u3 = (unit(r) for r in (1, 2, 3))
+    saving = (48 * (u1[0] + u3[0] - u2[1]) / u1[1],
+              48 * (u1[1] + u3[1] - u2[0]) / u1[0])
+    enclosure(saving, ["95.846609456084463", "95.846609456084464"], "Common H1-equivalent saving")
+    need(Q("95.846609456084463") < saving[0] <= saving[1] < Q("95.846609456084464"),
+         "Strict common saving enclosure")
+
+    # These checks cover the discrete steps in the packing proof.
+    for small in range(1, 17):
+        for large in range(small, 17):
+            before = moment(Counter([small, large]))
+            after = moment(Counter([large + 1]) + (Counter([small - 1]) if small > 1 else Counter()))
+            need(after[1] < before[0], "Moving rank to the larger child lowers the cost")
+
+    out = {
+        "status": "PASS_INDEPENDENT_LITERAL_AND_RATIONAL_BUDGET_REVIEW",
+        "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "source_pins": PINS,
+        "upstream_source_pins": low["source_pins"],
+        "selected_commit": BASE,
+        "selected_certificate": selected_path,
+        "selected_assembly": selected["certificate"],
+        "selected_b_snapshot": str(B),
+        "literal_words_checked": 24,
+        "unchanged_changed_scalar_sequences": 16,
+        "literal_invoices": invoices,
+        "exact_method": {"log_series": "64 positive atanh terms after binary reduction",
+                         "exp_degree": EXP_DEGREE, "outward_grid": str(GRID),
+                         "producer_imports": 0, "retained_engine_imports": 0},
+        "profile_intervals_checked": len(certificates),
+        "certificates": certificates,
+        "mixed_limits": mixed_limits,
+        "common_changed_exit_H1_equivalent_saving": encode(saving),
+        "discrete_packing_steps_checked": 136,
+        "scope": "Literal event invoices and conditional D25 histograms. No native phase replay, routed caller, recursive admission, finite map cost, precision, or kappa claim.",
+    }
+    (HERE / "REVIEW.json").write_text(json.dumps(out, indent=2, sort_keys=True) + "\n")
+    print("PASS", len(certificates), "exact profile intervals; 24 literal words; 16 unchanged scalar sequences")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/CHECKS.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/CHECKS.json
new file mode 100644
index 0000000000..b78f18224d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/CHECKS.json
@@ -0,0 +1,77 @@
+{
+  "checker_sha256": "40714657543e99faf87dea8f68e7a88eec9d7683940044ad0c937dbaf5e0ef5f",
+  "child_count": 1392,
+  "complete_native_profile": {
+    "1": 576,
+    "2": 144,
+    "5": 144,
+    "7": 272,
+    "8": 192,
+    "9": 64
+  },
+  "final_X_only_gauge_checked": true,
+  "native_rank_mass": 5600,
+  "new_complex_signs": 64,
+  "new_monomial_wrappers": 128,
+  "providers": {
+    "base": {
+      "complete_operator_equalities": 64,
+      "exact_state_coefficients_final": 32768,
+      "later_event_nonaccess_checks": 8064,
+      "local_Fourier_phase_values": 32768,
+      "local_operator_equalities": 128,
+      "signed_Pauli_columns": 9600,
+      "source_and_owner_assignment_bijection": true,
+      "wrong_sign_controls": 64,
+      "wrong_translation_controls": 64
+    },
+    "extra": {
+      "complete_operator_equalities": 64,
+      "exact_state_coefficients_final": 32768,
+      "later_event_nonaccess_checks": 8064,
+      "local_Fourier_phase_values": 32768,
+      "local_operator_equalities": 128,
+      "signed_Pauli_columns": 9600,
+      "source_and_owner_assignment_bijection": true,
+      "wrong_sign_controls": 64,
+      "wrong_translation_controls": 64
+    }
+  },
+  "scope": "Exact local operator and chronology contraction, all widths by tensorization. No rank saving or full finite supplier invoice.",
+  "source_pins": {
+    "controller": [
+      "encoded-controller/one-pair-current-codes-20261018/PROGRAM.json",
+      "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7"
+    ],
+    "full_gauge": [
+      "independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json",
+      "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89"
+    ],
+    "native": [
+      "oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz",
+      "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025"
+    ],
+    "packet": [
+      "bridge-access-20261017/rank9-completion-20261020/RANK9-PROGRAMS.json.gz",
+      "9a8e4f1e34b23f97435ea7d953f1a6e1a1059f88920f314712fa592be52ddaac"
+    ],
+    "permutation": [
+      "history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz",
+      "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9"
+    ],
+    "producer_proof": [
+      "bridge-access-20261017/rank9-completion-20261020/RANK9.md",
+      "a9271f13f08a25d48906051216200ed4424c52de2dabde4e7227eceffb49ef99"
+    ],
+    "triple": [
+      "bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-PROGRAMS.json.gz",
+      "b65a2b14a1e61c566063195d0ef363c7dae0d06bb2232e4c872275479f327419"
+    ],
+    "views": [
+      "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json",
+      "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"
+    ]
+  },
+  "status": "PASS_INDEPENDENT_RANK9_COMPLETION",
+  "unchanged_sign_primitive_price": 128
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..f46c95e6fd
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/FREEZE.json
@@ -0,0 +1,11 @@
+{
+  "files": {
+    "CHECKS.json": "26ed225989f554331212f833db3079cfdddbb3588bf1306f158c62001ae13c2f",
+    "NORMAL-HASHES.json": "a3af5577d7a1572978c6cccd285ca4b12b9793bde5675826a8e3120ffe2c9832",
+    "REVIEW.md": "91245e09657c37999259b1d34d08a6386242d5a4f4ddd6b10dcc7bb9a4f4f56a",
+    "check_rank9.py": "40714657543e99faf87dea8f68e7a88eec9d7683940044ad0c937dbaf5e0ef5f"
+  },
+  "normal_optimized_receipt_bytes_identical": true,
+  "scope": "Complete exact rank9 operator contraction and one-field native/monomial Clifford rank lower bound. No rank saving or complete supplier claim.",
+  "status": "FROZEN_INDEPENDENT_REVIEW"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/NORMAL-HASHES.json b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/NORMAL-HASHES.json
new file mode 100644
index 0000000000..7d5a9a3a36
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/NORMAL-HASHES.json
@@ -0,0 +1,3 @@
+{
+  "CHECKS.json": "26ed225989f554331212f833db3079cfdddbb3588bf1306f158c62001ae13c2f"
+}
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..3f495de6fb
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/REVIEW.md
@@ -0,0 +1,214 @@
+# Independent review of the last rank9 contraction
+
+The contraction is exact for all 64 preferred paths and both providers.
+It replaces one rank7 completion and one rank2 terminal child by one
+rank9 child on each path. It removes 64 children. It does not reduce
+the native rank mass, which remains 5,600.
+
+## Independent method
+
+The checker imports no producer code. `CHECKS.json` pins the emitted
+recipes, native words, permutation suffix, triple terminal, D25 views,
+controller, and final scalar gauge.
+
+The phase interpreter uses the convention
+
+```text
+i^s X_x Z_z.
+```
+
+A positive line gate is
+
+```text
+C_q = ((1+i)I+(1-i)X_q)/2.
+```
+
+If z dot q is one, its Pauli action changes x to x+q and s to s-1.
+If z dot q is zero, it fixes the Pauli operator. The inverse has the
+opposite phase change. Binary linear maps act by M on x and M^-T
+on z. Diagonal phases are checked from their exact quadratic form.
+These rules give a separate implementation of signed Pauli conjugation.
+
+The checker also applies each full circuit to the basis vector at
+address zero. It keeps Gaussian integer numerators and an exact power
+of two denominator. This check fixes the constant complex phase that
+a Pauli tableau cannot see.
+
+All circuit factors are unitary. Equal conjugation on all Pauli
+generators implies that two such circuits differ by one scalar.
+Equality on a nonzero state fixes that scalar. Thus the two checks
+prove operator equality on every input, not only on the tested basis
+vector.
+
+## Canonical completion and the exact terminal product
+
+Let M_p be the source endpoint adapter and T_p=M_p C_qp. The retained
+Y field is at T_p after its last scalar transfer. Its omitted native
+completion and target endpoint adapter have exact operator
+
+```text
+R_r = F9 C_qr^-1 C_qp^-1 M_p^-1.
+```
+
+The checker derives this operator from the actual serialized rank7
+recipe and both endpoint adapters. It verifies the complete signed
+Pauli map and global phase.
+
+The seven recorded complement vectors, together with q_r and q_p,
+form an orthonormal basis of the nine-dimensional root. For every
+one of its 512 characters, the checker verifies
+
+```text
+weight(chi)-sum_v (chi dot v) = 2 (Delta dot chi) mod 4.
+```
+
+Hence
+
+```text
+R_r = X_Delta (product_j C_uj) M_p^-1.
+```
+
+Let rho be the literal stage-two route, e its exit translation, A
+the inverse-triple owner map, and delta the complete triple Fourier
+translation. The preceding raw terminal contributes X_qr. The exact
+ordered terminal path is
+
+```text
+-X_delta C_a C_b^-1 P_A X_qr X_e P_rho R_r,
+a=q_p,                   b=A q_r.
+```
+
+Since P_A X_qr=X_b P_A and C_b^-1 X_b=C_b, this becomes
+
+```text
+-X_tau C_a C_b (product_j C_(A rho uj)) P_(A rho) M_p^-1,
+tau=delta+A(e+rho Delta).
+```
+
+The nine displayed directions are orthonormal on every actual path.
+Their full product therefore has Fourier rank nine. The checker also
+finds rank nine directly from the X components of the images of the
+25 Z generators.
+
+Each emitted right wrapper includes M_p^-1 and A rho. Each left
+wrapper includes the exact translation tau. The complete serialized
+wrappers, the positive H9 child, and the scalar minus sign are compared
+with the ordered old circuit. Wrong-sign and wrong-translation controls
+are rejected on every path.
+
+There is a matching local rank obstruction. For a Clifford operator,
+write its binary Pauli matrix as [[A,B],[C,D]], so B contains the X
+parts of the images of Z generators. Composition gives
+
+```text
+B_(12) = A_1 B_2+B_1 D_2,
+rank(B_(12)) <= rank(B_1)+rank(B_2).
+```
+
+A monomial Clifford has B=0. A rank-k native child, with monomial
+wrappers, has rank(B)=k. Consequently any such circuit on this one
+field has total native rank at least rank(B_target)=9. The old 7+2
+word and the new rank9 word both attain this local bound.
+
+Here the input basis is the physical computational-address basis of
+the deferred Y field at its canonical T_p cut. The target operator
+ends in the raw output-p chart after the full terminal. Its right
+side includes M_p^-1, and its left side includes the final translation.
+The rank computation uses that complete ordered operator. It does
+not remove the current frame by an unpriced Fourier change of basis.
+
+This obstruction allows arbitrary monomial Clifford wrappers between
+children. It does not cover cross-field scalar mixing, a changed
+target operator, productive centre sharing, or a general supplier.
+
+Before tensorization, cancel the common scalar minus sign in the two
+equal operators. The remaining single-column equality tensorizes at
+every width. Restore one scalar minus sign on the full field. This
+keeps the scalar sign separate from column phases in the wrappers.
+
+## Why the operation can be deferred
+
+The retained permutation64 word is the literal suffix of the complete
+native word. The checker locates each last scalar transfer and its
+actual rank7 target completion. It checks every later event for a
+read or write of that target. There is none.
+
+The pinned controller ends with the final forward call and then one
+X-only code. The checker verifies that every operand of the actual
+full scalar gauge is in the X bank. Thus deferring the 64 Y completions
+does not change any later local scalar input.
+
+The retained signed bank exchange is a physical array permutation
+with signs. It remains valid on arbitrary incomplete-frame arrays.
+On these 64 fields its Q-squared map is omitted, since that map has
+already been included in the exact contraction above.
+
+The output-to-source port map is a permutation. Each actual A rho
+is invertible and orthogonal, so its right action on the regular
+O(25,2) cover is a permutation as well. The combined source assignment
+is therefore bijective. No second copy or zero input is required.
+This proves the field assignment. It does not price its packed
+field-and-address permutation.
+
+## Exact invoice and its limit
+
+The complete profile changes from
+
+```text
+{1:576,2:208,5:144,7:336,8:192}
+```
+
+to
+
+```text
+{1:576,2:144,5:144,7:272,8:192,9:64}.
+```
+
+The latter has 1,392 children and rank mass 5,600. The 64 new child
+recipes have 128 monomial wrappers. Their 64 complex negative signs
+cost 128 real scalar primitives; these signs replace the same signs
+in the previous terminal. The signed bank exchange remains. No owned
+or private field is added.
+
+For 0<sigma<1, strict subadditivity gives
+
+```text
+64 (9^sigma-7^sigma-2^sigma) < 0.
+```
+
+Thus the contraction reduces the native child moment at fixed field
+volume. This is not a positive-exponent supplier. In the inherited
+224-field, D25 normalization, all child ranks are below 25 and
+
+```text
+(1/224) sum_r count(r) (r/25) = 5600/(224*25) = 1.
+```
+
+For every b>0 with sigma=1-b, each term (r/25)^(1-b) is strictly
+larger than r/25. The normalized native moment remains above one.
+The contraction cannot by itself cross the native admissibility
+threshold.
+
+The proof preserves the scalar response. It does not supply the
+complete finite precision bound, full-cover correction, packed map
+price, or revised recursive row-hosting certificate. Those obligations
+remain as stated in the producer packet.
+
+## Reproduction and credit
+
+Run `python3 -I -B check_rank9.py` and
+`python3 -O -I -B check_rank9.py`. Both must end with
+`PASS_INDEPENDENT_RANK9_COMPLETION` and produce identical receipt bytes.
+
+Per provider, the review checks 64 complete and 128 local operator
+equalities, 9,600 signed Pauli columns, all 32,768 local Fourier phase
+values, and the exact Gaussian state images. The receipt gives the
+state coefficient and chronology counts.
+
+The bridge-access lane supplied the contraction and literal wrappers.
+The history lane supplied the permutation64 word. The controller
+lane supplied the current five-cut program. Earlier independent
+reviews supply the complete triple-terminal and scalar-gauge context.
+This review supplies separate phase, chronology, and invoice checks.
+AI assistance was used. No PR, publication, rank saving, or kappa
+improvement is claimed.
diff --git a/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/check_rank9.py b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/check_rank9.py
new file mode 100644
index 0000000000..3cc03fca83
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/bridge-review-20261017/rank9-completion-review-20261020/check_rank9.py
@@ -0,0 +1,339 @@
+"""Check the complete rank9 contraction with an independent phase interpreter."""
+
+from collections import Counter
+from functools import lru_cache
+from hashlib import sha256
+from pathlib import Path
+import gzip
+import json
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+SELF_PIN = sha256(Path(__file__).read_bytes()).hexdigest()
+N = 25
+UNIT = tuple(1 << j for j in range(N))
+SOURCES = {
+    "packet": ("bridge-access-20261017/rank9-completion-20261020/RANK9-PROGRAMS.json.gz",
+               "9a8e4f1e34b23f97435ea7d953f1a6e1a1059f88920f314712fa592be52ddaac"),
+    "native": ("oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz",
+               "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025"),
+    "permutation": ("history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz",
+                    "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9"),
+    "triple": ("bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-PROGRAMS.json.gz",
+               "b65a2b14a1e61c566063195d0ef363c7dae0d06bb2232e4c872275479f327419"),
+    "views": ("bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json",
+              "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"),
+    "producer_proof": ("bridge-access-20261017/rank9-completion-20261020/RANK9.md",
+                       "a9271f13f08a25d48906051216200ed4424c52de2dabde4e7227eceffb49ef99"),
+    "controller": ("encoded-controller/one-pair-current-codes-20261018/PROGRAM.json",
+                   "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7"),
+    "full_gauge": ("independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json",
+                   "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def parity(x):
+    return x.bit_count() & 1
+
+
+def act(rows, x):
+    return sum(parity(row & x) << j for j, row in enumerate(rows))
+
+
+def transpose(rows):
+    return tuple(sum(((row >> j) & 1) << i for i, row in enumerate(rows)) for j in range(len(rows)))
+
+
+def act_columns(columns, x):
+    result = 0
+    for j, column in enumerate(columns):
+        if x >> j & 1:
+            result ^= column
+    return result
+
+
+def rank(vectors):
+    basis = {}
+    for x in vectors:
+        while x:
+            j = x.bit_length()-1
+            if j in basis:
+                x ^= basis[j]
+            else:
+                basis[j] = x
+                break
+    return len(basis)
+
+
+@lru_cache(None)
+def inverse(rows):
+    size = len(rows)
+    left, right = list(rows), [1 << j for j in range(size)]
+    for j in range(size):
+        pivot = next(i for i in range(j, size) if left[i] >> j & 1)
+        left[j], left[pivot] = left[pivot], left[j]
+        right[j], right[pivot] = right[pivot], right[j]
+        for i in range(size):
+            if i != j and left[i] >> j & 1:
+                left[i] ^= left[j]
+                right[i] ^= right[j]
+    need(tuple(left) == tuple(1 << j for j in range(size)), "Invertible affine matrix")
+    return tuple(right)
+
+
+def monomial(record):
+    if record is None:
+        return []
+    size = len(record["matrix_rows"])
+    need(size in (9, 25), "Declared monomial dimension")
+    rows = tuple(record["matrix_rows"]) + UNIT[size:]
+    quadratic = tuple(record["quadratic_rows"]) + (0,)*(N-size)
+    linear = tuple(record["linear_Z4"]) + (0,)*(N-size)
+    need(all(((quadratic[i] >> j) & 1) == ((quadratic[j] >> i) & 1)
+             for i in range(N) for j in range(N)), "Symmetric quadratic phase")
+    need(all(((quadratic[i] >> i) & 1) == linear[i] % 2 for i in range(N)),
+         "Quadratic phase diagonal convention")
+    inverse(rows)
+    return [("D", quadratic, linear), ("P", rows), ("X", record["offset"]),
+            ("PHASE", record["phase"])]
+
+
+def native(record):
+    return (monomial(record["right"]) +
+            [("C", 1 << j, 1) for j in range(record["rank"])] +
+            monomial(record["left"]))
+
+
+def adjoint(circuit):
+    out = []
+    for gate in reversed(circuit):
+        tag = gate[0]
+        if tag == "P":
+            out.append(("P", inverse(gate[1])))
+        elif tag == "D":
+            out.append(("D", gate[1], tuple((-x) % 4 for x in gate[2])))
+        elif tag in ("C", "PHASE"):
+            out.append((*gate[:-1], -gate[-1]))
+        else:
+            need(tag == "X", "Adjoint gate")
+            out.append(gate)
+    return out
+
+
+def phase_value(gate, x):
+    value = sum(c for j, c in enumerate(gate[2]) if x >> j & 1)
+    for j, row in enumerate(gate[1]):
+        if x >> j & 1:
+            value += 2*parity((row >> (j+1)) & (x >> (j+1)))
+    return value % 4
+
+
+def pauli(circuit, x, z):
+    power = 0
+    for gate in circuit:
+        tag = gate[0]
+        if tag == "P":
+            x = act(gate[1], x)
+            z = act(transpose(inverse(gate[1])), z)
+        elif tag == "X":
+            power += 2*parity(z & gate[1])
+        elif tag == "D":
+            power += phase_value(gate, x)
+            z ^= act(gate[1], x)
+        elif tag == "C":
+            if parity(z & gate[1]):
+                x ^= gate[1]
+                power -= gate[2]
+        else:
+            need(tag == "PHASE", "Pauli interpreter opcode")
+    return x, z, power % 4
+
+
+def tableau(circuit):
+    return ([pauli(circuit, 1 << j, 0) for j in range(N)] +
+            [pauli(circuit, 0, 1 << j) for j in range(N)])
+
+
+def rotate(pair, power):
+    a, b = pair
+    return ((a, b), (-b, a), (-a, -b), (b, -a))[power % 4]
+
+
+def state_zero(circuit):
+    state, denominator = {0: (1, 0)}, 0
+    for gate in circuit:
+        tag = gate[0]
+        if tag == "C":
+            out = {}
+            sign, direction = gate[2], gate[1]
+            for x, (a, b) in state.items():
+                for address, value in ((x, (a-sign*b, b+sign*a)),
+                                       (x ^ direction, (a+sign*b, b-sign*a))):
+                    old = out.get(address, (0, 0))
+                    out[address] = old[0]+value[0], old[1]+value[1]
+            state = {x: c for x, c in out.items() if c != (0, 0)}
+            denominator += 1
+        elif tag == "P":
+            state = {act(gate[1], x): c for x, c in state.items()}
+        elif tag == "X":
+            state = {x ^ gate[1]: c for x, c in state.items()}
+        elif tag == "D":
+            state = {x: rotate(c, phase_value(gate, x)) for x, c in state.items()}
+        else:
+            need(tag == "PHASE", "Exact state interpreter opcode")
+            state = {x: rotate(c, gate[1]) for x, c in state.items()}
+    while denominator and all(a % 2 == b % 2 == 0 for a, b in state.values()):
+        state = {x: (a//2, b//2) for x, (a, b) in state.items()}
+        denominator -= 1
+    return state, denominator
+
+
+def equal(a, b, label):
+    ta, tb = tableau(a), tableau(b)
+    need(ta == tb, label+" signed Pauli generators")
+    need(state_zero(a) == state_zero(b), label+" exact global phase")
+    return ta
+
+
+def main():
+    data = {}
+    for name, (relative, pin) in SOURCES.items():
+        raw = (LANES/relative).read_bytes()
+        if relative.endswith(".gz"):
+            raw = gzip.decompress(raw)
+        need(sha256(raw).hexdigest() == pin, "Source pin "+name)
+        if not relative.endswith(".md"):
+            data[name] = json.loads(raw)
+    packet, permutation, triple = data["packet"], data["permutation"], data["triple"]
+    need(data["controller"]["program"][-2:] == [["forward", 2], ["code_X", 1, -1]],
+         "Only the final X code follows the last forward call")
+    final_cut = triple["five_scalar_codes"][-1]
+    need(final_cut["cut"] == "after_F2" and final_cut["side"] == "X"
+         and final_cut["scalar_gauge_sha256"] == SOURCES["full_gauge"][1],
+         "The exact final current-cut gauge")
+    for event in data["full_gauge"]["events"]:
+        need(event[0] in ("add", "scale") and 0 <= event[1] < 112,
+             "The final gauge writes only X fields")
+        if event[0] == "add":
+            need(0 <= event[2] < 112, "The final gauge reads only X fields")
+    views = {(row["stage"], row["port"]): row for row in data["views"]["entries"]}
+    q = {p: views[0, p]["q"] for p in range(112)}
+    active = set(permutation["active_ports"])
+    paths = [row for row in triple["path_records"]["T_inverse"] if row["target"] in active]
+    need(len(paths) == 64 and len({row["target"] for row in paths}) == 64, "Unique terminal paths")
+    paths = {row["target"]: row for row in paths}
+    reports = {}
+    for provider in ("base", "extra"):
+        word = permutation["providers"][provider]["forward"]
+        whole = data["native"]["providers"][provider]["forward"]
+        need(whole["events"][whole["inherited_64_first_event"]:] == word["events"], "Literal native suffix")
+        adapters = {(row["port"], row["role"]): row for row in word["endpoint_adapters"]}
+        records = packet["providers"][provider]
+        need(len(records) == 64 and {row["output_port"] for row in records} ==
+             {row["source_port"] for row in records} == active, "Full cover source-port bijection")
+        checks, coefficients, later_events = 0, 0, 0
+        for record in records:
+            p, r = record["output_port"], record["source_port"]
+            path = paths[p]
+            need(path["source"] == r and path["coefficient"] == "-1", "Actual preferred terminal path")
+            transfer = next(row for row in word["transfers"] if row["source_port"] == p)
+            need(transfer["target_port"] == r, "The final source and target pair")
+            position = transfer["event"]+2
+            event = word["events"][position]
+            need(position == record["removed_native_event"] and event[:2] == ["native", 112+r]
+                 and event[4] == 7 and event[5] == record["old_completion_recipe_key"],
+                 "Actual removed completion")
+            need(event[2] == transfer["frame"], "The target is at the actual source line frame")
+            for later in word["events"][position+1:]:
+                touched = [later[1]] if later[0] == "native" else later[1][1:3]
+                need(112+r not in touched, "No later local target read or write")
+                later_events += 1
+            completion = word["native_recipes"][event[5]]
+            need(completion == whole["native_recipes"][event[5]], "Actual complete-core child recipe")
+            source_adapter = native(adapters[p, "source"])
+            target_adapter = native(adapters[r, "target"])
+            local = native(completion)+adjoint(target_adapter)
+            conventional = (adjoint(source_adapter) + [("C", q[p], -1), ("C", q[r], -1)] +
+                            [("C", 1 << j, 1) for j in range(9)])
+            equal(local, conventional, "Canonical completion")
+            complement = record["local_seven_axes"]
+            basis = [q[r], q[p]]+complement
+            need(len(complement) == 7 and all(x < 512 for x in basis) and
+                 all(parity(x & y) == (i == j) for i, x in enumerate(basis) for j, y in enumerate(basis)),
+                 "Exact local orthonormal complement")
+            delta = record["local_full_translation"]
+            for chi in range(512):
+                difference = (chi.bit_count()-sum(parity(x & chi) for x in basis)) % 4
+                need(difference == 2*parity(delta & chi), "All local full-frame Fourier phases")
+            factored = adjoint(source_adapter)+[("C", x, 1) for x in complement]+[("X", delta)]
+            equal(local, factored, "Seven-axis local factor")
+            route = path["route_columns"]
+            rho = views[2, r]["route_columns"]
+            composed = [act_columns(route, column) for column in rho]
+            need(route == record["terminal_route_columns"] and rho == record["stage2_route_columns"]
+                 and composed == record["cover_route_columns"], "Literal owner routes")
+            need(rank(composed) == N and all(parity(x & y) == (i == j)
+                 for i, x in enumerate(composed) for j, y in enumerate(composed)), "Cover-group owner map")
+            exit_shift = views[2, r]["literal_stage_alignment"]["exit_Y"]
+            a, b = path["lines"]
+            need(a == q[p] and b == act_columns(route, q[r]), "The two terminal lines")
+            axes = [a, b]+[act_columns(composed, x) for x in complement]
+            tau = path["FULL_translation"] ^ act_columns(route, exit_shift ^ act_columns(rho, delta))
+            need(axes == record["native_axes"] and tau == record["output_translation"], "Nine axes and exact shift")
+            need(all(parity(x & y) == (i == j) for i, x in enumerate(axes) for j, y in enumerate(axes)),
+                 "Nine orthonormal directions")
+            actual = (local + [("P", transpose(rho)), ("X", exit_shift), ("X", q[r]),
+                              ("P", transpose(route)), ("C", b, -1), ("C", a, 1),
+                              ("X", path["FULL_translation"]), ("PHASE", 2)])
+            compiled = (monomial(record["right"])+[("C", 1 << j, 1) for j in range(9)] +
+                        monomial(record["left"])+[("PHASE", 2)])
+            t = equal(actual, compiled, "Complete contraction")
+            need(rank([x for x, z, power in t[N:]]) == 9, "Exact Fourier rank")
+            need(state_zero(actual) != state_zero(compiled[:-1]), "The negative sign is required")
+            wrong_left = dict(record["left"], offset=record["left"]["offset"] ^ 1)
+            wrong = monomial(record["right"])+[("C", 1 << j, 1) for j in range(9)]+monomial(wrong_left)
+            need(tableau(actual) != tableau(wrong), "A wrong translation is rejected")
+            need(record["source_field_before_signed_exchange"] == 112+r
+                 and record["source_field_after_signed_exchange"] == r
+                 and record["output_field"] == p and record["rank"] == 9
+                 and record["sign"] == -1, "Arbitrary-state exchange roles")
+            checks += 1
+            coefficients += len(state_zero(compiled)[0])
+        reports[provider] = {"complete_operator_equalities": checks, "local_operator_equalities": 2*checks,
+                             "signed_Pauli_columns": 3*checks*2*N,
+                             "exact_state_coefficients_final": coefficients,
+                             "local_Fourier_phase_values": checks*512,
+                             "later_event_nonaccess_checks": later_events,
+                             "wrong_sign_controls": checks, "wrong_translation_controls": checks,
+                             "source_and_owner_assignment_bijection": True}
+        print(provider, "PASS_INDEPENDENT_RANK9", flush=True)
+    before = {int(r): c for r, c in packet["complete_native_profile_before"].items()}
+    after = {int(r): c for r, c in packet["complete_native_profile_after"].items()}
+    expected = Counter(before)
+    expected.subtract({7: 64, 2: 64})
+    expected.update({9: 64})
+    need(dict(expected) == after and sum(r*c for r, c in before.items()) ==
+         sum(r*c for r, c in after.items()) == 5600, "Exact full-profile substitution")
+    need(sum(before.values())-sum(after.values()) == 64, "Child count reduction")
+    need(packet["new_wrapper_calls"] == 128 and packet["real_sign_primitives"] == 128
+         and packet["owned_fields"] == packet["private_fields"] == 0, "Local invoice")
+    need(sha256(Path(__file__).read_bytes()).hexdigest() == SELF_PIN, "Fixed checker")
+    receipt = {"status": "PASS_INDEPENDENT_RANK9_COMPLETION",
+               "checker_sha256": SELF_PIN, "source_pins": SOURCES, "providers": reports,
+               "complete_native_profile": after, "native_rank_mass": 5600,
+               "child_count": sum(after.values()), "new_monomial_wrappers": 128,
+               "new_complex_signs": 64, "unchanged_sign_primitive_price": 128,
+               "final_X_only_gauge_checked": True,
+               "scope": "Exact local operator and chronology contraction, all widths by tensorization. No rank saving or full finite supplier invoice."}
+    (HERE/"CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n")
+    print(receipt["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/BUDGET.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/BUDGET.json
new file mode 100644
index 0000000000..8659daf530
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/BUDGET.json
@@ -0,0 +1,555 @@
+{
+  "assembly_sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+  "calls": 3,
+  "checker_sha256": "d1ec38fa1eabda116ce6d5bbfe2fff20dd3803736266755395e5aac7f6ee7349",
+  "dimension": 25,
+  "engine_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "engine_pins": {
+    "base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482"
+  },
+  "gzip_pin_convention": "SHA256 after decompression",
+  "historical_selected_b": "67018507072324140917/40000000000000000000000",
+  "idle_profile": {},
+  "literal": {
+    "clean": {
+      "base/I": {
+        "children": 1520,
+        "input_views": 112,
+        "mass": 1808,
+        "native_side_map_bound": 3008,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "9": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 720,
+          "add:1": 312,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3216
+      },
+      "base/Q": {
+        "children": 1520,
+        "input_views": 128,
+        "mass": 1792,
+        "native_side_map_bound": 3040,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 720,
+          "add:1": 312,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3264
+      },
+      "extra/I": {
+        "children": 1520,
+        "input_views": 112,
+        "mass": 1808,
+        "native_side_map_bound": 3008,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "9": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 720,
+          "add:1": 312,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3216
+      },
+      "extra/Q": {
+        "children": 1520,
+        "input_views": 128,
+        "mass": 1792,
+        "native_side_map_bound": 3040,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 720,
+          "add:1": 312,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3264
+      }
+    },
+    "dual": {
+      "base/inverse_adjoint": {
+        "children": 1520,
+        "input_views": 128,
+        "mass": 1792,
+        "native_side_map_bound": 3040,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 312,
+          "add:1": 720,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3264
+      },
+      "base/selected_swap_conjugate": {
+        "children": 1520,
+        "input_views": 128,
+        "mass": 1792,
+        "native_side_map_bound": 3040,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 312,
+          "add:1": 720,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3264
+      },
+      "extra/inverse_adjoint": {
+        "children": 1520,
+        "input_views": 128,
+        "mass": 1792,
+        "native_side_map_bound": 3040,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 312,
+          "add:1": 720,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3264
+      },
+      "extra/selected_swap_conjugate": {
+        "children": 1520,
+        "input_views": 128,
+        "mass": 1792,
+        "native_side_map_bound": 3040,
+        "output_views": 96,
+        "profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "scalar": 8600,
+        "scalar_census": {
+          "add:-1": 312,
+          "add:1": 720,
+          "scale:-1": 30,
+          "scale:-1/2": 19,
+          "scale:-2": 19,
+          "scale:1/2": 33,
+          "scale:2": 33
+        },
+        "total_map_bound": 3264
+      }
+    }
+  },
+  "productive_width": 224,
+  "results": {
+    "one_I_two_Q": {
+      "hypothetical_H1_cleanup": {
+        "112": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "999903132550720507/1000000000000000000",
+                "249975783137680127/250000000000000000"
+              ],
+              "children": 68,
+              "next": [
+                "500041334817796197/500000000000000000",
+                "200016533927118479/200000000000000000"
+              ],
+              "rank_mass": 68
+            },
+            "2": {
+              "accepted": [
+                "249972240627135393/250000000000000000",
+                "999888962508541573/1000000000000000000"
+              ],
+              "children": 34,
+              "next": [
+                "200049523982467781/200000000000000000",
+                "500123809956169453/500000000000000000"
+              ],
+              "rank_mass": 68
+            }
+          },
+          "mass": 5504,
+          "moment": [
+            "987694610779432221/1000000000000000000",
+            "493847305389716111/500000000000000000"
+          ],
+          "profile": {
+            "1": 4288,
+            "2": 192,
+            "3": 144,
+            "8": 32,
+            "9": 16
+          }
+        },
+        "128": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "999903132550720507/1000000000000000000",
+                "249975783137680127/250000000000000000"
+              ],
+              "children": 52,
+              "next": [
+                "500041334817796197/500000000000000000",
+                "200016533927118479/200000000000000000"
+              ],
+              "rank_mass": 52
+            },
+            "2": {
+              "accepted": [
+                "499946148318056543/500000000000000000",
+                "999892296636113087/1000000000000000000"
+              ],
+              "children": 26,
+              "next": [
+                "50012547701995521/50000000000000000",
+                "1000250954039910421/1000000000000000000"
+              ],
+              "rank_mass": 52
+            }
+          },
+          "mass": 5520,
+          "moment": [
+            "495283602068691203/500000000000000000",
+            "990567204137382407/1000000000000000000"
+          ],
+          "profile": {
+            "1": 4304,
+            "2": 192,
+            "3": 144,
+            "8": 32,
+            "9": 16
+          }
+        },
+        "144": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "999903132550720507/1000000000000000000",
+                "249975783137680127/250000000000000000"
+              ],
+              "children": 36,
+              "next": [
+                "500041334817796197/500000000000000000",
+                "200016533927118479/200000000000000000"
+              ],
+              "rank_mass": 36
+            },
+            "2": {
+              "accepted": [
+                "4999478153818423/5000000000000000",
+                "999895630763684601/1000000000000000000"
+              ],
+              "children": 18,
+              "next": [
+                "500127144083740967/500000000000000000",
+                "200050857633496387/200000000000000000"
+              ],
+              "rank_mass": 36
+            }
+          },
+          "mass": 5536,
+          "moment": [
+            "993439797495332591/1000000000000000000",
+            "62089987343458287/62500000000000000"
+          ],
+          "profile": {
+            "1": 4320,
+            "2": 192,
+            "3": 144,
+            "8": 32,
+            "9": 16
+          }
+        }
+      },
+      "limits": {
+        "1": {
+          "accepted": [
+            "999903132550720507/1000000000000000000",
+            "249975783137680127/250000000000000000"
+          ],
+          "children": 180,
+          "next": [
+            "500041334817796197/500000000000000000",
+            "200016533927118479/200000000000000000"
+          ],
+          "rank_mass": 180
+        },
+        "2": {
+          "accepted": [
+            "249966405903885243/250000000000000000",
+            "999865623615540973/1000000000000000000"
+          ],
+          "children": 90,
+          "next": [
+            "500112140509669153/500000000000000000",
+            "1000224281019338307/1000000000000000000"
+          ],
+          "rank_mass": 180
+        }
+      },
+      "mass": 5392,
+      "moment": [
+        "483793228636890463/500000000000000000",
+        "967586457273780927/1000000000000000000"
+      ],
+      "profile": {
+        "1": 4176,
+        "2": 192,
+        "3": 144,
+        "8": 32,
+        "9": 16
+      },
+      "source_scope": "The local words are supplied. Their routed three-call composition and terminal are not admitted.",
+      "three_call_map_bound": 9744,
+      "three_call_scalar_subtotal": 25800
+    },
+    "three_Q": {
+      "hypothetical_H1_cleanup": {
+        "112": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "999918207008622093/1000000000000000000",
+                "499959103504311047/500000000000000000"
+              ],
+              "children": 84,
+              "next": [
+                "1000097744093493979/1000000000000000000",
+                "50004887204674699/50000000000000000"
+              ],
+              "rank_mass": 84
+            },
+            "2": {
+              "accepted": [
+                "999900702838871643/1000000000000000000",
+                "249975175709717911/250000000000000000"
+              ],
+              "children": 42,
+              "next": [
+                "1000259360242668977/1000000000000000000",
+                "500129680121334489/500000000000000000"
+              ],
+              "rank_mass": 84
+            }
+          },
+          "mass": 5488,
+          "moment": [
+            "492418545939691811/500000000000000000",
+            "984837091879383623/1000000000000000000"
+          ],
+          "profile": {
+            "1": 4288,
+            "2": 192,
+            "3": 144,
+            "8": 48
+          }
+        },
+        "128": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "999918207008622093/1000000000000000000",
+                "499959103504311047/500000000000000000"
+              ],
+              "children": 68,
+              "next": [
+                "1000097744093493979/1000000000000000000",
+                "50004887204674699/50000000000000000"
+              ],
+              "rank_mass": 68
+            },
+            "2": {
+              "accepted": [
+                "999904036966443157/1000000000000000000",
+                "499952018483221579/500000000000000000"
+              ],
+              "children": 34,
+              "next": [
+                "1000262694370240491/1000000000000000000",
+                "250065673592560123/250000000000000000"
+              ],
+              "rank_mass": 68
+            }
+          },
+          "mass": 5504,
+          "moment": [
+            "987709685237333807/1000000000000000000",
+            "61731855327333363/62500000000000000"
+          ],
+          "profile": {
+            "1": 4304,
+            "2": 192,
+            "3": 144,
+            "8": 48
+          }
+        },
+        "144": {
+          "limits": {
+            "1": {
+              "accepted": [
+                "999918207008622093/1000000000000000000",
+                "499959103504311047/500000000000000000"
+              ],
+              "children": 52,
+              "next": [
+                "1000097744093493979/1000000000000000000",
+                "50004887204674699/50000000000000000"
+              ],
+              "rank_mass": 52
+            },
+            "2": {
+              "accepted": [
+                "999907371094014671/1000000000000000000",
+                "62494210693375917/62500000000000000"
+              ],
+              "children": 26,
+              "next": [
+                "200053205699562401/200000000000000000",
+                "500133014248906003/500000000000000000"
+              ],
+              "rank_mass": 52
+            }
+          },
+          "mass": 5520,
+          "moment": [
+            "123822784824410499/125000000000000000",
+            "990582278595283993/1000000000000000000"
+          ],
+          "profile": {
+            "1": 4320,
+            "2": 192,
+            "3": 144,
+            "8": 48
+          }
+        }
+      },
+      "limits": {
+        "1": {
+          "accepted": [
+            "999918207008622093/1000000000000000000",
+            "499959103504311047/500000000000000000"
+          ],
+          "children": 196,
+          "next": [
+            "1000097744093493979/1000000000000000000",
+            "50004887204674699/50000000000000000"
+          ],
+          "rank_mass": 196
+        },
+        "2": {
+          "accepted": [
+            "999877363945871043/1000000000000000000",
+            "249969340986467761/250000000000000000"
+          ],
+          "children": 98,
+          "next": [
+            "1000236021349668377/1000000000000000000",
+            "500118010674834189/500000000000000000"
+          ],
+          "rank_mass": 196
+        }
+      },
+      "mass": 5376,
+      "moment": [
+        "964728938373732327/1000000000000000000",
+        "120591117296716541/125000000000000000"
+      ],
+      "profile": {
+        "1": 4176,
+        "2": 192,
+        "3": 144,
+        "8": 48
+      },
+      "source_scope": "The local words are supplied. Their routed three-call composition and terminal are not admitted.",
+      "three_call_map_bound": 9792,
+      "three_call_scalar_subtotal": 25800
+    }
+  },
+  "scope": "Native arithmetic only. The 112,128,144 H1 cleanup costs are hypotheses. No caller, terminal, host, precision, or current-frontier claim.",
+  "selected_certificate": "research/community-frontier1094-audit/ASSEMBLY.json",
+  "selected_result_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+  "source_pins": {
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json": "fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json": "96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+    "lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d",
+    "lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/REVIEW.json": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "status": "PASS_SOURCE_COUNTS_AND_EXACT_CONDITIONAL_BUDGET"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/FREEZE.json
new file mode 100644
index 0000000000..d1996daeaa
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "BUDGET.json": "30a59c5cda0ff3c6f9e6ad7f9f38ec98fbfe71d34c58ddf768964cda304ba30d",
+    "PROOF.md": "fe70d65702c7455c8146ceefc7d006114d24a2c7eb3e733bce1810806a19b096",
+    "REPRODUCTION.json": "069f9f302ffc5387abbfc6d22827a7f284d0c8264a98543fccb940fad840f89c",
+    "check_budget.py": "d1ec38fa1eabda116ce6d5bbfe2fff20dd3803736266755395e5aac7f6ee7349"
+  },
+  "frozen_utc": "2026-10-20T17:40:13.158282+00:00",
+  "independent_review": "Pending. Two independently written pinned exact engines agree.",
+  "normal_optimized_byte_identical": true,
+  "publication_authorized": false,
+  "schema": "clean-exchange-budget-freeze-v1",
+  "scope": "Counts all8 clean and dual words. Conditional three-call native budgets and112/128/144H1 cleanup targets; no admitted caller, cleanup, terminal, or complete supplier."
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/PROOF.md b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/PROOF.md
new file mode 100644
index 0000000000..4da47a0285
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/PROOF.md
@@ -0,0 +1,113 @@
+# Native budgets for the clean centre exchange
+
+## Result and scope
+
+For dimension 25, productive width 224, three local calls, and no idle jobs, the exact conditional native budgets are:
+
+| Three-call profile | Native mass | Extra H1 limit | Extra H2 limit |
+| --- | ---: | ---: | ---: |
+| Three Q-entry calls | 5,376 | 196 | 98 |
+| One I-entry and two Q-entry calls | 5,392 | 180 | 90 |
+
+The complete histograms before cleanup are:
+
+```text
+three Q:       4176 H1 + 192 H2 + 144 H3 + 48 H8
+one I, two Q:  4176 H1 + 192 H2 + 144 H3 + 32 H8 + 16 H9
+```
+
+The limits use the historical selected exponent
+
+```text
+b = 67018507072324140917 / 40000000000000000000000.
+```
+
+The checker binds this value to `certificates/selected-result.json` and its assembly at Git commit `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. This is a historical source pin. It is not a claim about the current frontier.
+
+All extra native work must fit within the stated allowance. The H1 and H2 columns are alternatives. They cannot both be used at their limits.
+
+The local words are supplied and checked. Their routed three-call composition is not supplied by this packet. In particular, the three-Q profile does not provide the initial Q-entry state for free. Any work that forms it must be included in the extra budget. No terminal, recursive host, complete finite invoice, or kappa improvement is claimed.
+
+## Hypothetical cleanup costs
+
+If one-bank cleanup can be implemented with the stated number of H1 children, the exact remaining budgets are:
+
+| Three-call profile | Cleanup H1 | Extra H1 left | Extra H2 left |
+| --- | ---: | ---: | ---: |
+| Three Q | 112 | 84 | 42 |
+| Three Q | 128 | 68 | 34 |
+| Three Q | 144 | 52 | 26 |
+| One I, two Q | 112 | 68 | 34 |
+| One I, two Q | 128 | 52 | 26 |
+| One I, two Q | 144 | 36 | 18 |
+
+The receipt gives a strict passing bound at each limit and a strict failing bound at the next child. These rows price proposed cleanup histograms. They do not give access to the required queries or construct their scatter, frame changes, phase corrections, restoration, or terminal output.
+
+A full 224-H1 terminal would give mass 5,600 in the three-Q case. Since every child rank is less than 25, that bill fails for every b>0. The one-I bill with that terminal has mass 5,616 and fails even at b=0. At the pinned exponent, such a terminal must lose at least 28 H1 or 44 H1, respectively, before any other native work is added.
+
+## Literal source count
+
+The clean-exchange producer freeze is
+
+```text
+new-core-transfer-20261017/low-displacement-20261020/
+clean-late-exchange-20261020/FREEZE.json
+SHA256 96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc
+```
+
+Its independent local review freeze is
+
+```text
+new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json
+SHA256 6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d
+```
+
+The separate inverse-adjoint and selected-swap conjugate use the producer's `DUAL-FREEZE.json`, with SHA256 `fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43`. Their local producer checks are bound. A separate review of those dual words is not part of the clean-exchange review cited above.
+
+This checker counts all eight serialized words: both clean entry variants and both dual variants, for both providers. It imports no producer code. Every native and scalar event uses a data role from 0 through 223. The count is:
+
+| Local entry | Literal native profile | Children | Native mass |
+| --- | --- | ---: | ---: |
+| Q, inverse-adjoint, or selected-swap conjugate | 1392 H1 + 64 H2 + 48 H3 + 16 H8 | 1,520 | 1,792 |
+| I | 1392 H1 + 64 H2 + 48 H3 + 16 H9 | 1,520 | 1,808 |
+
+In a Q or dual word, each of the 224 data fields has total native rank eight. In an I word, sixteen fields have rank nine and the other 208 have rank eight. All individual child ranks satisfy the dimension-25 size guard.
+
+Each local scalar word contains 1,032 unit complex ADDs, 96 scales of price two, and 38 scales of price four. Thus each word costs
+
+```text
+1032*8 + 96*2 + 38*4 = 8600
+```
+
+real scalar primitives. This total includes the FULL source code and the sixteen signed exchanges. Inverse-adjoint conversion and field relabeling keep the total price. The checker verifies their literal counts too. Their routed use is a separate obligation.
+
+The I-entry word has 112 input views, 96 output views, and a native side-map bound of 3,008. The checker verifies the identity records on both sides of each of its sixteen direct H9 children. The Q and dual words retain all side maps: 128 input views, 96 output views, and a native side-map bound of 3,040.
+
+The three-call scalar subtotal is 25,800 in both cases. The total map-call bounds are 9,792 for three Q calls and 9,744 for one I and two Q calls. These component subtotals omit the caller, cleanup, any required physical role conversion, map lowering, recursive children, and precision.
+
+The source phase and full 640-column proofs are pinned premises. This budget checker does not run them again. It verifies the invoices; it does not reclassify the productive exchange as an ordinary data response.
+
+## Exact arithmetic
+
+For a histogram H, the native moment is
+
+```text
+M_H(b) = sum_r H[r] * r/(25*224) * (25/r)^b.
+```
+
+The two pinned rational engines give:
+
+| Profile | Lower bound | Upper bound |
+| --- | ---: | ---: |
+| Three Q | 0.964728938373732327 | 0.964728938373732328 |
+| One I, two Q | 0.967586457273780926 | 0.967586457273780927 |
+
+For each proposed cleanup, the checker adds its H1 count to the full histogram. For each permitted extra rank, both engines agree on the integer limit. Each engine proves M<1 at that limit and M>1 at the next count. It is not enough for the two engine intervals merely to overlap: both strict inequalities are tested separately in each engine. No floating-point calculation determines a numerical claim.
+
+## Reproduction and credit
+
+Run `python3 -I -B check_budget.py` and repeat with `-O`. Both runs must give identical receipt bytes. The source, certificate, and engine hashes are stored in `BUDGET.json`. A separate review of this new budget is pending.
+
+The root and controller lanes supplied the clean coupled interface. The new-core-transfer lane emitted the local words. The new-native-recipes lane supplied the independent clean-exchange review. The cover-algebra lane supplied the selected-bank dual formulation. The earlier budget and bridge-review lanes supplied the exact engine and certificate binding methods. This packet used AI assistance.
+
+No PR, push, commit, or publication is authorized. Before any future PR description, read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..3f8e6a892b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/REPRODUCTION.json
@@ -0,0 +1,11 @@
+{
+  "commands": [
+    "python3 -I -B check_budget.py",
+    "python3 -I -B -O check_budget.py"
+  ],
+  "independent_exact_engines": 2,
+  "normal_optimized_byte_identical": true,
+  "receipt_sha256": "30a59c5cda0ff3c6f9e6ad7f9f38ec98fbfe71d34c58ddf768964cda304ba30d",
+  "source_phase_compilers_rerun": false,
+  "stdout_sha256": "cd8b95e91270899c677b14adb69d1c355de66a8f6262afede24814f4028bf8b4"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/check_budget.py b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/check_budget.py
new file mode 100644
index 0000000000..d5982d1f44
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/clean-exchange-budget-20261020/check_budget.py
@@ -0,0 +1,210 @@
+"""Count the frozen clean-exchange words and price their native profiles."""
+
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import subprocess
+import tempfile
+
+
+HERE = Path(__file__).resolve().parent
+CAMPAIGN = HERE.parents[2]
+REPO = CAMPAIGN.parents[1]
+LOCAL = "lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/"
+REVIEW = "lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/"
+PINS = {
+    LOCAL + "FREEZE.json": "96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc",
+    LOCAL + "run-normal/CHECKS.json": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b",
+    LOCAL + "run-normal/CLEAN-LATE-EXCHANGE.json.gz": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+    LOCAL + "DUAL-FREEZE.json": "fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43",
+    LOCAL + "dual-normal/CHECKS.json": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b",
+    LOCAL + "dual-normal/CLEAN-DUAL.json.gz": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+    REVIEW + "FREEZE.json": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d",
+    REVIEW + "normal/REVIEW.json": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5",
+}
+COMMIT = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f"
+SELECTED_PIN = "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+ASSEMBLY_PIN = "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045"
+ENGINE_ROOT = "research/complex-k492-owner-repair/vendor/multicold/engines/"
+ENGINE_PINS = {
+    "moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+}
+B = Q(67018507072324140917, 40000000000000000000000)
+D, W = 25, 224
+Q_PROFILE = Counter({1: 1392, 2: 64, 3: 48, 8: 16})
+I_PROFILE = Counter({1: 1392, 2: 64, 3: 48, 9: 16})
+
+
+def need(ok, text):
+    if not ok:
+        raise ValueError(text)
+
+
+def mass(profile):
+    return sum(r * n for r, n in profile.items())
+
+
+def pinned(raw, pin, label):
+    need(sha256(raw).hexdigest() == pin, "Source pin: " + label)
+    return json.loads(raw)
+
+
+def git_file(path):
+    return subprocess.check_output(["git", "-C", str(REPO), "show", COMMIT + ":" + path])
+
+
+def bounds(values):
+    lo, hi = max(a for a, b in values), min(b for a, b in values)
+    need(lo <= hi, "Exact engine intervals overlap")
+    scale = 10**18
+    return [str(Q((lo * scale).__floor__(), scale)), str(Q((hi * scale).__ceil__(), scale))]
+
+
+def count_words(payload, receipt, dual=False):
+    answer = {}
+    identity = {
+        "matrix_rows": [1 << i for i in range(9)], "linear_Z4": [0] * 9,
+        "quadratic_rows": [0] * 9, "offset": 0, "phase": 0,
+    }
+    for provider, variants in payload["providers"].items():
+        for variant, word in variants.items():
+            is_I = not dual and variant == "I"
+            expected = I_PROFILE if is_I else Q_PROFILE
+            native = [e for e in word["events"] if e[0] == "native"]
+            scalar = [e[1] for e in word["events"] if e[0] == "scalar"]
+            need(len(native) + len(scalar) == len(word["events"]), "Every event is counted")
+            profile = Counter(e[4] for e in native)
+            need(profile == expected, "Literal native profile")
+            fields = Counter()
+            for event in native:
+                need(0 <= event[1] < 224 and 2 * event[4]**2 < D**2, "Data role and child size")
+                fields[event[1]] += event[4]
+            need(len(fields) == 224 and Counter(fields.values()) ==
+                 (Counter({8: 208, 9: 16}) if is_I else Counter({8: 224})), "Per-field rank count")
+            census = Counter()
+            cost = 0
+            for gate in scalar:
+                need(len(gate) == 4 and 0 <= gate[1] < 224, "Scalar target")
+                coefficient = Q(gate[3])
+                if gate[0] == "add":
+                    need(0 <= gate[2] < 224 and abs(coefficient) == 1, "Unit data ADD")
+                    cost += 8
+                else:
+                    need(gate[0] == "scale" and coefficient in (-1, 2, Q(1, 2), -2, Q(-1, 2)),
+                         "Dyadic data SCALE")
+                    cost += 4 if coefficient in (-2, Q(-1, 2)) else 2
+                census[gate[0], str(coefficient)] += 1
+            report = receipt["reports"][provider][variant]
+            need(cost == report["real_scalar_primitives"] == 8600, "Scalar price")
+            need(len(native) == report["native_children"] == 1520, "Native count")
+            need(mass(profile) == report["native_mass"], "Native mass")
+            need(len(word["input_views"]) == report["explicit_input_monomial_views"] == (112 if is_I else 128),
+                 "Input view count")
+            need(len(word["output_views"]) == report["explicit_output_monomial_views"] == 96, "Output view count")
+            if is_I:
+                direct = [e for e in native if e[4] == 9]
+                need(len(direct) == 16, "Direct FULL count")
+                need(all(word["native_recipes"][e[5]] == {"rank": 9, "left": identity, "right": identity}
+                         for e in direct), "Direct FULL side maps are identity")
+            side_maps = 2 * len(native) - (32 if is_I else 0)
+            need(side_maps == report["native_side_map_upper_bound"], "Native side-map bound")
+            answer[provider + "/" + variant] = {
+                "profile": profile, "children": len(native), "mass": mass(profile),
+                "scalar": cost, "input_views": len(word["input_views"]), "output_views": 96,
+                "native_side_map_bound": side_maps,
+                "total_map_bound": side_maps + len(word["input_views"]) + 96,
+                "scalar_census": {op + ":" + coefficient: n for (op, coefficient), n in sorted(census.items())},
+            }
+    return answer
+
+
+def main():
+    source = {}
+    for path, pin in PINS.items():
+        raw = (CAMPAIGN / path).read_bytes()
+        if path.endswith(".gz"):
+            raw = gzip.decompress(raw)
+        source[path] = pinned(raw, pin, path)
+    selected = pinned(git_file("certificates/selected-result.json"), SELECTED_PIN, "selected result")
+    assembly = pinned(git_file(selected["certificate"]), ASSEMBLY_PIN, selected["certificate"])
+    need(selected["certificate_sha256"] == ASSEMBLY_PIN and Q(assembly["complex_lower"]) == B,
+         "Historical selected exponent")
+    literal = {
+        "clean": count_words(source[LOCAL + "run-normal/CLEAN-LATE-EXCHANGE.json.gz"],
+                             source[LOCAL + "run-normal/CHECKS.json"]),
+        "dual": count_words(source[LOCAL + "dual-normal/CLEAN-DUAL.json.gz"],
+                            source[LOCAL + "dual-normal/CHECKS.json"], True),
+    }
+    results = {}
+    with tempfile.TemporaryDirectory(prefix="clean-exchange-moment-") as folder:
+        engines = []
+        for i, (name, pin) in enumerate(ENGINE_PINS.items()):
+            raw = git_file(ENGINE_ROOT + name)
+            need(sha256(raw).hexdigest() == pin, "Exact engine pin")
+            path = Path(folder) / name
+            path.write_bytes(raw)
+            spec = importlib.util.spec_from_file_location("clean_exchange_engine_" + str(i), path)
+            engine = importlib.util.module_from_spec(spec)
+            spec.loader.exec_module(engine)
+            engines.append(engine)
+
+        def moments(profile):
+            values = [engines[0].moment(profile, D, W, B, False),
+                      engines[1].moment(D, W, list(profile.items()), B)]
+            bounds(values)
+            return values
+
+        def allowance(profile):
+            base = moments(profile)
+            need(all(hi < 1 for lo, hi in base), "Positive native headroom")
+            row = {"profile": profile, "mass": mass(profile), "moment": bounds(base), "limits": {}}
+            for rank in (1, 2):
+                unit = moments({rank: 1})
+                n = [((1 - hi) / uhi).__floor__() for (lo, hi), (ulo, uhi) in zip(base, unit)]
+                need(n[0] == n[1] and n[0] >= 0, "Both engines give the same allowance")
+                yes = moments(profile + Counter({rank: n[0]}))
+                no = moments(profile + Counter({rank: n[0] + 1}))
+                need(all(hi < 1 for lo, hi in yes) and all(lo > 1 for lo, hi in no), "Strict pass and next failure")
+                row["limits"][str(rank)] = {"children": n[0], "rank_mass": rank * n[0],
+                                             "accepted": bounds(yes), "next": bounds(no)}
+            return row
+
+        for name, i_count in (("three_Q", 0), ("one_I_two_Q", 1)):
+            profile = Counter({r: (3 - i_count) * n for r, n in Q_PROFILE.items()})
+            profile.update({r: i_count * n for r, n in I_PROFILE.items()})
+            profile = +profile
+            need(mass(profile) == 5376 + 16 * i_count, "Complete three-call native mass")
+            row = allowance(profile)
+            row["hypothetical_H1_cleanup"] = {
+                str(n): allowance(profile + Counter({1: n})) for n in (112, 128, 144)
+            }
+            row["three_call_scalar_subtotal"] = 25800
+            row["three_call_map_bound"] = 9792 - 48 * i_count
+            row["source_scope"] = "The local words are supplied. Their routed three-call composition and terminal are not admitted."
+            results[name] = row
+
+    receipt = {
+        "status": "PASS_SOURCE_COUNTS_AND_EXACT_CONDITIONAL_BUDGET",
+        "source_pins": PINS, "gzip_pin_convention": "SHA256 after decompression",
+        "engine_commit": COMMIT, "engine_pins": ENGINE_PINS,
+        "selected_certificate": selected["certificate"], "selected_result_sha256": SELECTED_PIN,
+        "assembly_sha256": ASSEMBLY_PIN, "historical_selected_b": str(B),
+        "dimension": D, "productive_width": W, "calls": 3, "idle_profile": {},
+        "literal": literal, "results": results,
+        "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "scope": "Native arithmetic only. The 112,128,144 H1 cleanup costs are hypotheses. No caller, terminal, host, precision, or current-frontier claim.",
+    }
+    (HERE / "BUDGET.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    for name, row in results.items():
+        print(name, "base", {r: v["children"] for r, v in row["limits"].items()})
+        print(name, "cleanup", {n: {r: v["children"] for r, v in c["limits"].items()}
+                               for n, c in row["hypothetical_H1_cleanup"].items()})
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/coalesced-reciprocal-budget-20261020/BUDGET.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/coalesced-reciprocal-budget-20261020/BUDGET.json
new file mode 100644
index 0000000000..333d606d40
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/coalesced-reciprocal-budget-20261020/BUDGET.json
@@ -0,0 +1,244 @@
+{
+  "ambient_dimension": 25,
+  "arithmetic_loader_sha256": "d1ec38fa1eabda116ce6d5bbfe2fff20dd3803736266755395e5aac7f6ee7349",
+  "assembly_sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+  "base_moment": [
+    "964432838859427253/1000000000000000000",
+    "482216419429713627/500000000000000000"
+  ],
+  "limits": {
+    "cleanup_0_rank_1": {
+      "accepted_moment": [
+        "999981181664060791/1000000000000000000",
+        "124997647708007599/125000000000000000"
+      ],
+      "maximum_count": 198,
+      "next_rejected_moment": [
+        "500080359374466339/500000000000000000",
+        "1000160718748932679/1000000000000000000"
+      ]
+    },
+    "cleanup_0_rank_2": {
+      "accepted_moment": [
+        "999939921835363303/1000000000000000000",
+        "124992490229420413/125000000000000000"
+      ],
+      "maximum_count": 99,
+      "next_rejected_moment": [
+        "1000298579239160637/1000000000000000000",
+        "500149289619580319/500000000000000000"
+      ]
+    },
+    "cleanup_64_rank_1": {
+      "accepted_moment": [
+        "999981181664060791/1000000000000000000",
+        "124997647708007599/125000000000000000"
+      ],
+      "maximum_count": 134,
+      "next_rejected_moment": [
+        "500080359374466339/500000000000000000",
+        "1000160718748932679/1000000000000000000"
+      ]
+    },
+    "cleanup_64_rank_2": {
+      "accepted_moment": [
+        "12499415729320617/12500000000000000",
+        "999953258345649361/1000000000000000000"
+      ],
+      "maximum_count": 67,
+      "next_rejected_moment": [
+        "500155957874723347/500000000000000000",
+        "200062383149889339/200000000000000000"
+      ]
+    }
+  },
+  "local_words": {
+    "base/backward_inverse_E": {
+      "endpoint_maps": 224,
+      "histogram": {
+        "1": 971,
+        "2": 237,
+        "3": 46,
+        "4": 12,
+        "5": 5,
+        "6": 11,
+        "7": 10
+      },
+      "native_side_map_bound": 2584,
+      "scalar": 6440
+    },
+    "base/backward_inverse_by_metric": {
+      "endpoint_maps": 224,
+      "histogram": {
+        "1": 971,
+        "2": 237,
+        "3": 46,
+        "4": 12,
+        "5": 5,
+        "6": 11,
+        "7": 10
+      },
+      "native_side_map_bound": 2584,
+      "scalar": 7080
+    },
+    "base/backward_transpose_E": {
+      "endpoint_maps": 224,
+      "histogram": {
+        "1": 971,
+        "2": 237,
+        "3": 46,
+        "4": 12,
+        "5": 5,
+        "6": 11,
+        "7": 10
+      },
+      "native_side_map_bound": 2584,
+      "scalar": 6440
+    },
+    "base/forward_E": {
+      "endpoint_maps": 224,
+      "histogram": {
+        "1": 971,
+        "2": 237,
+        "3": 46,
+        "4": 12,
+        "5": 5,
+        "6": 11,
+        "7": 10
+      },
+      "native_side_map_bound": 2584,
+      "scalar": 6440
+    },
+    "base/forward_inverse_adjoint_E": {
+      "endpoint_maps": 224,
+      "histogram": {
+        "1": 971,
+        "2": 237,
+        "3": 46,
+        "4": 12,
+        "5": 5,
+        "6": 11,
+        "7": 10
+      },
+      "native_side_map_bound": 2584,
+      "scalar": 6440
+    },
+    "base/forward_inverse_adjoint_by_metric": {
+      "endpoint_maps": 224,
+      "histogram": {
+        "1": 971,
+        "2": 237,
+        "3": 46,
+        "4": 12,
+        "5": 5,
+        "6": 11,
+        "7": 10
+      },
+      "native_side_map_bound": 2584,
+      "scalar": 7080
+    },
+    "extra/backward_inverse_E": {
+      "endpoint_maps": 224,
+      "histogram": {
+        "1": 971,
+        "2": 237,
+        "3": 46,
+        "4": 12,
+        "5": 5,
+        "6": 11,
+        "7": 10
+      },
+      "native_side_map_bound": 2584,
+      "scalar": 6440
+    },
+    "extra/backward_inverse_by_metric": {
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diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/BUDGET.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/BUDGET.json
new file mode 100644
index 0000000000..7af6aaac07
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/BUDGET.json
@@ -0,0 +1,1868 @@
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+            "50069558021622113/50000000000000000"
+          ],
+          "rank_mass": 200
+        },
+        "9": {
+          "accepted": [
+            "999595043759627187/1000000000000000000",
+            "249898760939906797/250000000000000000"
+          ],
+          "children": 22,
+          "next": [
+            "500602469990487849/500000000000000000",
+            "1001204939980975699/1000000000000000000"
+          ],
+          "rank_mass": 198
+        }
+      },
+      "local_children": 1212,
+      "local_correction_rank": 30,
+      "local_profile": {
+        "1": 1036,
+        "3": 48,
+        "4": 55,
+        "5": 55,
+        "6": 9,
+        "7": 9
+      },
+      "local_scalar_primitives": 5288,
+      "moment": [
+        "192835465377991987/200000000000000000",
+        "1883158841581953/1953125000000000"
+      ],
+      "native_mass": 5376,
+      "profile": {
+        "1": 3108,
+        "3": 144,
+        "4": 165,
+        "5": 165,
+        "6": 27,
+        "7": 27
+      },
+      "source_status": "Frozen literal native word",
+      "three_call_scalar_subtotal": 15864,
+      "unfused_terminal_H1": 224,
+      "unfused_terminal_moment": [
+        "40175745356050501/40000000000000000",
+        "502196816950631263/500000000000000000"
+      ]
+    },
+    "rank30_W112": {
+      "local_mass": 1824,
+      "local_profile": {
+        "1": 988,
+        "2": 48,
+        "5": 55,
+        "6": 55,
+        "7": 9,
+        "8": 9
+      },
+      "preterminal": {
+        "all_legal_ranks": {
+          "accepted": [
+            "249988403212701771/250000000000000000",
+            "199990722570161417/200000000000000000"
+          ],
+          "best_profile": {
+            "3": 1,
+            "17": 6
+          },
+          "maximum_child_rank": 17,
+          "next": [
+            "25003311858513121/25000000000000000",
+            "1000132474340524841/1000000000000000000"
+          ],
+          "next_best_profile": {
+            "4": 1,
+            "17": 6
+          },
+          "scope": "Arithmetic optimum by concavity. No access or native construction is supplied.",
+          "total_rank_limit": 105
+        },
+        "limits": {
+          "1": {
+            "accepted": [
+              "39994471600291239/40000000000000000",
+              "62491361875455061/62500000000000000"
+            ],
+            "children": 104,
+            "next": [
+              "1000041327092152861/1000000000000000000",
+              "500020663546076431/500000000000000000"
+            ],
+            "rank_mass": 104
+          },
+          "17": {
+            "accepted": [
+              "199883198419473829/200000000000000000",
+              "499707996048684573/500000000000000000"
+            ],
+            "children": 6,
+            "next": [
+              "50122683429174827/50000000000000000",
+              "1002453668583496541/1000000000000000000"
+            ],
+            "rank_mass": 102
+          },
+          "2": {
+            "accepted": [
+              "249960029544516533/250000000000000000",
+              "999840118178066133/1000000000000000000"
+            ],
+            "children": 52,
+            "next": [
+              "500099387790931733/500000000000000000",
+              "1000198775581863467/1000000000000000000"
+            ],
+            "rank_mass": 104
+          },
+          "4": {
+            "accepted": [
+              "999818471502652857/1000000000000000000",
+              "499909235751326429/500000000000000000"
+            ],
+            "children": 26,
+            "next": [
+              "1000534953745808553/1000000000000000000",
+              "500267476872904277/500000000000000000"
+            ],
+            "rank_mass": 104
+          },
+          "8": {
+            "accepted": [
+              "499898424975922967/500000000000000000",
+              "199959369990369187/200000000000000000"
+            ],
+            "children": 13,
+            "next": [
+              "31288379726310669/31250000000000000",
+              "1001228151241941409/1000000000000000000"
+            ],
+            "rank_mass": 104
+          },
+          "9": {
+            "accepted": [
+              "499449395807719199/500000000000000000",
+              "998898791615438399/1000000000000000000"
+            ],
+            "children": 11,
+            "next": [
+              "100050868783678691/100000000000000000",
+              "1000508687836786911/1000000000000000000"
+            ],
+            "rank_mass": 99
+          }
+        },
+        "moment": [
+          "981189933180604773/1000000000000000000",
+          "490594966590302387/500000000000000000"
+        ],
+        "native_mass": 5472,
+        "profile": {
+          "1": 2964,
+          "2": 144,
+          "5": 165,
+          "6": 165,
+          "7": 27,
+          "8": 27
+        }
+      },
+      "rank_excess_over_full_budget": 96,
+      "source_status": "Frozen literal changed-output word; global transport and terminal remain separate",
+      "terminal_comparator": {
+        "1": 224
+      },
+      "terminal_scope": "A 224-H1 bill is a comparator only. The changed outputs need a new global terminal proof.",
+      "with_terminal_comparator_moment": [
+        "510703120095953681/500000000000000000",
+        "1021406240191907363/1000000000000000000"
+      ],
+      "with_terminal_comparator_rank_mass": 5696
+    },
+    "rank30_W48_I64": {
+      "all_other_debt_after_terminal": {
+        "all_legal_ranks": {
+          "accepted": [
+            "999944614844723163/1000000000000000000",
+            "249986153711180791/250000000000000000"
+          ],
+          "best_profile": {
+            "9": 1,
+            "17": 15
+          },
+          "maximum_child_rank": 17,
+          "next": [
+            "500061588231296191/500000000000000000",
+            "1000123176462592383/1000000000000000000"
+          ],
+          "next_best_profile": {
+            "10": 1,
+            "17": 15
+          },
+          "scope": "Arithmetic optimum by concavity. No access or native construction is supplied.",
+          "total_rank_limit": 264
+        },
+        "limits": {
+          "1": {
+            "accepted": [
+              "499993912326384943/500000000000000000",
+              "999987824652769887/1000000000000000000"
+            ],
+            "children": 263,
+            "next": [
+              "1000167361737641773/1000000000000000000",
+              "500083680868820887/500000000000000000"
+            ],
+            "rank_mass": 263
+          },
+          "17": {
+            "accepted": [
+              "998334718623374651/1000000000000000000",
+              "249583679655843663/250000000000000000"
+            ],
+            "children": 15,
+            "next": [
+              "1001372395109502047/1000000000000000000",
+              "31292887347171939/31250000000000000"
+            ],
+            "rank_mass": 255
+          },
+          "2": {
+            "accepted": [
+              "499876845614457227/500000000000000000",
+              "199950738245782891/200000000000000000"
+            ],
+            "children": 131,
+            "next": [
+              "250028087158177947/250000000000000000",
+              "1000112348632711789/1000000000000000000"
+            ],
+            "rank_mass": 262
+          },
+          "4": {
+            "accepted": [
+              "999340917136583933/1000000000000000000",
+              "499670458568291967/500000000000000000"
+            ],
+            "children": 65,
+            "next": [
+              "1000057399379739629/1000000000000000000",
+              "100005739937973963/100000000000000000"
+            ],
+            "rank_mass": 260
+          },
+          "8": {
+            "accepted": [
+              "124821401576814861/125000000000000000",
+              "998571212614518889/1000000000000000000"
+            ],
+            "children": 32,
+            "next": [
+              "500001256952307181/500000000000000000",
+              "1000002513904614363/1000000000000000000"
+            ],
+            "rank_mass": 256
+          },
+          "9": {
+            "accepted": [
+              "999456561750570553/1000000000000000000",
+              "499728280875285277/500000000000000000"
+            ],
+            "children": 29,
+            "next": [
+              "125133307246489883/125000000000000000",
+              "200213291594383813/200000000000000000"
+            ],
+            "rank_mass": 261
+          }
+        },
+        "moment": [
+          "952769571331463721/1000000000000000000",
+          "476384785665731861/500000000000000000"
+        ],
+        "native_mass": 5312,
+        "profile": {
+          "1": 3188,
+          "2": 144,
+          "4": 165,
+          "5": 165,
+          "6": 27,
+          "7": 27
+        }
+      },
+      "full_per_call_restoration_rank": 288,
+      "local_mass": 1696,
+      "local_profile": {
+        "1": 988,
+        "2": 48,
+        "4": 55,
+        "5": 55,
+        "6": 9,
+        "7": 9
+      },
+      "preterminal": {
+        "all_legal_ranks": {
+          "accepted": [
+            "499966089661180041/500000000000000000",
+            "999932179322360083/1000000000000000000"
+          ],
+          "best_profile": {
+            "13": 1,
+            "17": 28
+          },
+          "maximum_child_rank": 17,
+          "next": [
+            "1000110635772409079/1000000000000000000",
+            "25002765894310227/25000000000000000"
+          ],
+          "next_best_profile": {
+            "14": 1,
+            "17": 28
+          },
+          "scope": "Arithmetic optimum by concavity. No access or native construction is supplied.",
+          "total_rank_limit": 489
+        },
+        "limits": {
+          "1": {
+            "accepted": [
+              "499993912326384943/500000000000000000",
+              "999987824652769887/1000000000000000000"
+            ],
+            "children": 487,
+            "next": [
+              "1000167361737641773/1000000000000000000",
+              "500083680868820887/500000000000000000"
+            ],
+            "rank_mass": 487
+          },
+          "17": {
+            "accepted": [
+              "997608205931728201/1000000000000000000",
+              "498804102965864101/500000000000000000"
+            ],
+            "children": 28,
+            "next": [
+              "1000645882417855597/1000000000000000000",
+              "500322941208927799/500000000000000000"
+            ],
+            "rank_mass": 476
+          },
+          "2": {
+            "accepted": [
+              "199941402688582651/200000000000000000",
+              "124963376680364157/125000000000000000"
+            ],
+            "children": 243,
+            "next": [
+              "1000065670846710589/1000000000000000000",
+              "100006567084671059/100000000000000000"
+            ],
+            "rank_mass": 486
+          },
+          "4": {
+            "accepted": [
+              "124995512248144499/125000000000000000",
+              "999964097985155993/1000000000000000000"
+            ],
+            "children": 122,
+            "next": [
+              "1000680580228311687/1000000000000000000",
+              "125085072528538961/125000000000000000"
+            ],
+            "rank_mass": 488
+          },
+          "8": {
+            "accepted": [
+              "249965660753996261/250000000000000000",
+              "199972528603197009/200000000000000000"
+            ],
+            "children": 61,
+            "next": [
+              "500646972153040259/500000000000000000",
+              "1001293944306080519/1000000000000000000"
+            ],
+            "rank_mass": 488
+          },
+          "9": {
+            "accepted": [
+              "999487660272980749/1000000000000000000",
+              "3997950641091923/4000000000000000"
+            ],
+            "children": 54,
+            "next": [
+              "1001097556494329261/1000000000000000000",
+              "500548778247164631/500000000000000000"
+            ],
+            "rank_mass": 486
+          }
+        },
+        "moment": [
+          "228138316080040283/250000000000000000",
+          "912553264320161133/1000000000000000000"
+        ],
+        "native_mass": 5088,
+        "profile": {
+          "1": 2964,
+          "2": 144,
+          "4": 165,
+          "5": 165,
+          "6": 27,
+          "7": 27
+        }
+      },
+      "restoration_scope": "If all 96 missing ranks are paid after every call, the full mass reaches DW and no positive b passes. This does not prove that the debt is necessary.",
+      "source_status": "Frozen literal changed-output word; global transport and terminal remain separate",
+      "terminal_comparator": {
+        "1": 224
+      },
+      "terminal_scope": "A 224-H1 bill is a comparator only. The changed outputs need a new global terminal proof.",
+      "with_terminal_comparator_moment": [
+        "952769571331463721/1000000000000000000",
+        "476384785665731861/500000000000000000"
+      ],
+      "with_terminal_comparator_rank_mass": 5312
+    }
+  },
+  "selected_b_snapshot": "67018507072324140917/40000000000000000000000",
+  "source_pins": {
+    "lanes/bridge-access-20261017/rank9-completion-20261020/CHECKS.json": "c4b92b37441c095ff3c4d51ea920dd918edd54113764d76ce721a30ec435a2b0",
+    "lanes/bridge-access-20261017/rank9-completion-20261020/FREEZE.json": "6177f89c88b503765a724e8c1baa934da582c490089dbe29e0f6ce2371f9904b",
+    "lanes/budget-geometry-20261017/matched-native-budget-20261018/MATCHED-NATIVE-BUDGET.json": "a1832aeb1d82498f423637ba8cab0ff11262383665ed440159759bc54fe5775e",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS-FREEZE.json": "f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json": "b36bee542add54bac48e409c6a4a054b3bca5fba9c98d5513a90a6a92628d576",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-PROGRAM.json.gz": "7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-CHECKS.json": "8acc084b5cd1d9513fdd3373eede998bd08e7f3fe1624f9fd41f758d4de7cb82",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+  },
+  "status": "PASS_TWO_EXACT_ENGINES_WITH_EXPLICIT_SOURCE_SCOPE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/FREEZE.json
new file mode 100644
index 0000000000..a7a90b5f3d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "BUDGET.json": "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2",
+    "PROOF.md": "00059239aa0376fd731454d7bda1149e3c7f8b938eb4d4534684b69f204c2eba",
+    "REPRODUCTION.json": "8307dabd8ac3515dfdbc83af0c073eca793f07d60866aee18c3386baa939356f",
+    "check_budget.py": "ba1d4a4777e85be4a2930f17bf7c15a39a7b7cd1386f9255d5a607e160e55b96"
+  },
+  "frozen_utc": "2026-10-20T15:40:30.649317+00:00",
+  "independent_review": "Two independent pinned exact arithmetic engines agree. A separate review of this new packet is pending.",
+  "normal_optimized_byte_identical": true,
+  "publication_authorized": false,
+  "schema": "low-displacement-budget-freeze-v1",
+  "scope": "Exact source counts and D25 native budgets for raw and changed-output rank30/rank16 words, plus the matched H9 contraction. Global changed-code composition and complete finite supplier are not proved."
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/PROOF.md b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/PROOF.md
new file mode 100644
index 0000000000..9212dd8dba
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/PROOF.md
@@ -0,0 +1,122 @@
+# Native budgets for the low-displacement responses
+
+## Result and scope
+
+The exact native histograms give the following one-pair budgets:
+
+| Local response | Native profile | Children per call | Local scalar cost | Extra H1 limit | Extra H2 limit | Extra total rank limit |
+| --- | --- | ---: | ---: | ---: | ---: | ---: |
+| Rank thirty | {1:1036,3:48,4:55,5:55,6:9,7:9} | 1,212 | 5,288 | 199 | 99 | 200 |
+| Odd-grid rank sixteen | {1:1520,2:64,3:48} | 1,632 | 7,384 | 195 | 97 | 196 |
+
+Both local native words are frozen. The rank-sixteen row uses only the corrected v2 source. The earlier draft is not an input. Both local masses are 1,792. Their child distributions differ, and so do their recursive moments.
+
+The table assumes D=25, productive width W=224, three local calls, and no idle jobs. It uses
+
+    b = 67018507072324140917 / 40000000000000000000000.
+
+This is the fixed selected-rate snapshot used in the earlier budget packet. The source of the current frontier is a separate audit. All allowances must pay for the terminal and every other added native operation together.
+
+This packet does not prove the global controller, routed access to its codes, the odd-grid contract, a recursive host, or a complete finite supplier. The local correction rank does not supply any of these obligations.
+
+## Exact source count
+
+The rank-thirty source is `new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json`, with SHA256 `efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24`. The extension freeze has SHA256 `aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689`.
+
+The checker reads every native, scalar, and monomial event in both directions and both providers. It imports no producer code. Every event uses only the 224 data roles. In each raw word, each data role has total native rank eight. The source phase proofs and 640-column replays are pinned premises; this checker does not run them again.
+
+The checker independently prices each scalar coefficient. A complex ADD with coefficient of absolute value one, two, or three costs eight, ten, or twelve real primitives in the stated lowering. A negative unit scale or positive double or half scale costs two. A negative double or half scale costs four. The counts agree with the two source invoices.
+
+The local map bounds, including two side maps per child and all 224 endpoint maps, are 2,648 for rank thirty and 3,488 for rank sixteen. Thus the three-call component subtotals are:
+
+| Local response | Real scalar subtotal | Map-call bound |
+| --- | ---: | ---: |
+| Rank thirty | 15,864 | 7,944 |
+| Rank sixteen | 22,152 | 10,464 |
+
+These omit all controller codes, odd scans, terminal operations, map lowering, recursive work, and precision. In particular, inverse scales with denominators five and seven are not free scalar primitives.
+
+The source bounds the rank-thirty word's top-level prefix row one-norm by 46 forward and 30 backward. The rank-sixteen bound is 22 in both directions. These are different from the older matching word's bound. They must be used in the eventual precision account. They do not bound recursive child interiors.
+
+## Exact moment and terminal bounds
+
+For a native histogram H, use
+
+    M_H(b) = sum_r H[r] * r/(DW) * (D/r)^b.
+
+The two pinned rational engines evaluate the complete three-call histogram. Their outward bounds are:
+
+| Local response | Lower bound | Upper bound |
+| --- | ---: | ---: |
+| Rank thirty | 0.964177326889959935 | 0.964177326889959936 |
+| Rank sixteen | 0.964968717039954015 | 0.964968717039954016 |
+
+For each extra-child limit, both engines prove M<1 at the stated count and M>1 at the next count. The receipt includes these bounds for ranks 1, 2, 4, 8, 9, and 17. No floating-point result determines a threshold.
+
+Both complete preterminal profiles have native mass 5,376. A terminal of mass 224 gives 5,600=DW. Every child rank is below D, so that full bill has M(b)>1 for every b>0. The full 224-H1 terminal must lose at least 25 H1 in the rank-thirty case or 29 H1 in the rank-sixteen case at the stated b.
+
+The last column of the first table permits every legal integer child rank. The strict size guard gives maximum rank 17 because 2*17^2<25^2<2*18^2. For 0<b<1, r^(1-b) is increasing and concave. For a fixed sum of ranks, move mass from a smaller non-maximal rank to a larger one. This cannot increase the cost. Repeat until all but at most one nonzero rank are 17. Therefore the cheapest distribution of n ranks is floor(n/17) copies of rank 17 and one remainder.
+
+For rank thirty, 11 H17 + H13 passes and 11 H17 + H14 fails. For rank sixteen, 11 H17 + H9 passes and 11 H17 + H10 fails. The cheapest cost increases with n. Thus no terminal and debt invoice of more than 200 or 196 total ranks can pass. These are favorable arithmetic bounds. They do not construct those grouped children.
+
+## What the smaller correction ranks could enable
+
+A decoder must be constructed before the local correction rank can be used as a native invoice. The following rows are targets, not consequences of a rank factorization:
+
+| Local response | Hypothetical terminal | Extra H1 left for all other work |
+| --- | ---: | ---: |
+| Rank thirty | 60 H1 | 139 |
+| Rank thirty | 180 H1 | 19 |
+| Rank sixteen | 32 H1 | 163 |
+| Rank sixteen | 96 H1 | 99 |
+
+The second terminal in each pair has count six times the local correction rank. This numerical choice does not prove that three routed stages can be served by two line passes on their local correction coordinates. The queries, scatters, code changes, borrowed state, restoration, and odd-grid conversions must be implemented at their actual cuts.
+
+The smaller correction rank is useful only if such an access theorem or circuit reduces the complete native invoice. It does not improve the preterminal moment by itself: the more fragmented rank-sixteen word has less native headroom than the rank-thirty word.
+
+## Changed exits
+
+The producer subsequently supplied four literal changed-output words. Their `CODED-EXITS-FREEZE.json` has SHA256 `f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936`. This checker binds the corrected payload and counts all sixteen provider and direction words independently.
+
+| Response and exit code | Literal native profile | Mass | Children | Local map bound |
+| --- | --- | ---: | ---: | ---: |
+| Rank30 W48/I64 | {1:988,2:48,4:55,5:55,6:9,7:9} | 1,696 | 1,164 | 2,552 |
+| Rank30 W112 | {1:988,2:48,5:55,6:55,7:9,8:9} | 1,824 | 1,164 | 2,488 |
+| Rank16 W48/I64 | {1:1472,2:112} | 1,696 | 1,584 | 3,392 |
+| Rank16 W112 | {1:1408,2:112,3:64} | 1,824 | 1,584 | 3,328 |
+
+Each scalar cost is unchanged from the corresponding raw word. Each word has 48 inline monomial exits. The map bounds include these exits, all endpoint maps, and two side maps per native child. In W48/I64, 96 data fields have total native rank seven and 128 have rank eight. In W112, the corresponding ranks are seven and nine. These are per-field totals; the largest individual child is at most eight.
+
+A terminal with bill 224 H1 is only a comparator for these changed outputs. It is not an admitted decoder for their output code. Under that comparator, the W48/I64 budgets are:
+
+| Local response | Moment interval before other debt | Extra H1 debt | Extra H2 debt | Extra total-rank limit |
+| --- | --- | ---: | ---: | ---: |
+| Rank thirty | [0.952769571331463721,0.952769571331463722] | 263 | 131 | 264 |
+| Rank sixteen | [0.953560961481457801,0.953560961481457802] | 258 | 129 | 259 |
+
+The total-rank limits use the same favorable grouping theorem. The best final profiles are 15 H17 + H9 and 15 H17 + H4. The next total rank fails. These allowances must pay for all missing stage transport, controller work, endpoint restoration, and any other native debt.
+
+If all 96 missing ranks are restored after each of the three calls, the debt is 288 ranks. Together with a terminal of mass 224, that restores total mass DW. No positive b then passes. This is a conditional obstruction to that invoice; it does not prove that each call must pay the full restoration separately.
+
+The uniform W112 variants leave only 104 H1 for rank thirty or 99 H1 for rank sixteen before any terminal. A terminal of mass 224 gives total rank 5,696, which exceeds DW by 96. That combination fails even at b=0. A useful uniform-code construction must change this terminal account or remove other work.
+
+The changed local output contracts are proved by the producer. Their reuse across the three stages and their terminal compatibility remain open. A 96-rank mass reduction alone was not used to compute any moment.
+
+## The matched H7 plus H2 contraction
+
+The bridge lane implements a separate change to the older matched word. On 64 permutation ports, it combines the last F2 H7 child with the terminal H2 into one H9. The arithmetic replacement is
+
+    3*{1:160,2:48,5:48,7:112,8:64}
+      + 96 H1 + 64 H9 - 64 H7.
+
+This has the same mass as the old complete bill. Its moment lies in [1.002547757087305755,1.002547757087305756]. With the other children fixed, at most 81 of the 96 H1 can remain. It still needs a 15-H1 reduction. The contraction lowers the moment but does not cross the next integer target.
+
+The old matched profile is pinned to its frozen budget receipt. The bridge construction is pinned to `rank9-completion-20261020/FREEZE.json`, with SHA256 `6177f89c88b503765a724e8c1baa934da582c490089dbe29e0f6ce2371f9904b`. This checker checks the resulting complete profile against that source receipt. The producer emitted the wrappers and checked their phases. Independent native review is pending. This budget check does not rerun those wrapper checks or prove the complete recursive invoice.
+
+## Reproduction and credit
+
+Run `python3 -I -B check_budget.py` and repeat with `-O`. The two runs must give identical receipt bytes. The source and engine hashes are in `BUDGET.json`.
+
+The root supplied the rank-two mode construction and the odd-grid direction. The new-core-transfer lane supplied the complete native words and corrected extension metadata. The native-escape lane owns rational code admission. The bridge lane proposed the H9 contraction. The earlier budget and independent-review lanes supplied the exact arithmetic and source-count methods. This packet used AI assistance.
+
+No PR, push, commit, or publication is authorized. Before any future PR description, read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..7ef1c9bba6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/REPRODUCTION.json
@@ -0,0 +1,11 @@
+{
+  "checker_sha256": "ba1d4a4777e85be4a2930f17bf7c15a39a7b7cd1386f9255d5a607e160e55b96",
+  "commands": [
+    "python3 -I -B check_budget.py",
+    "python3 -I -B -O check_budget.py"
+  ],
+  "receipt_sha256": "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2",
+  "scope": "Literal invoice and exact arithmetic only; source phase compilers were not rerun.",
+  "status": "PASS_NORMAL_OPTIMIZED_BYTE_IDENTICAL",
+  "stdout": "rank30 H1 199 H2 99 any rank 200\nodd_rank16 H1 195 H2 97 any rank 196\nrank30_W48_I64 H1 debt 263 any rank debt 264\nodd_rank16_W48_I64 H1 debt 258 any rank debt 259\n"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/check_budget.py b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/check_budget.py
new file mode 100644
index 0000000000..8f091c9fec
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/low-displacement-budget-20261020/check_budget.py
@@ -0,0 +1,274 @@
+"""Price the native words at the fixed selected-rate snapshot."""
+
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from math import isqrt
+from pathlib import Path
+import subprocess
+import tempfile
+
+
+HERE = Path(__file__).resolve().parent
+CAMPAIGN = HERE.parents[2]
+REPO = CAMPAIGN.parents[1]
+SOURCE = "lanes/new-core-transfer-20261017/low-displacement-20261020/"
+MATCHED_BUDGET = "lanes/budget-geometry-20261017/matched-native-budget-20261018/MATCHED-NATIVE-BUDGET.json"
+FUSION = "lanes/bridge-access-20261017/rank9-completion-20261020/"
+PINS = {
+    SOURCE + "NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24",
+    SOURCE + "native-normal-v2/NATIVE-CHECKS.json": "8acc084b5cd1d9513fdd3373eede998bd08e7f3fe1624f9fd41f758d4de7cb82",
+    SOURCE + "native-normal-v2/NATIVE-PROGRAM.json.gz": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    SOURCE + "EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689",
+    SOURCE + "odd16-normal-v2/EXTENSION-CHECKS.json": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197",
+    SOURCE + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    SOURCE + "CODED-EXITS-FREEZE.json": "f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936",
+    SOURCE + "coded-normal/CODED-EXITS-CHECKS.json": "b36bee542add54bac48e409c6a4a054b3bca5fba9c98d5513a90a6a92628d576",
+    SOURCE + "coded-normal/CODED-EXITS-PROGRAM.json.gz": "7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d",
+    MATCHED_BUDGET: "a1832aeb1d82498f423637ba8cab0ff11262383665ed440159759bc54fe5775e",
+    FUSION + "FREEZE.json": "6177f89c88b503765a724e8c1baa934da582c490089dbe29e0f6ce2371f9904b",
+    FUSION + "CHECKS.json": "c4b92b37441c095ff3c4d51ea920dd918edd54113764d76ce721a30ec435a2b0",
+}
+COMMIT = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f"
+ENGINE_ROOT = "research/complex-k492-owner-repair/vendor/multicold/engines/"
+ENGINE_PINS = {
+    "moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+}
+B = Q(67018507072324140917, 40000000000000000000000)
+D, W, CALLS = 25, 224, 3
+RANK30 = Counter({1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9})
+ODD16 = Counter({1: 1520, 2: 64, 3: 48})
+CHANGED = {
+    "rank30_W48_I64": Counter({1: 988, 2: 48, 4: 55, 5: 55, 6: 9, 7: 9}),
+    "rank30_W112": Counter({1: 988, 2: 48, 5: 55, 6: 55, 7: 9, 8: 9}),
+    "odd_rank16_W48_I64": Counter({1: 1472, 2: 112}),
+    "odd_rank16_W112": Counter({1: 1408, 2: 112, 3: 64}),
+}
+
+
+def need(ok, text):
+    if not ok:
+        raise ValueError(text)
+
+
+def mass(profile):
+    return sum(r * n for r, n in profile.items())
+
+
+def bounds(values):
+    lo, hi = max(v[0] for v in values), min(v[1] for v in values)
+    need(lo <= hi, "Both exact engines overlap")
+    scale = 10**18
+    return [str(Q((lo * scale).__floor__(), scale)), str(Q((hi * scale).__ceil__(), scale))]
+
+
+def literal_invoice(receipt, payload, expected_profile, expected_scalar,
+                    field_rank_census=None, endpoint_count=224, inline_maps=0, fraction_pairs=False):
+    if field_rank_census is None:
+        field_rank_census = Counter({8: 224})
+    literal = {}
+    for provider, directions in payload["providers"].items():
+        for direction, word in directions.items():
+            native = [e for e in word["events"] if e[0] == "native"]
+            scalar = [e[1] for e in word["events"] if e[0] == "scalar"]
+            monomial = [e for e in word["events"] if e[0] == "monomial"]
+            need(len(native) + len(scalar) + len(monomial) == len(word["events"]), "Every local event is priced")
+            need(len(monomial) == inline_maps and all(0 <= e[1] < 224 for e in monomial), "Inline monomial census")
+            profile = Counter(e[4] for e in native)
+            need(profile == expected_profile, "Literal native profile")
+            fields = Counter()
+            for event in native:
+                need(0 <= event[1] < 224, "Native child uses data")
+                fields[event[1]] += event[4]
+            need(len(fields) == 224 and Counter(fields.values()) == field_rank_census, "Per-field rank census")
+            need(all(g[0] in ("add", "scale") and 0 <= g[1] < 224
+                     and (g[0] != "add" or 0 <= g[2] < 224) for g in scalar), "Scalar work uses data")
+            if fraction_pairs:
+                need(all(len(g) == (5 if g[0] == "add" else 4) for g in scalar), "Numerator-denominator gate schema")
+                census = Counter((g[0], Q(*g[-2:])) for g in scalar)
+            else:
+                need(all(len(g) == 4 and isinstance(g[3], str) for g in scalar), "Fraction-string gate schema")
+                census = Counter((g[0], Q(g[3])) for g in scalar)
+            scalar_cost = 0
+            for (op, coefficient), count in census.items():
+                if op == "add":
+                    need(abs(coefficient) in (1, 2, 3), "Admitted integer ADD coefficients")
+                    cost = {1: 8, 2: 10, 3: 12}[abs(coefficient)]
+                else:
+                    need(coefficient in (-1, 2, Q(1, 2), -2, Q(-1, 2)), "Admitted dyadic scales")
+                    cost = 4 if coefficient in (-2, Q(-1, 2)) else 2
+                scalar_cost += count * cost
+            bill = receipt["reports"][direction] if "reports" in receipt else receipt[provider][direction]
+            need(scalar_cost == bill["real_scalar_primitives"] == expected_scalar, "Literal scalar invoice")
+            need(bill["native_children"] == len(native) == sum(expected_profile.values()), "Literal native count")
+            need(bill["native_mass"] == mass(profile), "Receipt native mass")
+            need(len(word["endpoint_adapters"]) == bill.get("endpoint_maps", bill.get("external_endpoint_maps"))
+                 == endpoint_count, "Endpoint count")
+            literal[provider + "/" + direction] = {
+                "profile": profile, "children": len(native), "native_mass": mass(profile),
+                "scalar_primitives": scalar_cost, "map_bound": 2 * len(native) + endpoint_count + inline_maps,
+                "field_rank_census": field_rank_census, "endpoint_maps": endpoint_count, "inline_maps": inline_maps,
+                "scalar_census": {op + ":" + str(c): n for (op, c), n in sorted(census.items())},
+            }
+    return literal
+
+
+def main():
+    source = {}
+    for path, pin in PINS.items():
+        raw = (CAMPAIGN / path).read_bytes()
+        if path.endswith(".gz"):
+            raw = gzip.decompress(raw)
+        need(sha256(raw).hexdigest() == pin, "Source pin: " + path)
+        source[path] = json.loads(raw)
+    literal = {
+        "rank30": literal_invoice(source[SOURCE + "native-normal-v2/NATIVE-CHECKS.json"],
+                                  source[SOURCE + "native-normal-v2/NATIVE-PROGRAM.json.gz"], RANK30, 5288),
+        "odd_rank16": literal_invoice(source[SOURCE + "odd16-normal-v2/EXTENSION-CHECKS.json"],
+                                      source[SOURCE + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz"], ODD16, 7384),
+    }
+    changed_words = source[SOURCE + "coded-normal/CODED-EXITS-PROGRAM.json.gz"]["providers_by_response_and_code"]
+    changed_receipts = source[SOURCE + "coded-normal/CODED-EXITS-CHECKS.json"]["receipts"]
+    for family, prefix, scalar in (("rank30", "rank30", 5288), ("rank16", "odd_rank16", 7384)):
+        for code in ("W48_I64", "W112"):
+            name = prefix + "_" + code
+            census = Counter({7: 96, 8 if code == "W48_I64" else 9: 128})
+            literal[name] = literal_invoice(changed_receipts[family][code],
+                                           {"providers": changed_words[family][code]}, CHANGED[name], scalar,
+                                           census, 176 if code == "W48_I64" else 112, 48, fraction_pairs=True)
+
+    results = {}
+    with tempfile.TemporaryDirectory(prefix="low-displacement-moment-") as folder:
+        engines = []
+        for i, (name, pin) in enumerate(ENGINE_PINS.items()):
+            raw = subprocess.check_output(["git", "-C", str(REPO), "show", COMMIT + ":" + ENGINE_ROOT + name])
+            need(sha256(raw).hexdigest() == pin, "Exact engine pin")
+            path = Path(folder) / name
+            path.write_bytes(raw)
+            spec = importlib.util.spec_from_file_location("low_displacement_engine_" + str(i), path)
+            engine = importlib.util.module_from_spec(spec)
+            spec.loader.exec_module(engine)
+            engines.append(engine)
+
+        def moments(profile):
+            values = [engines[0].moment(profile, D, W, B, False),
+                      engines[1].moment(D, W, list(profile.items()), B)]
+            bounds(values)
+            return values
+
+        def allowance(profile):
+            base = moments(profile)
+            need(all(hi < 1 for lo, hi in base), "Positive native headroom")
+            answer = {"moment": bounds(base), "native_mass": mass(profile), "profile": profile, "limits": {}}
+            for rank in (1, 2, 4, 8, 9, 17):
+                unit = moments({rank: 1})
+                counts = [((1 - hi) / unit_hi).__floor__() for (lo, hi), (unit_lo, unit_hi) in zip(base, unit)]
+                need(counts[0] == counts[1], "Both engines give the same integer allowance")
+                n = counts[0]
+                yes, no = moments(profile + Counter({rank: n})), moments(profile + Counter({rank: n + 1}))
+                need(all(hi < 1 for lo, hi in yes) and all(lo > 1 for lo, hi in no), "Strict allowance and next failure")
+                answer["limits"][str(rank)] = {"children": n, "rank_mass": n * rank,
+                                               "accepted": bounds(yes), "next": bounds(no)}
+            rank_max = isqrt((D * D - 1) // 2)
+
+            def packed(n):
+                q, r = divmod(n, rank_max)
+                return Counter({rank_max: q}) + (Counter({r: 1}) if r else Counter())
+
+            lo, hi = 0, D * W - mass(profile)
+            need(all(a > 1 for a, b in moments(profile + packed(hi))), "Full rank budget fails")
+            while hi - lo > 1:
+                mid = (hi + lo) // 2
+                at = moments(profile + packed(mid))
+                if all(b < 1 for a, b in at):
+                    lo = mid
+                else:
+                    need(all(a > 1 for a, b in at), "Exact packed-rank sign")
+                    hi = mid
+            answer["all_legal_ranks"] = {
+                "maximum_child_rank": rank_max, "total_rank_limit": lo, "best_profile": packed(lo),
+                "accepted": bounds(moments(profile + packed(lo))),
+                "next_best_profile": packed(hi), "next": bounds(moments(profile + packed(hi))),
+                "scope": "Arithmetic optimum by concavity. No access or native construction is supplied.",
+            }
+            return answer
+
+        for name, local, scalar, correction, status in (
+            ("rank30", RANK30, 5288, 30, "Frozen literal native word"),
+            ("odd_rank16", ODD16, 7384, 16, "Frozen literal native word; rational code and global admission remain separate"),
+        ):
+            need(mass(local) == 1792 and all(2 * r * r < D * D for r in local), "Local rank and size")
+            whole = Counter({r: CALLS * n for r, n in local.items()})
+            row = allowance(whole)
+            row.update({"local_profile": local, "local_children": sum(local.values()),
+                        "local_scalar_primitives": scalar, "three_call_scalar_subtotal": CALLS * scalar,
+                        "source_status": status, "local_correction_rank": correction,
+                        "unfused_terminal_H1": 224,
+                        "H1_removal_from_unfused_terminal": 224 - row["limits"]["1"]["children"],
+                        "unfused_terminal_moment": bounds(moments(whole + Counter({1: 224})))})
+            need(mass(whole) == 5376 and mass(whole + Counter({1: 224})) == D * W, "Complete raw rank account")
+            for count in (2 * correction, 6 * correction):
+                row.setdefault("hypothetical_H1_terminal_targets", {})[str(count)] = {
+                    "moment": bounds(moments(whole + Counter({1: count}))),
+                    "remaining_H1": row["limits"]["1"]["children"] - count,
+                    "scope": "An arithmetic target only. Local correction rank does not provide routed terminal access.",
+                }
+            results[name] = row
+            print(name, "H1", row["limits"]["1"]["children"], "H2", row["limits"]["2"]["children"],
+                  "any rank", row["all_legal_ranks"]["total_rank_limit"], flush=True)
+
+        for name, local in CHANGED.items():
+            need(all(2 * r * r < D * D for r in local), "Changed-output child size")
+            whole = Counter({r: CALLS * n for r, n in local.items()})
+            row = {"local_profile": local, "local_mass": mass(local), "preterminal": allowance(whole),
+                   "source_status": "Frozen literal changed-output word; global transport and terminal remain separate",
+                   "terminal_comparator": {"1": 224},
+                   "terminal_scope": "A 224-H1 bill is a comparator only. The changed outputs need a new global terminal proof."}
+            complete = whole + Counter({1: 224})
+            row["with_terminal_comparator_moment"] = bounds(moments(complete))
+            row["with_terminal_comparator_rank_mass"] = mass(complete)
+            if name.endswith("W48_I64"):
+                need(mass(local) == 1696 and mass(complete) + 288 == D * W, "Full per-call restoration loses")
+                row["all_other_debt_after_terminal"] = allowance(complete)
+                row["full_per_call_restoration_rank"] = 288
+                row["restoration_scope"] = "If all 96 missing ranks are paid after every call, the full mass reaches DW and no positive b passes. This does not prove that the debt is necessary."
+                print(name, "H1 debt", row["all_other_debt_after_terminal"]["limits"]["1"]["children"],
+                      "any rank debt", row["all_other_debt_after_terminal"]["all_legal_ranks"]["total_rank_limit"], flush=True)
+            else:
+                need(mass(local) == 1824 and mass(complete) == D * W + 96, "Uniform output with full terminal exceeds rank budget")
+                row["rank_excess_over_full_budget"] = 96
+            results[name] = row
+
+        matched = Counter({1: 160, 2: 48, 5: 48, 7: 112, 8: 64})
+        need(source[MATCHED_BUDGET]["literal_local_invoice"]["base/forward"]["native_profile"]
+             == {str(r): n for r, n in matched.items()}, "Pinned matched comparator")
+        fusion_base = Counter({r: CALLS * n for r, n in matched.items()})
+        fusion_base[7] -= 64
+        fusion_base[9] += 64
+        fusion = allowance(fusion_base)
+        fusion["remaining_terminal_H1"] = 96
+        fusion["minimum_H1_saving"] = 96 - fusion["limits"]["1"]["children"]
+        fusion["complete_moment"] = bounds(moments(fusion_base + Counter({1: 96})))
+        need({str(r): n for r, n in (fusion_base + Counter({1: 96})).items()}
+             == source[FUSION + "CHECKS.json"]["complete_native_profile_after"], "Pinned rank-nine completion profile")
+        need(source[FUSION + "CHECKS.json"]["complete_native_rank"] == 5600, "Rank-nine completion mass")
+        fusion["scope"] = "The frozen bridge construction replaces the final 64 H7 and 64 terminal H2 by 64 H9. Its independent native review is pending. This checker binds its profile and prices it; it does not rerun the wrapper phase checks."
+        results["matched_H7_H2_fusion"] = fusion
+
+    out = {"status": "PASS_TWO_EXACT_ENGINES_WITH_EXPLICIT_SOURCE_SCOPE",
+           "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+           "source_pins": PINS, "gzip_pin_convention": "Decompressed bytes",
+           "engine_commit": COMMIT, "engine_pins": ENGINE_PINS,
+           "dimension": D, "productive_width": W, "calls": CALLS, "idle_profile": {},
+           "selected_b_snapshot": str(B), "literal_native_invoices": literal, "results": results,
+           "W48_scope": "The frozen changed-exit histograms are counted literally. Global transport and terminal compatibility remain unproved. No mass-only pricing shortcut is used.",
+           "global_scope": "A hypothetical three-call D25 placement is priced. Routed codes, terminal access, recursive host and complete finite costs remain separate."}
+    (HERE / "BUDGET.json").write_text(json.dumps(out, indent=2, sort_keys=True) + "\n")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/matched-native-budget-20261018/MATCHED-NATIVE-BUDGET.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/matched-native-budget-20261018/MATCHED-NATIVE-BUDGET.json
new file mode 100644
index 0000000000..230d9d8085
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/matched-native-budget-20261018/MATCHED-NATIVE-BUDGET.json
@@ -0,0 +1,1410 @@
+{
+  "checker_sha256": "77465e802789742559dea96cf8276405f93f58a4e7901f5a2b649080a163048f",
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+  "scope": "Pinned local responses and structural one-pair paid terminal. Changed outputs need global composition. No complete finite supplier or kappa claim.",
+  "selected_b": "67018507072324140917/40000000000000000000000",
+  "selected_b_scope": "The exact selected-rate snapshot used on 2026-10-18. No claim that this is the current selected rate.",
+  "source_pins": {
+    "lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-CHECKS.json": "3ef62a5e133fddc32926c8c4f3f009e32178cb369a37ccd6880d5a740c6b9acf",
+    "lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-FREEZE.json": "0a20fdae1f2497088e0e62e72960d81c44c48805b5685b08710ceed898bc22ce",
+    "lanes/budget-geometry-20261017/centre-service-budget-20261018/CENTRE-SERVICE-BUDGET.json": "e61c1689f01c47d71ba88d57077b0600b8b5f524eb3168d0c872a9a2303cfe55",
+    "lanes/history-encoding/one-pair-admission-20261018/CHECKS.json": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944",
+    "lanes/history-encoding/one-pair-admission-20261018/FREEZE.json": "0c27631267119efca1a416f0f299a2ce398a87fea313611341133b7c3736d8ed",
+    "lanes/independent-review-20261018/helper-free-invoice/REVIEW.json": "e75477a65040b75122854b4023101743ce9ce2e6510ecaeb29e08b4d9ffc25b0",
+    "lanes/oblique-native-20261017/matched-left-gauge/FREEZE.json": "663aa9d98092507f1393f46cfcc03f85c1906e0559ba0553f9d636e2fbec2f93",
+    "lanes/oblique-native-20261017/matched-left-gauge/LEFT-GAUGE-PROGRAM.json.gz": "437f96b00ae04f410c55f3501ac28bc103e0b416005459c661ac02794c0f9891",
+    "lanes/oblique-native-20261017/matched-left-gauge/LEFT-GAUGE-RECEIPT.json": "1b910b246fd062163528507569bfa4aa11004dda2cd6e59bc2bd52550e527c67",
+    "lanes/oblique-native-20261017/matched-native-involution/FREEZE.json": "b35eae3fb4b53f51cfbed6bec8968b950c70e65bfe777cbe0d15e86c36dd4ab5",
+    "lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz (decompressed)": "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025",
+    "lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-RECEIPT.json": "7bc873d627e022d4677b740633c9cd5f86c5e675d84460d538b4b6314c79536c",
+    "lanes/oblique-native-20261017/matched-scalar-optimization/CHECKS.json": "2000cd9b5deb37f5fb9aef416fbd2b28b9dbbc0df6612eb1956e088f3418f8a8",
+    "lanes/oblique-native-20261017/matched-scalar-optimization/FREEZE.json": "c6abc3f2b659fbd0a55549038e927c032810c67bded610843fff7416d1cc3f83",
+    "lanes/oblique-native-20261017/matched-scalar-optimization/OPTIMIZED-PROGRAM.json.gz": "c820a5881174edce5425a7eae6f255ea800dc39be2f7f326cc299a6e5c0072b9"
+  },
+  "status": "PASS_TWO_EXACT_ENGINES_WITH_CONDITIONAL_GLOBAL_SCOPE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/FREEZE.json
new file mode 100644
index 0000000000..6a807d5b79
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/FREEZE.json
@@ -0,0 +1,13 @@
+{
+  "files": {
+    "MIXED-BUDGET.json": "7359fbab24858a21ea9879fff0b61883134ee3bb754916085689136f6d833224",
+    "PROOF.md": "6a6514195645d0cf508b3f560275e3970fa71dc1e8f29cf62038a7be0d8a7772",
+    "REPRODUCTION.json": "097bb57410d27add5f88dc1f9d86c07ef2dd7badfcb2cd864de71972640681c3",
+    "check_mixed_budget.py": "72e3fa1dc402c04448bd9c908e52b29b2b3286bbd13944b1988c75c78e400748"
+  },
+  "frozen_utc": "2026-10-20T15:47:09.052849+00:00",
+  "independent_review": "Pending. Rational bounds are derived from the pinned earlier two-engine receipt.",
+  "normal_optimized_byte_identical": true,
+  "publication_authorized": false,
+  "schema": "mixed-exit-budget-freeze-v1"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/MIXED-BUDGET.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/MIXED-BUDGET.json
new file mode 100644
index 0000000000..5c83fcf3b9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/MIXED-BUDGET.json
@@ -0,0 +1,265 @@
+{
+  "checker_sha256": "72e3fa1dc402c04448bd9c908e52b29b2b3286bbd13944b1988c75c78e400748",
+  "method": "Rational interval arithmetic and linearity in the native histogram",
+  "rows": {
+    "odd_rank16": {
+      "1": {
+        "H1_saving_from_full_restoration": 30,
+        "changed_calls": 1,
+        "limits": {
+          "1": {
+            "accepted": [
+              "64988719301753098511/65000000000000000000",
+              "3249435965087654931/3250000000000000000"
+            ],
+            "children": 66,
+            "next": [
+              "65000389212269771137/65000000000000000000",
+              "9750058381840465687/9750000000000000000"
+            ],
+            "rank_mass": 66
+          },
+          "2": {
+            "accepted": [
+              "6061364478714812179/6062500000000000000",
+              "96981831659436995027/97000000000000000000"
+            ],
+            "children": 33,
+            "next": [
+              "19403324285521067249/19400000000000000000",
+              "9701662142760533641/9700000000000000000"
+            ],
+            "rank_mass": 66
+          }
+        },
+        "moment": [
+          "987977003194657003/1000000000000000000",
+          "246994250798664251/250000000000000000"
+        ],
+        "profile": {
+          "1": 4736,
+          "2": 240,
+          "3": 96
+        },
+        "rank_mass": 5504
+      },
+      "2": {
+        "H1_saving_from_full_restoration": 30,
+        "changed_calls": 2,
+        "limits": {
+          "1": {
+            "accepted": [
+              "32495254677837348271/32500000000000000000",
+              "12998101871134939343/13000000000000000000"
+            ],
+            "children": 162,
+            "next": [
+              "4062636204136960573/4062500000000000000",
+              "7800261511942964321/7800000000000000000"
+            ],
+            "rank_mass": 162
+          },
+          "2": {
+            "accepted": [
+              "19396512501685443971/19400000000000000000",
+              "48491281254213610057/48500000000000000000"
+            ],
+            "children": 81,
+            "next": [
+              "24254338069148890309/24250000000000000000",
+              "97017352276595561497/97000000000000000000"
+            ],
+            "rank_mass": 162
+          }
+        },
+        "moment": [
+          "485384491169028701/500000000000000000",
+          "970768982338057403/1000000000000000000"
+        ],
+        "profile": {
+          "1": 4688,
+          "2": 288,
+          "3": 48
+        },
+        "rank_mass": 5408
+      },
+      "3": {
+        "H1_saving_from_full_restoration": 30,
+        "changed_calls": 3,
+        "limits": {
+          "1": {
+            "accepted": [
+              "64992299409596294573/65000000000000000000",
+              "6499229940959629481/6500000000000000000"
+            ],
+            "children": 258,
+            "next": [
+              "65003969320112967199/65000000000000000000",
+              "19501190796033890231/19500000000000000000"
+            ],
+            "rank_mass": 258
+          },
+          "2": {
+            "accepted": [
+              "48491646678708722423/48500000000000000000",
+              "96983293357417445201/97000000000000000000"
+            ],
+            "children": 129,
+            "next": [
+              "97018083125585786227/97000000000000000000",
+              "12127260390698223323/12125000000000000000"
+            ],
+            "rank_mass": 258
+          }
+        },
+        "moment": [
+          "953560961481457801/1000000000000000000",
+          "476780480740728901/500000000000000000"
+        ],
+        "profile": {
+          "1": 4640,
+          "2": 336,
+          "3": 0
+        },
+        "rank_mass": 5312
+      }
+    },
+    "rank30": {
+      "1": {
+        "H1_saving_from_full_restoration": 25,
+        "changed_calls": 1,
+        "limits": {
+          "1": {
+            "accepted": [
+              "298479924702064210477/298500000000000000000",
+              "596959849404128421977/597000000000000000000"
+            ],
+            "children": 71,
+            "next": [
+              "597067033043796937229/597000000000000000000",
+              "298533516521898469129/298500000000000000000"
+            ],
+            "rank_mass": 71
+          },
+          "2": {
+            "accepted": [
+              "49487061797789695579/49500000000000000000",
+              "10997124843953265703/11000000000000000000"
+            ],
+            "children": 35,
+            "next": [
+              "33003210226185109069/33000000000000000000",
+              "16501605113092554563/16500000000000000000"
+            ],
+            "rank_mass": 70
+          }
+        },
+        "moment": [
+          "2961556839133988771/3000000000000000000",
+          "1480778419566994387/1500000000000000000"
+        ],
+        "profile": {
+          "1": 3284,
+          "2": 48,
+          "3": 96,
+          "4": 165,
+          "5": 165,
+          "6": 27,
+          "7": 27
+        },
+        "rank_mass": 5504
+      },
+      "2": {
+        "H1_saving_from_full_restoration": 25,
+        "changed_calls": 2,
+        "limits": {
+          "1": {
+            "accepted": [
+              "298488145180458010679/298500000000000000000",
+              "596976290360916022957/597000000000000000000"
+            ],
+            "children": 167,
+            "next": [
+              "597083474000584537633/597000000000000000000",
+              "298541737000292269619/298500000000000000000"
+            ],
+            "rank_mass": 167
+          },
+          "2": {
+            "accepted": [
+              "49487434756810480489/49500000000000000000",
+              "32991623171206987081/33000000000000000000"
+            ],
+            "children": 83,
+            "next": [
+              "11001152955177433003/11000000000000000000",
+              "16501729432766149549/16500000000000000000"
+            ],
+            "rank_mass": 166
+          }
+        },
+        "moment": [
+          "2909932776564189967/3000000000000000000",
+          "290993277656418997/300000000000000000"
+        ],
+        "profile": {
+          "1": 3236,
+          "2": 96,
+          "3": 48,
+          "4": 165,
+          "5": 165,
+          "6": 27,
+          "7": 27
+        },
+        "rank_mass": 5408
+      },
+      "3": {
+        "H1_saving_from_full_restoration": 25,
+        "changed_calls": 3,
+        "limits": {
+          "1": {
+            "accepted": [
+              "99498788552950603627/99500000000000000000",
+              "198997577105901207979/199000000000000000000"
+            ],
+            "children": 263,
+            "next": [
+              "199033304985790712679/199000000000000000000",
+              "99516652492895356703/99500000000000000000"
+            ],
+            "rank_mass": 263
+          },
+          "2": {
+            "accepted": [
+              "49487807715831265399/49500000000000000000",
+              "32991871810554177053/33000000000000000000"
+            ],
+            "children": 131,
+            "next": [
+              "3000337045898135359/3000000000000000000",
+              "100011234863271179/100000000000000000"
+            ],
+            "rank_mass": 262
+          }
+        },
+        "moment": [
+          "952769571331463721/1000000000000000000",
+          "476384785665731861/500000000000000000"
+        ],
+        "profile": {
+          "1": 3188,
+          "2": 144,
+          "3": 0,
+          "4": 165,
+          "5": 165,
+          "6": 27,
+          "7": 27
+        },
+        "rank_mass": 5312
+      }
+    }
+  },
+  "scope": "Conditional native histogram only. The changed-call placement and the 224 H1 terminal are not admitted.",
+  "selected_b_snapshot": "67018507072324140917/40000000000000000000000",
+  "source_sha256": "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/PROOF.md b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/PROOF.md
new file mode 100644
index 0000000000..238c6cce6f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/PROOF.md
@@ -0,0 +1,52 @@
+# Budgets with one or two changed exits
+
+## Result and scope
+
+This addendum uses D=25, productive width 224, three local calls, and no idle jobs. It uses the same exact exponent snapshot as `low-displacement-budget-20261020/BUDGET.json`. Its SHA256 is `12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2`.
+
+Let k calls use the W48/I64 exit. Let the other 3-k calls use the raw exit of the same response family. Add a terminal comparator of 224 H1. The exact remaining allowances are:
+
+| Response | Changed calls k | Extra H1 limit | Extra H2 limit |
+| --- | ---: | ---: | ---: |
+| Rank thirty | 1 | 71 | 35 |
+| Rank thirty | 2 | 167 | 83 |
+| Rank thirty | 3 | 263 | 131 |
+| Rank sixteen | 1 | 66 | 33 |
+| Rank sixteen | 2 | 162 | 81 |
+| Rank sixteen | 3 | 258 | 129 |
+
+Each limit must pay for all added native work. The table does not allow both limits at the same time. For example, the first row allows 71 H1 with no other added children, or 35 H2 with no other added children.
+
+These are conditional histograms. The table does not prove that a changed-output word can be put at any selected stage. It does not construct a 224-H1 decoder for the changed global output. The output code, routed access, phases, arbitrary borrowed state, restoration, and recursive host remain separate obligations. No finite cost or kappa improvement is claimed.
+
+The one-call rows give a useful construction target. A construction can try a single changed exit at the final stage. It need not first solve repeated transport between three changed exits. If that construction also admits the stated terminal comparator, its other native work must fit within the first or fourth row.
+
+## Proof
+
+For a native histogram H, the moment is
+
+    M(H) = sum_r H[r] * r/(25*224) * (25/r)^b.
+
+It is linear in H. Let R and C be the three-call raw and changed histograms, each with the same 224-H1 terminal comparator. The k-call histogram is
+
+    H_k = ((3-k)R + kC)/3.
+
+Thus M(H_k)=((3-k)M(R)+kM(C))/3. The frozen source gives outward rational bounds for both endpoint moments. This identity gives an outward rational interval for each mixed moment.
+
+The checker also derives the cost of one H1 or H2 from the frozen bounds. If A is the raw preterminal moment, B is its moment after n copies of one child rank, and u is the cost of one such child, then B-A=nu. Therefore
+
+    (B_lower-A_upper)/n <= u <= (B_upper-A_lower)/n.
+
+The checker uses these exact rational intervals. For each stated limit n, it verifies that the upper bound for M(H_k)+nu is less than one. It verifies that the lower bound with n+1 copies is greater than one. The three-call limits also agree with the earlier frozen packet. No floating-point calculation determines a result.
+
+The complete mass before other debt is 5,600-96k. Restoring 96 ranks after each changed call raises it to 5,600=DW. If every child rank is below D, that restored bill has moment greater than one for every b>0. This does not prove that such restoration is necessary.
+
+For an all-H1 restoration, the exact table requires at least 25 H1 to be removed from 96k in the rank-thirty case, or 30 in the rank-sixteen case. These differences hold for k=1, 2, and 3 at the stated exponent. They are budget targets, not lower bounds on a legal decoder.
+
+## Verification and credit
+
+Run `python3 -I -B check_mixed_budget.py` and repeat with `-O`. The two runs must produce identical receipt bytes. The checker verifies the frozen source hash and the dimension, width, and number of calls. It then uses only rational interval operations. It does not repeat the source native replay or its phase compiler. A separate review of this addendum is pending.
+
+The root and new-core-transfer lane supplied the response construction and the raw and changed native words. The earlier budget packet supplied the exact source counts and two-engine moment bounds. This addendum used AI assistance.
+
+No PR, push, commit, or publication is authorized. Before any future PR description, read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..05903ff6d9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/REPRODUCTION.json
@@ -0,0 +1,9 @@
+{
+  "commands": [
+    "python3 -I -B check_mixed_budget.py",
+    "python3 -I -B -O check_mixed_budget.py"
+  ],
+  "normal_optimized_byte_identical": true,
+  "receipt_sha256": "7359fbab24858a21ea9879fff0b61883134ee3bb754916085689136f6d833224",
+  "stdout_sha256": "9723ad92bd2ba37c2272384db6d9fe9123e69841b79ccf53a209abaa31df0b93"
+}
diff --git a/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/check_mixed_budget.py b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/check_mixed_budget.py
new file mode 100644
index 0000000000..f012520e6f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/budget-geometry-20261017/mixed-exit-budget-20261020/check_mixed_budget.py
@@ -0,0 +1,91 @@
+"""Price one or two changed exits from the frozen rational bounds."""
+
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE = HERE.parent / "low-displacement-budget-20261020" / "BUDGET.json"
+PIN = "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2"
+
+
+def need(ok, text):
+    if not ok:
+        raise ValueError(text)
+
+
+def interval(value):
+    lo, hi = map(Q, value)
+    need(lo <= hi, "Ordered interval")
+    return lo, hi
+
+
+def encode(value):
+    return [str(x) for x in value]
+
+
+def main():
+    raw_bytes = SOURCE.read_bytes()
+    need(sha256(raw_bytes).hexdigest() == PIN, "Frozen source pin")
+    source = json.loads(raw_bytes)
+    need((source["dimension"], source["productive_width"], source["calls"]) == (25, 224, 3),
+         "One-pair schedule")
+    rows = {}
+    for family in ("rank30", "odd_rank16"):
+        raw = source["results"][family]
+        coded = source["results"][family + "_W48_I64"]
+        a = interval(raw["unfused_terminal_moment"])
+        b = interval(coded["with_terminal_comparator_moment"])
+        before = interval(raw["moment"])
+        units = {}
+        for rank in (1, 2):
+            n = raw["limits"][str(rank)]["children"]
+            accepted = interval(raw["limits"][str(rank)]["accepted"])
+            units[rank] = ((accepted[0] - before[1]) / n,
+                           (accepted[1] - before[0]) / n)
+            need(0 < units[rank][0] <= units[rank][1], "Positive unit interval")
+        rows[family] = {}
+        for count in (1, 2, 3):
+            base = tuple(((3 - count) * a[i] + count * b[i]) / 3 for i in (0, 1))
+            need(base[1] < 1, "Positive budget with the terminal comparator")
+            profile = Counter({int(r): (3 - count) * n for r, n in raw["local_profile"].items()})
+            profile.update({int(r): count * n for r, n in coded["local_profile"].items()})
+            profile[1] += 224
+            rank_mass = sum(r * n for r, n in profile.items())
+            need(rank_mass == 5600 - 96 * count, "Complete rank count")
+            result = {"changed_calls": count, "profile": profile, "rank_mass": rank_mass,
+                      "moment": encode(base), "limits": {}}
+            for rank, unit in units.items():
+                n = ((1 - base[1]) / unit[1]).__floor__()
+                yes = tuple(base[i] + n * unit[i] for i in (0, 1))
+                no = tuple(base[i] + (n + 1) * unit[i] for i in (0, 1))
+                need(n >= 0 and yes[1] < 1 < no[0], "Strict limit and next failure")
+                result["limits"][str(rank)] = {
+                    "children": n, "rank_mass": n * rank,
+                    "accepted": encode(yes), "next": encode(no),
+                }
+            result["H1_saving_from_full_restoration"] = 96 * count - result["limits"]["1"]["children"]
+            rows[family][str(count)] = result
+        for rank in (1, 2):
+            need(rows[family]["3"]["limits"][str(rank)]["children"]
+                 == coded["all_other_debt_after_terminal"]["limits"][str(rank)]["children"],
+                 "The three-call endpoint agrees with the frozen source")
+    receipt = {
+        "source_sha256": PIN,
+        "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "selected_b_snapshot": source["selected_b_snapshot"],
+        "method": "Rational interval arithmetic and linearity in the native histogram",
+        "scope": "Conditional native histogram only. The changed-call placement and the 224 H1 terminal are not admitted.",
+        "rows": rows,
+    }
+    (HERE / "MIXED-BUDGET.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    for family, entries in rows.items():
+        print(family, [(k, r["limits"]["1"]["children"], r["limits"]["2"]["children"])
+                       for k, r in entries.items()])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json
new file mode 100644
index 0000000000..0cb76e6370
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json
@@ -0,0 +1,1523 @@
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+  "ordinary_inverse_both_orders": true,
+  "phase_ledger_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+  "phase_source_sha256": "cf39b15752fcb96cc22b9013dce38e13a4399d99b30dc9f53eef788d5ded2bf4",
+  "q_labels": [
+    11,
+    19,
+    35,
+    67,
+    131,
+    259,
+    13,
+    21,
+    37,
+    69,
+    133,
+    261,
+    41,
+    73,
+    137,
+    265,
+    49,
+    81,
+    145,
+    273,
+    161,
+    289,
+    193,
+    321,
+    385,
+    14,
+    22,
+    38,
+    70,
+    134,
+    262,
+    26,
+    74,
+    138,
+    266,
+    50,
+    146,
+    274,
+    98,
+    162,
+    290,
+    194,
+    322,
+    386,
+    28,
+    44,
+    140,
+    268,
+    84,
+    148,
+    276,
+    100,
+    164,
+    292,
+    196,
+    324,
+    388,
+    56,
+    88,
+    152,
+    280,
+    104,
+    168,
+    296,
+    200,
+    328,
+    392,
+    112,
+    176,
+    304,
+    208,
+    336,
+    400,
+    224,
+    352,
+    416,
+    448,
+    508,
+    506,
+    502,
+    494,
+    478,
+    446,
+    382,
+    254,
+    505,
+    501,
+    493,
+    477,
+    445,
+    381,
+    253,
+    499,
+    491,
+    475,
+    443,
+    379,
+    251,
+    487,
+    471,
+    439,
+    375,
+    247,
+    463,
+    431,
+    367,
+    239,
+    415,
+    351,
+    223,
+    319,
+    191
+  ],
+  "scope": "Exact matrices and binary label geometry. No carried-frame or supplier cost claim.",
+  "selected_determinant": "-1/4",
+  "selected_inverse": [
+    {
+      "1": "2"
+    },
+    {
+      "0": "2"
+    }
+  ],
+  "selected_ports": [
+    0,
+    15
+  ],
+  "status": "PASS_MATCHING_GEOMETRY_AND_TWO_PORT_UNITS",
+  "unique_common_isotropic_matching": [
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ],
+    [
+      [
+        0,
+        5
+      ],
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        3
+      ]
+    ]
+  ],
+  "vertex_matching_span_rank_counts": [
+    {
+      "4": 15
+    },
+    {
+      "4": 15
+    },
+    {
+      "4": 15
+    },
+    {
+      "4": 15
+    },
+    {
+      "4": 15
+    },
+    {
+      "4": 15
+    },
+    {
+      "4": 15
+    },
+    {
+      "4": 15
+    }
+  ]
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/FREEZE.json
new file mode 100644
index 0000000000..e0a88ee15f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/FREEZE.json
@@ -0,0 +1,12 @@
+{
+  "files": {
+    "ROW-CAPTURE.md": "0caea104839f0e9726c892ab2b21c2c3501deb818ab0c844e4fa5234cb870eee",
+    "check_row_capture.py": "ccf661107a790c3d858a3f2bd4d8adc5269f588bfd989bd2e2029e26cbb14081",
+    "run-normal/CHECKS.json": "7054fe6350d900561111b81f2ce46057edb62aef1f5581c4adac66f1c1742081",
+    "run-normal/ROW-CAPTURE.json": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+  },
+  "independent_review": "queued in new-native-recipes-20261017",
+  "normal_optimized_byte_identical": true,
+  "scope": "Exact normalized row code, scalar words, encoded response, and arbitrary-baseline late query. Native emission, routed admission, and full supplier closure remain separate.",
+  "status": "PASS_EXACT_ROW_CAPTURE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/ROW-CAPTURE.md b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/ROW-CAPTURE.md
new file mode 100644
index 0000000000..3b316dc1b6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/ROW-CAPTURE.md
@@ -0,0 +1,258 @@
+# A centre capture that changes only sixteen output rows
+
+The actual rank-sixteen response has a dyadic code on its existing data
+fields. The code changes sixteen selected rows and leaves the other
+ninety-six rows unchanged. Its inverse changes the same sixteen rows.
+Both words cost 1,760 real scalar primitives. They use no additional
+field, native child, or odd division.
+
+This code gives a concrete forward-service interface. First apply the
+code to the current I-frame Y bank. Keep the original source paths and
+the ninety-six ordinary target paths. Replace the sixteen selected
+target paths by full F9 children. At the completed source cut, add the
+specified centre query to those sixteen FULL targets.
+
+The scalar algebra is checked here. The native emitter and the routed
+cut check are separate packets. A complete supplier decoder is still
+open.
+
+## Exact source and pivots
+
+The pinned native source is
+
+```text
+new-core-transfer-20261017/low-displacement-20261020/
+odd16-normal-v2/EXTENSION-PROGRAM.json.gz
+decompressed SHA256
+d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4
+```
+
+Its response is E=I+UV, where U has sixteen columns and V has sixteen
+rows. The first eight centre coordinates come from the six-mode blocks.
+The other eight come from the eight-port cliques. The exact action is
+
+```text
+H = I+VU = diag(-5 I8,-7 I8).
+```
+
+Select these physical pivots, in this order:
+
+```text
+P = [0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23].
+```
+
+Let R be the other ninety-six ports. The first eight pivots form four
+complete physical pair blocks:
+
+```text
+(0,27), (36,111), (20,46), (7,57).
+```
+
+The matrix V_P has determinant 16. It is a dyadic unit. Its eight-port
+part is the signed pair code, with the stated order of its centre
+coordinates. Its remaining part is identity. It commutes with H.
+
+Put W=V_P^-1 V and write W=[I,B] in P,R order. This W is a rectangular
+reader. It is not the Clifford gauge called W in other campaign notes.
+Define
+
+```text
+C = [ I   B ],          C^-1 = [ I  -B ].
+    [ 0   I ]                  [ 0   I ]
+```
+
+Thus C records the normalized centre query in P and retains the original
+ordinary values in R. Each selected target can have any initial value.
+The inverse subtracts the same query from the unchanged R sources.
+There is no clean-record premise.
+
+The large selected rows have twenty coefficients of magnitude 1/2.
+The small selected rows have seven unit coefficients. For each large
+row, scale the target by 2, add the twenty signed unit sources, and
+scale the target by 1/2. The price is 164 per large row. Each small row
+costs 56. Hence each complete code costs
+
+```text
+8*164 + 8*56 = 1760.
+```
+
+## The encoded response
+
+Let A=U_R V_P. Exact multiplication gives
+
+```text
+C E C^-1 = [ H   0 ].
+           [ A   I ]
+```
+
+The centre action is diagonal. A lower fanout into the ordinary fields
+remains. The code does not turn the complete response into a diagonal
+matrix.
+
+The selected rows of CE are HW. The ordinary rows are the original
+ordinary rows of E. In the literal paired-mode chart, CE has nonzero
+diagonal entries on exactly the sixteen selected pivots. All other
+mode diagonal entries remain zero.
+
+These facts permit a narrower native change than full diagonalization:
+the new response needs different target paths on sixteen fields.
+
+## A forward service with FULL centre outputs
+
+Let x,y be arbitrary local data. The physical entry is
+
+```text
+X = Qx,       Y = y.
+```
+
+The original forward service has physical output
+
+```text
+X = F9 x,     Y = F9 q(y+Ex),       q=Q^-1.
+```
+
+Use the following ordered construction.
+
+1. Apply C to Y in the common I frame.
+2. Run all original X paths and all original Y paths on R.
+3. Apply a full F9 child to each selected Y field.
+4. After all X fields are FULL, add HWx to the selected Y fields.
+
+The resulting exact physical output is
+
+```text
+X   = F9 x,
+Y_P = F9 W(y+Ex),
+Y_R = F9 q_R (y+Ex)_R.
+```
+
+For step 4, every source is F9 x and every selected target is already
+F9 Wy. Therefore the additive map is a common-frame scalar query. Its
+literal word preserves every arbitrary target baseline. It costs 3,424
+real scalar primitives, with no scratch field or odd division.
+The coefficients with numerators 5 and 7 are ordinary dyadic ADD
+coefficients under the pinned scalar tariff.
+
+The complete large selected pair blocks are material. Removing their
+target pair code and inverse code does not change an ordinary target.
+The original forward target operations do not feed any X source.
+The small selected pivots have no target pair-code dependency.
+The native packet must check these statements on every actual event.
+
+Removing sixteen target progress paths of mass 8 and inserting sixteen
+children of rank 9 gives the provisional mass change
+
+```text
+-16*8 + 16*9 = +16.
+```
+
+This count is not the full recursive bill. The emitted child profile,
+native phases, endpoint adapters, scalar removals, and hosting checks
+remain the responsibility of the complete native packet.
+
+At a routed stage, a selected Y output must use the X FULL exit view.
+It must not keep the old Y-hole exit view. Under the next stage's old
+current-Y view, these selected inputs have an exterior Q_p factor,
+while the ordinary inputs have exterior I. The changed service is not
+automatically an old all-I Y input.
+
+## A narrower transition
+
+Suppose two routed codes use the same physical pivot set and both have
+the form C_s=[[I,B_s],[0,I]]. The B_s entries can be spatial operators.
+Keep the phase order exactly. Then
+
+```text
+C_t q C_s^-1 Q
+  = [ I   B_t - q_P B_s Q_R ].
+    [ 0             I       ]
+```
+
+There is no product of the two correction terms: each term has rows in
+P and columns in R. The transition leaves all ninety-six R fields
+unchanged and uses them only as sources.
+
+This statement is stronger than a displacement-rank bound. It still
+does not supply the phase-coded reader q_P B_s Q_R at a legal cut.
+Sixteen changed outputs do not imply sixteen native children.
+
+## Use in the last call of the one-pair controller
+
+For the actual symmetric, noninvolutive native response, the legal
+five-code content word is
+
+```text
+F0;
+X <- E0 X;
+Y <- E1^-1 Y;
+B1, with backward cross term -E1;
+X <- E1^-1 X;
+Y <- E2 Y;
+F2;
+X <- E1 X.
+```
+
+It has content endpoint
+
+```text
+(-y,T x),       T=E2 E1^-1 E0.
+```
+
+Using the new capture only in F2 changes this to the physical endpoint
+
+```text
+X   = -F25 y,
+Y_P = F25 [C2 T x]_P,
+Y_R = F25 q_R (T x)_R.
+```
+
+This equation includes every original borrowed Y input: its
+coefficient in the final Y bank is zero. It does not make X a further
+clean data record. X retains arbitrary original y.
+
+To see the remaining decoder precisely, put z=E1^-1 E0 x. Write
+
+```text
+c = [C2 E2 z]_P = H W2 z,
+b = (E2 z)_R.
+```
+
+Then the content inverse of the last E2 factor is
+
+```text
+d   = H^-1 c,
+z_R = b - A2 d,
+z_P = d - B2 z_R.
+```
+
+The centre c is FULL, while b remains in its ordinary hole frames.
+The lower fanout and the last reader therefore have phase and access
+obligations. The earlier factors E0^-1 E1 also remain. No 16-line
+terminal decoder follows from these equations.
+
+## Checks, credit, and status
+
+Run from the workspace root:
+
+```text
+python3 -I -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/row-capture-20261020/check_row_capture.py
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/row-capture-20261020/check_row_capture.py --output work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/row-capture-20261020/run-optimized
+```
+
+Both runs must report PASS_EXACT_ROW_CAPTURE and produce identical
+payload and receipt bytes. The checker reads the pinned response and
+pair-code data. It imports no producer. It checks both code inverse
+orders, the selected minor, all encoded-response entries, the sixteen
+mode diagonal entries, both scalar words, and all 224 columns of the
+final arbitrary-baseline query.
+
+The new-core lane supplied the actual rank-sixteen response. The
+bridge-access lane found the complete-pair pivot matching and supplied
+the native chronology and exit-view requirement. This lane supplied the
+row-only normalized code and its ordered transition. The root proposed
+the full-F9 selected-target replacement. The new-core lane emits that
+complete native word; the new-native-recipes lane reviews it.
+
+AI assistance was used. No PR, commit, push, or publication is
+authorized. Before any future PR description, read
+/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/check_row_capture.py b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/check_row_capture.py
new file mode 100644
index 0000000000..a272e4244f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/check_row_capture.py
@@ -0,0 +1,269 @@
+#!/usr/bin/env python3
+"""Check the exact row capture and its local output interface."""
+
+from fractions import Fraction as F
+from pathlib import Path
+import argparse
+import gzip
+import hashlib
+import json
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parent.parent
+N = 112
+P = [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23]
+PINS = {
+    "native": (
+        "new-core-transfer-20261017/low-displacement-20261020/"
+        "odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+        "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    ),
+    "pairs": (
+        "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json",
+        "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    ),
+}
+
+
+def need(value, message):
+    if not value:
+        raise ValueError(message)
+
+
+def load(name):
+    path, pin = PINS[name]
+    raw = (LANES / path).read_bytes()
+    if path.endswith(".gz"):
+        raw = gzip.decompress(raw)
+    need(hashlib.sha256(raw).hexdigest() == pin, "source pin: " + name)
+    return json.loads(raw)
+
+
+def matrix(rows):
+    return [{int(j): F(a) for j, a in row.items() if F(a)} for row in rows]
+
+
+def identity(n):
+    return [{i: F(1)} for i in range(n)]
+
+
+def addrow(a, b, scale=F(1)):
+    out = dict(a)
+    for j, v in b.items():
+        out[j] = out.get(j, F(0)) + scale * v
+        if not out[j]:
+            del out[j]
+    return out
+
+
+def mul(a, b):
+    out = []
+    for row in a:
+        acc = {}
+        for k, v in row.items():
+            acc = addrow(acc, b[k], v)
+        out.append(acc)
+    return out
+
+
+def inv(a):
+    n = len(a)
+    left = [[a[i].get(j, F(0)) for j in range(n)] for i in range(n)]
+    right = [[F(i == j) for j in range(n)] for i in range(n)]
+    determinant = F(1)
+    for j in range(n):
+        pivot = next((i for i in range(j, n) if left[i][j]), None)
+        need(pivot is not None, "singular minor")
+        if pivot != j:
+            left[j], left[pivot] = left[pivot], left[j]
+            right[j], right[pivot] = right[pivot], right[j]
+            determinant *= -1
+        value = left[j][j]
+        determinant *= value
+        left[j] = [x / value for x in left[j]]
+        right[j] = [x / value for x in right[j]]
+        for i in range(n):
+            if i != j and left[i][j]:
+                value = left[i][j]
+                left[i] = [x - value * y for x, y in zip(left[i], left[j])]
+                right[i] = [x - value * y for x, y in zip(right[i], right[j])]
+    return [
+        {j: v for j, v in enumerate(row) if v} for row in right
+    ], determinant
+
+
+def dumpmatrix(a):
+    return [{str(j): str(v) for j, v in sorted(row.items())} for row in a]
+
+
+def lower_shear(c, sign=1):
+    word = []
+    for p in P:
+        row = dict(c[p])
+        need(row.pop(p) == 1, "unit pivot coefficient")
+        need(not (set(row) & set(P)), "pivot source in capture shear")
+        half = any(v.denominator == 2 for v in row.values())
+        scale = 2 if half else 1
+        if half:
+            word.append(["scale", p, None, "2"])
+        for j, v in sorted(row.items()):
+            value = sign * scale * v
+            need(value in (-1, 1), "non-unit scaled capture coefficient")
+            word.append(["add", p, j, str(value)])
+        if half:
+            word.append(["scale", p, None, "1/2"])
+    return word
+
+
+def lower_query(rows, targets, source_offset):
+    word = []
+    for p, row in zip(targets, rows):
+        denominators = {v.denominator for v in row.values()}
+        need(denominators <= {1, 2}, "query coefficient denominator")
+        scale = 2 if 2 in denominators else 1
+        if scale == 2:
+            word.append(["scale", p, None, "2"])
+        for j, v in sorted(row.items()):
+            value = scale * v
+            word.append(["add", p, source_offset + j, str(value)])
+        if scale == 2:
+            word.append(["scale", p, None, "1/2"])
+    return word
+
+
+def replay(word, size):
+    rows = identity(size)
+    price = 0
+    for op, target, source, raw in word:
+        value = F(raw)
+        numerator, denominator = abs(value.numerator), value.denominator
+        need(denominator & (denominator - 1) == 0, "dyadic tariff")
+        if op == "add":
+            rows[target] = addrow(rows[target], rows[source], value)
+            price += 2 * (3 + numerator.bit_length() - 1
+                          + numerator.bit_count() + denominator.bit_length() - 1)
+        else:
+            need(op == "scale", "opcode")
+            need(numerator & (numerator - 1) == 0, "power-of-two scale")
+            rows[target] = {j: v * value for j, v in rows[target].items()}
+            price += 2 * (abs(numerator.bit_length() - denominator.bit_length())
+                          + int(value < 0))
+    return rows, price
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "run-normal")
+    args = parser.parse_args()
+    model = load("native")["model"]
+    flags = load("pairs")
+    e = matrix(model["response"])
+    u = matrix(model["correction_U"])
+    v = matrix(model["correction_V"])
+    base = identity(N)
+    uv = mul(u, v)
+    need(e == [addrow(a, b) for a, b in zip(base, uv)], "E factor")
+    vp = [{j: row.get(p, F(0)) for j, p in enumerate(P) if row.get(p)}
+          for row in v]
+    vpi, det_vp = inv(vp)
+    w = mul(vpi, v)
+    need(all(row.get(p, F(0)) == (i == j)
+             for i, row in enumerate(w) for j, p in enumerate(P)),
+         "normalized pivot minor")
+    c = [dict(row) for row in base]
+    ci = [dict(row) for row in base]
+    for p, row in zip(P, w):
+        c[p] = row
+        ci[p] = addrow({p: F(2)}, row, -1)
+    need(mul(c, ci) == base and mul(ci, c) == base, "capture inverse")
+    h = mul(v, u)
+    h = [addrow(a, b) for a, b in zip(identity(16), h)]
+    need(h == [{i: F(-5 if i < 8 else -7)} for i in range(16)],
+         "centre action")
+    need(mul(h, vp) == mul(vp, h), "pivot minor and centre action")
+    lower = mul(u, vp)
+    k = [dict(row) for row in base]
+    for i, p in enumerate(P):
+        k[p] = {p: h[i][i]}
+    for r in set(range(N)) - set(P):
+        for j, value in lower[r].items():
+            k[r][P[j]] = value
+    need(mul(mul(c, e), ci) == k, "encoded response")
+    ce = mul(c, e)
+    need([ce[p] for p in P] == mul(h, w), "selected response")
+    need(all(ce[r] == e[r] for r in set(range(N)) - set(P)),
+         "ordinary response changed")
+    pair = identity(N)
+    for record in flags["pair_codes"]:
+        ports = record["ports"]
+        need(not (set(ports) & set(P)) or set(ports) <= set(P),
+             "partial selected pair")
+        for p, row in zip(ports, record["matrix"]):
+            pair[p] = {q: F(a) for q, a in zip(ports, row) if a}
+    pairi, _ = inv(pair)
+    cmode = mul(mul(pair, c), pairi)
+    emode = mul(mul(pair, e), pairi)
+    cemode = mul(mul(pair, ce), pairi)
+    need(mul(cmode, emode) == cemode, "mode response order")
+    need({i for i, row in enumerate(cemode) if row.get(i)} == set(P),
+         "selected diagonal support")
+    code_word = lower_shear(c)
+    inverse_word = lower_shear(c, -1)
+    got, code_price = replay(code_word, N)
+    goti, inverse_price = replay(inverse_word, N)
+    need(got == c and goti == ci, "literal capture words")
+    need(code_price == inverse_price == 1760, "capture invoice")
+    query_word = lower_query([ce[p] for p in P], P, N)
+    rows, query_price = replay(query_word, 2 * N)
+    expected = identity(2 * N)
+    for p in P:
+        expected[p] = addrow(expected[p], {N+j: a for j, a in ce[p].items()})
+    need(rows == expected, "arbitrary-baseline final query")
+    need(query_price == 3424, "final query invoice")
+    payload = {
+        "schema": "row-only-rank16-capture-v1",
+        "source_pins": PINS,
+        "pivots": P,
+        "ordinary_ports": sorted(set(range(N)) - set(P)),
+        "pivot_minor": dumpmatrix(vp),
+        "pivot_minor_inverse": dumpmatrix(vpi),
+        "pivot_minor_determinant": str(det_vp),
+        "centre_reader": dumpmatrix(w),
+        "response": dumpmatrix(e),
+        "code": dumpmatrix(c),
+        "code_inverse": dumpmatrix(ci),
+        "encoded_response": dumpmatrix(k),
+        "selected_capture_response": dumpmatrix(ce),
+        "mode_capture_response": dumpmatrix(cemode),
+        "scalar_word": code_word,
+        "inverse_scalar_word": inverse_word,
+        "final_query_word": query_word,
+        "final_query_field_convention": "Y=0..111; FULL X=112..223",
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode()
+    (args.output / "ROW-CAPTURE.json").write_bytes(raw)
+    receipt = {
+        "status": "PASS_EXACT_ROW_CAPTURE",
+        "payload_sha256": hashlib.sha256(raw).hexdigest(),
+        "pivot_minor_determinant": str(det_vp),
+        "code_and_inverse_scalar_price": code_price,
+        "code_native_children": 0,
+        "code_extra_fields": 0,
+        "code_fixed_odd_scans": 0,
+        "final_query_scalar_price": query_price,
+        "final_query_real_fixed_odd_scans": 0,
+        "final_query_borrowed_baseline_columns_checked": 224,
+        "changed_mode_diagonal_ports": P,
+        "native_capture_emitted_here": False,
+        "supplier_terminal_closed": False,
+    }
+    (args.output / "CHECKS.json").write_text(
+        json.dumps(receipt, indent=2, sort_keys=True) + "\n"
+    )
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/run-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/run-normal/CHECKS.json
new file mode 100644
index 0000000000..17953f768b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/run-normal/CHECKS.json
@@ -0,0 +1,32 @@
+{
+  "changed_mode_diagonal_ports": [
+    0,
+    27,
+    36,
+    111,
+    20,
+    7,
+    57,
+    46,
+    1,
+    3,
+    6,
+    8,
+    17,
+    18,
+    24,
+    23
+  ],
+  "code_and_inverse_scalar_price": 1760,
+  "code_extra_fields": 0,
+  "code_fixed_odd_scans": 0,
+  "code_native_children": 0,
+  "final_query_borrowed_baseline_columns_checked": 224,
+  "final_query_real_fixed_odd_scans": 0,
+  "final_query_scalar_price": 3424,
+  "native_capture_emitted_here": false,
+  "payload_sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7",
+  "pivot_minor_determinant": "16",
+  "status": "PASS_EXACT_ROW_CAPTURE",
+  "supplier_terminal_closed": false
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json
new file mode 100644
index 0000000000..79b36b6188
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json
@@ -0,0 +1,10667 @@
+{
+  "centre_reader": [
+    {
+      "0": "1",
+      "13": "1/2",
+      "14": "1/2",
+      "15": "-1/2",
+      "2": "1/2",
+      "25": "1/2",
+      "51": "1/2",
+      "52": "1/2",
+      "53": "-1/2",
+      "70": "1/2",
+      "71": "1/2",
+      "72": "1/2",
+      "76": "1/2",
+      "78": "1/2",
+      "81": "-1/2",
+      "87": "1/2",
+      "89": "1/2",
+      "90": "1/2",
+      "91": "1/2",
+      "92": "1/2",
+      "99": "1/2"
+    },
+    {
+      "13": "-1/2",
+      "14": "-1/2",
+      "15": "1/2",
+      "2": "1/2",
+      "25": "1/2",
+      "27": "1",
+      "51": "-1/2",
+      "52": "-1/2",
+      "53": "1/2",
+      "70": "1/2",
+      "71": "1/2",
+      "72": "1/2",
+      "76": "1/2",
+      "78": "-1/2",
+      "81": "1/2",
+      "87": "1/2",
+      "89": "1/2",
+      "90": "1/2",
+      "91": "1/2",
+      "92": "-1/2",
+      "99": "-1/2"
+    },
+    {
+      "104": "-1/2",
+      "106": "-1/2",
+      "11": "-1/2",
+      "110": "-1/2",
+      "13": "1/2",
+      "15": "1/2",
+      "21": "1/2",
+      "36": "1",
+      "37": "1/2",
+      "41": "1/2",
+      "43": "1/2",
+      "47": "1/2",
+      "51": "-1/2",
+      "53": "-1/2",
+      "61": "1/2",
+      "63": "1/2",
+      "70": "1/2",
+      "72": "-1/2",
+      "89": "1/2",
+      "9": "-1/2",
+      "91": "-1/2"
+    },
+    {
+      "104": "1/2",
+      "106": "-1/2",
+      "11": "-1/2",
+      "110": "1/2",
+      "111": "1",
+      "13": "-1/2",
+      "15": "1/2",
+      "21": "1/2",
+      "37": "-1/2",
+      "41": "1/2",
+      "43": "-1/2",
+      "47": "1/2",
+      "51": "1/2",
+      "53": "-1/2",
+      "61": "-1/2",
+      "63": "1/2",
+      "70": "1/2",
+      "72": "1/2",
+      "89": "-1/2",
+      "9": "1/2",
+      "91": "-1/2"
+    },
+    {
+      "10": "-1/2",
+      "105": "1/2",
+      "110": "1/2",
+      "14": "1/2",
+      "16": "1/2",
+      "2": "1/2",
+      "20": "1",
+      "21": "1/2",
+      "25": "-1/2",
+      "37": "1/2",
+      "42": "-1/2",
+      "44": "-1/2",
+      "47": "-1/2",
+      "52": "-1/2",
+      "62": "1/2",
+      "71": "1/2",
+      "78": "1/2",
+      "79": "-1/2",
+      "90": "-1/2",
+      "94": "1/2",
+      "99": "-1/2"
+    },
+    {
+      "10": "1/2",
+      "104": "-1/2",
+      "105": "-1/2",
+      "106": "-1/2",
+      "11": "1/2",
+      "16": "-1/2",
+      "41": "-1/2",
+      "42": "-1/2",
+      "43": "-1/2",
+      "44": "-1/2",
+      "61": "1/2",
+      "62": "1/2",
+      "63": "1/2",
+      "7": "1",
+      "76": "-1/2",
+      "79": "-1/2",
+      "81": "1/2",
+      "87": "1/2",
+      "9": "1/2",
+      "92": "1/2",
+      "94": "-1/2"
+    },
+    {
+      "10": "1/2",
+      "104": "1/2",
+      "105": "1/2",
+      "106": "1/2",
+      "11": "1/2",
+      "16": "1/2",
+      "41": "1/2",
+      "42": "1/2",
+      "43": "1/2",
+      "44": "1/2",
+      "57": "1",
+      "61": "1/2",
+      "62": "1/2",
+      "63": "1/2",
+      "76": "1/2",
+      "79": "-1/2",
+      "81": "1/2",
+      "87": "-1/2",
+      "9": "1/2",
+      "92": "1/2",
+      "94": "-1/2"
+    },
+    {
+      "10": "-1/2",
+      "105": "1/2",
+      "110": "1/2",
+      "14": "1/2",
+      "16": "-1/2",
+      "2": "-1/2",
+      "21": "-1/2",
+      "25": "1/2",
+      "37": "1/2",
+      "42": "-1/2",
+      "44": "1/2",
+      "46": "1",
+      "47": "1/2",
+      "52": "-1/2",
+      "62": "1/2",
+      "71": "1/2",
+      "78": "-1/2",
+      "79": "1/2",
+      "90": "-1/2",
+      "94": "-1/2",
+      "99": "1/2"
+    },
+    {
+      "1": "1",
+      "19": "1",
+      "5": "1",
+      "54": "1",
+      "64": "1",
+      "73": "1",
+      "82": "1",
+      "83": "1"
+    },
+    {
+      "22": "1",
+      "3": "1",
+      "4": "1",
+      "50": "1",
+      "60": "1",
+      "69": "1",
+      "80": "1",
+      "84": "1"
+    },
+    {
+      "35": "1",
+      "38": "1",
+      "39": "1",
+      "40": "1",
+      "6": "1",
+      "77": "1",
+      "85": "1",
+      "86": "1"
+    },
+    {
+      "103": "1",
+      "107": "1",
+      "108": "1",
+      "109": "1",
+      "12": "1",
+      "45": "1",
+      "8": "1",
+      "88": "1"
+    },
+    {
+      "17": "1",
+      "29": "1",
+      "30": "1",
+      "56": "1",
+      "58": "1",
+      "67": "1",
+      "93": "1",
+      "95": "1"
+    },
+    {
+      "101": "1",
+      "18": "1",
+      "32": "1",
+      "34": "1",
+      "49": "1",
+      "65": "1",
+      "68": "1",
+      "98": "1"
+    },
+    {
+      "24": "1",
+      "26": "1",
+      "28": "1",
+      "48": "1",
+      "66": "1",
+      "75": "1",
+      "96": "1",
+      "97": "1"
+    },
+    {
+      "100": "1",
+      "102": "1",
+      "23": "1",
+      "31": "1",
+      "33": "1",
+      "55": "1",
+      "59": "1",
+      "74": "1"
+    }
+  ],
+  "code": [
+    {
+      "0": "1",
+      "13": "1/2",
+      "14": "1/2",
+      "15": "-1/2",
+      "2": "1/2",
+      "25": "1/2",
+      "51": "1/2",
+      "52": "1/2",
+      "53": "-1/2",
+      "70": "1/2",
+      "71": "1/2",
+      "72": "1/2",
+      "76": "1/2",
+      "78": "1/2",
+      "81": "-1/2",
+      "87": "1/2",
+      "89": "1/2",
+      "90": "1/2",
+      "91": "1/2",
+      "92": "1/2",
+      "99": "1/2"
+    },
+    {
+      "1": "1",
+      "19": "1",
+      "5": "1",
+      "54": "1",
+      "64": "1",
+      "73": "1",
+      "82": "1",
+      "83": "1"
+    },
+    {
+      "2": "1"
+    },
+    {
+      "22": "1",
+      "3": "1",
+      "4": "1",
+      "50": "1",
+      "60": "1",
+      "69": "1",
+      "80": "1",
+      "84": "1"
+    },
+    {
+      "4": "1"
+    },
+    {
+      "5": "1"
+    },
+    {
+      "35": "1",
+      "38": "1",
+      "39": "1",
+      "40": "1",
+      "6": "1",
+      "77": "1",
+      "85": "1",
+      "86": "1"
+    },
+    {
+      "10": "1/2",
+      "104": "-1/2",
+      "105": "-1/2",
+      "106": "-1/2",
+      "11": "1/2",
+      "16": "-1/2",
+      "41": "-1/2",
+      "42": "-1/2",
+      "43": "-1/2",
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+      "87": "1/2",
+      "9": "1/2",
+      "92": "1/2",
+      "94": "-1/2"
+    },
+    {
+      "103": "1",
+      "107": "1",
+      "108": "1",
+      "109": "1",
+      "12": "1",
+      "45": "1",
+      "8": "1",
+      "88": "1"
+    },
+    {
+      "9": "1"
+    },
+    {
+      "10": "1"
+    },
+    {
+      "11": "1"
+    },
+    {
+      "12": "1"
+    },
+    {
+      "13": "1"
+    },
+    {
+      "14": "1"
+    },
+    {
+      "15": "1"
+    },
+    {
+      "16": "1"
+    },
+    {
+      "17": "1",
+      "29": "1",
+      "30": "1",
+      "56": "1",
+      "58": "1",
+      "67": "1",
+      "93": "1",
+      "95": "1"
+    },
+    {
+      "101": "1",
+      "18": "1",
+      "32": "1",
+      "34": "1",
+      "49": "1",
+      "65": "1",
+      "68": "1",
+      "98": "1"
+    },
+    {
+      "19": "1"
+    },
+    {
+      "10": "-1/2",
+      "105": "1/2",
+      "110": "1/2",
+      "14": "1/2",
+      "16": "1/2",
+      "2": "1/2",
+      "20": "1",
+      "21": "1/2",
+      "25": "-1/2",
+      "37": "1/2",
+      "42": "-1/2",
+      "44": "-1/2",
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+      "79": "-1/2",
+      "90": "-1/2",
+      "94": "1/2",
+      "99": "-1/2"
+    },
+    {
+      "21": "1"
+    },
+    {
+      "22": "1"
+    },
+    {
+      "100": "1",
+      "102": "1",
+      "23": "1",
+      "31": "1",
+      "33": "1",
+      "55": "1",
+      "59": "1",
+      "74": "1"
+    },
+    {
+      "24": "1",
+      "26": "1",
+      "28": "1",
+      "48": "1",
+      "66": "1",
+      "75": "1",
+      "96": "1",
+      "97": "1"
+    },
+    {
+      "25": "1"
+    },
+    {
+      "26": "1"
+    },
+    {
+      "13": "-1/2",
+      "14": "-1/2",
+      "15": "1/2",
+      "2": "1/2",
+      "25": "1/2",
+      "27": "1",
+      "51": "-1/2",
+      "52": "-1/2",
+      "53": "1/2",
+      "70": "1/2",
+      "71": "1/2",
+      "72": "1/2",
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+      "90": "1/2",
+      "91": "1/2",
+      "92": "-1/2",
+      "99": "-1/2"
+    },
+    {
+      "28": "1"
+    },
+    {
+      "29": "1"
+    },
+    {
+      "30": "1"
+    },
+    {
+      "31": "1"
+    },
+    {
+      "32": "1"
+    },
+    {
+      "33": "1"
+    },
+    {
+      "34": "1"
+    },
+    {
+      "35": "1"
+    },
+    {
+      "104": "-1/2",
+      "106": "-1/2",
+      "11": "-1/2",
+      "110": "-1/2",
+      "13": "1/2",
+      "15": "1/2",
+      "21": "1/2",
+      "36": "1",
+      "37": "1/2",
+      "41": "1/2",
+      "43": "1/2",
+      "47": "1/2",
+      "51": "-1/2",
+      "53": "-1/2",
+      "61": "1/2",
+      "63": "1/2",
+      "70": "1/2",
+      "72": "-1/2",
+      "89": "1/2",
+      "9": "-1/2",
+      "91": "-1/2"
+    },
+    {
+      "37": "1"
+    },
+    {
+      "38": "1"
+    },
+    {
+      "39": "1"
+    },
+    {
+      "40": "1"
+    },
+    {
+      "41": "1"
+    },
+    {
+      "42": "1"
+    },
+    {
+      "43": "1"
+    },
+    {
+      "44": "1"
+    },
+    {
+      "45": "1"
+    },
+    {
+      "10": "-1/2",
+      "105": "1/2",
+      "110": "1/2",
+      "14": "1/2",
+      "16": "-1/2",
+      "2": "-1/2",
+      "21": "-1/2",
+      "25": "1/2",
+      "37": "1/2",
+      "42": "-1/2",
+      "44": "1/2",
+      "46": "1",
+      "47": "1/2",
+      "52": "-1/2",
+      "62": "1/2",
+      "71": "1/2",
+      "78": "-1/2",
+      "79": "1/2",
+      "90": "-1/2",
+      "94": "-1/2",
+      "99": "1/2"
+    },
+    {
+      "47": "1"
+    },
+    {
+      "48": "1"
+    },
+    {
+      "49": "1"
+    },
+    {
+      "50": "1"
+    },
+    {
+      "51": "1"
+    },
+    {
+      "52": "1"
+    },
+    {
+      "53": "1"
+    },
+    {
+      "54": "1"
+    },
+    {
+      "55": "1"
+    },
+    {
+      "56": "1"
+    },
+    {
+      "10": "1/2",
+      "104": "1/2",
+      "105": "1/2",
+      "106": "1/2",
+      "11": "1/2",
+      "16": "1/2",
+      "41": "1/2",
+      "42": "1/2",
+      "43": "1/2",
+      "44": "1/2",
+      "57": "1",
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+    {
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+    }
+  ],
+  "source_pins": {
+    "native": [
+      "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+      "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+    ],
+    "pairs": [
+      "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json",
+      "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"
+    ]
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/COMPLETION-LIMITS.md b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/COMPLETION-LIMITS.md
new file mode 100644
index 0000000000..d3ebca903f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/COMPLETION-LIMITS.md
@@ -0,0 +1,187 @@
+# Limits and two consequences of the row completion
+
+This addendum uses the immutable `ROW-INVOLUTION.json` source with hash
+`a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b`.
+It does not change the earlier freeze.
+
+## Rank clarification
+
+In the general theorem in `ROW-INVOLUTION.md`, the sentence “The change
+has rank \(r\)” means
+\(\operatorname{rank}(A-I)=r\). It does not mean that
+\(\operatorname{rank}(A-E)=r\) for every source. For the actual source,
+the two ranks are both 16. The addendum checks the second rank
+separately.
+
+## Sixteen row changes are necessary
+
+Let \(E\) be the actual pinned 112-port response. Allow arbitrary new
+values in a set of its rows, including new coefficients across the
+old component boundary. Require the resulting matrix to be a unit
+over \(\mathbb Z[1/2]\).
+
+At least sixteen rows must change: eight in the large 48-port
+component and eight in the small 64-port component.
+
+The large component is similar, by a dyadic unit, to eight signed
+blocks \(I-dd^T\) of size six. Modulo 5, each block has exactly one
+left-null direction. Thus its left nullspace has dimension eight.
+The small component has eight blocks \(I-dd^T\) of size eight.
+Modulo 7, its left nullspace also has dimension eight. The exact
+physical matrix ranks are 40 modulo 5 on the large component and
+56 modulo 7 on the small component.
+
+Suppose fewer than eight large rows change. The eight-dimensional
+old left nullspace contains a nonzero vector whose coefficients
+at all these changed rows are zero. Extend that vector by zero
+on the small component. It still annihilates the new matrix
+modulo 5: its coefficients vanish on every modified large row,
+and its coefficients on all small rows are zero. The new matrix
+cannot be a dyadic unit. The same argument modulo 7 applies to
+the small rows. This proof does not restrict the coefficients in
+the modified rows.
+
+The sixteen-row involution attains this lower bound. This is an
+exact lower bound for row replacement of this fixed response.
+It does not apply to changes in columns, native transfer
+weights outside the selected rows, odd-denominator arithmetic,
+or a different initial response.
+
+## Uniqueness at displacement rank sixteen
+
+The retained ordinary factor \(U_R\) has rank sixteen. The checker
+verifies this rank over the rationals.
+
+Let \(A'\) be an involution that has the same 96 ordinary rows as
+\(E\), and suppose \(\operatorname{rank}(A'-I)=16\). Its retained
+ordinary displacement rows are \(U_RV\), which have rank sixteen.
+They therefore span the full row space of \(A'-I\). This row
+space is the row space of \(V\), so there is a unique matrix
+\(U'\) such that
+
+\[
+A'=I+U'V,\qquad U'_R=U_R.
+\]
+
+Both \(U'\) and \(V\) have rank sixteen. The involution identity
+then gives
+
+\[
+0=U'(2I+VU')V,\qquad VU'=-2I.
+\]
+
+Since \(V_P\) has an inverse, this forces
+
+\[
+U'_P=V_P^{-1}(-2I-V_RU_R).
+\]
+
+Thus \(A'=A\), the frozen row involution. This stronger uniqueness
+statement uses the actual rank of \(U_R\). It is not a claim about
+other pivot sets or involutions with larger displacement rank.
+
+## A symmetric unit with a cheaper selected query
+
+Let \(\Pi_P\) be the diagonal projector on the sixteen pivots. The
+actual normalized row code satisfies
+
+\[
+S=CA=E-\Pi_P=C^TDC,\qquad D=I-2\Pi_P.
+\]
+
+In one signed block, with \(b=d_R^T\),
+
+\[
+S=
+\begin{pmatrix}
+-1&-b\\
+-b^T&I-b^Tb
+\end{pmatrix},
+\qquad
+S^{-1}=
+\begin{pmatrix}
+k-2&-b\\
+-b^T&I
+\end{pmatrix}.
+\]
+
+The complete physical response is symmetric and dyadic. It has
+determinant one. Its displacement from the identity has rank 32,
+which is larger than the rank of \(A-I\).
+
+The selected query is
+
+\[
+Y_P\mathrel{+}=S[P,*]X=-V_P^{-1}VX.
+\]
+
+It costs 1,904 scalar primitives on the existing common-frame
+fields. This is a different response from the selected rows of
+\(A\), whose query costs 2,960. There is no pricing discrepancy.
+
+A scalar word for \(S\) applies the actual pair code, the signed
+block capture, the pivot signs, the transposed capture, and the
+inverse pair code. It costs 2,508 scalar primitives. Its literal
+inverse has the same price. Both words use no extra fields.
+
+Only the selected diagonal entries differ from the old response.
+This supplies another input for the row-replacement native
+emitter. The inverse has ordinary diagonal entries, so the
+existing off-diagonal native grammar does not automatically
+implement it. No native inverse or complete caller is claimed.
+
+## The diagonal metric of the involution
+
+In each signed block, define
+
+\[
+M_{pp}=k-3,\qquad M_{ii}=-1\quad(i\ne p).
+\]
+
+Then \(A=I+Md\,d^T\), and
+
+\[
+A^T=M^{-1}AM,\qquad A^TM^{-1}A=M^{-1}.
+\]
+
+The physical pair code preserves this diagonal matrix: its
+selected pairs have the same value 3 on both ports, and its
+ordinary pairs have value \(-1\) on both ports. The small
+selected values are 5.
+
+For any diagonal unitary phase \(Z\) on the selected ports,
+put \(L=ZA\). Since \(M\) commutes with \(Z\),
+
+\[
+L^*=M^{-1}L^{-1}M.
+\]
+
+This is an exact operator identity. The inverse metric contains
+\(1/3\) and \(1/5\), so it is not a dyadic unit. A caller that uses
+these factors must prove the required divisibility of its live
+values and include the scalar cost. This addendum does not
+provide that caller.
+
+## Validation
+
+Run:
+
+```sh
+python3 check_completion_limits.py
+python3 -O check_completion_limits.py --output limits-optimized
+```
+
+Both runs produce `PASS_ROW_COMPLETION_LIMITS` and byte-identical
+payloads and receipts. The checks use exact rational and finite
+field arithmetic. They verify both modular ranks, the ordinary
+factor rank, both symmetric inverse orders, all literal scalar
+words, the arbitrary-baseline selected query, and the metric
+identities. Native emission, phase admission at a caller cut,
+and complete supplier pricing remain separate.
+
+The coordinated independent review supplied the stronger
+uniqueness argument and checked the nullspace lower-bound
+argument. The bridge and native review workers supplied
+independent forms of the symmetric completion. This packet
+records the exact combined statement and producer checks.
+AI assistance was used throughout.
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/FREEZE.json
new file mode 100644
index 0000000000..fa445f736e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/FREEZE.json
@@ -0,0 +1,11 @@
+{
+  "files": {
+    "ROW-INVOLUTION.md": "c8470cc2280a057cbebf4a31ee679495990b200a6d6c033cc39e459eb2cf139f",
+    "check_row_involution.py": "a675e5578de4bc264524f7c1a75c5685a1967a65f7d3cd020fb0dc19352d31e9",
+    "run-normal/CHECKS.json": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6",
+    "run-normal/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+    "run-optimized/CHECKS.json": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6",
+    "run-optimized/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "scope": "Exact dyadic row-involution algebra and scalar words; native service and supplier composition are separate."
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/LIMITS-FREEZE.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/LIMITS-FREEZE.json
new file mode 100644
index 0000000000..9ff85ed1e0
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/LIMITS-FREEZE.json
@@ -0,0 +1,12 @@
+{
+  "files": {
+    "COMPLETION-LIMITS.md": "91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607",
+    "check_completion_limits.py": "f07260347b3b5a955c475a25f87873dded309f9bd0bd1ad382c5a21c5acb16bb",
+    "limits-normal/CHECKS.json": "eb60b314a3cb6896c6afd33b8dc88d422f5ce12ac5ab73ce9a704950c6975276",
+    "limits-normal/COMPLETION-LIMITS.json": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa",
+    "limits-optimized/CHECKS.json": "eb60b314a3cb6896c6afd33b8dc88d422f5ce12ac5ab73ce9a704950c6975276",
+    "limits-optimized/COMPLETION-LIMITS.json": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa"
+  },
+  "scope": "Row-completion bounds, uniqueness, symmetric dyadic unit, and metric identities; no native or supplier claim.",
+  "source_freeze_sha256": "538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2"
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/ROW-INVOLUTION.md b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/ROW-INVOLUTION.md
new file mode 100644
index 0000000000..d80508fa11
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/ROW-INVOLUTION.md
@@ -0,0 +1,219 @@
+# A rank-sixteen involution from sixteen row replacements
+
+This packet constructs an exact dyadic involution on the 112 actual data
+ports. It changes only sixteen rows of the pinned response. It also gives
+its transpose, scalar programs, and the sixteen final query rows. It does
+not claim a complete supplier or a terminal decoder.
+
+## General row completion
+
+Work over a commutative ring in which 2 is a unit. Let
+
+\[
+E=I+UV,\qquad U\in R^{n\times r},\quad V\in R^{r\times n}.
+\]
+
+Select \(r\) rows \(P\), and let \(R\) also denote the complementary index
+set when it occurs as a subscript. Assume the square minor \(V_P\) has an
+inverse over the ring. Keep \(U_R\), and set
+
+\[
+\widetilde U_P=V_P^{-1}(-2I-V_RU_R),\qquad
+A=I+\widetilde U V.
+\]
+
+Then \(V\widetilde U=-2I\). Thus
+
+\[
+A^2
+=I+\widetilde U(2I+V\widetilde U)V
+=I.
+\]
+
+All rows outside \(P\) still equal the corresponding rows of \(E\).
+The change has rank \(r\) over any field of characteristic other than
+2. Indeed, \(V\widetilde U=-2I\) makes both factors full rank. The
+determinant identity gives \(\det A=(-1)^r\). The space
+\(\operatorname{im}\widetilde U\) is the \(-1\) eigenspace, and
+\(\ker V\) is the \(+1\) eigenspace.
+
+More generally, replace \(-2I\) by \(K-I\), for an arbitrary \(r\)-square
+matrix \(K\). This gives
+
+\[
+V A=K V,\qquad \det A=\det K.
+\]
+
+If \(K\) is a unit, then
+
+\[
+A^{-1}=I-\widetilde U K^{-1}V.
+\]
+
+The construction is unique within the stated factor family: \(V\), the
+rows \(U_R\), and the desired matrix \(V\widetilde U\) determine
+\(\widetilde U_P\). This is not a uniqueness claim for all possible row
+completions.
+
+## Actual signed blocks
+
+The pinned native response has eight signed blocks of size six and
+eight blocks of size eight. In the pair chart, each block is
+
+\[
+E_k=I-dd^{T},\qquad d_i\in\{1,-1\}.
+\]
+
+Choose one pivot \(p\) with \(d_p=1\). The completion is
+
+\[
+A_k=I+\bigl((k-2)e_p-d\bigr)d^{T}.
+\]
+
+Since \(d^{T}((k-2)e_p-d)=-2\), this is an involution. In pivot and
+complement order it is
+
+\[
+A_k=
+\begin{pmatrix}
+k-2 &(k-3)d_R^{T}\\
+-d_R&I-d_Rd_R^{T}
+\end{pmatrix}.
+\]
+
+All nonpivot rows are unchanged. In \(A_k^T\), all nonpivot columns are
+unchanged. Its nonpivot row support is the old support. Only its pivot
+column coefficients change: multiply the old coefficients by
+\(-(k-3)\), which is \(-3\) or \(-5\). The sixteen pivot diagonal
+entries are the only nonzero diagonal entries.
+
+The actual pivot order is
+
+```text
+0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23.
+```
+
+The first eight ports form four complete physical pair blocks. Thus
+the pair matrix \(H\) preserves the pivot set and its complement.
+On the large component \(H^T H=2I\); on the small component \(H=I\).
+These components do not mix. Consequently
+
+\[
+(H^{-1}A_{\rm mode}H)^T
+=H^{-1}A_{\rm mode}^{T}H.
+\]
+
+The physical matrix \(A\) therefore preserves the 96 ordinary response
+rows. Its transpose preserves the 96 ordinary columns. The checker
+constructs \(A\) once from the general \(U,V,V_P\) formula and once
+from the signed block formula. The results agree exactly.
+
+For the complete 112-port matrix,
+
+\[
+A^2=(A^T)^2=I,\quad
+\operatorname{rank}(A-I)=16,\quad
+\det A=1,\quad
+\operatorname{tr}A=80.
+\]
+
+All coefficients are dyadic. No inverse by 3, 5, or 7 is needed.
+
+## Query code and scalar programs
+
+Retain the normalized row code from the source packet:
+
+\[
+C=\begin{pmatrix}I&B\\0&I\end{pmatrix},\qquad
+V_P^{-1}V=[I,B].
+\]
+
+The completed response has the exact form
+
+\[
+C A C^{-1}
+=\begin{pmatrix}-I&0\\ U_RV_P&I\end{pmatrix}.
+\]
+
+This is a lower triangular code. The lower block is present and must
+not be discarded.
+
+The packet gives two scalar implementations of \(A\). A direct
+physical implementation uses \(C\), a lower shear, pivot signs, and
+\(C^{-1}\). It costs 5,600 real scalar primitives. A shorter word
+first applies the actual pair code. In each block, it executes:
+
+1. Add \(d_R^Tx_R\) to \(x_p\).
+2. Subtract \(d_Rx_p\) from \(x_R\).
+3. Negate \(x_p\).
+4. Subtract the updated \(d_R^Tx_R\) from \(x_p\).
+
+It then applies the inverse pair code. This word costs 3,276 scalar
+primitives. Transpose each gate and reverse the order to obtain a
+word for \(A^T\) at the same price. Both words use the existing data
+fields only. They require a common admissible frame for their scalar
+operations.
+
+The final selected-target queries have arbitrary target baselines:
+
+\[
+Y_P\mathrel{+}=A[P,*]X,\qquad
+Y_P\mathrel{+}=A^T[P,*]X.
+\]
+
+Their literal prices are 2,960 and 1,984 scalar primitives,
+respectively. Their sources must all be in the same completed FULL
+frame as the selected targets. The programs contain only dyadic
+ADDs and power-of-two SCALEs. They use no extra fields.
+
+## Native application and scope
+
+The earlier row-replacement service removes the selected target
+paths, advances the sixteen selected targets by full rank-nine
+children, and adds the selected response rows after all source
+fields reach FULL. The 96 other target paths remain in place.
+
+For \(A\), those retained response rows are unchanged. For \(A^T\),
+their off-diagonal support is unchanged in the actual mode chart.
+The transfer weights on the pivot columns must be changed as
+specified above. These facts supply exact inputs to the separate
+native emitter. This packet does not replace its native replay.
+
+The intended hybrid forward output has selected FULL fields and
+96 ordinary hole fields. A formal transpose does not by itself
+restore the original raw output contract. A backward service and
+any conversion to the raw contract require separate complete
+words, phase checks, and costs. In particular, \(A^{-1}=A\) is an
+algebraic fact, not an automatic composition rule for the mixed
+native frames.
+
+The construction removes the old odd centre eigenvalues from the
+response. It does not prove that the actual responses at different
+supplier stages are equal, or that the final raw phase can be
+removed at no cost.
+
+## Source and validation
+
+The checker pins the previous row-capture checker and payload, the
+complete rank-sixteen native response, and the actual pair flags.
+The source paths and hashes are in `ROW-INVOLUTION.json`.
+
+Run:
+
+```sh
+python3 check_row_involution.py
+python3 -O check_row_involution.py --output run-optimized
+```
+
+Both runs produce `PASS_EXACT_ROW_INVOLUTION` and byte-identical
+payloads and receipts. The checks include the two independent
+matrix constructions, both involution identities, exact
+displacement rank, all 112 matrix columns, all 224 query columns
+with arbitrary baselines, transpose support, and both scalar
+programs. No complete supplier cost or kappa improvement is
+claimed.
+
+This work uses the row-capture construction and native clique
+response from the coordinated centre-information campaign.
+AI agents developed the algebra, programs, and checks. Independent
+review is pending at this freeze and will use a separate packet.
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/check_completion_limits.py b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/check_completion_limits.py
new file mode 100644
index 0000000000..56e271ef78
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/check_completion_limits.py
@@ -0,0 +1,179 @@
+#!/usr/bin/env python3
+"""Check the row bound, uniqueness premise, and symmetric completion."""
+
+from fractions import Fraction as F
+from pathlib import Path
+import argparse
+import hashlib
+import importlib.util
+import json
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE_PIN = "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+CHECKER_PIN = "a675e5578de4bc264524f7c1a75c5685a1967a65f7d3cd020fb0dc19352d31e9"
+HELPER_PIN = "ccf661107a790c3d858a3f2bd4d8adc5269f588bfd989bd2e2029e26cbb14081"
+
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def read(path, pin):
+    raw = path.read_bytes()
+    need(hashlib.sha256(raw).hexdigest() == pin, "source pin: " + str(path))
+    return raw
+
+
+def module(path, pin, name):
+    read(path, pin)
+    spec = importlib.util.spec_from_file_location(name, path)
+    result = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(result)
+    return result
+
+
+def finite_rank(a, ports, prime):
+    rows = [[int(row.get(j, 0).numerator) *
+             pow(int(row.get(j, F(0)).denominator), -1, prime) % prime
+             for j in ports] for row in (a[i] for i in ports)]
+    pivot = 0
+    for j in range(len(ports)):
+        found = next((i for i in range(pivot, len(rows)) if rows[i][j]), None)
+        if found is None:
+            continue
+        rows[pivot], rows[found] = rows[found], rows[pivot]
+        inverse = pow(rows[pivot][j], -1, prime)
+        rows[pivot] = [x * inverse % prime for x in rows[pivot]]
+        for i in range(pivot + 1, len(rows)):
+            value = rows[i][j]
+            if value:
+                rows[i] = [(x - value * y) % prime
+                           for x, y in zip(rows[i], rows[pivot])]
+        pivot += 1
+    return pivot
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "limits-normal")
+    args = parser.parse_args()
+    base = module(HERE / "check_row_involution.py", CHECKER_PIN, "frozen_involution")
+    h = module(HERE.parent / "row-capture-20261020/check_row_capture.py",
+               HELPER_PIN, "frozen_capture")
+    data = json.loads(read(HERE / "run-normal/ROW-INVOLUTION.json", SOURCE_PIN))
+    a = h.matrix(data["response"])
+    at = h.matrix(data["response_transpose"])
+    e = h.matrix(data["original_response"])
+    c = h.matrix(data["row_code"])
+    ci = h.matrix(data["row_code_inverse"])
+    u = h.matrix(data["correction_U"])
+    p = data["pivots"]
+    rest = data["ordinary_ports"]
+    large = sorted(j for block in data["blocks"] if block["size"] == 6
+                   for j in block["ports"])
+    small = sorted(set(range(112)) - set(large))
+    need(len(large) == 48 and len(small) == 64, "component dimensions")
+    need(all(set(e[i]) <= set(large) for i in large), "large component support")
+    need(all(set(e[i]) <= set(small) for i in small), "small component support")
+    ranks = {"large_mod_5": finite_rank(e, large, 5),
+             "small_mod_7": finite_rank(e, small, 7)}
+    need(ranks == {"large_mod_5": 40, "small_mod_7": 56}, "modular nullities")
+    need(base.rank([u[i] for i in rest], 16) == 16, "ordinary factor rank")
+    identity = h.identity(112)
+    difference = [h.addrow(x, y, -1) for x, y in zip(a, e)]
+    need(base.rank(difference, 112) == 16, "actual row update rank")
+    signature = [{i: F(-1 if i in p else 1)} for i in range(112)]
+    symmetric = h.mul(c, a)
+    direct = [h.addrow(row, {i: F(1)}, -1) if i in p else row
+              for i, row in enumerate(e)]
+    need(symmetric == direct, "diagonal completion")
+    need(symmetric == base.transpose(symmetric, 112), "symmetric response")
+    need(symmetric == h.mul(h.mul(base.transpose(c, 112), signature), c),
+         "symmetric congruence")
+    symmetric_inverse = h.mul(h.mul(ci, signature), base.transpose(ci, 112))
+    need(h.mul(symmetric, symmetric_inverse) == identity, "right inverse")
+    need(h.mul(symmetric_inverse, symmetric) == identity, "left inverse")
+    need(base.rank([h.addrow(x, y, -1)
+                    for x, y in zip(symmetric, identity)], 112) == 32,
+         "symmetric displacement rank")
+    query = h.lower_query([symmetric[i] for i in p], p, 112)
+    actual, query_price = h.replay(query, 224)
+    expected = h.identity(224)
+    for i in p:
+        expected[i] = h.addrow(expected[i],
+                              {112 + j: value for j, value in symmetric[i].items()})
+    need(actual == expected and query_price == 1904, "symmetric query")
+    flags = h.load("pairs")
+    pair_word = []
+    for record in flags["pair_codes"]:
+        x, y = record["ports"]
+        (aa, bb), (cc, dd) = record["matrix"]
+        if aa != 1:
+            pair_word.append(["scale", x, None, str(aa)])
+        pair_word += [["add", x, y, str(bb)], ["scale", y, None, str(2 * dd)],
+                      ["add", y, x, str(F(cc, aa))]]
+    capture_mode_word = []
+    for block in data["blocks"]:
+        for port, sign in zip(block["ports"], block["signs"]):
+            if port != block["pivot"]:
+                capture_mode_word.append(["add", block["pivot"], port, sign])
+    signs_word = [["scale", port, None, "-1"] for port in p]
+    pair_inverse = base.inverse_word(pair_word)
+    symmetric_word = (pair_word + capture_mode_word + signs_word +
+                      base.transpose_word(capture_mode_word) + pair_inverse)
+    inverse_word = base.inverse_word(symmetric_word)
+    actual, scalar_price = h.replay(symmetric_word, 112)
+    actual_inverse, inverse_price = h.replay(inverse_word, 112)
+    need(actual == symmetric and actual_inverse == symmetric_inverse,
+         "symmetric scalar words")
+    need(scalar_price == inverse_price == 2508, "symmetric scalar tariff")
+    metric = h.identity(112)
+    for i in range(112):
+        metric[i] = {i: F(-1)}
+    for block in data["blocks"]:
+        metric[block["pivot"]] = {block["pivot"]: F(block["size"] - 3)}
+    metric_inverse = [{i: 1 / metric[i][i]} for i in range(112)]
+    need(h.mul(h.mul(metric_inverse, a), metric) == at, "diagonal similarity")
+    need(h.mul(h.mul(at, metric_inverse), a) == metric_inverse,
+         "inverse metric preservation")
+    need(h.mul(h.mul(a, metric), at) == metric, "metric preservation")
+    payload = {
+        "schema": "row-completion-limits-v1",
+        "source_payload_sha256": SOURCE_PIN,
+        "large_ports": large, "small_ports": small, "pivots": p,
+        "symmetric_response": h.dumpmatrix(symmetric),
+        "symmetric_response_inverse": h.dumpmatrix(symmetric_inverse),
+        "symmetric_query_word": query,
+        "symmetric_word": symmetric_word,
+        "symmetric_inverse_word": inverse_word,
+        "metric": h.dumpmatrix(metric),
+        "metric_inverse": h.dumpmatrix(metric_inverse),
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode()
+    (args.output / "COMPLETION-LIMITS.json").write_bytes(raw)
+    receipt = {
+        "status": "PASS_ROW_COMPLETION_LIMITS",
+        "payload_sha256": hashlib.sha256(raw).hexdigest(),
+        "modular_ranks": ranks,
+        "minimum_dyadic_unit_row_changes": 16,
+        "ordinary_factor_rank": 16,
+        "actual_rank_A_minus_E": 16,
+        "symmetric_displacement_rank": 32,
+        "symmetric_determinant": "1",
+        "symmetric_query_scalar": query_price,
+        "symmetric_word_and_inverse_scalar": scalar_price,
+        "metric_values": ["-1", "3", "5"],
+        "inverse_metric_contains_odd_denominators": True,
+        "native_services_emitted_here": False,
+        "supplier_terminal_closed": False,
+    }
+    (args.output / "CHECKS.json").write_text(
+        json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/check_row_involution.py b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/check_row_involution.py
new file mode 100644
index 0000000000..6e1d8167af
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/check_row_involution.py
@@ -0,0 +1,297 @@
+#!/usr/bin/env python3
+"""Check a dyadic involution that changes sixteen response rows."""
+
+from fractions import Fraction as F
+from pathlib import Path
+import argparse
+import hashlib
+import importlib.util
+import json
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE = HERE.parent / "row-capture-20261020"
+HELPER_PIN = "ccf661107a790c3d858a3f2bd4d8adc5269f588bfd989bd2e2029e26cbb14081"
+CAPTURE_PIN = "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+N = 112
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def pinned(path, pin):
+    raw = path.read_bytes()
+    require(hashlib.sha256(raw).hexdigest() == pin, "source pin: " + str(path))
+    return raw
+
+
+def transpose(a, width):
+    result = [{} for _ in range(width)]
+    for i, row in enumerate(a):
+        for j, value in row.items():
+            result[j][i] = value
+    return result
+
+
+def rank(a, width):
+    rows = [[row.get(j, F(0)) for j in range(width)] for row in a]
+    pivot_row = 0
+    for j in range(width):
+        found = next((i for i in range(pivot_row, len(rows)) if rows[i][j]), None)
+        if found is None:
+            continue
+        rows[pivot_row], rows[found] = rows[found], rows[pivot_row]
+        value = rows[pivot_row][j]
+        rows[pivot_row] = [x / value for x in rows[pivot_row]]
+        for i in range(pivot_row + 1, len(rows)):
+            value = rows[i][j]
+            if value:
+                rows[i] = [x - value * y
+                           for x, y in zip(rows[i], rows[pivot_row])]
+        pivot_row += 1
+        if pivot_row == len(rows):
+            break
+    return pivot_row
+
+
+def inverse_word(word):
+    result = []
+    for op, target, source, raw in reversed(word):
+        value = F(raw)
+        result.append([op, target, source,
+                       str(-value if op == "add" else 1 / value)])
+    return result
+
+
+def transpose_word(word):
+    return [[op, source, target, value] if op == "add"
+            else [op, target, None, value]
+            for op, target, source, value in reversed(word)]
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=HERE / "run-normal")
+    args = parser.parse_args()
+    helper_path = SOURCE / "check_row_capture.py"
+    pinned(helper_path, HELPER_PIN)
+    spec = importlib.util.spec_from_file_location("frozen_row_capture", helper_path)
+    h = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(h)
+    capture = json.loads(pinned(SOURCE / "run-normal/ROW-CAPTURE.json", CAPTURE_PIN))
+    model = h.load("native")["model"]
+    flags = h.load("pairs")
+    p = capture["pivots"]
+    pset = set(p)
+    rest = sorted(set(range(N)) - pset)
+    eye = h.identity(N)
+    e = h.matrix(model["response"])
+    u = h.matrix(model["correction_U"])
+    v = h.matrix(model["correction_V"])
+    vp = h.matrix(capture["pivot_minor"])
+    vpi = h.matrix(capture["pivot_minor_inverse"])
+    c = h.matrix(capture["code"])
+    ci = h.matrix(capture["code_inverse"])
+    modified_u = [dict(row) for row in u]
+    ordinary_u = [dict(row) if i in rest else {} for i, row in enumerate(u)]
+    vu_ordinary = h.mul(v, ordinary_u)
+    desired = [h.addrow({i: F(-2)}, row, -1)
+               for i, row in enumerate(vu_ordinary)]
+    selected_u = h.mul(vpi, desired)
+    for port, row in zip(p, selected_u):
+        modified_u[port] = row
+    require(h.mul(v, modified_u) == [{i: F(-2)} for i in range(16)],
+            "centre contraction")
+    correction = h.mul(modified_u, v)
+    a = [h.addrow(x, y) for x, y in zip(eye, correction)]
+    at = transpose(a, N)
+    require(h.mul(a, a) == eye, "A squared")
+    require(h.mul(at, at) == eye, "transpose squared")
+    require(all(a[i] == e[i] for i in rest), "ordinary row preservation")
+    require(all(at[i].get(j, F(0)) == e[i].get(j, F(0))
+                for i in range(N) for j in rest), "ordinary column preservation")
+    require(rank(correction, N) == 16, "displacement rank")
+    require(all(x.denominator & (x.denominator - 1) == 0
+                for row in a for x in row.values()), "dyadic entries")
+    require(sum(a[i].get(i, F(0)) for i in range(N)) == 80, "trace")
+    pair = h.identity(N)
+    for record in flags["pair_codes"]:
+        ports = record["ports"]
+        require(not (set(ports) & pset) or set(ports) <= pset,
+                "selected pair closure")
+        for port, row in zip(ports, record["matrix"]):
+            pair[port] = {q: F(x) for q, x in zip(ports, row) if x}
+    pairi, _ = h.inv(pair)
+    mode_e = h.mul(h.mul(pair, e), pairi)
+    mode_a = h.mul(h.mul(pair, a), pairi)
+    mode_at = h.mul(h.mul(pair, at), pairi)
+    require(mode_at == transpose(mode_a, N), "physical transpose in mode chart")
+    blocks = []
+    for group in model["vertex_assignments"]:
+        ports = group["ordered_carriers_a_b_c"]
+        blocks.append((ports, list(map(F, group["signs"]))))
+    blocks += [(ports, [F(1)] * len(ports)) for ports in model["small_cliques"]]
+    direct = h.identity(N)
+    expected_mode_e = h.identity(N)
+    block_records = []
+    for ports, signs in blocks:
+        selected = pset & set(ports)
+        require(len(selected) == 1, "one pivot per block")
+        pivot = next(iter(selected))
+        d = dict(zip(ports, signs))
+        require(d[pivot] == 1, "positive pivot sign")
+        k = len(ports)
+        require(k in (6, 8), "block size")
+        for i in ports:
+            row_u = F(k - 2 if i == pivot else 0) - d[i]
+            direct[i] = h.addrow({i: F(1)}, d, row_u)
+            expected_mode_e[i] = h.addrow({i: F(1)}, d, -d[i])
+        block_records.append({
+            "ports": ports, "signs": [str(x) for x in signs],
+            "pivot": pivot, "size": k,
+            "pivot_column_transpose_multiplier": -(k - 3),
+        })
+    require(direct == mode_a, "independent signed block construction")
+    require(expected_mode_e == mode_e, "original signed block response")
+    require({i for i, row in enumerate(mode_a) if row.get(i)} == pset,
+            "mode diagonal support")
+    require({i for i, row in enumerate(a) if row.get(i)} == pset,
+            "physical diagonal support")
+    for block in block_records:
+        pivot = block["pivot"]
+        multiple = block["pivot_column_transpose_multiplier"]
+        for i in block["ports"]:
+            if i != pivot:
+                require(mode_at[i][pivot] == multiple * mode_e[i][pivot],
+                        "transpose weight slot")
+    for direction, response in (("A", mode_a), ("AT", mode_at)):
+        for i in rest:
+            require(set(response[i]) == set(mode_e[i]),
+                    direction + " ordinary native support")
+    encoded = h.mul(h.mul(c, a), ci)
+    expected_encoded = h.identity(N)
+    fanout = h.mul(modified_u, vp)
+    for i, port in enumerate(p):
+        expected_encoded[port] = {port: F(-1)}
+    for r in rest:
+        expected_encoded[r] = h.addrow(
+            expected_encoded[r], {p[j]: x for j, x in fanout[r].items()})
+    require(encoded == expected_encoded, "lower triangular encoded response")
+    queries = {}
+    query_prices = {}
+    for name, response in (("A", a), ("AT", at)):
+        word = h.lower_query([response[port] for port in p], p, N)
+        actual, price = h.replay(word, 2 * N)
+        expected = h.identity(2 * N)
+        for port in p:
+            expected[port] = h.addrow(
+                expected[port], {N + j: x for j, x in response[port].items()})
+        require(actual == expected, name + " arbitrary baseline query")
+        queries[name] = word
+        query_prices[name] = price
+    lower_word = []
+    for r in rest:
+        for j, value in sorted(fanout[r].items()):
+            lower_word.append(["add", r, p[j], str(value)])
+    gauge_word = list(capture["scalar_word"]) + lower_word
+    gauge_word += [["scale", port, None, "-1"] for port in p]
+    gauge_word += capture["inverse_scalar_word"]
+    actual, gauge_price = h.replay(gauge_word, N)
+    require(actual == a, "literal common frame involution")
+    require(h.replay(gauge_word + gauge_word, N)[0] == eye, "literal gauge square")
+    at_word = transpose_word(gauge_word)
+    actual_at, transpose_price = h.replay(at_word, N)
+    require(actual_at == at, "literal common frame transpose")
+    require(gauge_price == transpose_price, "transpose scalar invoice")
+    pair_word = []
+    for record in flags["pair_codes"]:
+        x, y = record["ports"]
+        (aa, bb), (cc, dd) = record["matrix"]
+        if aa != 1:
+            pair_word.append(["scale", x, None, str(aa)])
+        pair_word.append(["add", x, y, str(bb)])
+        pair_word.append(["scale", y, None, str(2 * dd)])
+        pair_word.append(["add", y, x, str(F(cc, aa))])
+    require(h.replay(pair_word, N)[0] == pair, "literal pair code")
+    pair_inverse_word = inverse_word(pair_word)
+    require(h.replay(pair_inverse_word, N)[0] == pairi, "literal inverse pair code")
+    mode_word = []
+    for record in block_records:
+        pivot = record["pivot"]
+        signed = list(zip(record["ports"], record["signs"]))
+        for port, sign in signed:
+            if port != pivot:
+                mode_word.append(["add", pivot, port, sign])
+        for port, sign in signed:
+            if port != pivot:
+                mode_word.append(["add", port, pivot, str(-F(sign))])
+        mode_word.append(["scale", pivot, None, "-1"])
+        for port, sign in signed:
+            if port != pivot:
+                mode_word.append(["add", pivot, port, str(-F(sign))])
+    require(h.replay(mode_word, N)[0] == mode_a, "literal signed block word")
+    short_word = pair_word + mode_word + pair_inverse_word
+    short_at_word = transpose_word(short_word)
+    short_a, short_price = h.replay(short_word, N)
+    short_at, short_at_price = h.replay(short_at_word, N)
+    require(short_a == a and short_at == at, "short physical words")
+    require(short_price == short_at_price < gauge_price, "short word tariff")
+    require(h.replay(short_word + short_word, N)[0] == eye,
+            "short word involution")
+    payload = {
+        "schema": "rank16-row-involution-v1",
+        "source_pins": {
+            "capture_checker": HELPER_PIN, "capture_payload": CAPTURE_PIN,
+            **{name: item[1] for name, item in h.PINS.items()},
+        },
+        "pivots": p, "ordinary_ports": rest,
+        "blocks": block_records,
+        "response": h.dumpmatrix(a),
+        "response_transpose": h.dumpmatrix(at),
+        "response_inverse": h.dumpmatrix(a),
+        "response_inverse_transpose": h.dumpmatrix(at),
+        "original_response": h.dumpmatrix(e),
+        "mode_response": h.dumpmatrix(mode_a),
+        "mode_response_transpose": h.dumpmatrix(mode_at),
+        "correction_U": h.dumpmatrix(modified_u),
+        "correction_V": h.dumpmatrix(v),
+        "row_code": h.dumpmatrix(c),
+        "row_code_inverse": h.dumpmatrix(ci),
+        "encoded_response": h.dumpmatrix(encoded),
+        "final_query_words": queries,
+        "query_field_convention": "Y=0..111; FULL X=112..223",
+        "common_frame_words": {"A": short_word, "AT": short_at_word},
+        "direct_physical_words": {"A": gauge_word, "AT": at_word},
+    }
+    args.output.mkdir(parents=True, exist_ok=True)
+    raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode()
+    (args.output / "ROW-INVOLUTION.json").write_bytes(raw)
+    receipt = {
+        "status": "PASS_EXACT_ROW_INVOLUTION",
+        "payload_sha256": hashlib.sha256(raw).hexdigest(),
+        "displacement_rank": 16,
+        "determinant": "1",
+        "trace": 80,
+        "negative_eigenvalue_multiplicity": 16,
+        "ordinary_rows_unchanged": 96,
+        "ordinary_columns_unchanged_in_transpose": 96,
+        "both_involution_orders": True,
+        "mode_and_physical_transpose_match": True,
+        "query_baseline_columns_each": 224,
+        "final_query_scalar_prices": query_prices,
+        "common_frame_scalar_price_each": short_price,
+        "direct_physical_scalar_price_each": gauge_price,
+        "all_arithmetic_dyadic": True,
+        "owned_fields": 0,
+        "native_service_emitted_here": False,
+        "supplier_terminal_closed": False,
+    }
+    (args.output / "CHECKS.json").write_text(
+        json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-normal/CHECKS.json
new file mode 100644
index 0000000000..d7fd204987
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-normal/CHECKS.json
@@ -0,0 +1,23 @@
+{
+  "actual_rank_A_minus_E": 16,
+  "inverse_metric_contains_odd_denominators": true,
+  "metric_values": [
+    "-1",
+    "3",
+    "5"
+  ],
+  "minimum_dyadic_unit_row_changes": 16,
+  "modular_ranks": {
+    "large_mod_5": 40,
+    "small_mod_7": 56
+  },
+  "native_services_emitted_here": false,
+  "ordinary_factor_rank": 16,
+  "payload_sha256": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa",
+  "status": "PASS_ROW_COMPLETION_LIMITS",
+  "supplier_terminal_closed": false,
+  "symmetric_determinant": "1",
+  "symmetric_displacement_rank": 32,
+  "symmetric_query_scalar": 1904,
+  "symmetric_word_and_inverse_scalar": 2508
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-normal/COMPLETION-LIMITS.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-normal/COMPLETION-LIMITS.json
new file mode 100644
index 0000000000..b42f2a964d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-normal/COMPLETION-LIMITS.json
@@ -0,0 +1,9144 @@
+{
+  "large_ports": [
+    0,
+    2,
+    7,
+    9,
+    10,
+    11,
+    13,
+    14,
+    15,
+    16,
+    20,
+    21,
+    25,
+    27,
+    36,
+    37,
+    41,
+    42,
+    43,
+    44,
+    46,
+    47,
+    51,
+    52,
+    53,
+    57,
+    61,
+    62,
+    63,
+    70,
+    71,
+    72,
+    76,
+    78,
+    79,
+    81,
+    87,
+    89,
+    90,
+    91,
+    92,
+    94,
+    99,
+    104,
+    105,
+    106,
+    110,
+    111
+  ],
+  "metric": [
+    {
+      "0": "3"
+    },
+    {
+      "1": "5"
+    },
+    {
+      "2": "-1"
+    },
+    {
+      "3": "5"
+    },
+    {
+      "4": "-1"
+    },
+    {
+      "5": "-1"
+    },
+    {
+      "6": "5"
+    },
+    {
+      "7": "3"
+    },
+    {
+      "8": "5"
+    },
+    {
+      "9": "-1"
+    },
+    {
+      "10": "-1"
+    },
+    {
+      "11": "-1"
+    },
+    {
+      "12": "-1"
+    },
+    {
+      "13": "-1"
+    },
+    {
+      "14": "-1"
+    },
+    {
+      "15": "-1"
+    },
+    {
+      "16": "-1"
+    },
+    {
+      "17": "5"
+    },
+    {
+      "18": "5"
+    },
+    {
+      "19": "-1"
+    },
+    {
+      "20": "3"
+    },
+    {
+      "21": "-1"
+    },
+    {
+      "22": "-1"
+    },
+    {
+      "23": "5"
+    },
+    {
+      "24": "5"
+    },
+    {
+      "25": "-1"
+    },
+    {
+      "26": "-1"
+    },
+    {
+      "27": "3"
+    },
+    {
+      "28": "-1"
+    },
+    {
+      "29": "-1"
+    },
+    {
+      "30": "-1"
+    },
+    {
+      "31": "-1"
+    },
+    {
+      "32": "-1"
+    },
+    {
+      "33": "-1"
+    },
+    {
+      "34": "-1"
+    },
+    {
+      "35": "-1"
+    },
+    {
+      "36": "3"
+    },
+    {
+      "37": "-1"
+    },
+    {
+      "38": "-1"
+    },
+    {
+      "39": "-1"
+    },
+    {
+      "40": "-1"
+    },
+    {
+      "41": "-1"
+    },
+    {
+      "42": "-1"
+    },
+    {
+      "43": "-1"
+    },
+    {
+      "44": "-1"
+    },
+    {
+      "45": "-1"
+    },
+    {
+      "46": "3"
+    },
+    {
+      "47": "-1"
+    },
+    {
+      "48": "-1"
+    },
+    {
+      "49": "-1"
+    },
+    {
+      "50": "-1"
+    },
+    {
+      "51": "-1"
+    },
+    {
+      "52": "-1"
+    },
+    {
+      "53": "-1"
+    },
+    {
+      "54": "-1"
+    },
+    {
+      "55": "-1"
+    },
+    {
+      "56": "-1"
+    },
+    {
+      "57": "3"
+    },
+    {
+      "58": "-1"
+    },
+    {
+      "59": "-1"
+    },
+    {
+      "60": "-1"
+    },
+    {
+      "61": "-1"
+    },
+    {
+      "62": "-1"
+    },
+    {
+      "63": "-1"
+    },
+    {
+      "64": "-1"
+    },
+    {
+      "65": "-1"
+    },
+    {
+      "66": "-1"
+    },
+    {
+      "67": "-1"
+    },
+    {
+      "68": "-1"
+    },
+    {
+      "69": "-1"
+    },
+    {
+      "70": "-1"
+    },
+    {
+      "71": "-1"
+    },
+    {
+      "72": "-1"
+    },
+    {
+      "73": "-1"
+    },
+    {
+      "74": "-1"
+    },
+    {
+      "75": "-1"
+    },
+    {
+      "76": "-1"
+    },
+    {
+      "77": "-1"
+    },
+    {
+      "78": "-1"
+    },
+    {
+      "79": "-1"
+    },
+    {
+      "80": "-1"
+    },
+    {
+      "81": "-1"
+    },
+    {
+      "82": "-1"
+    },
+    {
+      "83": "-1"
+    },
+    {
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diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-optimized/CHECKS.json
new file mode 100644
index 0000000000..d7fd204987
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-optimized/CHECKS.json
@@ -0,0 +1,23 @@
+{
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+  "inverse_metric_contains_odd_denominators": true,
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+  "payload_sha256": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa",
+  "status": "PASS_ROW_COMPLETION_LIMITS",
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+  "symmetric_determinant": "1",
+  "symmetric_displacement_rank": 32,
+  "symmetric_query_scalar": 1904,
+  "symmetric_word_and_inverse_scalar": 2508
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-optimized/COMPLETION-LIMITS.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-optimized/COMPLETION-LIMITS.json
new file mode 100644
index 0000000000..b42f2a964d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/limits-optimized/COMPLETION-LIMITS.json
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+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/CHECKS.json
new file mode 100644
index 0000000000..642d5829bc
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/CHECKS.json
@@ -0,0 +1,23 @@
+{
+  "all_arithmetic_dyadic": true,
+  "both_involution_orders": true,
+  "common_frame_scalar_price_each": 3276,
+  "determinant": "1",
+  "direct_physical_scalar_price_each": 5600,
+  "displacement_rank": 16,
+  "final_query_scalar_prices": {
+    "A": 2960,
+    "AT": 1984
+  },
+  "mode_and_physical_transpose_match": true,
+  "native_service_emitted_here": false,
+  "negative_eigenvalue_multiplicity": 16,
+  "ordinary_columns_unchanged_in_transpose": 96,
+  "ordinary_rows_unchanged": 96,
+  "owned_fields": 0,
+  "payload_sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+  "query_baseline_columns_each": 224,
+  "status": "PASS_EXACT_ROW_INVOLUTION",
+  "supplier_terminal_closed": false,
+  "trace": 80
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json
new file mode 100644
index 0000000000..9935a857d8
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json
@@ -0,0 +1,29746 @@
+{
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+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-optimized/CHECKS.json
new file mode 100644
index 0000000000..642d5829bc
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-optimized/CHECKS.json
@@ -0,0 +1,23 @@
+{
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+  "determinant": "1",
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+  "negative_eigenvalue_multiplicity": 16,
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+  "payload_sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+  "query_baseline_columns_each": 224,
+  "status": "PASS_EXACT_ROW_INVOLUTION",
+  "supplier_terminal_closed": false,
+  "trace": 80
+}
diff --git a/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-optimized/ROW-INVOLUTION.json b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-optimized/ROW-INVOLUTION.json
new file mode 100644
index 0000000000..9935a857d8
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-optimized/ROW-INVOLUTION.json
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+    "capture_payload": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7",
+    "native": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "pairs": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/encoded-controller/one-pair-current-codes-20261018/PROGRAM.json b/research/native-centre-capture/frozen/lanes/encoded-controller/one-pair-current-codes-20261018/PROGRAM.json
new file mode 100644
index 0000000000..c54e751a73
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/encoded-controller/one-pair-current-codes-20261018/PROGRAM.json
@@ -0,0 +1 @@
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diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json
new file mode 100644
index 0000000000..3924fe2465
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json
@@ -0,0 +1,27210 @@
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diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json
new file mode 100644
index 0000000000..961b84a24b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json
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diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/CHECKS.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/CHECKS.json
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diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json
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--- /dev/null
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diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json
new file mode 100644
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+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json
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+    {
+      "mode": "normal",
+      "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97",
+      "stdout": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE\nreceipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97\n"
+    },
+    {
+      "mode": "optimized",
+      "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97",
+      "stdout": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE\nreceipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97\n"
+    }
+  ],
+  "status": "PASS_BYTE_IDENTICAL"
+}
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..335ceedf21
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md
@@ -0,0 +1,158 @@
+# Independent review of the full rank-thirty response
+
+The frozen matrix and scalar-code packet passes. It gives an exact
+dyadic unit on all 112 ports, with correction rank 30. Both its response
+and its inverse retain the specified selected eight-port block. The
+ordinary 104-port block has an exact dyadic inverse. All four supplied
+common-frame scalar words have the stated map and price.
+
+No material finding remains in this scope. This review does not certify
+the separate native packet, helper progress, a routed cut, a terminal,
+or a complete supplier cost.
+
+## Response and selected interface
+
+The response on 48 ports is the signed pair conjugate of eight copies
+of the root's integer six-mode unit. At each vertex the two modes that
+meet selected physical ports occupy the first two a positions. The
+sign diagonal gives their two off-diagonal coefficients -alpha_v.
+The response and its inverse have the same a-to-a block. These facts
+preserve the old selected block in both physical matrices.
+
+The independent checker derives each vertex assignment from the
+pinned mode support and the original selected set. It then acts on
+physical basis columns in this order:
+
+```text
+signed pair code,
+selected sign diagonal,
+rank-one reflection and final coordinate exchange,
+selected sign diagonal,
+inverse pair code.
+```
+
+For the inverse it reverses the reflection and exchange. It does not
+import the producer or use the producer's matrix to define this action.
+All 112 columns in each direction agree with the frozen matrices,
+including the disjoint small-port response. Both full inverse orders
+are the identity.
+
+The selected block L is the old block, and L^-1 is the old inverse.
+Both multiplication orders are checked. For the ordinary block H,
+write the full inverse as
+
+```text
+E^-1 = [[L,N],[P,Q]].
+```
+
+The block inverse identity gives H^-1=Q-P L^-1 N. The supplied ordinary
+inverse passes both multiplication orders on all 104 columns; every
+coefficient is dyadic. The exact determinants are
+
+```text
+det(L)=1/16,       det(H)=2^21,       det(E)=2^25.
+```
+
+They also satisfy Jacobi's principal-minor identity
+det(H)=det(E) det((E^-1)_SS). No Schur-complement determinant has been
+substituted for the ordinary determinant.
+
+The supplied U and V have ranks 30 and satisfy E-I=UV on every physical
+column. The two disjoint parts contribute ranks 16 and 14. Since U is
+injective and V is onto its 30-dimensional output, this proves that
+the correction rank is exactly 30.
+
+## The small-port cover and its restricted optimum
+
+The fourteen cliques partition the 64 small ports. Eleven have size
+five and three have size three. The checker verifies each pairwise
+binary inner product from the actual q labels.
+
+On a clique of size k, I-J has eigenvalue 1-k on the constant vector
+and eigenvalue one on its complement. Therefore its inverse is
+I-J/(k-1), its determinant is 1-k, and its correction rank is one.
+For k=3 and k=5 these are dyadic units. The complete small determinant
+is (-4)^11(-2)^3=2^25.
+
+There is a short structural proof that the actual support has no
+nine-clique. Every small q satisfies q dot q=1 and q dot z=1 for z=45.
+The vector z is nonzero and isotropic. Nine pairwise orthogonal odd
+vectors in the nine-dimensional binary space would be an orthonormal
+basis. Expanding z in that basis would give z=sum(q_i), and hence
+z dot z=1. This contradicts z dot z=0.
+
+As a separate finite check, this review enumerates all cliques by
+increasing vertex extension. This differs from the producer's
+pivoted maximal-clique method. It finds exactly the same maximal
+cliques: 896 of size four and 64 of size eight. It also compares every
+maximal clique, not just the two counts.
+
+The fourteen-block optimum is valid within the stated disjoint
+dyadic rank-one clique model. More generally, if a k by k zero-diagonal
+block has rank(A-I)=1, write A=I+u*v. The diagonal equations imply
+v*u=-k, so det(A)=1-k. Dyadic invertibility requires k-1 to be a power
+of two. The clique-size bound leaves k=2,3,5. Twelve blocks cover at
+most sixty ports. Thirteen size-five blocks would cover sixty-five;
+replacing a size-five block by size three or two reduces the total by
+two or three, and cannot give sixty-four. Fourteen is therefore
+necessary and the supplied cover attains it.
+
+This argument does not apply to an odd-denominator representation,
+overlapping blocks, a correction of higher rank within a block, or a
+different native encoding. It is not a lower bound for the required
+computation.
+
+## Literal scalar words
+
+The review executes every supplied gate on each of the 112 independent
+input columns. Every input is arbitrary. All target and source indices
+are data fields; no initial zero, borrowed helper, or owned scratch is
+used. It checks E, E^-1, E^T, and E^-T separately.
+
+For a signed six-mode block, the in-place reflection code has twelve
+unit additions and one negation. The final exchange has three unit
+additions and one negation. This costs 124 real scalar primitives per
+vertex. The eight blocks cost 992. The physical pair code and inverse
+cost 940, so the 48-port scalar code costs 1932.
+
+For a clique of size k, the three groups of k-1 unit additions and
+one scale by -(k-1) implement I-J. Their costs are 102 for k=5 and
+52 for k=3. Thus the small code costs 1278 and each full word costs
+1932+1278=3210. Reversing or transposing the word preserves this
+invoice under the stated tariff.
+
+The independent column replay also accumulates the absolute row sums
+at every changed row. The maximum prefix row norms are 44 for E and
+E^-1, and 14 for E^T and E^-T. These bounds concern the scalar code
+alone. They do not bound a recursive child's internal state.
+
+The four words are valid at a common frame. This phrase is a binding
+premise. It does not provide access to fields in different hole frames,
+or make an accumulated controller chart free to change.
+
+## Reproduction
+
+Run from the workspace root:
+
+```text
+python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py
+```
+
+The expected status is `PASS_INDEPENDENT_RANK_THIRTY_RESPONSE`.
+The two receipts must be byte-identical. The checker authenticates
+the producer proof, checker, payload, receipt, freeze, and the two
+underlying input payloads. It does not run or import producer code.
+It uses exact integers and fractions.
+
+The new-core-transfer lane supplied the full response, clique cover,
+scalar words, and their producer checks. The root supplied the
+reciprocal six-mode construction. The actual pair coordinates and
+selected block come from the pinned cyclic and matching packets.
+This lane supplied the distinct column replay, clique enumeration,
+and the isotropic proof of the clique-size bound. OpenAI Codex
+assisted this work.
+
+No PR, push, or publication is authorized. Before any PR description,
+read
+/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py
new file mode 100644
index 0000000000..8d27eb2ff8
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py
@@ -0,0 +1,233 @@
+#!/usr/bin/env python3
+"""Check the full response with independent columns and clique extension."""
+
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+SOURCE = LANES / "new-core-transfer-20261017/low-displacement-20261020"
+PINS = {
+    "RESPONSE-FREEZE.json": "59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9",
+    "RESPONSE.md": "5ea5866231992c389ae2796f1534e0af90ca88bcedfa3fa9758d78f9457d2981",
+    "check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8",
+    "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c",
+    "run-normal/RESPONSE-CHECKS.json": "7f84440d79200b8c060aad07b910bb96f2bcdde95b07ddb8d41bcea1fcb09d5c",
+}
+
+
+def need(ok, label):
+    if not ok:
+        raise ValueError(label)
+
+
+def unit(n, j):
+    return [F(i == j) for i in range(n)]
+
+
+def sparse(rows):
+    return [{int(k): F(v) for k, v in row.items()} for row in rows]
+
+
+def apply(rows, x):
+    return [sum((v * x[j] for j, v in row.items()), F(0)) for row in rows]
+
+
+def eliminate(rows, width):
+    a = [dict(row) for row in rows]
+    pivot, det = 0, F(1)
+    for j in range(width):
+        p = next((i for i in range(pivot, len(a)) if a[i].get(j)), None)
+        if p is None:
+            continue
+        if p != pivot:
+            a[p], a[pivot] = a[pivot], a[p]
+            det = -det
+        value = a[pivot][j]
+        det *= value
+        for i in range(pivot + 1, len(a)):
+            value_i = a[i].get(j, F(0)) / value
+            if not value_i:
+                continue
+            for k, c in a[pivot].items():
+                new = a[i].get(k, F(0)) - value_i * c
+                if new:
+                    a[i][k] = new
+                else:
+                    a[i].pop(k, None)
+        pivot += 1
+        if pivot == len(a):
+            break
+    return pivot, det if pivot == width == len(a) else None
+
+
+def restrict(rows, ports):
+    return [{j: rows[p][q] for j, q in enumerate(ports) if q in rows[p]} for p in ports]
+
+
+def main():
+    for name, digest in PINS.items():
+        need(sha256((SOURCE / name).read_bytes()).hexdigest() == digest, "Producer pin")
+    packet = json.loads((SOURCE / "run-normal/RESPONSE-PROGRAM.json").read_text())
+    inputs = {}
+    for name, digest in packet["source_pins"].items():
+        raw = (LANES / name).read_bytes()
+        need(sha256(raw).hexdigest() == digest, "Inherited source pin")
+        inputs[Path(name).name] = json.loads(raw)
+    cyclic = inputs["CYCLIC-FLAGS.json"]
+    matching = inputs["MATCHED-INVOLUTION-PROGRAM.json"]
+    selected = matching["selected_ports"]
+    need(packet["selected_ports"] == selected, "Original selected set")
+    need(packet["ports"] == cyclic["ports"], "Actual binary directions")
+    assignments = []
+    for v, c in enumerate(cyclic["cyclic_carriers"]):
+        chosen = [p for p in c if set(map(int, cyclic["mode_rows"][str(p)])) & set(selected)]
+        need(len(chosen) == 2, "Selected mode count")
+        assignments.append({"vertex": v, "ordered_carriers_a_b_c":
+                            chosen + [p for p in c if p not in chosen],
+                            "signs": [1, (-1) ** v, 1, 1, 1, 1]})
+    need(assignments == packet["vertex_assignments"], "Selected-mode assignment")
+
+    def pair(x, inverse=False):
+        out = list(x)
+        for entry in cyclic["pair_codes"]:
+            ps, h = entry["ports"], entry["matrix"]
+            for i, p in enumerate(ps):
+                out[p] = sum((F(h[j][i], 2) if inverse else F(h[i][j])) * x[ps[j]]
+                             for j in range(2))
+        return out
+
+    def formula(x, inverse=False, wrong_sign=False):
+        coded, result = pair(x), list(x)
+        mixed = list(coded)
+        for entry in assignments:
+            ps, d = entry["ordered_carriers_a_b_c"], list(entry["signs"])
+            if wrong_sign:
+                d[1] = 1
+            values = [coded[p] * sign for p, sign in zip(ps, d)]
+            if inverse:
+                values[-2], values[-1] = values[-1], values[-2]
+            query = values[-2] - sum(values[:4])
+            values = [a + query for a in values[:4]] + [values[-2] + 2 * query, values[-1]]
+            if not inverse:
+                values[-2], values[-1] = values[-1], values[-2]
+            for p, sign, value in zip(ps, d, values):
+                mixed[p] = sign * value
+        result = pair(mixed, True)
+        for c in packet["small_cliques"]:
+            total = sum(x[p] for p in c) / (len(c) - 1 if inverse else 1)
+            for p in c:
+                result[p] = x[p] - total
+        return result
+
+    e, ei = sparse(packet["response"]), sparse(packet["response_inverse"])
+    columns, inverse_columns = [], []
+    for j in range(112):
+        x = unit(112, j)
+        a, b = formula(x), formula(x, True)
+        need(a == apply(e, x) and b == apply(ei, x), "Independent response columns")
+        need(formula(a, True) == formula(b) == x, "Full inverse orders")
+        columns.append(a)
+        inverse_columns.append(b)
+    need(any(formula(unit(112, p), wrong_sign=True) != formula(unit(112, p)) for p in selected),
+         "Reject omitted selected sign")
+    old_l = sparse(matching["selected_block"])
+    li = sparse(packet["selected_inverse"])
+    need(restrict(e, selected) == restrict(ei, selected) == old_l, "Both selected blocks")
+    need(all(apply(old_l, apply(li, unit(8, j))) == apply(li, apply(old_l, unit(8, j))) == unit(8, j)
+             for j in range(8)), "Selected inverse orders")
+    ordinary = sorted(set(range(112)) - set(selected))
+    need(ordinary == packet["ordinary_ports"], "Ordinary partition")
+    h, hi = restrict(e, ordinary), sparse(packet["ordinary_inverse"])
+    need(all(c.denominator & (c.denominator - 1) == 0 for row in hi for c in row.values()),
+         "Dyadic ordinary inverse")
+    need(all(apply(h, apply(hi, unit(104, j))) == apply(hi, apply(h, unit(104, j))) == unit(104, j)
+             for j in range(104)), "Ordinary inverse orders")
+    need(eliminate(old_l, 8)[1] == F(1, 16), "Selected determinant")
+    need(eliminate(e, 112)[1] == 2 ** 25, "Full determinant")
+    need(eliminate(h, 104)[1] == 2 ** 21, "Ordinary determinant")
+    u, v = sparse(packet["correction_U"]), sparse(packet["correction_V"])
+    need(eliminate(u, 30)[0] == eliminate(v, 112)[0] == 30, "Factor ranks")
+    for j in range(112):
+        x = unit(112, j)
+        need(apply(u, apply(v, x)) == [a - b for a, b in zip(columns[j], x)], "Correction factor")
+
+    word_receipts = {}
+    for name, gates in packet["common_frame_words"].items():
+        expected = inverse_columns if "inverse" in name else columns
+        if "transpose" in name:
+            expected = [list(row) for row in zip(*expected)]
+        prefix_norms = [F(0)] * len(gates)
+        price = 0
+        parsed = []
+        for kind, target, origin, text in gates:
+            c = F(text)
+            need(0 <= target < 112 and c != 0, "Literal field and coefficient")
+            need(c.denominator & (c.denominator - 1) == 0, "Dyadic gate")
+            a, b = abs(c.numerator), c.denominator
+            if kind == "add":
+                need(isinstance(origin, int) and 0 <= origin < 112 and origin != target,
+                     "Arbitrary-input addition")
+                price += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length())
+            else:
+                need(kind == "scale" and origin is None and a & (a - 1) == 0, "Unit scale")
+                price += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0))
+            parsed.append((kind, target, origin, c))
+        for j in range(112):
+            x = unit(112, j)
+            for k, (kind, target, origin, c) in enumerate(parsed):
+                x[target] = x[target] * c if kind == "scale" else x[target] + c * x[origin]
+                prefix_norms[k] += abs(x[target])
+            need(x == expected[j], "Literal word column " + name)
+        norm = max([F(1)] + prefix_norms)
+        need(price == 3210 and norm == (14 if "transpose" in name else 44), "Scalar invoice")
+        word_receipts[name] = {"columns": 112, "scalar": price, "prefix_row_norm": str(norm)}
+
+    small, q = packet["small_ports"], packet["ports"]
+    need(sorted(p for c in packet["small_cliques"] for p in c) == small, "Disjoint small cover")
+    need(Counter(map(len, packet["small_cliques"])) == {3: 3, 5: 11}, "Clique cover sizes")
+    need(all((q[p] & q[r]).bit_count() % 2 == (p == r)
+             for c in packet["small_cliques"] for p in c for r in c), "Actual clique cover")
+    need(all(q[p].bit_count() % 2 == (q[p] & 45).bit_count() % 2 == 1 for p in small)
+         and (45).bit_count() % 2 == 0, "Affine isotropic obstruction to size nine")
+    adjacent = [{r for r in small if r != p and (q[p] & q[r]).bit_count() % 2 == 0}
+                for p in range(112)]
+    maxima, visited = [], Counter()
+
+    def extend(chosen, options, common):
+        visited[len(chosen)] += 1
+        if not common:
+            maxima.append(tuple(chosen))
+        for i, p in enumerate(options):
+            extend(chosen + [p], [r for r in options[i + 1:] if r in adjacent[p]],
+                   common & adjacent[p])
+
+    extend([], small, set(small))
+    need(Counter(map(len, maxima)) == {4: 896, 8: 64}, "Separate maximal clique census")
+    need(sorted(maxima) == sorted(tuple(sorted(c)) for c in packet["maximal_small_cliques"]),
+         "Every reported maximal clique")
+    need(max(visited) == 8, "Maximum clique dimension")
+    receipt = {
+        "status": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE",
+        "producer_pins": PINS,
+        "source_pins": packet["source_pins"],
+        "response_columns_per_direction": 112,
+        "correction_rank": 30,
+        "determinants": {"selected": "1/16", "ordinary": str(2 ** 21), "full": str(2 ** 25)},
+        "word_checks": word_receipts,
+        "all_clique_sizes": dict(sorted(visited.items())),
+        "maximal_clique_sizes": dict(sorted(Counter(map(len, maxima)).items())),
+        "scope": "Matrix, scalar words, and actual graph. Native phases and routed terminal are separate.",
+    }
+    raw = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode()
+    (HERE / "CHECKS.json").write_bytes(raw)
+    print(receipt["status"])
+    print("receipt_sha256=" + sha256(raw).hexdigest())
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..00faa47794
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/FREEZE.json
@@ -0,0 +1,11 @@
+{
+  "files": {
+    "REPRODUCTION.json": "1a5c9c5c7e49ed3f171e40d2eeb24f3178f371b26cf747ef81c5091146967992",
+    "REVIEW.md": "e4a287d477eff6a8fd8ad672350b3898add189428bd28b7688822de715370f96",
+    "check_review.py": "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89",
+    "run-normal/CHECKS.json": "42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596",
+    "run-optimized/CHECKS.json": "42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596"
+  },
+  "scope": "Matrix, scalar capture, route, and ordered entry code only. Native phase review is separate. No complete supplier or kappa claim.",
+  "status": "FROZEN_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE_REVIEW"
+}
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..59be9f1328
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/REPRODUCTION.json
@@ -0,0 +1,7 @@
+{
+  "normal": "run-normal/CHECKS.json",
+  "optimized": "run-optimized/CHECKS.json",
+  "producer_sources_unchanged": true,
+  "receipt_sha256": "42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596",
+  "status": "PASS_BYTE_IDENTICAL_NORMAL_AND_OPTIMIZED"
+}
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..626b633931
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/REVIEW.md
@@ -0,0 +1,229 @@
+# Independent review of the route32 response and capture codes
+
+Result: PASS within the scope below. There is no material finding in the
+frozen producer packet. This review makes the target of the transported
+code explicit.
+
+## Scope and inputs
+
+The producer packet is
+`new-core-transfer-20261017/low-displacement-20261020/route32`.
+Its freeze hash is
+`28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af`.
+The exact input hashes are in `check_review.py` and the receipt.
+
+This review covers the 112 by 112 response, its rational inverse, both
+scalar capture codes, their literal inverses, their entry translations,
+their costs, and their relation to the actual route labels. It does not
+repeat the native phase review. It does not establish a complete supplier,
+a physical terminal, a recursive precision bound, or a kappa improvement.
+
+The review checker imports no producer code. It reconstructs the groups
+from the frozen cyclic pair geometry and the prior selected-mode
+assignment. It evaluates response columns from signed block sums. A
+separate reverse interpreter checks each scalar output row. A forward row
+interpreter checks the maximum norm and denominator of every prefix.
+
+## Response and selection
+
+Let H be the actual pair code. Its large-sector two by two blocks have
+entries in {+1,-1} and satisfy H H^T=2I. It is the identity on the small
+sector. Each pair has one route label.
+
+The route is the least element r of the ordered root space for which
+q_p dot r=1. The exact class sizes are
+
+```text
+r=30: 64 ports
+r=45: 32 ports
+r=75: 16 ports.
+```
+
+Each large vertex has four modes in class 30 and two in class 75.
+Each old small eight-clique has four modes in each of classes 30 and 45.
+The split gives eight large four-mode blocks, eight large two-mode
+blocks, and sixteen small four-mode blocks.
+
+For a block of size k with sign vector d, put
+
+```text
+M=I-dd^T,
+M^-1=I-dd^T/(k-1).
+```
+
+Since d^T d=k, the two products are I. The eigenvalue on d is 1-k;
+the other k-1 eigenvalues are 1. Thus each block contributes one to
+rank(M-I). The physical response is E=H^-1 M H. It follows that
+
+```text
+rank(E-I)=32,
+det(E)=(-3)^24(-1)^8=3^24=282429536481.
+```
+
+The checker independently verifies both inverse orders on all 112 input
+columns. It also verifies the serialized rank32 correction factors, their
+ranks, physical symmetry, and the zero physical diagonal.
+
+The old selected-eight principal block is the zero matrix. It is not a
+valid selected interface for this response. The packet uses empty
+selection, so its ordinary response is the entire invertible E.
+The inverse has no odd denominator other than three. It is a rational
+unit; a dyadic inverse implementation is not asserted.
+
+## Pivot code
+
+In one block let p be the first port. The direct formula for the pivot
+code P is
+
+```text
+(Pz)_p = sum_i d_i z_i,
+(Pz)_i = d_i z_i-d_p z_p       for i != p.
+```
+
+Hence P d=k e_p and the p-th row of P is d^T. Therefore
+d^T P^-1=e_p^T, and
+
+```text
+P(I-dd^T)P^-1 = I-k e_p e_p^T.
+```
+
+The complete code C is the direct sum of these P blocks after H.
+It puts the 32 centre sums in existing pivot fields and keeps 80
+independent complement coordinates. No zero input is required.
+
+The reverse interpreter verifies all 640 output rows for both literal
+inverse orders. All events refer to fields 0 through 111, so the other
+528 fields remain arbitrary and unchanged. The full scalar cost is
+1,870 units in each direction. The maximum prefix row one-norm is 8
+forward and 4 backward. The maximum binary denominator height is zero
+forward and three backward.
+
+## Four-mode reflection code
+
+For each four-mode block, put
+
+```text
+s=d-2d_p e_p,
+S=I-ss^T/2.
+```
+
+Then s^T s=4 and s^T d=2. Consequently S^2=I,
+rank(S-I)=1, and S d=2d_p e_p. As S is symmetric,
+
+```text
+S(I-dd^T)S = I-4 e_p e_p^T.
+```
+
+The producer's no-scratch word has the same matrix. To see this
+directly, write t=sum_(i!=p) d_i z_i. After its first four groups of
+operations, the pivot is (d_p/2)(d_p z_p+t). Each complement output
+is then z_i+(d_i d_p/2)z_p-(d_i/2)t. These are the rows of S.
+
+The word has nine unit ADDs and scales -2 and 1/2. Under the source
+tariff, its cost is 9*8+4+2=78. The complete code uses this word on
+24 four-mode blocks and the pivot word on the eight two-mode blocks.
+It includes the actual H pair code.
+
+The independent full cost is 2,486 units in each direction. All 640
+literal output rows and both inverse orders pass. The maximum prefix
+row one-norm is 8 forward and 4 backward. The maximum binary
+denominator height is one forward and two backward. There are no
+owned fields, native children, or odd-division events.
+
+For either complete code,
+
+```text
+C E C^-1 = D,
+D = diag(-3 on 24 pivots, -1 on 8 pivots, +1 on 80 complements).
+```
+
+The pivot positions are those in the frozen payload. This equation
+does not assign a physical implementation to D^-1 at another frame.
+In particular, D^-1 contains 24 factors -1/3.
+
+## Route and ordered-frame use
+
+Every nonzero response coefficient and every scalar ADD in both
+capture words connects equal route labels. Thus the response and
+codes commute with diag(A_(r_p)) for any chosen spatial operators A_r.
+This is an exact block-matrix identity.
+
+For the actual unshifted D11 stages, the transvection direction is
+u=(511 xor r) xor e_(8+s), with s=1,2. The checker verifies the
+complete eleven columns of each route matrix and their orthogonality.
+Equal r gives the same route matrix, permutation, and ordered circuit
+P_kappa^-1 F9 P_kappa. It therefore gives the same phase as well.
+This permits the stated commutation with these advances.
+
+This conclusion does not cover added field-dependent views or phase
+corrections. It does not permit Q to commute with C. The checker
+rejects that commutation on the actual payload.
+
+The literal input word is C Q^2: all 112 input translations occur
+before the scalar code. The reverse interpreter retains the translation
+label on each original source field. It checks all 640 outputs and
+the literal spatial inverse. The invoice includes 112 explicit maps
+in addition to the scalar invoice.
+
+For clarity, the formal output code q C q diagonalizes the response
+Q E q, where q=Q^-1:
+
+```text
+(q C q)(Q E q)(Q C^-1 Q)
+  = q C E C^-1 Q
+  = q D Q
+  = D.
+```
+
+Only adjacent inverse cancellations and commutation of the diagonal
+scalar D with Q are used. This is not a formula for conjugating E
+alone, and it does not give a native-free implementation of q C q.
+
+The relative q spaces have dimensions one on the eight two-mode
+blocks and three on the other 24 blocks. Only the eight one-dimensional
+spaces lie in the common root space. Thus route preservation alone
+does not prove a common-root encoding or terminal cost.
+
+## Restricted partition minimum
+
+The reviewed maximal-clique list contains 896 four-cliques and 64
+eight-cliques. Every eight-clique has four ports in each small route
+class. The largest monochromatic clique has size four.
+
+This gives a sharp rank32 minimum in the following restricted family.
+Use the same H. Partition each large vertex into route-homogeneous
+blocks, with no block shared by two vertices. Partition the small
+sector into route-homogeneous cliques. Use I-dd^T on every block.
+Do not mix the large and small sectors.
+
+Each large vertex needs at least two blocks because it has two route
+classes. The eight vertices therefore need at least 16 blocks. The
+64 small ports need at least 16 cliques because a monochromatic
+clique has at most four ports. Each block contributes one to
+rank(E-I), so the total rank is at least 32. The packet attains 32.
+
+This is a minimum for this partition family. It is not a lower bound
+for arbitrary native responses, other pair codes, shared blocks,
+cross-sector constructions, or centre-information encoding.
+
+## Reproduction and credit
+
+Run from the workspace root:
+
+```text
+python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py --out /tmp/route32-review-normal
+python3 -O work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py --out /tmp/route32-review-optimized
+```
+
+Each output directory must be absent before its run. The expected
+status is `PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE`.
+The normal and optimized receipts have the same bytes.
+The checker also rejects an omitted scalar transfer and the wrong
+side of the Q^2 entry translations.
+
+The route split and reflection formula came from the coordinating
+researcher. The producer built the exact model and literal words.
+The common-root geometry, cyclic pair code, and complete clique
+list are earlier campaign inputs, with their hashes in the receipt.
+This review adds an independent derivation and exact replay.
+AI assistance was used. No publication is authorized.
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py
new file mode 100644
index 0000000000..66ba64bcbf
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py
@@ -0,0 +1,393 @@
+#!/usr/bin/env python3
+"""Check the route response and capture words from exact input columns."""
+
+import argparse
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+SOURCE = LANES / "new-core-transfer-20261017/low-displacement-20261020"
+PINS = {
+    "route32/FREEZE.json": "28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af",
+    "route32/ROUTE32.md": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28",
+    "route32/emit_model.py": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711",
+    "route32/model-normal/ROUTE32-MODEL.json": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52",
+    "route32/model-normal/CHECKS.json": "69ee6905c99ab4d93f48d828c378f6c902d5e8a9844df68acbc8971158d76502",
+    "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c",
+}
+INHERITED = {
+    "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json":
+        "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json":
+        "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd",
+    "independent-review-20261017/rank-thirty-review-20261020/FREEZE.json":
+        "15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189",
+}
+OLD_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+
+
+def need(test, label):
+    if not test:
+        raise ValueError(label)
+
+
+def sparse(rows):
+    return [{int(j): F(c) for j, c in row.items() if F(c)} for row in rows]
+
+
+def unit(n, j):
+    return [F(i == j) for i in range(n)]
+
+
+def apply(rows, x):
+    return [sum((c * x[j] for j, c in row.items()), F(0)) for row in rows]
+
+
+def rows_from_columns(columns):
+    return [{j: c for j, c in enumerate(row) if c} for row in zip(*columns)]
+
+
+def eliminate(rows, width):
+    a = [dict(row) for row in rows]
+    count, determinant = 0, F(1)
+    for column in range(width):
+        found = next((i for i in range(count, len(a)) if a[i].get(column)), None)
+        if found is None:
+            continue
+        if found != count:
+            a[found], a[count] = a[count], a[found]
+            determinant = -determinant
+        pivot = a[count][column]
+        determinant *= pivot
+        for i in range(count + 1, len(a)):
+            factor = a[i].get(column, F(0)) / pivot
+            if factor:
+                for j, coefficient in a[count].items():
+                    value = a[i].get(j, F(0)) - factor * coefficient
+                    if value:
+                        a[i][j] = value
+                    else:
+                        a[i].pop(j, None)
+        count += 1
+        if count == len(a):
+            break
+    return count, determinant if count == width == len(a) else None
+
+
+def binary_span(values):
+    out = {0}
+    for v in values:
+        out |= {x ^ v for x in out}
+    return out
+
+
+def add(row, key, value):
+    value += row.get(key, F(0))
+    if value:
+        row[key] = value
+    else:
+        row.pop(key, None)
+
+
+def reverse_output(word, output):
+    row = {(output, 0): F(1)}
+    for kind, target, origin, text in reversed(word):
+        c = F(text)
+        terms = [(key, value) for key, value in row.items() if key[0] == target]
+        if kind == "add":
+            for (_, mask), value in terms:
+                add(row, (origin, mask), c * value)
+        elif kind == "scale":
+            for key, value in terms:
+                add(row, key, (c - 1) * value)
+        else:
+            need(kind == "translate" and c.denominator == 1, "Translation type")
+            for key, _ in terms:
+                del row[key]
+            for (_, mask), value in terms:
+                add(row, (target, mask ^ int(c)), value)
+    return row
+
+
+def inverse_word(word):
+    return [[kind, target, origin,
+             str(-F(text) if kind == "add" else 1 / F(text) if kind == "scale" else F(text))]
+            for kind, target, origin, text in reversed(word)]
+
+
+def word_invoice(word, routes):
+    price, maps = 0, 0
+    for kind, target, origin, text in word:
+        need(isinstance(target, int) and 0 <= target < 112, "Data field target")
+        c = F(text)
+        if kind == "translate":
+            need(origin is None and c.denominator == 1 and 0 <= c < 512, "Translation label")
+            maps += 1
+            continue
+        a, b = abs(c.numerator), c.denominator
+        need(c and b & (b - 1) == 0, "Dyadic nonzero coefficient")
+        if kind == "add":
+            need(isinstance(origin, int) and 0 <= origin < 112 and origin != target,
+                 "Data field source")
+            need(routes[origin] == routes[target], "Every scalar meeting preserves route")
+            price += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length())
+        else:
+            need(kind == "scale" and origin is None and a & (a - 1) == 0, "Dyadic unit scale")
+            price += 2 * (abs(a.bit_length() - b.bit_length()) + int(c < 0))
+    return {"scalar_units": price, "translation_maps": maps, "native_children": 0,
+            "owned_fields": 0}
+
+
+def prefix_bounds(word):
+    rows = [{j: F(1)} for j in range(112)]
+    norm, height = F(1), 0
+    for kind, target, origin, text in word:
+        c = F(text)
+        if kind == "scale":
+            rows[target] = {j: value * c for j, value in rows[target].items()}
+        else:
+            need(kind == "add", "Scalar prefix type")
+            for j, value in rows[origin].items():
+                add(rows[target], j, c * value)
+        norm = max(norm, sum(map(abs, rows[target].values()), F(0)))
+        for value in rows[target].values():
+            b = value.denominator
+            need(b & (b - 1) == 0, "Dyadic prefix")
+            height = max(height, b.bit_length() - 1)
+    return {"maximum_row_one_norm": str(norm), "binary_height": height}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    for name, pin in PINS.items():
+        need(sha256((SOURCE / name).read_bytes()).hexdigest() == pin, "Producer pin " + name)
+    for name, pin in INHERITED.items():
+        need(sha256((LANES / name).read_bytes()).hexdigest() == pin, "Source pin " + name)
+    raw = gzip.decompress((SOURCE / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz").read_bytes())
+    need(sha256(raw).hexdigest() == OLD_PIN, "Rank-sixteen source pin")
+    old = json.loads(raw)["model"]
+    model = json.loads((SOURCE / "route32/model-normal/ROUTE32-MODEL.json").read_text())
+    cyclic = json.loads((LANES / next(k for k in INHERITED if k.endswith("CYCLIC-FLAGS.json"))).read_text())
+    geometry = json.loads((LANES / next(k for k in INHERITED if k.endswith("GEOMETRY.json"))).read_text())
+    rank30 = json.loads((SOURCE / "run-normal/RESPONSE-PROGRAM.json").read_text())
+    q = cyclic["ports"]
+    need(q == model["ports"] == old["ports"] == geometry["q_labels"], "Actual q labels")
+    root = binary_span([30, 45, 75, 384])
+    need(sorted(root) == model["root_space"] == geometry["common_even_isotropic_space"],
+         "Actual root space")
+    routes = [min(r for r in root if (r & v).bit_count() % 2) for v in q]
+    need(routes == model["port_routes"] and Counter(routes) == {30: 64, 45: 32, 75: 16},
+         "Actual route labels")
+    need(model["selected_ports"] == [] and model["ordinary_ports"] == list(range(112)),
+         "Empty selection")
+
+    def pair(x, inverse=False):
+        y = list(x)
+        for record in cyclic["pair_codes"]:
+            ports, h = record["ports"], record["matrix"]
+            need(routes[ports[0]] == routes[ports[1]], "Pair route")
+            for i, p in enumerate(ports):
+                y[p] = sum((F(h[j][i], 2) if inverse else F(h[i][j])) * x[ports[j]]
+                           for j in range(2))
+        return y
+
+    groups = []
+    for vertex, carriers in enumerate(cyclic["cyclic_carriers"]):
+        selected = [p for p in carriers if set(map(int, cyclic["mode_rows"][str(p)]))
+                    & set(old["selected_ports"])]
+        need(len(selected) == 2, "Original selected modes")
+        ports = selected + [p for p in carriers if p not in selected]
+        signs = [1, (-1) ** vertex, 1, 1, 1, 1]
+        for route in sorted({routes[p] for p in ports}):
+            group = [(p, d) for p, d in zip(ports, signs) if routes[p] == route]
+            groups.append(([p for p, _ in group], [d for _, d in group], route, "large"))
+    for clique in old["small_cliques"]:
+        need(len(clique) == 8, "Original small clique size")
+        for route in sorted({routes[p] for p in clique}):
+            ports = [p for p in clique if routes[p] == route]
+            groups.append((ports, [1] * len(ports), route, "small"))
+    need(sorted(p for ps, _, _, _ in groups for p in ps) == list(range(112)), "Mode partition")
+    need(Counter((kind, len(ps)) for ps, _, _, kind in groups)
+         == {("large", 4): 8, ("large", 2): 8, ("small", 4): 16}, "Group counts")
+    relative = Counter()
+    inside = 0
+    for (ps, signs, route, kind), record in zip(groups, model["groups"]):
+        need((ps, signs, route, kind) == (record["ports"], record["signs"],
+                                       record["route"], record["kind"]), "Actual group binding")
+        need(record["pivot"] == ps[0] and record["centre_multiplier"] == 1 - len(ps),
+             "Pivot placement")
+        span = binary_span([q[p] ^ q[ps[0]] for p in ps])
+        need(binary_span(record["relative_q_basis"]) == span, "Relative q space")
+        dim = len(span).bit_length() - 1
+        relative[dim] += 1
+        inside += span <= root
+        need(record["relative_q_rank"] == dim
+             and record["relative_q_in_common_root"] == (span <= root), "Relative q claims")
+        if kind == "small":
+            need(all((q[p] & q[t]).bit_count() % 2 == (p == t) for p in ps for t in ps),
+                 "Actual small orthonormal clique")
+    need(relative == {1: 8, 3: 24} and inside == 8, "Root membership scope")
+
+    def mode_action(x, inverse=False):
+        y = list(x)
+        for ps, signs, _, _ in groups:
+            total = sum(d * x[p] for p, d in zip(ps, signs))
+            if inverse:
+                total /= len(ps) - 1
+            for p, d in zip(ps, signs):
+                y[p] -= d * total
+        return y
+
+    def response(x, inverse=False):
+        return pair(mode_action(pair(x), inverse), True)
+
+    e, ei = sparse(model["response"]), sparse(model["response_inverse"])
+    u, v = sparse(model["correction_U"]), sparse(model["correction_V"])
+    need(len(u) == 112 and len(v) == 32, "Correction dimensions")
+    for j in range(112):
+        x = unit(112, j)
+        a, b = response(x), response(x, True)
+        need(apply(e, x) == a and apply(ei, x) == b, "Independent response column")
+        need(response(a, True) == response(b) == x, "Both response inverse orders")
+        need(apply(u, apply(v, x)) == [a_i - x_i for a_i, x_i in zip(a, x)], "UV correction")
+        need(apply(sparse(model["mode_response"]), x) == mode_action(x), "Mode response")
+        need(apply(sparse(model["mode_inverse"]), x) == mode_action(x, True), "Mode inverse")
+    need(eliminate(u, 32)[0] == eliminate(v, 112)[0] == 32, "Rank32 factors")
+    need(eliminate(e, 112)[1] == 3 ** 24 == int(model["full_determinant"]), "Full determinant")
+    need(all(not row.get(p) for p, row in enumerate(e)), "Physical zero diagonal")
+    need(all(e[p].get(t, F(0)) == e[t].get(p, F(0)) for p in range(112) for t in range(112)),
+         "Physical response symmetry")
+    need(all(routes[p] == routes[t] for p, row in enumerate(e) for t in row), "Response route")
+    old_selected = old["selected_ports"]
+    need(all(not e[p].get(t) for p in old_selected for t in old_selected), "Old selected block is zero")
+    need(sparse(model["old_selected_block"]) == [{} for _ in range(8)]
+         and model["old_selected_determinant"] == "0", "Old selected report")
+    need(set(c.denominator for row in ei for c in row.values()) <= {1, 2, 3, 6},
+         "Only odd inverse denominator three")
+    diagonal = [F(1)] * 112
+    for ps, _, _, _ in groups:
+        diagonal[ps[0]] = 1 - len(ps)
+    need(sparse(model["diagonal_response"]) == [{p: c} for p, c in enumerate(diagonal)],
+         "Actual diagonal response")
+
+    def code_formula(x, reflection=False):
+        z = pair(x)
+        result = list(z)
+        for ps, d, _, _ in groups:
+            p = ps[0]
+            if reflection and len(ps) == 4:
+                s = [-d[0]] + d[1:]
+                total = sum(s_i * z[t] for t, s_i in zip(ps, s)) / 2
+                for t, s_i in zip(ps, s):
+                    result[t] = z[t] - s_i * total
+            else:
+                result[p] = sum(d_i * z[t] for t, d_i in zip(ps, d))
+                for t, d_i in zip(ps[1:], d[1:]):
+                    result[t] = d_i * z[t] - d[0] * z[p]
+        return result
+
+    receipts = {}
+    for name, code in model["codes"].items():
+        word, inverse, entry = code["word"], code["inverse_word"], code["entry_word"]
+        need(inverse == inverse_word(word), "Literal scalar inverse " + name)
+        need(entry[:112] == [["translate", p, None, str(q[p])] for p in range(112)]
+             and entry[112:] == word, "Ordered entry code " + name)
+        expected = rows_from_columns([code_formula(unit(112, j), name == "reflection") for j in range(112)])
+        need(expected == sparse(code["code"]), "Formula code " + name)
+        literal = [{p: c for (p, mask), c in reverse_output(word, i).items() if mask == 0}
+                   for i in range(112)]
+        need(literal == expected, "Independent reverse scalar outputs " + name)
+        inverse_rows = [{p: c for (p, mask), c in reverse_output(inverse, i).items() if mask == 0}
+                        for i in range(112)]
+        need(inverse_rows == sparse(code["inverse_code"]), "Independent reverse inverse outputs")
+        for j in range(112):
+            x = unit(112, j)
+            need(apply(expected, apply(e, apply(inverse_rows, x))) == [diagonal[i] * x[i] for i in range(112)],
+                 "Conjugated centre diagonal")
+        for order in (word + inverse, inverse + word):
+            need(all(reverse_output(order, i) == {(i, 0): 1} for i in range(640)),
+                 "All640 literal inverse outputs")
+        for i in range(640):
+            want = {(p, q[p]): c for p, c in expected[i].items()} if i < 112 else {(i, 0): F(1)}
+            need(reverse_output(entry, i) == want, "All640 ordered entry outputs")
+            need(reverse_output(entry + inverse_word(entry), i) == {(i, 0): 1},
+                 "All640 spatial inverse outputs")
+        need(any(reverse_output(word + entry[:112], i) != reverse_output(entry, i) for i in range(112)),
+             "Reject free Q-square commutation")
+        mutation = list(word)
+        mutation.pop(next(i for i, event in enumerate(word) if event[0] == "add"))
+        need(any(reverse_output(mutation, i) != reverse_output(word, i) for i in range(112)),
+             "Reject omitted scalar transfer")
+        invoice, inverse_invoice = word_invoice(word, routes), word_invoice(inverse, routes)
+        entry_invoice = word_invoice(entry, routes)
+        need(invoice["scalar_units"] == inverse_invoice["scalar_units"] == (1870 if name == "pivot" else 2486),
+             "Independent scalar invoice")
+        need(entry_invoice["translation_maps"] == 112 and entry_invoice["scalar_units"] == invoice["scalar_units"],
+             "Entry translation invoice")
+        forward_bounds, backward_bounds = prefix_bounds(word), prefix_bounds(inverse)
+        need(forward_bounds == {"maximum_row_one_norm": "8", "binary_height": int(name == "reflection")}
+             and backward_bounds == {"maximum_row_one_norm": "4", "binary_height": 3 - int(name == "reflection")},
+             "Exact prefix bounds")
+        receipts[name] = {"events": len(word), "invoice": invoice, "inverse_invoice": inverse_invoice,
+                          "entry_invoice": entry_invoice, "prefix": forward_bounds,
+                          "inverse_prefix": backward_bounds, "all_output_rows": 640}
+
+    reflection_checks = 0
+    for ps, d, _, _ in groups:
+        if len(ps) != 4:
+            continue
+        s = [-d[0]] + d[1:]
+        matrix = [{j: F(i == j) - F(s[i] * s[j], 2) for j in range(4)} for i in range(4)]
+        need(apply(matrix, d) == [2 * d[0], 0, 0, 0], "Signed reflection query")
+        delta = [{j: c - (i == j) for j, c in row.items() if c != (i == j)} for i, row in enumerate(matrix)]
+        need(eliminate(delta, 4)[0] == 1, "Reflection displacement rank")
+        for j in range(4):
+            x = unit(4, j)
+            need(apply(matrix, apply(matrix, x)) == x, "Reflection involution")
+        reflection_checks += 1
+
+    maxima = rank30["maximal_small_cliques"]
+    need(Counter(map(len, maxima)) == {4: 896, 8: 64}, "Reviewed clique list")
+    need(all(Counter(routes[p] for p in clique) == {30: 4, 45: 4}
+             for clique in maxima if len(clique) == 8), "All64 eight-cliques cross routes")
+    need(max(max(Counter(routes[p] for p in clique).values()) for clique in maxima) == 4,
+         "Restricted monochromatic clique bound")
+    route_columns = {}
+    for stage in (1, 2):
+        for route in sorted(set(routes)):
+            direction = (511 ^ route) ^ (1 << (8 + stage))
+            need(direction.bit_count() % 2 == 0, "Even transvection direction")
+            columns = [(1 << j) ^ (direction if (direction >> j) & 1 else 0) for j in range(11)]
+            need(all((a & b).bit_count() % 2 == (i == j)
+                     for i, a in enumerate(columns) for j, b in enumerate(columns)), "Orthogonal route")
+            route_columns[f"{stage}:{route}"] = columns
+    receipt = {
+        "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE",
+        "producer_pins": PINS, "inherited_pins": INHERITED, "rank16_raw_sha256": OLD_PIN,
+        "response_columns_per_direction": 112, "response_symmetric": True,
+        "correction_rank": 32, "determinant": str(3 ** 24),
+        "selection": [], "old_selected_block": "zero",
+        "centre_multipliers": {"-3": 24, "-1": 8, "1": 80},
+        "reflection_blocks": reflection_checks, "code_receipts": receipts,
+        "relative_q_rank_counts": dict(sorted(relative.items())), "blocks_inside_root": inside,
+        "route_classes": dict(sorted(Counter(routes).items())), "actual_kappa_columns": route_columns,
+        "restricted_monochromatic_maximum_clique": 4,
+        "scope": "Exact response, scalar capture words, and route binding. Native phases and a complete caller have separate reviews.",
+    }
+    data = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode()
+    (args.out / "CHECKS.json").write_bytes(data)
+    print(receipt["status"])
+    print("receipt_sha256=" + sha256(data).hexdigest())
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/run-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/run-normal/CHECKS.json
new file mode 100644
index 0000000000..5455bfc745
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/run-normal/CHECKS.json
@@ -0,0 +1,183 @@
+{
+  "actual_kappa_columns": {
+    "1:30": [
+      992,
+      2,
+      4,
+      8,
+      16,
+      961,
+      929,
+      865,
+      737,
+      481,
+      1024
+    ],
+    "1:45": [
+      1,
+      976,
+      4,
+      8,
+      962,
+      32,
+      914,
+      850,
+      722,
+      466,
+      1024
+    ],
+    "1:75": [
+      1,
+      2,
+      944,
+      8,
+      932,
+      916,
+      64,
+      820,
+      692,
+      436,
+      1024
+    ],
+    "2:30": [
+      1504,
+      2,
+      4,
+      8,
+      16,
+      1473,
+      1441,
+      1377,
+      1249,
+      512,
+      481
+    ],
+    "2:45": [
+      1,
+      1488,
+      4,
+      8,
+      1474,
+      32,
+      1426,
+      1362,
+      1234,
+      512,
+      466
+    ],
+    "2:75": [
+      1,
+      2,
+      1456,
+      8,
+      1444,
+      1428,
+      64,
+      1332,
+      1204,
+      512,
+      436
+    ]
+  },
+  "blocks_inside_root": 8,
+  "centre_multipliers": {
+    "-1": 8,
+    "-3": 24,
+    "1": 80
+  },
+  "code_receipts": {
+    "pivot": {
+      "all_output_rows": 640,
+      "entry_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 1870,
+        "translation_maps": 112
+      },
+      "events": 276,
+      "inverse_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 1870,
+        "translation_maps": 0
+      },
+      "inverse_prefix": {
+        "binary_height": 3,
+        "maximum_row_one_norm": "4"
+      },
+      "invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 1870,
+        "translation_maps": 0
+      },
+      "prefix": {
+        "binary_height": 0,
+        "maximum_row_one_norm": "8"
+      }
+    },
+    "reflection": {
+      "all_output_rows": 640,
+      "entry_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 2486,
+        "translation_maps": 112
+      },
+      "events": 368,
+      "inverse_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 2486,
+        "translation_maps": 0
+      },
+      "inverse_prefix": {
+        "binary_height": 2,
+        "maximum_row_one_norm": "4"
+      },
+      "invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 2486,
+        "translation_maps": 0
+      },
+      "prefix": {
+        "binary_height": 1,
+        "maximum_row_one_norm": "8"
+      }
+    }
+  },
+  "correction_rank": 32,
+  "determinant": "282429536481",
+  "inherited_pins": {
+    "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd",
+    "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    "independent-review-20261017/rank-thirty-review-20261020/FREEZE.json": "15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189"
+  },
+  "old_selected_block": "zero",
+  "producer_pins": {
+    "route32/FREEZE.json": "28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af",
+    "route32/ROUTE32.md": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28",
+    "route32/emit_model.py": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711",
+    "route32/model-normal/CHECKS.json": "69ee6905c99ab4d93f48d828c378f6c902d5e8a9844df68acbc8971158d76502",
+    "route32/model-normal/ROUTE32-MODEL.json": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52",
+    "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c"
+  },
+  "rank16_raw_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+  "reflection_blocks": 24,
+  "relative_q_rank_counts": {
+    "1": 8,
+    "3": 24
+  },
+  "response_columns_per_direction": 112,
+  "response_symmetric": true,
+  "restricted_monochromatic_maximum_clique": 4,
+  "route_classes": {
+    "30": 64,
+    "45": 32,
+    "75": 16
+  },
+  "scope": "Exact response, scalar capture words, and route binding. Native phases and a complete caller have separate reviews.",
+  "selection": [],
+  "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/run-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/run-optimized/CHECKS.json
new file mode 100644
index 0000000000..5455bfc745
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/route32-capture-review-20261020/run-optimized/CHECKS.json
@@ -0,0 +1,183 @@
+{
+  "actual_kappa_columns": {
+    "1:30": [
+      992,
+      2,
+      4,
+      8,
+      16,
+      961,
+      929,
+      865,
+      737,
+      481,
+      1024
+    ],
+    "1:45": [
+      1,
+      976,
+      4,
+      8,
+      962,
+      32,
+      914,
+      850,
+      722,
+      466,
+      1024
+    ],
+    "1:75": [
+      1,
+      2,
+      944,
+      8,
+      932,
+      916,
+      64,
+      820,
+      692,
+      436,
+      1024
+    ],
+    "2:30": [
+      1504,
+      2,
+      4,
+      8,
+      16,
+      1473,
+      1441,
+      1377,
+      1249,
+      512,
+      481
+    ],
+    "2:45": [
+      1,
+      1488,
+      4,
+      8,
+      1474,
+      32,
+      1426,
+      1362,
+      1234,
+      512,
+      466
+    ],
+    "2:75": [
+      1,
+      2,
+      1456,
+      8,
+      1444,
+      1428,
+      64,
+      1332,
+      1204,
+      512,
+      436
+    ]
+  },
+  "blocks_inside_root": 8,
+  "centre_multipliers": {
+    "-1": 8,
+    "-3": 24,
+    "1": 80
+  },
+  "code_receipts": {
+    "pivot": {
+      "all_output_rows": 640,
+      "entry_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 1870,
+        "translation_maps": 112
+      },
+      "events": 276,
+      "inverse_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 1870,
+        "translation_maps": 0
+      },
+      "inverse_prefix": {
+        "binary_height": 3,
+        "maximum_row_one_norm": "4"
+      },
+      "invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 1870,
+        "translation_maps": 0
+      },
+      "prefix": {
+        "binary_height": 0,
+        "maximum_row_one_norm": "8"
+      }
+    },
+    "reflection": {
+      "all_output_rows": 640,
+      "entry_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 2486,
+        "translation_maps": 112
+      },
+      "events": 368,
+      "inverse_invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 2486,
+        "translation_maps": 0
+      },
+      "inverse_prefix": {
+        "binary_height": 2,
+        "maximum_row_one_norm": "4"
+      },
+      "invoice": {
+        "native_children": 0,
+        "owned_fields": 0,
+        "scalar_units": 2486,
+        "translation_maps": 0
+      },
+      "prefix": {
+        "binary_height": 1,
+        "maximum_row_one_norm": "8"
+      }
+    }
+  },
+  "correction_rank": 32,
+  "determinant": "282429536481",
+  "inherited_pins": {
+    "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd",
+    "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    "independent-review-20261017/rank-thirty-review-20261020/FREEZE.json": "15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189"
+  },
+  "old_selected_block": "zero",
+  "producer_pins": {
+    "route32/FREEZE.json": "28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af",
+    "route32/ROUTE32.md": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28",
+    "route32/emit_model.py": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711",
+    "route32/model-normal/CHECKS.json": "69ee6905c99ab4d93f48d828c378f6c902d5e8a9844df68acbc8971158d76502",
+    "route32/model-normal/ROUTE32-MODEL.json": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52",
+    "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c"
+  },
+  "rank16_raw_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+  "reflection_blocks": 24,
+  "relative_q_rank_counts": {
+    "1": 8,
+    "3": 24
+  },
+  "response_columns_per_direction": 112,
+  "response_symmetric": true,
+  "restricted_monochromatic_maximum_clique": 4,
+  "route_classes": {
+    "30": 64,
+    "45": 32,
+    "75": 16
+  },
+  "scope": "Exact response, scalar capture words, and route binding. Native phases and a complete caller have separate reviews.",
+  "selection": [],
+  "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..dcbbcdfedf
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/FREEZE.json
@@ -0,0 +1,12 @@
+{
+  "files": {
+    "REPRODUCTION.md": "ca560dd3d8799cb57167dd1ed3f7a5a1ba8e7c189ce48e3c6d76dcc45dac5373",
+    "REVIEW.md": "a136f1ae9960a93b9e399d84853c4899eb6a39fd42d1464a97a1c32bbdfb6f31",
+    "check_review.py": "2b5f8c6231e42d6299c6dba249d0c86d6dab1a9db97cadcf8e902c3d01a8a2e3",
+    "verified-normal/CHECKS.json": "57039f8f9603f4b101a3960bfca4472f9617855213c8247c2470d84f31171f92",
+    "verified-optimized/CHECKS.json": "57039f8f9603f4b101a3960bfca4472f9617855213c8247c2470d84f31171f92"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Actual row involution, sharp dyadic row count, fixed-pivot uniqueness, symmetric unit, metric identities and scalar words. No native service or caller.",
+  "status": "PASS_INDEPENDENT_ROW_COMPLETION_REVIEW"
+}
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/REPRODUCTION.md b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/REPRODUCTION.md
new file mode 100644
index 0000000000..9b78edb33a
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/REPRODUCTION.md
@@ -0,0 +1,28 @@
+# Reproduction
+
+Run from `/Users/aliromman/Projects/IntegerMultiplicationBounds`.
+Use one process at a time. Each output directory must be new.
+
+```text
+python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/row-involution-review-20261020/check_review.py --out NEW_NORMAL_DIRECTORY
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/row-involution-review-20261020/check_review.py --out NEW_OPTIMIZED_DIRECTORY
+```
+
+Both runs must print:
+
+```text
+PASS_INDEPENDENT_ROW_INVOLUTION
+```
+
+The retained final runs are `verified-normal` and `verified-optimized`. Their
+`CHECKS.json` files must be equal byte for byte. The checker uses
+exact rational arithmetic and explicit failure conditions.
+
+The earlier `normal` and `optimized` directories contain the complete
+base review before the symmetric and metric addendum was bound.
+
+The old native response and physical pair geometry are pinned inputs.
+No producer function is imported or replayed. The imported helper is
+a frozen earlier independent matrix checker; its hash is in the
+receipt. The new review derives its response matrices from the signed
+blocks and uses reverse output propagation for the literal words.
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..739492cea4
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/REVIEW.md
@@ -0,0 +1,414 @@
+# Independent review of the actual row-involution completion
+
+Status: PASS within the stated scope.
+
+The frozen construction gives a dyadic involution A on the actual 112
+ports. It preserves all 96 ordinary rows of the old response E. Its
+transpose, the two scalar implementations, and both late queries pass
+independent exact checks. No native word or complete caller is
+established by this review.
+
+The producer freeze is
+`538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2`.
+The proof hash is
+`c8470cc2280a057cbebf4a31ee679495990b200a6d6c033cc39e459eb2cf139f`.
+The payload hash is
+`a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b`.
+This review also binds the separate limits freeze
+`775c1b565ec0aa969f2dbecebb04f4b9a82a561e7e7d842c2b1abae7a75509a6`,
+with proof
+`91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607`
+and payload
+`25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa`.
+
+## General construction and its uniqueness scope
+
+Work over a commutative ring in which 2 is a unit. Let
+`E=I+UV`, with `U` of size `n by r` and `V` of size `r by n`.
+Let `P` have r indices and let `R` be its complement. Assume that
+`V_P` has an inverse over the ring. Set
+
+```text
+U'_R = U_R,
+U'_P = V_P^-1 (-2I-V_R U_R).
+```
+
+Then `VU'=-2I` and
+
+```text
+A^2 = (I+U'V)^2 = I+U'(2I+VU')V = I.
+```
+
+Every row in R is unchanged. The identity `VU'=-2I` supplies a left
+inverse for `U'` and a right inverse for V. Over a field of
+characteristic other than two, both factors have rank r, so
+`rank(A-I)=r`. Also
+
+```text
+det(A) = det(I+VU') = (-1)^r.
+```
+
+The decomposition into `im(U')` and `ker(V)` is direct. A acts as
+minus identity on the first summand and identity on the second.
+This proves the eigenspace statements.
+
+The frozen proof's phrase "the change has rank r" refers to `A-I`.
+It must not be read as a general statement about `A-E`. For example,
+E can already equal A. The producer accepted this wording
+clarification without changing the frozen proof.
+
+The stated uniqueness claim is valid. Within the fixed factor family,
+V, `U_R`, and the desired value of `VU'` determine `U'_P` through
+the invertible minor. The source does not assert uniqueness among
+all possible row completions.
+
+The general K extension is also valid. Replace `-2I` by `K-I`.
+Then `VA=KV` and `det(A)=det(K)`. If K is a unit, direct
+multiplication on both sides gives
+
+```text
+A^-1 = I-U' K^-1 V.
+```
+
+No commutation between K and `U'` or V is used. This algebra does
+not supply a scalar tariff for an arbitrary K.
+
+## Independent construction from the actual signed blocks
+
+The reviewer reads the pinned old native response and the pinned
+physical pair flags. It does not import the producer's code. One
+matrix helper from a prior independent review is pinned and used
+for exact elimination and reverse output propagation.
+
+In the mode chart, the old response consists of eight signed blocks
+of size six and eight signed blocks of size eight:
+
+```text
+E_k = I-dd^T.
+```
+
+For the actual selected pivot p, the source signs satisfy `d_p=1`.
+The reviewer constructs
+
+```text
+u'_k = (k-2)e_p-d,
+A_k = I+u'_k d^T.
+```
+
+The contraction `d^T u'_k=-2` proves each block involutive. Its
+nonpivot rows equal the old rows. Its selected row is
+
+```text
+(k-2) x_p + (k-3) d_R^T x_R.
+```
+
+The checker constructs the physical matrices from these blocks and
+the actual pair code H. It also reconstructs the old factor matrices
+U and V. They agree with the source factors, in the source's exact
+centre-coordinate order.
+
+The actual pivot order is
+
+```text
+0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23.
+```
+
+The selected minor obeys
+
+```text
+V_P V_P^T = diag(2 I8,I8).
+```
+
+Thus its inverse can be formed from its transpose and these sixteen
+diagonal units. The reviewer checks both inverse orders, then
+reconstructs the general completion formula above. It agrees with
+the independent signed-block construction on every entry.
+
+The final exact facts are
+
+```text
+A^2 = (A^T)^2 = I,
+rank(A-I) = 16,
+rank(A-E) = 16,
+det(A) = 1,
+trace(A) = 80.
+```
+
+The equality `rank(A-E)=16` is an additional fact of this actual
+source. It is not a consequence claimed for every input to the
+general theorem.
+
+## The physical transpose uses the pair metric
+
+For a general pair matrix H, transposition does not pass through
+similarity unchanged. If `A=H^-1 A_mode H`, then
+
+```text
+H A^T H^-1 = G A_mode^T G^-1,
+G = H H^T.
+```
+
+For the actual H,
+
+```text
+G = diag(2 I48,I64).
+```
+
+The actual mode response does not mix these two components. Thus G
+commutes with `A_mode^T`, and the right side is exactly
+`A_mode^T`. The checker verifies the metric, the commutation, and
+the resulting physical transpose. It does not assume that H is
+orthogonal with unit scale.
+
+All 96 ordinary physical rows of A equal those of E. All 96
+ordinary columns of `A^T` equal those of E. In each mode block,
+the nonpivot row support of `A^T` is the old support. Its
+pivot-column coefficients are the old coefficients multiplied by
+`-(k-3)`, which is -3 or -5. A native emitter must change those
+weights explicitly.
+
+## Stronger uniqueness for this actual pivot set
+
+The exact retained factor `U_R` has rank 16. Since V has full row
+rank, the ordinary displacement rows `(E-I)_R=U_R V` have row
+space equal to the full row space of V.
+
+Let Z be any rational matrix with the same 96 ordinary rows as E,
+`rank(Z-I)=16`, and `Z^2=I`. The retained displacement rows
+already span a 16-dimensional space. Therefore every row of `Z-I`
+lies in `row(V)`, and there is a matrix T with
+
+```text
+Z-I = T V,    T_R=U_R.
+```
+
+The rank of T is 16. The involution equation gives
+`T(2I+VT)V=0`. A left inverse of T and a right inverse of V imply
+`VT=-2I`. The invertible selected minor now forces
+
+```text
+T_P = V_P^-1(-2I-V_R U_R).
+```
+
+Hence Z=A. This proves uniqueness among all rank-sixteen involutive
+row completions for this fixed actual set P, not only within a
+factor family chosen in advance. It applies in particular to dyadic
+candidates. It does not assert uniqueness for a different pivot set
+or for a completion of larger displacement rank.
+
+## A sharp dyadic row-count bound
+
+The producer proposed this separate extension during review. The
+reviewer derived it independently and checked the required actual
+modular ranks.
+
+The old physical response is block diagonal on its large 48-port
+component and its small 64-port component. Modulo five, the large
+component has rank 40 and left-nullity eight. Modulo seven, the
+small component has rank 56 and left-nullity eight.
+
+These nullities also follow from the signed blocks. A six-mode block
+has one null direction modulo five, since `d^T d=6=1 mod 5`.
+An eight-mode block has one null direction modulo seven. The pair
+code is invertible modulo both primes, so similarity preserves the
+nullities.
+
+Suppose a new matrix changes fewer than eight rows in the large
+component. In its eight-dimensional old left kernel modulo five,
+impose zero on the coordinates of those changed rows. A nonzero
+vector remains. Extend it by zero on the small component. It
+annihilates the original matrix, and it annihilates every row
+replacement because its coefficients vanish at every changed row.
+It is therefore a nonzero left-null vector of the new matrix.
+
+Any matrix with an inverse over `Z[1/2]` remains invertible modulo
+five. The preceding conclusion is a contradiction. Thus at least
+eight large rows must change. The same argument modulo seven
+requires at least eight small rows.
+
+Consequently every dyadic-unit row replacement of this fixed E
+changes at least sixteen rows. The replacement entries can mix the
+two components; the proof still applies. A is a dyadic involution
+and changes exactly eight rows in each component, so it attains the
+bound.
+
+This is a bound on row replacement in the stated common scalar
+representation. It excludes neither odd-grid inverses nor changes
+to the columns, the frames, or the required interface. It is not a
+native lower bound or a lower bound for the required computation.
+
+## Literal words, arbitrary state, and exact prices
+
+The short scalar word first applies H. In each mode block it forms
+`x_p+d_R^T x_R`, subtracts its signed fanout from the ordinary
+coordinates, negates the pivot, and subtracts the updated reader.
+An explicit expansion gives
+
+```text
+x'_p = (k-2)x_p+(k-3)d_R^T x_R,
+x'_R = -d_R x_p+(I-d_R d_R^T)x_R.
+```
+
+The word then applies `H^-1`. Each size-six block costs 122 old
+real scalar units, and each size-eight block costs 170. H and its
+inverse each cost 470. The total is
+`8*122+8*170+2*470=3276`.
+
+Reversing the order and transposing each elementary gate gives the
+literal transpose word with the same invoice. The longer direct
+physical word has cost 5600. The checker verifies both
+implementations and their squares by reverse propagation on all
+640 arbitrary field inputs. The other 528 fields are unchanged.
+A separate forward pass checks the exact scalar invoice and every
+prefix.
+
+The late query words preserve arbitrary target baselines. They
+add `A[P,*]X` or `A^T[P,*]X` into the selected Y fields. They
+leave all source fields and all other fields unchanged. All 640
+outputs pass the reverse check, including the 224 data inputs.
+
+| Word | Old real scalar units | Prefix row one-norm | Binary denominator height |
+| --- | ---: | ---: | ---: |
+| Short A | 3276 | 68 | 1 |
+| Short transpose | 3276 | 18 | 1 |
+| Direct A | 5600 | 69 | 2 |
+| Direct transpose | 5600 | 14 | 2 |
+| Late A query | 2960 | 70 | 1 |
+| Late transpose query | 1984 | 30 | 1 |
+
+Every SCALE is a signed power of two. No owned field, CLEAR, or
+odd-arithmetic service occurs. These are scalar words in a common
+admissible frame. The prefix bounds do not include any recursive
+native child, owner map, or routed chart conversion.
+
+The normalized row code also satisfies
+
+```text
+C A C^-1 = [[-I,0],[U_R V_P,I]].
+```
+
+The lower fanout is retained in both the proof and the check.
+It must not be replaced by a diagonal code without a further word.
+
+## Symmetric completion and its general form
+
+The addendum gives a distinct response
+
+```text
+S = C A = E-Pi_P = C^T D C,
+D = I-2 Pi_P.
+```
+
+The checker constructs S directly from the old E and the selected
+diagonal projector. It does not obtain S from a producer matrix.
+It then checks all three other expressions, symmetry, both inverse
+orders, determinant one, and `rank(S-I)=32`. Thus the displacement
+rank is larger than that of A, although only the same sixteen rows
+change from E.
+
+There is a general proof of the congruence. Suppose E is symmetric,
+`E=I+UV`, `V_P` is invertible, and `E[P,P]=0`. Set
+`B=V_P^-1 V_R`. The zero selected block gives
+`U_P=-V_P^-1`, so the selected ordinary block of E is `-B`.
+Symmetry then gives `U_R V_P=-B^T`. Therefore
+
+```text
+E = [[0,-B],[-B^T,I-B^T B]],
+E-Pi_P = [[-I,-B],[-B^T,I-B^T B]]
+       = [[I,0],[B^T,I]] [[-I,0],[0,I]] [[I,B],[0,I]].
+```
+
+The outer matrices are the transpose pair `C^T,C`. They are units
+over the same coefficient ring. Consequently the symmetric
+completion is a unit, with
+
+```text
+S^-1 = C^-1 D C^-T.
+```
+
+This proof does not require the actual block sizes, an eigenvalue
+bound, or division by an odd integer. The selected diagonal
+completion is enough under its stated zero-minor and factor
+hypotheses. In an operator setting with an adjoint, the same
+ordered block proof holds with every transpose replaced by the
+adjoint, provided E is self-adjoint and the specified inverse
+minor exists. It does not make the resulting operator codes free.
+
+In one actual mode block, the literal word first forms
+`x_p+d_R^T x_R`, negates the pivot, and adds the signed fanout
+of that negated pivot into `x_R`. This is S. It has two signed ADD passes and
+one pivot sign. Its reverse word is the exact inverse. The
+complete physical word, including H and its inverse, costs
+`8*82+8*114+2*470=2508` old real units in each direction.
+
+The selected rows are exactly `-V_P^-1 V`. The late query therefore
+costs 1904 units. Its arbitrary target baseline is retained.
+Both complete scalar words, both literal inverse orders, and
+the late query pass all 640 reverse-output checks.
+
+| Symmetric word | Old real scalar units | Prefix row one-norm | Binary denominator height |
+| --- | ---: | ---: | ---: |
+| S | 2508 | 22 | 1 |
+| Inverse of S | 2508 | 28 | 1 |
+| Late S query | 1904 | 24 | 1 |
+
+The ordinary diagonal entries of `S^-1` are nonzero. The original
+off-diagonal native grammar therefore does not supply a native
+inverse of S by an automatic substitution. The scalar inverse
+word is a common-frame service with its own access premise.
+
+## The involution's diagonal metric
+
+Define a second metric M by `M_pp=k-3` at each block pivot and
+`M_ii=-1` on its nonpivot coordinates. In a mode block,
+
+```text
+A = I+M d d^T.
+```
+
+It follows directly that
+
+```text
+A^T = M^-1 A M,
+A^T M^-1 A = M^-1.
+```
+
+The actual physical pair code commutes with M: every selected
+large pair has value 3 on both coordinates, every ordinary pair
+has value -1 on both, and the small component has no pair code.
+The checker verifies the physical identities and all metric
+entries. The inverse metric has denominators three and five.
+
+Let Z be any field-diagonal unitary spatial operator that commutes
+with M, and put `L=ZA`. No commutation between Z and A is needed:
+
+```text
+L^* = A^T Z^-1
+    = M^-1 A M Z^-1
+    = M^-1 A Z^-1 M
+    = M^-1 L^-1 M.
+```
+
+This is an ordered identity at every spatial width. It is not a
+dyadic implementation of the metric wrapper. A caller that
+executes `M^-1` must establish its representation and arithmetic
+service. The identity does not require odd arithmetic in every
+implementation of `A^T`; the separately checked 3276-unit word
+already implements that matrix using dyadic units.
+
+## Native and caller scope
+
+The review supplies exact response matrices, query rows, transfer
+weights, scalar implementations, and an actual transpose identity
+for the separate native emitter. It does not verify a new native
+program. In particular, `A^-1=A` does not imply that the hybrid
+FULL/hole output types compose with an old backward input.
+
+The stage responses can differ after routing. Their ordered
+composition, legal current-source access, final raw output, helper
+progress, and complete recursive cost remain obligations of the
+caller. No complete supplier or kappa improvement is claimed.
+
+AI assistance was used. No PR, push, or publication is authorized.
+Before any PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/check_review.py b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/check_review.py
new file mode 100644
index 0000000000..348bdae45f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/check_review.py
@@ -0,0 +1,318 @@
+#!/usr/bin/env python3
+"""Check the row involution from signed blocks and reverse output rows."""
+
+import argparse
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+SOURCE = LANES / "controller-followthrough-20261017/row-involution-20261020"
+PINS = {
+    "FREEZE.json": "538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2",
+    "ROW-INVOLUTION.md": "c8470cc2280a057cbebf4a31ee679495990b200a6d6c033cc39e459eb2cf139f",
+    "check_row_involution.py": "a675e5578de4bc264524f7c1a75c5685a1967a65f7d3cd020fb0dc19352d31e9",
+    "run-normal/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+    "run-normal/CHECKS.json": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6",
+    "LIMITS-FREEZE.json": "775c1b565ec0aa969f2dbecebb04f4b9a82a561e7e7d842c2b1abae7a75509a6",
+    "COMPLETION-LIMITS.md": "91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607",
+    "check_completion_limits.py": "f07260347b3b5a955c475a25f87873dded309f9bd0bd1ad382c5a21c5acb16bb",
+    "limits-normal/COMPLETION-LIMITS.json": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa",
+    "limits-normal/CHECKS.json": "eb60b314a3cb6896c6afd33b8dc88d422f5ce12ac5ab73ce9a704950c6975276",
+}
+OLD = LANES / "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz"
+OLD_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+PAIR = LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json"
+PAIR_PIN = "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"
+HELPER = LANES / "independent-review-20261017/route32-capture-review-20261020/check_review.py"
+HELPER_PIN = "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89"
+
+
+def need(test, label):
+    if not test:
+        raise ValueError(label)
+
+
+def eye(n):
+    return [{i: F(1)} for i in range(n)]
+
+
+def add(row, j, value):
+    value += row.get(j, F(0))
+    if value:
+        row[j] = value
+    else:
+        row.pop(j, None)
+
+
+def multiply(a, b):
+    result = []
+    for row in a:
+        out = {}
+        for j, c in row.items():
+            for t, value in b[j].items():
+                add(out, t, c * value)
+        result.append(out)
+    return result
+
+
+def transpose(a, width):
+    out = [{} for _ in range(width)]
+    for i, row in enumerate(a):
+        for j, c in row.items():
+            out[j][i] = c
+    return out
+
+
+def difference(a, b):
+    out = [dict(row) for row in a]
+    for row, subtract in zip(out, b):
+        for j, c in subtract.items():
+            add(row, j, -c)
+    return out
+
+
+def modular_rank(rows, columns, prime):
+    a = [[int(row.get(j, F(0)).numerator % prime) *
+          pow(row.get(j, F(0)).denominator, -1, prime) % prime
+          for j in columns] for row in rows]
+    count = 0
+    for j in range(len(columns)):
+        found = next((i for i in range(count, len(a)) if a[i][j]), None)
+        if found is None:
+            continue
+        a[count], a[found] = a[found], a[count]
+        scale = pow(a[count][j], -1, prime)
+        a[count] = [x * scale % prime for x in a[count]]
+        for i in range(count + 1, len(a)):
+            factor = a[i][j]
+            if factor:
+                a[i] = [(x - factor * y) % prime for x, y in zip(a[i], a[count])]
+        count += 1
+        if count == len(a):
+            break
+    return count
+
+
+def scalar_invoice(word, width):
+    rows = eye(width)
+    cost, norm, height = 0, F(1), 0
+    for kind, target, origin, text in word:
+        c = F(text)
+        a, b = abs(c.numerator), c.denominator
+        need(0 <= target < width and c and b & (b - 1) == 0, "Dyadic field event")
+        if kind == "add":
+            need(0 <= origin < width and origin != target, "Distinct ADD fields")
+            cost += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length())
+            for j, value in rows[origin].items():
+                add(rows[target], j, c * value)
+        else:
+            need(kind == "scale" and origin is None and a & (a - 1) == 0, "Unit SCALE")
+            cost += 2 * (abs(a.bit_length() - b.bit_length()) + int(c < 0))
+            rows[target] = {j: c * value for j, value in rows[target].items()}
+        norm = max(norm, sum(map(abs, rows[target].values()), F(0)))
+        height = max(height, *(x.denominator.bit_length() - 1 for x in rows[target].values()))
+    return rows, {"old_real_scalar_units": cost, "prefix_row_one_norm": str(norm),
+                  "binary_denominator_height": height}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    for name, pin in PINS.items():
+        need(sha256((SOURCE / name).read_bytes()).hexdigest() == pin, "Producer pin " + name)
+    need(sha256(HELPER.read_bytes()).hexdigest() == HELPER_PIN, "Independent helper pin")
+    need(sha256(PAIR.read_bytes()).hexdigest() == PAIR_PIN, "Pair source pin")
+    raw = gzip.decompress(OLD.read_bytes())
+    need(sha256(raw).hexdigest() == OLD_PIN, "Actual response pin")
+    old = json.loads(raw)["model"]
+    source = json.loads((SOURCE / "run-normal/ROW-INVOLUTION.json").read_text())
+    limits = json.loads((SOURCE / "limits-normal/COMPLETION-LIMITS.json").read_text())
+    flags = json.loads(PAIR.read_text())
+    spec = importlib.util.spec_from_file_location("independent_matrix", HELPER)
+    r = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(r)
+    pivots = [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23]
+    need(source["pivots"] == pivots, "Actual pivot order")
+    pset = set(pivots)
+    rest = sorted(set(range(112)) - pset)
+    groups = [(x["ordered_carriers_a_b_c"], x["signs"]) for x in old["vertex_assignments"]]
+    groups += [(ports, [1] * len(ports)) for ports in old["small_cliques"]]
+    need(sorted(p for ports, _ in groups for p in ports) == list(range(112)), "Block partition")
+    h, hi = eye(112), eye(112)
+    large = set()
+    for record in flags["pair_codes"]:
+        ps, matrix = record["ports"], record["matrix"]
+        need(not (set(ps) & pset) or set(ps) <= pset, "Complete selected pair")
+        large.update(ps)
+        for i, p in enumerate(ps):
+            h[p] = {ps[j]: F(matrix[i][j]) for j in range(2) if matrix[i][j]}
+            hi[p] = {ps[j]: F(matrix[j][i], 2) for j in range(2) if matrix[j][i]}
+    need(len(large) == 48, "Actual large component")
+    need(multiply(h, hi) == multiply(hi, h) == eye(112), "Actual pair inverses")
+    metric = [{i: F(2 if i in large else 1)} for i in range(112)]
+    need(multiply(h, transpose(h, 112)) == metric, "Physical transpose metric")
+    mode_e, mode_a = eye(112), eye(112)
+    mode_u, mode_v = [{} for _ in range(112)], []
+    for j, (ps, signs) in enumerate(groups):
+        d = dict(zip(ps, map(F, signs)))
+        selected = pset & set(ps)
+        need(len(selected) == 1, "One pivot per signed block")
+        p = next(iter(selected))
+        need(d[p] == 1 and len(ps) in (6, 8), "Actual signed pivot")
+        mode_v.append(d)
+        for i in ps:
+            mode_u[i] = {j: -d[i]}
+            for t, sign in d.items():
+                add(mode_e[i], t, -d[i] * sign)
+                add(mode_a[i], t, (F(len(ps) - 2 if i == p else 0) - d[i]) * sign)
+    e = multiply(hi, multiply(mode_e, h))
+    a = multiply(hi, multiply(mode_a, h))
+    at = transpose(a, 112)
+    u, v = multiply(hi, mode_u), multiply(mode_v, h)
+    need(e == r.sparse(old["response"]), "Independent old response")
+    need(u == r.sparse(old["correction_U"]) and v == r.sparse(old["correction_V"]), "Actual factor gauge")
+    need(a == r.sparse(source["response"]) and at == r.sparse(source["response_transpose"]),
+         "Independent signed-block response columns")
+    need(multiply(metric, transpose(mode_a, 112)) == multiply(transpose(mode_a, 112), metric),
+         "No cross-metric component")
+    need(multiply(h, multiply(at, hi)) == transpose(mode_a, 112), "Physical transpose through pair chart")
+    need(multiply(a, a) == multiply(at, at) == eye(112), "Both involutions")
+    need(all(a[i] == e[i] for i in rest), "All96 ordinary rows")
+    need(all(at[i].get(j, F(0)) == e[i].get(j, F(0)) for i in range(112) for j in rest),
+         "All96 ordinary transpose columns")
+    need(r.eliminate(difference(a, eye(112)), 112)[0] == 16, "Rank(A-I)")
+    need(r.eliminate(difference(a, e), 112)[0] == 16, "Separate actual rank(A-E)")
+    need(r.eliminate([u[i] for i in rest], 16)[0] == 16, "Ordinary factors force full rank")
+    need(r.eliminate(a, 112) == (112, F(1)), "Full determinant")
+    need(sum(a[i].get(i, F(0)) for i in range(112)) == 80, "Trace")
+    vp = [{j: row.get(p, F(0)) for j, p in enumerate(pivots) if row.get(p)} for row in v]
+    vpt = transpose(vp, 16)
+    gram = [{i: F(2 if i < 8 else 1)} for i in range(16)]
+    need(multiply(vp, vpt) == gram, "Actual selected Gram")
+    gram_inverse = [{i: 1 / row[i]} for i, row in enumerate(gram)]
+    vpi = multiply(vpt, gram_inverse)
+    need(multiply(vp, vpi) == multiply(vpi, vp) == eye(16), "Selected inverse both orders")
+    ordinary_u = [u[i] if i in rest else {} for i in range(112)]
+    desired = difference([{i: F(-2)} for i in range(16)], multiply(v, ordinary_u))
+    completed_u = [dict(row) for row in ordinary_u]
+    for p, row in zip(pivots, multiply(vpi, desired)):
+        completed_u[p] = row
+    need(multiply(v, completed_u) == [{i: F(-2)} for i in range(16)], "General completion contraction")
+    need(difference(a, eye(112)) == multiply(completed_u, v), "General completion matches signed formula")
+    c = eye(112)
+    for p, row in zip(pivots, multiply(vpi, v)):
+        c[p] = row
+    ci = difference(eye(112), difference(c, eye(112)))
+    need(multiply(c, ci) == multiply(ci, c) == eye(112), "Normalized code inverse")
+    need(c == r.sparse(source["row_code"]) and ci == r.sparse(source["row_code_inverse"]), "Code binding")
+    encoded = eye(112)
+    fanout = multiply(u, vp)
+    for p in pivots:
+        encoded[p] = {p: F(-1)}
+    for i in rest:
+        for j, value in fanout[i].items():
+            add(encoded[i], pivots[j], value)
+    need(multiply(c, multiply(a, ci)) == encoded == r.sparse(source["encoded_response"]),
+         "Lower triangular encoded response")
+    reports = {}
+    for section, price in (("common_frame_words", 3276), ("direct_physical_words", 5600)):
+        for name, expected in (("A", a), ("AT", at)):
+            word = source[section][name]
+            forward, invoice = scalar_invoice(word, 112)
+            need(forward == expected and invoice["old_real_scalar_units"] == price, "Full scalar invoice")
+            for i in range(640):
+                want = {(j, 0): value for j, value in expected[i].items()} if i < 112 else {(i, 0): F(1)}
+                need(r.reverse_output(word, i) == want, "All640 reverse scalar outputs")
+                need(r.reverse_output(word + word, i) == {(i, 0): F(1)}, "All640 literal square")
+            reports[section + "/" + name] = invoice
+    for name, response, price in (("A", a, 2960), ("AT", at, 1984)):
+        word = source["final_query_words"][name]
+        expected = eye(224)
+        for p in pivots:
+            for j, value in response[p].items():
+                add(expected[p], 112 + j, value)
+        forward, invoice = scalar_invoice(word, 224)
+        need(forward == expected and invoice["old_real_scalar_units"] == price, "Late query invoice")
+        for i in range(640):
+            want = {(j, 0): value for j, value in expected[i].items()} if i < 224 else {(i, 0): F(1)}
+            need(r.reverse_output(word, i) == want, "All640 arbitrary-baseline query outputs")
+        reports["late_query/" + name] = invoice
+    projector = [{i: F(1)} if i in pset else {} for i in range(112)]
+    signature = [{i: F(-1 if i in pset else 1)} for i in range(112)]
+    symmetric = difference(e, projector)
+    symmetric_inverse = multiply(ci, multiply(signature, transpose(ci, 112)))
+    need(symmetric == transpose(symmetric, 112) == multiply(c, a), "Symmetric completion")
+    need(symmetric == multiply(transpose(c, 112), multiply(signature, c)), "Exact congruence")
+    need(symmetric == r.sparse(limits["symmetric_response"]) and
+         symmetric_inverse == r.sparse(limits["symmetric_response_inverse"]), "Symmetric source binding")
+    need(multiply(symmetric, symmetric_inverse) == multiply(symmetric_inverse, symmetric) == eye(112),
+         "Both symmetric inverse orders")
+    need(r.eliminate(difference(symmetric, eye(112)), 112)[0] == 32, "Symmetric displacement rank")
+    need(r.eliminate(symmetric, 112) == (112, F(1)), "Symmetric determinant")
+    for name, key, expected in (("S", "symmetric_word", symmetric),
+                                ("S_inverse", "symmetric_inverse_word", symmetric_inverse)):
+        word = limits[key]
+        forward, invoice = scalar_invoice(word, 112)
+        need(forward == expected and invoice["old_real_scalar_units"] == 2508, "Symmetric literal invoice")
+        for i in range(640):
+            want = {(j, 0): value for j, value in expected[i].items()} if i < 112 else {(i, 0): F(1)}
+            need(r.reverse_output(word, i) == want, "All640 symmetric outputs")
+        reports["common_frame_words/" + name] = invoice
+    for first, second in (("symmetric_word", "symmetric_inverse_word"),
+                          ("symmetric_inverse_word", "symmetric_word")):
+        need(all(r.reverse_output(limits[first] + limits[second], i) == {(i, 0): F(1)}
+                 for i in range(640)), "Both literal symmetric inverse orders")
+    expected = eye(224)
+    for p in pivots:
+        for j, value in symmetric[p].items():
+            add(expected[p], 112 + j, value)
+    forward, invoice = scalar_invoice(limits["symmetric_query_word"], 224)
+    need(forward == expected and invoice["old_real_scalar_units"] == 1904, "Symmetric late query")
+    for i in range(640):
+        want = {(j, 0): value for j, value in expected[i].items()} if i < 224 else {(i, 0): F(1)}
+        need(r.reverse_output(limits["symmetric_query_word"], i) == want,
+             "All640 symmetric arbitrary-baseline query outputs")
+    reports["late_query/S"] = invoice
+    response_metric = [{i: F(-1)} for i in range(112)]
+    for ps, _ in groups:
+        p = next(iter(pset & set(ps)))
+        response_metric[p] = {p: F(len(ps) - 3)}
+    response_metric_inverse = [{i: 1 / row[i]} for i, row in enumerate(response_metric)]
+    need(response_metric == r.sparse(limits["metric"]) and
+         response_metric_inverse == r.sparse(limits["metric_inverse"]), "Response metric binding")
+    need(multiply(h, response_metric) == multiply(response_metric, h), "Metric preserved by pair chart")
+    need(at == multiply(response_metric_inverse, multiply(a, response_metric)), "Weighted transpose")
+    need(multiply(at, multiply(response_metric_inverse, a)) == response_metric_inverse,
+         "Inverse metric preservation")
+    need({value.denominator for row in response_metric_inverse for value in row.values()} == {1, 3, 5},
+         "Odd inverse-metric services remain")
+    small = sorted(set(range(112)) - large)
+    modular = {"large_mod5_rank": modular_rank([e[i] for i in sorted(large)], sorted(large), 5),
+               "small_mod7_rank": modular_rank([e[i] for i in small], small, 7)}
+    need(modular == {"large_mod5_rank": 40, "small_mod7_rank": 56}, "Actual modular row obstruction")
+    receipt = {
+        "status": "PASS_INDEPENDENT_ROW_INVOLUTION",
+        "producer_pins": PINS, "old_response_pin": OLD_PIN, "pair_pin": PAIR_PIN,
+        "independent_helper_pin": HELPER_PIN, "reports": reports,
+        "ordinary_factor_rank": 16, "rank_A_minus_I": 16, "rank_A_minus_E": 16,
+        "determinant": "1", "trace": 80, "unchanged_ordinary_rows": 96,
+        "symmetric_displacement_rank": 32, "symmetric_determinant": "1",
+        "modular_ranks": modular, "arbitrary_input_fields": 640,
+        "scope": "Exact completion algebra, actual transpose metric, scalar words and baseline queries. No native service or caller.",
+    }
+    output = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode()
+    (args.out / "CHECKS.json").write_bytes(output)
+    print(receipt["status"])
+    print("receipt_sha256=" + sha256(output).hexdigest())
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/verified-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/verified-normal/CHECKS.json
new file mode 100644
index 0000000000..e90c9de0ce
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/verified-normal/CHECKS.json
@@ -0,0 +1,79 @@
+{
+  "arbitrary_input_fields": 640,
+  "determinant": "1",
+  "independent_helper_pin": "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89",
+  "modular_ranks": {
+    "large_mod5_rank": 40,
+    "small_mod7_rank": 56
+  },
+  "old_response_pin": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+  "ordinary_factor_rank": 16,
+  "pair_pin": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+  "producer_pins": {
+    "COMPLETION-LIMITS.md": "91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607",
+    "FREEZE.json": "538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2",
+    "LIMITS-FREEZE.json": "775c1b565ec0aa969f2dbecebb04f4b9a82a561e7e7d842c2b1abae7a75509a6",
+    "ROW-INVOLUTION.md": "c8470cc2280a057cbebf4a31ee679495990b200a6d6c033cc39e459eb2cf139f",
+    "check_completion_limits.py": "f07260347b3b5a955c475a25f87873dded309f9bd0bd1ad382c5a21c5acb16bb",
+    "check_row_involution.py": "a675e5578de4bc264524f7c1a75c5685a1967a65f7d3cd020fb0dc19352d31e9",
+    "limits-normal/CHECKS.json": "eb60b314a3cb6896c6afd33b8dc88d422f5ce12ac5ab73ce9a704950c6975276",
+    "limits-normal/COMPLETION-LIMITS.json": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa",
+    "run-normal/CHECKS.json": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6",
+    "run-normal/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "rank_A_minus_E": 16,
+  "rank_A_minus_I": 16,
+  "reports": {
+    "common_frame_words/A": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 3276,
+      "prefix_row_one_norm": "68"
+    },
+    "common_frame_words/AT": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 3276,
+      "prefix_row_one_norm": "18"
+    },
+    "common_frame_words/S": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2508,
+      "prefix_row_one_norm": "22"
+    },
+    "common_frame_words/S_inverse": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2508,
+      "prefix_row_one_norm": "28"
+    },
+    "direct_physical_words/A": {
+      "binary_denominator_height": 2,
+      "old_real_scalar_units": 5600,
+      "prefix_row_one_norm": "69"
+    },
+    "direct_physical_words/AT": {
+      "binary_denominator_height": 2,
+      "old_real_scalar_units": 5600,
+      "prefix_row_one_norm": "14"
+    },
+    "late_query/A": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2960,
+      "prefix_row_one_norm": "70"
+    },
+    "late_query/AT": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 1984,
+      "prefix_row_one_norm": "30"
+    },
+    "late_query/S": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 1904,
+      "prefix_row_one_norm": "24"
+    }
+  },
+  "scope": "Exact completion algebra, actual transpose metric, scalar words and baseline queries. No native service or caller.",
+  "status": "PASS_INDEPENDENT_ROW_INVOLUTION",
+  "symmetric_determinant": "1",
+  "symmetric_displacement_rank": 32,
+  "trace": 80,
+  "unchanged_ordinary_rows": 96
+}
diff --git a/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/verified-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/verified-optimized/CHECKS.json
new file mode 100644
index 0000000000..e90c9de0ce
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/independent-review-20261017/row-involution-review-20261020/verified-optimized/CHECKS.json
@@ -0,0 +1,79 @@
+{
+  "arbitrary_input_fields": 640,
+  "determinant": "1",
+  "independent_helper_pin": "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89",
+  "modular_ranks": {
+    "large_mod5_rank": 40,
+    "small_mod7_rank": 56
+  },
+  "old_response_pin": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+  "ordinary_factor_rank": 16,
+  "pair_pin": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+  "producer_pins": {
+    "COMPLETION-LIMITS.md": "91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607",
+    "FREEZE.json": "538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2",
+    "LIMITS-FREEZE.json": "775c1b565ec0aa969f2dbecebb04f4b9a82a561e7e7d842c2b1abae7a75509a6",
+    "ROW-INVOLUTION.md": "c8470cc2280a057cbebf4a31ee679495990b200a6d6c033cc39e459eb2cf139f",
+    "check_completion_limits.py": "f07260347b3b5a955c475a25f87873dded309f9bd0bd1ad382c5a21c5acb16bb",
+    "check_row_involution.py": "a675e5578de4bc264524f7c1a75c5685a1967a65f7d3cd020fb0dc19352d31e9",
+    "limits-normal/CHECKS.json": "eb60b314a3cb6896c6afd33b8dc88d422f5ce12ac5ab73ce9a704950c6975276",
+    "limits-normal/COMPLETION-LIMITS.json": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa",
+    "run-normal/CHECKS.json": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6",
+    "run-normal/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "rank_A_minus_E": 16,
+  "rank_A_minus_I": 16,
+  "reports": {
+    "common_frame_words/A": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 3276,
+      "prefix_row_one_norm": "68"
+    },
+    "common_frame_words/AT": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 3276,
+      "prefix_row_one_norm": "18"
+    },
+    "common_frame_words/S": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2508,
+      "prefix_row_one_norm": "22"
+    },
+    "common_frame_words/S_inverse": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2508,
+      "prefix_row_one_norm": "28"
+    },
+    "direct_physical_words/A": {
+      "binary_denominator_height": 2,
+      "old_real_scalar_units": 5600,
+      "prefix_row_one_norm": "69"
+    },
+    "direct_physical_words/AT": {
+      "binary_denominator_height": 2,
+      "old_real_scalar_units": 5600,
+      "prefix_row_one_norm": "14"
+    },
+    "late_query/A": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2960,
+      "prefix_row_one_norm": "70"
+    },
+    "late_query/AT": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 1984,
+      "prefix_row_one_norm": "30"
+    },
+    "late_query/S": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 1904,
+      "prefix_row_one_norm": "24"
+    }
+  },
+  "scope": "Exact completion algebra, actual transpose metric, scalar words and baseline queries. No native service or caller.",
+  "status": "PASS_INDEPENDENT_ROW_INVOLUTION",
+  "symmetric_determinant": "1",
+  "symmetric_displacement_rank": 32,
+  "trace": 80,
+  "unchanged_ordinary_rows": 96
+}
diff --git a/research/native-centre-capture/frozen/lanes/interface-proof/verify_native_lift.py b/research/native-centre-capture/frozen/lanes/interface-proof/verify_native_lift.py
new file mode 100644
index 0000000000..fb72255b9c
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/interface-proof/verify_native_lift.py
@@ -0,0 +1,336 @@
+"""Check the exact native lift and the finite local bill.
+
+The checker does not import the emitter or the Clifford compiler. It uses
+Pauli conjugation and a separate exact state interpreter. The scalar map is
+owned by the independent transpose replay in the adjacent review lane.
+"""
+from collections import Counter
+from fractions import Fraction
+from functools import lru_cache
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import json
+import resource
+import subprocess
+import tarfile
+import time
+
+BASE = 'bce54fb3f895cbe5cd4c0eb477c3afeed100190f'
+ARCHIVE = 'research/community-frontier1042-audit/selected-replay.tar.gz'
+ARCHIVE_HASH = '22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754'
+PINS = {
+    'CANONICAL-WORD.json.gz': '16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219',
+    'LOCAL-PROGRAMS.json.gz': '241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a',
+    'CLIFFORD-RECIPES.json': 'd0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731',
+    'RESIDUAL-ADAPTERS.json': '383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c',
+}
+
+
+def require(condition, label):
+    if not condition:
+        raise ValueError(label)
+
+
+def load(repo):
+    args = ['git', 'show', BASE + ':' + ARCHIVE]
+    proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE)
+    digest = sha256()
+    while chunk := proc.stdout.read(65536):
+        digest.update(chunk)
+    require(proc.wait() == 0 and digest.hexdigest() == ARCHIVE_HASH, 'archive pin')
+    proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE)
+    values = {}
+    with tarfile.open(fileobj=proc.stdout, mode='r|gz') as archive:
+        for entry in archive:
+            name = entry.name.removeprefix('slots/local/')
+            if entry.name.startswith('slots/local/') and name in PINS:
+                raw = archive.extractfile(entry).read()
+                require(sha256(raw).hexdigest() == PINS[name], name + ' pin')
+                values[name] = json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw)
+    require(proc.wait() == 0 and set(values) == set(PINS), 'source extraction')
+    return values
+
+
+def parity(value):
+    return value.bit_count() % 2
+
+
+def mul(matrix, vector):
+    return sum(parity(row & vector) << i for i, row in enumerate(matrix))
+
+
+def transpose(matrix):
+    return tuple(sum(((row >> j) & 1) << i for i, row in enumerate(matrix)) for j in range(len(matrix)))
+
+
+def inverse(matrix):
+    n = len(matrix)
+    rows = [row | (1 << (n+i)) for i, row in enumerate(matrix)]
+    for j in range(n):
+        pivot = next((i for i in range(j, n) if rows[i] >> j & 1), None)
+        require(pivot is not None, 'singular binary chart')
+        rows[j], rows[pivot] = rows[pivot], rows[j]
+        for i in range(n):
+            if i != j and rows[i] >> j & 1:
+                rows[i] ^= rows[j]
+    require([row & ((1 << n)-1) for row in rows] == [1 << i for i in range(n)], 'binary inverse')
+    return tuple(row >> n for row in rows)
+
+
+def extend(vectors, n):
+    columns, pivots = [], {}
+    for value in tuple(vectors) + tuple(1 << i for i in range(n)):
+        reduced = value
+        while reduced:
+            j = reduced.bit_length()-1
+            if j not in pivots:
+                pivots[j] = reduced
+                columns.append(value)
+                break
+            reduced ^= pivots[j]
+    require(len(columns) == n, 'frame basis extension')
+    return tuple(columns)
+
+
+def adjoint(circuit):
+    out = []
+    for gate in reversed(circuit):
+        if gate[0] == 'P':
+            out.append(('P', inverse(gate[1])))
+        elif gate[0] == 'D':
+            out.append(('D', gate[1], tuple(-a % 4 for a in gate[2])))
+        elif gate[0] == 'C':
+            out.append(('C', gate[1], -gate[2]))
+        elif gate[0] == 'phase':
+            out.append(('phase', -gate[1] % 4))
+        else:
+            require(gate[0] == 'X', 'adjoint gate type')
+            out.append(gate)
+    return tuple(out)
+
+
+def fourier(rank):
+    return tuple(('C', 1 << i, 1) for i in range(rank))
+
+
+def frame(vectors, n):
+    rank = len(vectors)
+    if rank == 0:
+        return ()
+    if rank == n:
+        return fourier(n)
+    matrix = transpose(extend(vectors, n))
+    columns = transpose(inverse(matrix))
+    quadratic = tuple((1 << i) ^ sum(parity(a & b) << j for j, b in enumerate(columns)) for i, a in enumerate(columns))
+    diagonal = tuple((row >> i) & 1 for i, row in enumerate(quadratic))
+    chart = (('P', matrix), ('D', quadratic, diagonal))
+    return adjoint(chart) + fourier(rank) + chart
+
+
+def monomial(record):
+    matrix = tuple(record['matrix_rows'])
+    quadratic = tuple(record['quadratic_rows'])
+    linear = tuple(record['linear_Z4'])
+    require(transpose(quadratic) == quadratic, 'quadratic symmetry')
+    require(len(matrix) == len(quadratic) == len(linear) == 9, 'monomial dimension')
+    require(all(a % 2 == (quadratic[i] >> i) & 1 for i, a in enumerate(linear)), 'diagonal parity')
+    inverse(matrix)
+    return (('D', quadratic, linear), ('P', matrix), ('X', record['offset']), ('phase', record['phase']))
+
+
+def recipe(record):
+    rank = record['rank']
+    require(isinstance(rank, int) and 0 <= rank <= 9, 'child rank')
+    if rank == 0:
+        require(record['right'] is None, 'rank zero right factor')
+        return monomial(record['left'])
+    return monomial(record['right']) + fourier(rank) + monomial(record['left'])
+
+
+def tableau(circuit, n=9):
+    rows = [(1 << i, 0, 0) for i in range(n)] + [(0, 1 << i, 0) for i in range(n)]
+    for gate in circuit:
+        tag = gate[0]
+        out = []
+        inverse_transpose = transpose(inverse(gate[1])) if tag == 'P' else None
+        for x, z, phase in rows:
+            if tag == 'P':
+                x, z = mul(gate[1], x), mul(inverse_transpose, z)
+            elif tag == 'X':
+                phase += 2 * parity(z & gate[1])
+            elif tag == 'C':
+                if parity(z & gate[1]):
+                    x ^= gate[1]
+                    phase += 3 * gate[2]
+            elif tag == 'D':
+                quadratic, linear = gate[1:]
+                phase += sum(linear[i] for i in range(n) if x >> i & 1)
+                phase += 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(n) if x >> i & 1)
+                z ^= mul(quadratic, x)
+            else:
+                require(tag == 'phase', 'tableau gate type')
+            out.append((x, z, phase % 4))
+        rows = out
+    return tuple(rows)
+
+
+@lru_cache(maxsize=512)
+def action(gate):
+    if gate[0] == 'P':
+        return tuple(mul(gate[1], x) for x in range(512))
+    require(gate[0] == 'D', 'state action type')
+    quadratic, linear = gate[1:]
+    return tuple((sum(linear[i] for i in range(9) if x >> i & 1)
+                  + 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(9) if x >> i & 1)) % 4 for x in range(512))
+
+
+def rotate(pair, power):
+    a, b = pair
+    return ((a, b), (-b, a), (-a, -b), (b, -a))[power % 4]
+
+
+def state(circuit, basis=0):
+    value = [(0, 0)] * 512
+    value[basis] = (1, 0)
+    denominator = 0
+    for gate in circuit:
+        tag = gate[0]
+        if tag == 'P':
+            moved = [(0, 0)] * 512
+            for source, target in enumerate(action(gate)):
+                moved[target] = value[source]
+            value = moved
+        elif tag == 'X':
+            value = [value[x ^ gate[1]] for x in range(512)]
+        elif tag == 'D':
+            value = [rotate(pair, p) for pair, p in zip(value, action(gate))]
+        elif tag == 'phase':
+            value = [rotate(pair, gate[1]) for pair in value]
+        elif tag == 'C':
+            direction, sign = gate[1:]
+            moved = []
+            for x, (a, b) in enumerate(value):
+                c, d = value[x ^ direction]
+                moved.append((a-sign*b+c+sign*d, b+sign*a+d-sign*c))
+            value = moved
+            denominator += 1
+        else:
+            raise ValueError('state gate type')
+        while denominator and all((a | b) % 2 == 0 for a, b in value):
+            value = [(a//2, b//2) for a, b in value]
+            denominator -= 1
+    return value, denominator
+
+
+def equal(actual, expected, label):
+    require(tableau(actual) == tableau(expected), label + ': Pauli action')
+    require(state(actual) == state(expected), label + ': global phase')
+
+
+def scalar_cost(gate):
+    if gate[0] in ('copy', 'clear'):
+        return 1
+    value = Fraction(*gate[-2:])
+    numerator, denominator = abs(value.numerator), value.denominator
+    require(numerator > 0 and denominator & (denominator-1) == 0, 'nonzero dyadic scalar')
+    if gate[0] == 'scale':
+        require(numerator & (numerator-1) == 0, 'dyadic scale unit')
+        return abs(numerator.bit_length()-denominator.bit_length()) + (value < 0)
+    require(gate[0] == 'add', 'scalar type')
+    return 3 + numerator.bit_length()-1 + numerator.bit_count() + denominator.bit_length()-1
+
+
+def main(args):
+    start = time.monotonic()
+    data = load(args.repo)
+    word = data['CANONICAL-WORD.json.gz']
+    old = data['LOCAL-PROGRAMS.json.gz']
+    phase = data['CLIFFORD-RECIPES.json']
+    residual = data['RESIDUAL-ADAPTERS.json']['recipes']
+    changed_raw = gzip.decompress(args.changed.read_bytes())
+    require(sha256(changed_raw).hexdigest() == 'fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877', 'changed payload pin')
+    changed = json.loads(changed_raw)
+    require(set(changed) == {'forward', 'backward'}, 'orientation inventory')
+    native = lambda events: [e for e in events if e[0] in ('climb', 'adapter', 'residual_adapter')]
+    invoices = {}
+    for name, events in changed.items():
+        require(native(events) == native(old[name]), 'persistent native stream')
+        require(all(e[0] in ('scalar', 'phase', 'climb', 'adapter', 'residual_adapter') for e in events), 'event grammar')
+        first = events.index(['phase', 'centre_dirty_correction'])
+        last = events.index(['phase', 'A'])
+        prefix = [e[1] for e in events[first+1:last]]
+        require(all(e[0] == 'scalar' and e[2] == 0 for e in events[first+1:last]), 'correction frame')
+        scalars = [e[1] for e in events if e[0] == 'scalar']
+        paid = Counter(e[5] for e in events if e[0] == 'climb')
+        invoices[name] = {
+            'events': len(events), 'scalar_macros': len(scalars),
+            'real_component_primitive_bound': 2*sum(map(scalar_cost, scalars)),
+            'prefix_macros': dict(Counter(e[0] for e in prefix)),
+            'prefix_real_component_primitive_bound': 2*sum(map(scalar_cost, prefix)),
+            'paid_profile': dict(sorted(paid.items())),
+            'paid_rank_sum': sum(rank*count for rank, count in paid.items()),
+            'persistent_native_events': len(native(events)),
+        }
+    used = {(e[3], e[4]) for e in changed['forward'] if e[0] == 'climb'}
+    children = {(r['old'], r['new']): r for r in phase['children']}
+    require(len(children) == len(phase['children']) and used <= set(children), 'child recipe binding')
+    frames = [frame(tuple(vectors), 9) for vectors in word['frames']]
+    for i, (a, b) in enumerate(sorted(used)):
+        record = children[a, b]
+        require(record['rank'] == len(word['frames'][b])-len(word['frames'][a]), 'paid frame difference')
+        equal(recipe(record), adjoint(frames[a])+frames[b], 'child '+str((a, b)))
+        if i % 500 == 0:
+            print('phase edges', i, '/', len(used), flush=True)
+    endpoints = {(r['role'], r['port']): r for r in phase['endpoint_adapters']}
+    require(set(endpoints) == {(role, p) for role in ('source', 'target') for p in range(112)}, 'endpoint coverage')
+    for (role, port), record in endpoints.items():
+        q = word['ports'][port]
+        conventional = (('C', q, 1),) if role == 'source' else (('C', q, -1),)+fourier(9)
+        expected_frame = word['start'][port] if role == 'source' else word['final'][112+port]
+        require(record['frame'] == expected_frame and record['rank'] == 0, 'endpoint frame binding')
+        equal(recipe(record), adjoint(conventional)+frames[expected_frame], 'endpoint '+str((role, port)))
+    used_residual = set()
+    for event in changed['forward']:
+        if event[0] == 'residual_adapter':
+            _, position, register, entry, *tail = event
+            terminal = tail[0] if tail else 1
+            key = str(entry) if terminal == 1 else str(entry)+':'+str(terminal)
+            require(key in residual and position in ('pre', 'post'), 'residual binding')
+            require(entry == word['start'][register] and terminal == word['final'][register], 'residual boundary')
+            used_residual.add(key)
+    for key in sorted(used_residual):
+        record = residual[key]
+        entry = record['frame']
+        terminal = record.get('terminal', 1)
+        equal(recipe(record), adjoint(frames[entry])+frames[terminal], 'residual '+key)
+    probe = next(r for r in children.values() if r['left']['phase'] != 0 or r['right'] and r['right']['phase'] != 0)
+    correct = recipe(probe)
+    corrupt = tuple(gate for gate in correct if gate[0] != 'phase')
+    if state(corrupt) == state(correct):
+        corrupt = correct+(('phase', 1),)
+    require(tableau(corrupt) == tableau(correct) and state(corrupt) != state(correct), 'global phase negative control')
+    require(state(corrupt, 1) != state(correct, 1), 'phase control second input')
+    report = {
+        'status': 'PASS_INDEPENDENT_NATIVE_FRAME_LIFT_AND_FINITE_LOCAL_BILL',
+        'base': BASE, 'archive_sha256': ARCHIVE_HASH, 'member_sha256': PINS,
+        'changed_payload_sha256': sha256(changed_raw).hexdigest(),
+        'checked_unique_persistent_edges': len(used), 'checked_endpoint_adapters': len(endpoints),
+        'checked_residual_recipes': len(used_residual), 'finite_local_invoice': invoices,
+        'exact_operator_method': 'Pauli conjugation and exact Gaussian dyadic zero state; no compiler import',
+        'negative_controls': ['wrong global phase with the same Pauli action, on basis inputs 0 and 1'],
+        'all_tensor_powers': 'Base operators are exactly equal, so their tensor powers are equal for every positive integer. The common frame conjugation proof gives the full array map.',
+        'not_claimed': ['global chart or owner admission', 'recursive supplier admission', 'new kappa', 'fresh all-size compiler proof'],
+        'seconds': time.monotonic()-start, 'max_rss_bytes': resource.getrusage(resource.RUSAGE_SELF).ru_maxrss,
+    }
+    args.out.write_text(json.dumps(report, indent=2, sort_keys=True)+'\n')
+    print(report['status'], flush=True)
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--repo', type=Path, required=True)
+    parser.add_argument('--changed', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    main(parser.parse_args())
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz
new file mode 100644
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS-FREEZE.json
new file mode 100644
index 0000000000..e8cf8b08f3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS-FREEZE.json
@@ -0,0 +1,13 @@
+{
+  "files": {
+    "CODED-EXITS.md": "1860726ae7a210bc7ed8c4afc93cdf251bad8a7d90fd8b353157752434c2c4c8",
+    "EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689",
+    "NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24",
+    "coded-normal/CODED-EXITS-CHECKS.json": "b36bee542add54bac48e409c6a4a054b3bca5fba9c98d5513a90a6a92628d576",
+    "coded-normal/CODED-EXITS-PROGRAM.json.gz": "aad4decc178d7b9ac19ef4b97d3b77d56854c26714f063e1ff6fa762cf2b6b08",
+    "emit_coded_exits.py": "3d6c9283a2217306bae8f998891439e5cff435a7b3d7575c9481c115f411a282"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Exact changed output contracts; independent review and complete supplier duties remain separate.",
+  "status": "PASS_CHANGED_NATIVE_EXITS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS.md
new file mode 100644
index 0000000000..7ea08ea65b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS.md
@@ -0,0 +1,115 @@
+# Exact output codes for both low-displacement responses
+
+The native exits of both new responses admit the previous common
+left output code W. The uniform output code no longer requires
+rank-nine children. For the rank-sixteen response, its maximum child
+rank is three. This is a local representation result. It does not
+remove W or prove a complete supplier.
+
+Let
+
+```text
+W = S_e0 C_45 S_e0
+```
+
+be the literal circuit in the pinned isotropic-pair-gauge packet.
+The new emitter uses the frozen exit compiler and its exact physical
+phase checks. It applies that compiler to the new words' actual
+ordered source bases.
+
+Two output representations are emitted:
+
+* W48_I64 applies W to both data banks on the 48 paired ports.
+* W112 applies W to both data banks on all 112 data ports.
+
+At a coded port p, the exact physical output is
+
+```text
+X_p = W F9 x'_p,
+Y_p = W F9 Q_p^-1 y'_p.
+```
+
+At an uncoded port, omit the initial W. The input convention remains
+X=Qx, Y=y. The response itself does not change. In particular, there
+is no commutation of W with Q and no free re-interpretation as a raw
+endpoint.
+
+## Actual exit replacement
+
+For each coded source with last canonical frame Gamma_U, the final
+edge is the exact operator W F9 Gamma_U^-1. All such sources share
+the same W F9 frame. The inverse physical pair code remains legal.
+
+For each coded target with last frame Gamma_V, the new intrinsic
+exit is W F9 Q_p^-1 Gamma_V^-1. The old external target adapter is
+removed. A rank-zero intrinsic exit is an explicit monomial event;
+it is not omitted.
+
+The new six-mode paths reach rank six before the source exit.
+The exact coded source exit has rank two, in place of rank three.
+The 48 pair-mode target exits become monomial. These calculations
+use the actual source bases and phase maps; the result is not
+inferred from a mass subtraction.
+
+The small-clique exits depend on the clique size. In the
+rank-sixteen word they start from rank-seven flags. Under the
+uniform W output, the source exits have rank three and the target
+exits rank two. The earlier matching word started its small sources
+on lines and required rank-nine exits under the same W output.
+The new flags therefore resolve that specific native-rank issue.
+Recursive hosting remains a separate obligation.
+
+## Complete local invoices
+
+Every row below applies to both providers and both directions.
+The scalar operation sequence is unchanged.
+
+| Response and output code | Native profile | Children | Mass | Real scalar primitives |
+| --- | --- | ---: | ---: | ---: |
+| Rank30, W48_I64 | 988 H1 + 48 H2 + 55 H4 + 55 H5 + 9 H6 + 9 H7 | 1164 | 1696 | 5288 |
+| Rank30, W112 | 988 H1 + 48 H2 + 55 H5 + 55 H6 + 9 H7 + 9 H8 | 1164 | 1824 | 5288 |
+| Rank16, W48_I64 | 1472 H1 + 112 H2 | 1584 | 1696 | 7384 |
+| Rank16, W112 | 1408 H1 + 112 H2 + 64 H3 | 1584 | 1824 | 7384 |
+
+Each word has 48 inline monomial exits. W48_I64 retains 176 external
+endpoint adapters; W112 retains 112. There are at most two side maps
+per native child, in addition to the listed inline monomial and
+external endpoint maps. These maps are not claimed to be free.
+
+All 640 input columns remain independent. The 416 other fields keep
+their original values and frames. There is no owned or private
+workspace. The forward and backward scalar prefix bounds remain
+46 and 30 for rank thirty, and 22 in both directions for rank sixteen.
+
+## Verification and use
+
+The source event schema is converted exactly to the frozen exit
+compiler's rational scalar schema. The converted raw word is
+replayed before any exit changes. Each output word is then checked
+on all 640 columns, including every equal-frame scalar access and
+every exact native or monomial source frame. The serialized packet
+is read back and replayed again.
+
+Every changed physical exit receives a fresh compiler lowering and
+an independent Pauli and exact Gaussian-state comparison. The old
+native phases remain pinned. The source pair-code metadata comes
+from the exact cyclic-family payload.
+
+Run emit_coded_exits.py with --out naming a new directory. Repeat
+with optimized Python and a different new output directory. The
+expected status is PASS_LOW_DISPLACEMENT_CODED_EXITS. Both payloads
+and receipts must be byte-identical.
+
+The W48_I64 mass saving is useful only if the caller can consume the
+mixed representation. The uniform W112 representation has a larger
+mass but a uniform exterior code. Neither word proves a free stage
+transition, a free terminal inverse, helper progress, or the final
+recursive cost. The complete controller must retain the stated
+ordered physical outputs.
+
+The coherent-port and root lanes supplied W. The oblique-native
+lane supplied the exact exit compiler and its previous matching
+application. This packet binds that construction to the new cyclic
+paths and proves the resulting profiles. AI assistance was used.
+No PR or publication is authorized. Before any future description,
+read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json
new file mode 100644
index 0000000000..61c4e93cc1
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "EXTENSIONS.md": "2328ec60c1cf89efe7661b3696839f8eb32a95e11c67a62dd653781a8b0ed5fb",
+    "NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24",
+    "emit_followthrough.py": "b03568530696ab810070ba3243b59dd74740fb634fe7f26b2cbdb1d3283d045f",
+    "odd16-normal-v2/EXTENSION-CHECKS.json": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197",
+    "odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b",
+    "reciprocal-normal-v2/EXTENSION-CHECKS.json": "cfea59ca775a7350c2e9bcded1c52f2f19df12465f6d8736fd2a907599839adc",
+    "reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz": "825f27e5b3705dace14c75ae53aa21ea94b9dc69284bbdbd3377591fbcce7439"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Independent native review, odd-grid admission and the global supplier remain separate.",
+  "status": "PASS_RECIPROCAL_LARGE_AND_ODD_GRID_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md
new file mode 100644
index 0000000000..af1bd759d0
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md
@@ -0,0 +1,190 @@
+# Reciprocal and odd-grid extensions
+
+These are two separate extensions of the frozen native paths.
+The first realizes the reciprocal response on the 48 paired ports.
+The second lowers the full correction rank from thirty to sixteen
+by permitting odd denominators in later scalar inverse codes.
+The original rank-thirty packets remain unchanged.
+
+## A native reciprocal response on the large sector
+
+Replace the six-mode matrix B by B^-T on the 48 paired ports.
+Both matrices have zero diagonal, so every new nonzero coefficient
+has its own existing cyclic transfer event. Keep the small
+fourteen-clique response C.
+
+The new complete response is
+
+```text
+A = E48^-T direct_sum C.
+```
+
+The raw backward native call therefore gives
+
+```text
+x <- x - (E48^-1 direct_sum C) y.
+```
+
+This proves native reciprocal access on the large sector. It does
+not prove a reciprocal response on all 112 ports, because C^-1 has
+nonzero diagonal and is not emitted by the small-clique paths.
+
+Every native frame, edge, recipe, and endpoint adapter is identical
+to the frozen rank-thirty path. Only scalar coefficients and their
+nonzero event positions change. The full response, its inverse, all
+640 input columns in both directions, and all four common-frame
+scalar codes are checked. Every scalar code costs 3210. The native
+invoice remains 5288 real scalar primitives and
+
+```text
+1036 H1 + 48 H3 + 55 H4 + 55 H5 + 9 H6 + 9 H7.
+```
+
+The original selected block L and the ordinary principal unit are
+preserved. The forward prefix row one-norm is 30; the backward
+bound is 46. The proof uses the 1141 frozen native phase records
+and 224 frozen endpoint records, with exact binary-frame matching.
+
+## Sixteen correction coordinates with odd-grid inverses
+
+The actual small-port orthogonality graph has a disjoint partition
+into eight eight-cliques. The literal partition is in the payload.
+The checker verifies every pairwise orthogonality equation and the
+complete disjoint cover.
+
+At each large vertex use
+
+```text
+B_v = I6-d_v d_v^T,
+B_v^-1 = I6-d_v d_v^T/5,
+```
+
+where d_v is the same sign vector used for the selected-compatible
+rank-two block. Conjugate by the actual physical pair code H.
+The physical large response has eight correction coordinates.
+Equivalently, let K contain the eight signed twelve-port rows
+d_v^T H. Then
+
+```text
+K K^T = 12 I8,
+E48 = I48-K^T K/2,
+E48^-1 = I48-K^T K/10.
+```
+
+On each small eight-clique use
+
+```text
+C8 = I8-J8,
+C8^-1 = I8-J8/7.
+```
+
+Each clique contributes one correction coordinate. The full
+response E is symmetric, has determinant 35^8, and satisfies
+rank(E-I)=16. The payload contains exact factors U,V with
+E-I=UV and ranks sixteen. Both full inverse products are checked.
+
+The selected block of E remains the previous L. However, the
+selected block of E^-1 is (4I+L)/5. Therefore
+
+```text
+det(E_U,U) = 7^8 * 31^4 / 16,
+((E^-1)_S,S)^-1 = 10(4I-L)/31.
+```
+
+The payload includes the new ordinary inverse and checks both of
+its 104-column inverse products. This exposes the factor 31 needed
+by the selected ordinary normalization. A controller with no
+selected split can avoid that additional principal-inverse
+requirement. It still needs its own complete code and terminal
+construction.
+
+The inverse coefficients 1/5 and 1/7 are not ordinary dyadic unit
+scales. Their exact implementation needs the retained odd-grid
+contract, conversion of all relevant root streams including
+borrowed streams, a bound on odd denominator height, complete
+native-child endpoint closure, and exact final conversion. Those
+obligations belong to the separate odd-grid packet. This native
+packet neither prices those divisions as free nor assumes them to
+be forbidden.
+
+## Literal native implementation and invoice
+
+All native transfer coefficients in the rank-sixteen word are signed
+integers of absolute value one. The large sector uses the frozen
+six-mode cyclic paths, with all 240 off-diagonal coefficients.
+Its pair-code cost is 1880 and its transfer cost is 1920.
+
+For each eight-clique, use the same cyclic line-flag construction as
+in NATIVE.md, now with depths one through seven. The source and
+target flags are equal at each transfer and remain nested. A source
+finishes with rank two after its rank-seven flag. A target finishes
+with rank one in its own rank-eight hole.
+
+Each small port contributes fourteen H1 children and one H2 child.
+The complete local word has the following invoice in either
+direction:
+
+| Quantity | Count |
+| --- | ---: |
+| Rank-one children | 1520 |
+| Rank-two children | 64 |
+| Rank-three children | 48 |
+| All native children | 1632 |
+| Native mass | 1792 |
+| Real scalar primitives | 7384 |
+| Endpoint adapters | 224 |
+| Native side-map upper bound | 3264 |
+
+The small transfer cost is 448 unit ADDs, or 3584 real primitives.
+The complete scalar count is 1880+1920+3584=7384. This is the
+native word's scalar count only.
+
+The phase table contains 685 entries inherited by exact frame-pair
+identity and 876 new entries. Each new entry is compiled and checked
+with the independent Pauli and exact Gaussian-state interpreter.
+The 224 endpoint adapters are unchanged. Both providers have the
+same actual data directions and receive the complete checked word.
+
+Every output is replayed on all 640 independent input columns.
+The 416 other fields remain arbitrary and unchanged. No owned or
+private field is used. The complete prefix row one-norm is at most
+22 in either direction. Every native child still has a Gaussian
+dyadic endpoint. This last statement does not replace the global
+odd-grid precision proof.
+
+The exact physical conventions remain X=Qx at entry and
+(F9 x', F9 Q^-1 y') at exit. No changed-exit W48/I64 histogram is
+claimed in this packet. No source response is moved through Q.
+
+## Reproduction and scope
+
+Run emit_followthrough.py with --kind reciprocal-large or
+--kind odd-grid-rank16, and --out naming a new directory. Repeat
+with optimized Python and a different new directory. The expected
+statuses are PASS_RECIPROCAL_LARGE and PASS_ODD_GRID_RANK16.
+The final v2 outputs must be byte-identical between the two modes.
+
+The earlier extension directories are retained as drafts. Their
+scalar/native maps passed, but their copied matrix metadata included
+an old ordinary inverse. The final emitter constructs a new model
+from only valid shared geometry, computes the new inverse, and
+checks both inverse products. Only the v2 outputs are frozen.
+
+The rank-sixteen extension changes the allowed representation. It
+does not contradict a dyadic-only obstruction. Its native child
+distribution also differs from the rank-thirty and matching words;
+mass alone is not a recursive price comparison.
+
+The generic current-cut controller still leaves the ordered code
+E2 E1^-T E0 and the physical conjugation Q(...)Q^-1. Native local
+correctness does not supply access to that code's queries or
+scatters. Helper progress, recursive hosting, the complete precision
+bound, terminal removal, and the final supplier bound remain open.
+
+The root identified odd-grid admission as the relevant escape. The
+native-escape lane is responsible for that contract. The root's
+reciprocal matrix, the independent-review cyclic flag family, and
+the earlier pair-code and common-frame scalar constructions are
+the other predecessors. AI assistance was used. No publication is
+authorized. Before any future PR description, read
+/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json
new file mode 100644
index 0000000000..26466669a7
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json
@@ -0,0 +1,12 @@
+{
+  "files": {
+    "NATIVE.md": "6c6d0cd1d93f270f16765183b8512a81a533b0bb5a2712506d677e27bbfa74d5",
+    "RESPONSE-FREEZE.json": "59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9",
+    "emit_native.py": "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745",
+    "native-normal-v2/NATIVE-CHECKS.json": "8acc084b5cd1d9513fdd3373eede998bd08e7f3fe1624f9fd41f758d4de7cb82",
+    "native-normal-v2/NATIVE-PROGRAM.json.gz": "aca3b3364b73e3c2115ede3082088e7566d789273711031381e44406c0ae793c"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Independent producer review and global supplier duties remain separate.",
+  "status": "PASS_NATIVE_DATA_RESPONSE_AND_PHASES"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE.md
new file mode 100644
index 0000000000..f547931fc9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE.md
@@ -0,0 +1,149 @@
+# Native realization of the rank-thirty response
+
+The literal native word implements the full response E from
+RESPONSE.md in both directions:
+
+```text
+F(x,y,h) = (x, y+E x, h),
+B(x,y,h) = (x-E^T y, y, h).
+```
+
+The physical input convention is X=Qx and Y=y. The physical output
+convention is X=F9 x' and Y=F9 Q^-1 y'. All 640 input columns are
+independent. The 416 fields outside the two data banks remain
+unchanged. No owned field or private field is used. This is a local
+data service; it does not supply productive progress for those other
+fields.
+
+The exact local invoice, in either direction, is
+
+| Quantity | Count |
+| --- | ---: |
+| Rank-one children | 1036 |
+| Rank-three children | 48 |
+| Rank-four children | 55 |
+| Rank-five children | 55 |
+| Rank-six children | 9 |
+| Rank-seven children | 9 |
+| All native children | 1212 |
+| Native mass | 1792 |
+| Real scalar primitives | 5288 |
+| Endpoint adapters | 224 |
+| Native side-map upper bound | 2424 |
+
+The implementation checks 1141 distinct native edges and 224 endpoint
+adapters with the independent Pauli and exact Gaussian-state
+interpreter. These checks include global phase. They are separate
+from the scalar-column replay.
+
+## The large 48-port word
+
+The pinned cyclic family supplies the exact paths and the
+parameterized scalar events. At each of eight vertices there are six
+pair-mode carriers. For every ordered pair of distinct modes, one
+source flag and one target flag have the same actual binary frame.
+The corresponding coefficient of the signed rank-two block is
+substituted at that event. A zero coefficient omits that ADD only;
+the fixed native path is retained.
+
+The source and target pair codes use the exact pinned short factors.
+The source pair code is applied after the two source lines reach
+their pair plane. The target code is applied while both targets are
+at I. The inverse source code is applied at FULL. The inverse target
+code is applied at the common pair-perpendicular frame, before the
+two targets reach their individual holes.
+
+There are 176 nonzero mode coefficients. Of these, 136 are signed
+units, 32 have absolute value two, and eight have absolute value
+three. Their real ADD cost is 1504. The pair codes and inverse codes
+cost 1880 across both data banks. The large-sector scalar cost is
+therefore 3384. Its native profile is 624 H1 + 48 H3.
+
+In the backward word, each source carrier receives the negative
+coefficient times the corresponding target carrier. Since the pair
+code H obeys H H^T=2I, removal of both codes gives the exact negative
+transpose -E^T. No scalar response is moved through Q.
+
+## The 64-port clique word
+
+For each clique q0,...,q(k-1), the labels are orthonormal over F2.
+At depth d=1,...,k-1, advance source i to
+
+```text
+S_i(d) = span(q_i,...,q_(i+d-1))
+```
+
+and target j to
+
+```text
+T_j(d) = span(q_(j-d),...,q_(j-1)).
+```
+
+Indices are cyclic. Then S_i(d)=T_(i+d)(d). Apply the signed unit
+coefficient of I-J_k at this common frame. Every off-diagonal ordered
+pair occurs exactly once.
+
+Each source starts at its own line. Each target starts at I. After
+the last transfer, advance each source to FULL and each target to
+its own hole. Every target flag excludes its own q label and is
+contained in that hole. Thus every native edge is nested, with
+positive rank. No frame change on nonzero data is free.
+
+For a five-clique, each port contributes seven H1 children, one H4,
+and one H5. For a three-clique, each port contributes three H1, one
+H6, and one H7. The eleven five-cliques and three three-cliques give
+
+```text
+412 H1 + 55 H4 + 55 H5 + 9 H6 + 9 H7.
+```
+
+There are 238 signed unit ADDs, with real scalar cost 1904.
+
+## Phase and complete replay
+
+The frame table is in canonical binary row form. For each native
+edge old -> new, the compiler lowers the exact operator
+Gamma_new Gamma_old^-1. A separate interpreter checks all Pauli
+images and one exact Gaussian-state column. Together these checks
+determine the complete Clifford operator and its global phase.
+The child rank is independently checked against the frame-dimension
+difference.
+
+For each physical source line Q_p and each target convention
+F9 Q_p^-1, an explicit rank-zero adapter relates the convention to
+the canonical endpoint frame. All 224 adapters receive the same
+independent exact phase check. Both pinned providers have the same
+data directions. The new word is consequently the same for both;
+the checker verifies that premise from each provider.
+
+The serialized words are read back and replayed on all 640 input
+columns. Every scalar ADD has exactly equal source and target
+frames. Every native edge has the declared entry frame and a
+nested exit. Every final data frame and every untouched field is
+checked. Deletion of one nonzero transfer is rejected.
+
+The maximum top-level prefix row one-norm is 46 forward and 30
+backward. This does not bound the internal state of recursive
+children. The complete recursive precision and host invoice remain
+separate.
+
+Run emit_native.py with --out and a new directory. Repeat with
+optimized Python and a different new directory. The expected status
+is PASS_LOW_DISPLACEMENT_NATIVE. Both payloads and receipts must be
+byte-identical. The empty first-attempt directory is retained. That
+attempt stopped before phase compilation because its temporary
+binary-basis routine did not produce a unique row form. The final
+emitter uses complete binary row reduction and checks every common
+frame explicitly.
+
+The response remains asymmetric on the 48-port sector. This packet
+emits the raw backward transpose. It does not emit the full inverse
+as a native response: the small clique inverse has nonzero diagonal.
+The general-unit controller can use the explicit common-frame
+inverse codes, subject to its own routed access and terminal duties.
+
+The root reciprocal response, the independent-review cyclic flags,
+the controller's pair geometry, and the oblique-native phase
+construction are the predecessors. AI assistance was used. This
+packet does not change the selected frontier or claim a complete
+kappa improvement. No publication is authorized.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE-FREEZE.json
new file mode 100644
index 0000000000..f3cd7e48e4
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE-FREEZE.json
@@ -0,0 +1,11 @@
+{
+  "files": {
+    "RESPONSE.md": "5ea5866231992c389ae2796f1534e0af90ca88bcedfa3fa9758d78f9457d2981",
+    "check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8",
+    "run-normal/RESPONSE-CHECKS.json": "7f84440d79200b8c060aad07b910bb96f2bcdde95b07ddb8d41bcea1fcb09d5c",
+    "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Native phase and routed terminal review remain open.",
+  "status": "PASS_EXACT_RESPONSE_AND_SCALAR_CODES"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md
new file mode 100644
index 0000000000..0ee7aebbb6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md
@@ -0,0 +1,165 @@
+# A rank-thirty correction on the actual 112 ports
+
+This packet gives an exact unit response E on the actual 112 data ports.
+It has rank(E-I)=30. The previous signed matching has correction rank
+56. The new response keeps the useful selected eight-port principal
+block L. Both E and E^-1 have selected block L. The ordinary principal
+block is also a dyadic unit.
+
+The packet also gives complete in-place scalar words for E, E^-1, E^T,
+and E^-T. Each word costs 3210 real scalar primitives at a common
+frame. It uses no owned or borrowed field. These are port-code and
+matrix results. Native phase lowering, routed access, the physical
+terminal, helper progress, and the complete supplier cost are separate.
+
+## The 48-port reciprocal part
+
+The signed pair code H comes from the pinned cyclic family. Its 24
+two-field blocks satisfy H H^T=2I. The six coded fields at each of
+eight vertices have their actual carrier labels in the payload.
+
+Use the root's reciprocal six-mode matrix. Write a=(a0,a1,a2,a3),
+s=sum(a), and define
+
+```text
+E6(a,b,c)    = (a-s*1+b*1, c, -2s+3b),
+E6^-1(a,b,c) = (a-s*1+c*1, -2s+3c, b).
+```
+
+Both matrices are integer units with determinant one and zero
+diagonal. Their correction rank is two. The root proof establishes
+the general construction and the sharp rank-two lower bound.
+
+At each vertex, put its two modes that meet the selected physical
+ports in the first two a positions. Fill the other four positions in
+the source order. Conjugate the block by the sign diagonal
+
+```text
+D_v = diag(1, alpha_v, 1, 1, 1, 1),
+alpha_v = (-1)^v.
+```
+
+The two selected-mode off-diagonal entries of both D_v E6 D_v and
+D_v E6^-1 D_v are -alpha_v. All their diagonal entries are zero.
+Consequently the physical selected block is exactly the old L after
+the pair code is removed. The full physical 48-port response is
+H^-1 (direct_sum_v D_v E6 D_v) H. It has determinant one and
+correction rank sixteen. Its inverse is explicitly given by the same
+formula with E6^-1.
+
+This assignment is significant for the existing selected interface:
+L^2=I/2 and det(L)=1/16 remain valid. It is not an arbitrary rank-two
+block that loses the selected principal unit.
+
+The mode word uses E6=P R, where P exchanges b and c. The reflection
+R is implemented without a scratch field. With d_i the four a signs,
+execute
+
+```text
+b -= sum_i d_i a_i
+a_i += d_i b                 for each i
+b *= -1
+b += sum_i d_i a_i
+exchange b,c
+```
+
+The exchange is four priced scalar instructions: three unit ADDs and
+one negative unit scale. Thus each six-mode word costs 124. The eight
+words cost 992. The physical pair code and its inverse cost 940 on
+one bank. This gives 1932 for the complete 48-port scalar code.
+
+The reflection factor alone has nonzero diagonal. Its scalar code
+does not prove that it can be used as a free native transfer.
+
+## A fourteen-block cover of the other 64 ports
+
+The exact orthogonality graph joins ports p,r when q_p dot q_r=0.
+All 64 q labels have odd norm. Exhaustive maximal-clique enumeration
+finds 896 maximal cliques of size four and 64 of size eight. In
+particular, this fixed support has no nine-clique.
+
+The payload gives a disjoint cover by eleven five-cliques and three
+three-cliques. On a clique of size k use
+
+```text
+C_k = I-J_k,       C_k^-1 = I-J_k/(k-1).
+```
+
+Here J_k is the all-ones matrix. Each C_k is a dyadic unit, has zero
+diagonal, and differs from identity by rank one. Thus the 64-port
+part has correction rank fourteen and determinant 2^25.
+
+Fourteen is optimal within disjoint dyadic rank-one clique blocks of
+sizes two, three, and five. A cover with at most twelve blocks covers
+at most sixty ports. Thirteen five-blocks cover sixty-five ports, and
+replacing a size five by size three or two decreases this number by
+two or three, never by one. The graph has no size nine block. This is
+a lower bound for this stated clique model, not a lower bound for all
+native constructions or terminal decoders.
+
+An in-place word for C_k is
+
+```text
+a += sum(rest)
+b -= a                       for each remaining field b
+a *= -(k-1)
+a -= sum(rest)
+```
+
+The word uses 3(k-1) unit ADDs and one dyadic scale. Its cost is 102
+when k=5 and 52 when k=3. The complete small code costs
+11*102+3*52=1278. Reverse the word and invert its instructions to
+obtain the inverse. The inverse has nonzero diagonal and is not
+claimed to belong to the direct native zero-diagonal family.
+
+## Complete code and principal inverse
+
+Combine the two disjoint responses. The resulting E has determinant
+2^25 and correction rank thirty. The payload gives exact matrices U,V
+with 30 columns and rows, respectively, such that E-I=UV. Both U and
+V have rank thirty.
+
+Let S be the old selected eight ports and U0 its complement. Partition
+E^-1 as [[L,N],[P,Q]]. Then
+
+```text
+(E_U0,U0)^-1 = Q-P L^-1 N.
+```
+
+Both multiplication orders are checked on all 104 ordinary columns.
+Every inverse coefficient is dyadic. The ordinary determinant is
+2^21. The selected determinant is 1/16.
+
+The combined scalar word costs 1932+1278=3210. Its reverse gives
+E^-1. Reverse the instruction order and transpose each elementary
+operation to give E^T; apply both operations to give E^-T. Every word
+is checked on all 112 columns. The maximum prefix row one-norm is
+44 for E and E^-1, and 14 for E^T and E^-T. These are bounds for the
+top-level scalar word only.
+
+The generic five-code controller can use a native forward response
+E and raw backward response E^T, provided each common-frame code is
+legally bound at its stated cut. Its residual is still the ordered
+operator E2 E1^-T E0. The physical terminal sees
+Q(E2 E1^-T E0)Q^-1. Rank thirty in one local chart does not provide
+free access to those correction coordinates in a routed hole frame.
+
+## Reproduction and credit
+
+The checker requires a new output directory and preserves all source
+packets. Run it once with ordinary Python and once with optimized
+Python, with different output directories. The expected status is
+PASS_LOW_DISPLACEMENT_RESPONSE. The two payloads and receipts must
+be byte-identical.
+
+The root supplied the reciprocal rank-two matrix and its proof. The
+independent-review lane supplied the complete cyclic zero-diagonal
+family. The controller and oblique-native lanes supplied the actual
+signed pair coordinates and the selected matching interface. The
+encoded-controller lane supplied the legal-cut general-unit
+controller and the three-field I-J code. This packet binds the
+selected principal units, gives the actual fourteen-clique cover,
+and extends the scalar code to five fields. AI assistance was used.
+
+No PR or publication is authorized. Before any future PR description,
+read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py
new file mode 100644
index 0000000000..17a70cda41
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py
@@ -0,0 +1,339 @@
+#!/usr/bin/env python3
+"""Bind the rank-two response and the small clique cover to actual ports."""
+
+import argparse
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+PINS = {
+    "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json":
+        "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json":
+        "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902",
+}
+CLIQUES = [
+    [5, 34, 40, 85, 97], [3, 32, 38, 50, 95], [24, 48, 67, 80, 82],
+    [23, 35, 55, 65, 68], [1, 17, 66, 75, 83], [8, 12, 45, 107, 109],
+    [29, 49, 54, 56, 108], [26, 30, 64, 73, 96], [4, 33, 69, 74, 88],
+    [18, 22, 84], [19, 28, 77], [39, 58, 86], [6, 98, 100, 101, 102],
+    [31, 59, 60, 93, 103],
+]
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(relative):
+    raw = (LANES / relative).read_bytes()
+    need(sha256(raw).hexdigest() == PINS[relative], "Source pin " + relative)
+    return json.loads(raw)
+
+
+def identity(n):
+    return [{i: F(1)} for i in range(n)]
+
+
+def add(target, source, coefficient=F(1)):
+    for key, value in source.items():
+        target[key] = target.get(key, F(0)) + coefficient * value
+        if not target[key]:
+            del target[key]
+
+
+def product(a, b):
+    result = []
+    for row in a:
+        value = {}
+        for j, coefficient in row.items():
+            add(value, b[j], coefficient)
+        result.append(value)
+    return result
+
+
+def transpose(a, n):
+    result = [{} for _ in range(n)]
+    for i, row in enumerate(a):
+        for j, value in row.items():
+            result[j][i] = value
+    return result
+
+
+def restrict(a, ports):
+    index = {p: i for i, p in enumerate(ports)}
+    return [{index[p]: value for p, value in a[row].items() if p in index}
+            for row in ports]
+
+
+def rank(rows, columns):
+    rows = [dict(row) for row in rows]
+    pivot = 0
+    for column in range(columns):
+        found = next((i for i in range(pivot, len(rows)) if rows[i].get(column)), None)
+        if found is None:
+            continue
+        rows[pivot], rows[found] = rows[found], rows[pivot]
+        c = rows[pivot][column]
+        rows[pivot] = {p: v / c for p, v in rows[pivot].items()}
+        for i in range(pivot + 1, len(rows)):
+            if rows[i].get(column):
+                add(rows[i], rows[pivot], -rows[i][column])
+        pivot += 1
+    return pivot
+
+
+def determinant(rows):
+    rows = [dict(row) for row in rows]
+    result = F(1)
+    for column in range(len(rows)):
+        found = next((i for i in range(column, len(rows)) if rows[i].get(column)), None)
+        if found is None:
+            return F(0)
+        if found != column:
+            rows[column], rows[found] = rows[found], rows[column]
+            result = -result
+        c = rows[column][column]
+        result *= c
+        for i in range(column + 1, len(rows)):
+            if rows[i].get(column):
+                add(rows[i], rows[column], -rows[i][column] / c)
+    return result
+
+
+def inverse_word(word):
+    return [[op, target, origin, str(1 / F(c) if op == "scale" else -F(c))]
+            for op, target, origin, c in reversed(word)]
+
+
+def transpose_word(word):
+    return [[op, target if op == "scale" else origin,
+             origin if op == "scale" else target, c]
+            for op, target, origin, c in reversed(word)]
+
+
+def replay(word):
+    state = identity(112)
+    maximum = F(1)
+    for op, target, origin, coefficient in word:
+        c = F(coefficient)
+        if op == "scale":
+            state[target] = {p: c * v for p, v in state[target].items() if c * v}
+        else:
+            need(op == "add" and target != origin, "Scalar word grammar")
+            add(state[target], state[origin], c)
+        maximum = max(maximum, sum(abs(c) for c in state[target].values()))
+    return state, maximum
+
+
+def price(word):
+    result = 0
+    for op, _, _, coefficient in word:
+        c = F(coefficient)
+        a, b = abs(c.numerator), c.denominator
+        need(a and not b & (b - 1), "Dyadic coefficient")
+        if op == "scale":
+            need(not a & (a - 1), "Dyadic unit scale")
+            result += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0))
+        else:
+            result += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length())
+    return result
+
+
+def maximal_cliques(ports, q):
+    n = len(ports)
+    adjacent = [sum(1 << j for j, r in enumerate(ports)
+                    if i != j and not (q[p] & q[r]).bit_count() % 2)
+                for i, p in enumerate(ports)]
+    result = []
+
+    def visit(chosen, possible, excluded):
+        if not possible and not excluded:
+            result.append(chosen)
+            return
+        options = possible | excluded
+        pivot = max((i for i in range(n) if options >> i & 1),
+                    key=lambda i: (adjacent[i] & possible).bit_count(), default=0)
+        todo = possible & ~adjacent[pivot]
+        while todo:
+            bit = todo & -todo
+            i = bit.bit_length() - 1
+            todo -= bit
+            visit(chosen | bit, possible & adjacent[i], excluded & adjacent[i])
+            possible -= bit
+            excluded |= bit
+
+    visit(0, (1 << n) - 1, 0)
+    return [[ports[i] for i in range(n) if mask >> i & 1] for mask in sorted(result)]
+
+
+def encoded(rows):
+    return [{str(p): str(c) for p, c in sorted(row.items())} for row in rows]
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    cyclic = read(next(name for name in PINS if "CYCLIC" in name))
+    matching = read(next(name for name in PINS if "MATCHED" in name))
+    selected, small = matching["selected_ports"], matching["small_ports"]
+    selected_set = set(selected)
+    q = cyclic["ports"]
+    h = identity(112)
+    codes = []
+    for pair in cyclic["pair_codes"]:
+        a, b = pair["ports"]
+        aa, ab = pair["matrix"][0]
+        ba, bb = pair["matrix"][1]
+        h[a], h[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)}
+        if aa != 1:
+            codes.append(["scale", a, None, str(aa)])
+        codes.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)],
+                      ["add", b, a, str(ba * aa)]])
+    hi = transpose(h, 112)
+    for p in cyclic["affected_ports"]:
+        hi[p] = {k: v / 2 for k, v in hi[p].items()}
+    need(product(h, hi) == identity(112), "Actual pair inverse")
+    mode = identity(112)
+    mode_inverse = identity(112)
+    mode_u, mode_v = [{} for _ in range(112)], []
+    mode_word, assignments = [], []
+    for vertex, group in enumerate(cyclic["cyclic_carriers"]):
+        chosen = [p for p in group if selected_set.intersection(map(int, cyclic["mode_rows"][str(p)]))]
+        rest = [p for p in group if p not in chosen]
+        need(len(chosen) == 2 and len(rest) == 4, "Two selected modes per vertex")
+        order = chosen + rest
+        signs = [1, 1 if vertex % 2 == 0 else -1, 1, 1, 1, 1]
+        e = [{j: F((i == j) - 1) for j in range(4) if i != j} | {4: F(1)}
+             for i in range(4)]
+        e += [{5: F(1)}, {0: F(-2), 1: F(-2), 2: F(-2), 3: F(-2), 4: F(3)}]
+        swap = [0, 1, 2, 3, 5, 4]
+        ei = [{swap[j]: c for j, c in e[swap[i]].items()} for i in range(6)]
+        need(product(e, ei) == product(ei, e) == identity(6), "Six-mode reciprocal pair")
+        for i, p in enumerate(order):
+            mode[p] = {order[j]: c * signs[i] * signs[j] for j, c in e[i].items()}
+            mode_inverse[p] = {order[j]: c * signs[i] * signs[j] for j, c in ei[i].items()}
+        offset = len(mode_v)
+        local_u = [[1, 0]] * 4 + [[0, 1], [2, -1]]
+        local_v = [[-1, -1, -1, -1, 1, 0], [0, 0, 0, 0, -1, 1]]
+        for i, p in enumerate(order):
+            mode_u[p].update({offset + j: F(value * signs[i])
+                             for j, value in enumerate(local_u[i]) if value})
+        mode_v.extend([{order[j]: F(value * signs[j]) for j, value in enumerate(row) if value}
+                       for row in local_v])
+        a, b, c = order[:4], order[4], order[5]
+        for i, p in enumerate(a):
+            mode_word.append(["add", b, p, str(-signs[i])])
+        for i, p in enumerate(a):
+            mode_word.append(["add", p, b, str(signs[i])])
+        mode_word.append(["scale", b, None, "-1"])
+        for i, p in enumerate(a):
+            mode_word.append(["add", b, p, str(signs[i])])
+        mode_word.extend([["add", b, c, "1"], ["add", c, b, "-1"],
+                          ["add", b, c, "1"], ["scale", c, None, "-1"]])
+        assignments.append({"vertex": vertex, "ordered_carriers_a_b_c": order, "signs": signs})
+    need(replay(mode_word)[0] == mode, "In-place rank-two mode code")
+    response, response_inverse = product(hi, product(mode, h)), product(hi, product(mode_inverse, h))
+    u, v = product(hi, mode_u), product(mode_v, h)
+    small_word = []
+    need(sorted(p for group in CLIQUES for p in group) == sorted(small), "Exact disjoint64 cover")
+    for group in CLIQUES:
+        k = len(group)
+        need(k in (3, 5), "Dyadic clique size")
+        need(all((q[p] & q[r]).bit_count() % 2 == int(p == r)
+                 for p in group for r in group), "Actual orthonormal clique")
+        for p in group:
+            response[p] = {r: F(-1) for r in group if r != p}
+            response_inverse[p] = {r: F(int(p == r)) - F(1, k - 1) for r in group}
+            u[p] = {len(v): F(-1)}
+        v.append({p: F(1) for p in group})
+        a, rest = group[0], group[1:]
+        small_word.extend([["add", a, p, "1"] for p in rest])
+        small_word.extend([["add", p, a, "-1"] for p in rest])
+        small_word.append(["scale", a, None, str(1 - k)])
+        small_word.extend([["add", a, p, "-1"] for p in rest])
+    word = codes + mode_word + inverse_word(codes) + small_word
+    common_words = {"E": word, "inverse_E": inverse_word(word),
+                    "transpose_E": transpose_word(word),
+                    "inverse_transpose_E": transpose_word(inverse_word(word))}
+    expected = {"E": response, "inverse_E": response_inverse,
+                "transpose_E": transpose(response, 112),
+                "inverse_transpose_E": transpose(response_inverse, 112)}
+    word_receipts = {}
+    for name, gates in common_words.items():
+        actual, maximum = replay(gates)
+        need(actual == expected[name], "Full112 scalar code " + name)
+        need(replay(gates + inverse_word(gates))[0] == identity(112), "Both code orders " + name)
+        word_receipts[name] = {"real_scalar_primitives": price(gates),
+                               "prefix_row_l1_bound": str(maximum), "owned_fields": 0}
+    need(product(response, response_inverse) == product(response_inverse, response) == identity(112),
+         "Full112 reciprocal products")
+    correction = [dict(row) for row in response]
+    for i in range(112):
+        add(correction[i], {i: F(-1)})
+    need(product(u, v) == correction and rank(u, 30) == rank(v, 112) == 30,
+         "Exact full rank30 correction factor")
+    l = restrict(response, selected)
+    li = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_inverse"]]
+    old_l = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_block"]]
+    need(l == restrict(response_inverse, selected) == old_l, "Both selected blocks retain L")
+    need(product(l, li) == identity(8), "Selected inverse")
+    ordinary = sorted(set(range(112)) - selected_set)
+    p = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(selected)
+          if response_inverse[r].get(s)} for r in ordinary]
+    n = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(ordinary)
+          if response_inverse[r].get(s)} for r in selected]
+    ordinary_inverse = restrict(response_inverse, ordinary)
+    for row, update in zip(ordinary_inverse, product(product(p, li), n)):
+        add(row, update, -1)
+    ordinary_block = restrict(response, ordinary)
+    need(product(ordinary_block, ordinary_inverse) == product(ordinary_inverse, ordinary_block)
+         == identity(104), "Both ordinary104 inverse orders")
+    need(all(not c.denominator & (c.denominator - 1)
+             for row in ordinary_inverse for c in row.values()), "Dyadic ordinary inverse")
+    maxima = maximal_cliques(small, q)
+    histogram = Counter(map(len, maxima))
+    need(histogram == {4: 896, 8: 64}, "Exhaustive maximal clique census")
+    # A separate exhaustive extension pass checks the absence of a ninth vertex.
+    need(all(not any(p not in clique and all(not (q[p] & q[r]).bit_count() % 2 for r in clique)
+                     for p in small) for clique in maxima), "Each reported clique is maximal")
+    receipt = {
+        "status": "PASS_LOW_DISPLACEMENT_RESPONSE",
+        "source_pins": PINS, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "correction_rank_large48": 16, "correction_rank_small64": 14, "correction_rank_full112": 30,
+        "selected_determinant": str(determinant(l)),
+        "full_determinant": str(determinant(response)),
+        "ordinary104_determinant": str(determinant(ordinary_block)),
+        "small_clique_sizes": dict(sorted(Counter(map(len, CLIQUES)).items())),
+        "all_maximal_small_clique_sizes": dict(sorted(histogram.items())),
+        "common_frame_scalar_codes": word_receipts,
+        "scope": "Exact port matrices, principal units, scalar codes and geometry. Native phases and terminal access are separate.",
+    }
+    payload = {
+        "source_pins": PINS, "ports": q, "selected_ports": selected, "ordinary_ports": ordinary,
+        "large_ports": cyclic["affected_ports"], "small_ports": small,
+        "vertex_assignments": assignments, "mode_response": encoded(mode),
+        "mode_inverse": encoded(mode_inverse), "small_cliques": CLIQUES,
+        "response": encoded(response), "response_inverse": encoded(response_inverse),
+        "correction_U": encoded(u), "correction_V": encoded(v),
+        "selected_block": encoded(l), "selected_inverse": encoded(li),
+        "ordinary_inverse": encoded(ordinary_inverse), "common_frame_words": common_words,
+        "maximal_small_cliques": maxima,
+    }
+    raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode()
+    (args.out / "RESPONSE-PROGRAM.json").write_bytes(raw)
+    receipt["payload_sha256"] = sha256(raw).hexdigest()
+    (args.out / "RESPONSE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md
new file mode 100644
index 0000000000..5fcb324c5b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md
@@ -0,0 +1,190 @@
+# A native inverse-adjoint for the clean centre exchange
+
+The Q-entry clean word has a literal inverse-adjoint with the same
+native profile and scalar price. Its selected-bank conjugate has the
+same price too. The conjugate is emitted by changing the field labels
+of every instruction. It does not need extra physical swap instructions.
+
+Both providers pass all 640 arbitrary input columns and restore all 416
+auxiliary fields. Each word costs 8,600 real scalar primitives and has
+native mass 1,792. This packet supplies a local physical operation.
+The routed two-call construction and the full supplier bill are
+separate.
+
+## The actual content blocks
+
+Use the selected ports P, the other ports U, and the normalized reader
+L=[I,B] from `CLEAN-LATE-EXCHANGE.md`. Put D=E_UP. Exact multiplication
+on the source matrices gives
+
+```text
+D = -B^T,        E_U x = u + D(a+Bu),        x=(a,u).
+```
+
+These are identities of the actual response. They are not assumptions
+about an arbitrary row code.
+
+Let the selected target content be z and the ordinary target content
+be v. The clean word has content map
+
+```text
+alpha = a+Bu,
+M(a,u,z,v) = (-z, u, alpha, v+u+D alpha).
+```
+
+Its inverse is obtained directly from its output:
+
+```text
+a = third - B second,
+u = second,
+z = -first,
+v = fourth - second - D third.
+```
+
+Thus its inverse-transpose is
+
+```text
+M^(-T)(a,u,z,v) = (-z, u+Da-v, a+Bv, v).
+```
+
+Let S exchange only the selected X and Y coordinates. Then
+
+```text
+Bswapclean = S M^(-T) S,
+Bswapclean(a,u,z,v) = (z+Bv, u+Dz-v, -a, v).
+```
+
+The checker derives M^(-T) from the complete stored inverse of M.
+It compares the result with these block equations and checks both
+inverse product orders. No inverse of E or odd division is used.
+
+## Physical operator and exact order
+
+Let A_in and A_out denote the block diagonal physical entry and exit
+operators. For the Q-entry clean word, they are unitary:
+
+```text
+A_in  = diag(Q_X, Q_P on selected Y, I_U on ordinary Y),
+A_out = diag(F9_X, F9_P on selected Y, F9 q_U on ordinary Y).
+```
+
+The actual operation is W=A_out M A_in^-1. Therefore
+
+```text
+W^(-*) = A_out M^(-T) A_in^-1.
+```
+
+All content coefficients here are real. The notation * denotes the
+Hilbert adjoint of the complete physical operator, including phases.
+This statement does not replace an adjoint with a transpose for a
+general complex response.
+
+Suppose the original chronological gates are G1,...,Gn. The physical
+operator is Gn...G1. Its inverse-adjoint is
+
+```text
+Gn^(-*) ... G1^(-*).
+```
+
+The chronological order is unchanged. Every native gate and endpoint
+view is unitary, so its inverse-adjoint is exactly the same operator,
+including its global phase. For the scalar instructions:
+
+```text
+target += c source   becomes   source -= c target,
+target *= c          becomes   target *= 1/c.
+```
+
+The emitter applies these rules to every scalar instruction. All scalar
+reads still use two fields in the same current frame. Native frame
+progress is unchanged. The full column replay checks the resulting
+word, including every borrowed helper.
+
+## Selected-bank conjugation without added swaps
+
+At each selected port, both input fields have the same Q frame and
+both output fields have the same FULL frame. Their exact input
+monomial records are also equal. Consequently S commutes with A_in
+and A_out.
+
+The conjugated physical operator can be written
+
+```text
+S W^(-*) S
+  = (S Gn^(-*) S) ... (S G1^(-*) S).
+```
+
+Each adjacent pair S S cancels. To emit this circuit, replace every
+selected field index p with 112+p, and vice versa, in every instruction
+and boundary binding. This is a different, explicit circuit on the
+same physical fields. It is not an unpriced swap of live data.
+
+The emitter stores this field permutation. It checks all input records
+by their physical target, frame, port, and complete monomial recipe.
+The ninety-six ordinary output records keep their fields. The native
+recipes and frame lists are unchanged byte for byte. The entry and exit
+frame arrays are invariant under the selected permutation.
+
+The exact physical Bswapclean result is
+
+```text
+input:
+  X = Q(a,u),        Y_P = Q_P z,        Y_U = v;
+
+output:
+  X_P = F9(z+Bv),    X_U = F9(u+Dz-v),
+  Y_P = -F9 a,       Y_U = F9 q_U v.
+```
+
+The unpermuted inverse-adjoint is also stored as a separate complete
+word. It has content (-z,u+Da-v,a+Bv,v) with the same physical exit
+frames.
+
+## Invoice and checks
+
+For both variants and both providers, the complete local invoice is
+
+```text
+scalar primitives              8600
+native profile                 1392 H1 + 64 H2 + 48 H3 + 16 H8
+native mass                    1792
+native children                1520
+input monomial views           128
+output monomial views           96
+native side-map upper bound    3040
+extra boundary swap steps         0
+extra owned or private fields     0
+odd divisions                    0
+```
+
+Inverting the real power-of-two scales keeps their price. Transposing
+and negating the ADDs also keeps their price. The H8 wrappers remain
+charged.
+
+The exact content prefix row one-norm is 12. The additional binary
+denominator height is two. These are bounds at the emitted operation
+boundaries. They do not include recursive child precision or primitive
+internal roundoff.
+
+The normal and optimized runs produce identical payloads and receipts.
+The serialized programs are replayed. A wrong code ADD sign and a wrong
+exchange ADD sign are rejected in all four complete words.
+
+```text
+python3 emit_dual.py --out <new-directory>
+python3 -O emit_dual.py --out <another-new-directory>
+```
+
+Both commands refuse an existing output directory.
+
+This construction uses the frozen clean exchange and its reviewed
+native dependencies. The independent clean-exchange review is
+`new-native-recipes-20261017/clean-centre-exchange-review-20261020`,
+with freeze SHA256
+`6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d`.
+The cover-algebra lane supplied the useful selected-bank formulation.
+AI agents prepared this literal circuit and its checks.
+
+The matching input types make this local conjugation legal. They do
+not by themselves establish the next routed service, its scalar code,
+its output decoder, or a complete multiplication bound.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md
new file mode 100644
index 0000000000..83ca026c25
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md
@@ -0,0 +1,192 @@
+# Clean centre rows from a late productive exchange
+
+This packet forms the sixteen selected centre rows without a clean
+target or an extra field. It puts the old selected target values into
+the selected source fields. All 416 auxiliary fields can have arbitrary
+initial values and return unchanged.
+
+Two distinct input contracts are supplied. Initial formation accepts
+selected targets in I. Reuse accepts selected targets in their positive
+line frame Q. Both words cost 8,600 real scalar primitives. Their native
+masses are 1,808 and 1,792, respectively. These are complete local
+invoices. A full supplier still needs its routed caller, helper host,
+recursive bill, and precision bound.
+
+## Exact inputs and source code
+
+The source response is the frozen rank-sixteen response E. Select the
+ordered physical ports
+
+```text
+P = [0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23].
+```
+
+Write U for the other ninety-six ports. The normalized reader L has
+the form L=[I,B] in P,U order. The existing row code is
+
+```text
+C = [ I  B ],       C^-1 = [ I -B ].
+    [ 0  I ]              [ 0  I ]
+```
+
+The literal C word uses no extra field and costs 1,760 real scalar
+primitives. It accepts arbitrary source values.
+
+The exact reader and code come from
+`controller-followthrough-20261017/row-capture-20261020`.
+The exact retained native paths come from
+`row-only-capture-20261020`. The I-entry variant uses the reviewed
+direct-FULL formation paths. The Q-entry variant uses the reviewed
+line-entry prefix in `fixed-reader-reuse-20261020`. Every source file
+and review pin is stored in the payload.
+
+Let q=Q^-1. Here Q has one positive line operator on each port, and F9
+is the common full nine-coordinate operator.
+
+For initial formation the physical inputs are
+
+```text
+X = Qx,       Y = y.
+```
+
+For reuse they are
+
+```text
+X = Qx,       Y_P = Q_P z,       Y_U = y_U.
+```
+
+The x, y, and z values in each stated contract are independent and
+arbitrary. In particular, z does not have to be a centre value. The
+contract does not assume any relation between z and x.
+
+## Literal construction
+
+First run the complete retained source paths and the ninety-six
+ordinary target paths. None of these events reads a selected target.
+Then advance the sixteen selected targets to FULL. Initial formation
+uses sixteen rank-nine children. Reuse uses sixteen rank-eight
+line-to-FULL children, with their actual nontrivial wrappers.
+
+At this cut all X fields and all selected Y fields are FULL. The
+content is
+
+```text
+X = x,
+Y_P = b,
+Y_U = (y+Ex)_U,
+```
+
+where b=y_P for formation and b=z for reuse. The ordinary Y fields
+retain the physical exterior q_U. Apply C to X at the common FULL
+cut. Thus X_P=Lx and X_U=x_U. For every p in P, perform the following
+three unit ADDs in this order:
+
+```text
+Y_p += X_p
+X_p -= Y_p
+Y_p += X_p
+```
+
+For arbitrary values a and b, these three steps map (a,b) to (-b,a).
+They cost 24 real scalar primitives per selected pair. No extra sign
+instruction or temporary field is needed.
+
+The exact physical result is therefore
+
+```text
+X_P = -F9 b,          X_U = F9 x_U,
+Y_P = F9 Lx,          Y_U = F9 q_U (y+Ex)_U.
+```
+
+The sixteen centre values in Y_P contain no old Y contribution. The
+old selected target state is still present, with a minus sign, in
+X_P. The construction changes the productive data interface; it does
+not erase that state.
+
+## Full-domain correctness
+
+The content map is invertible. If its output content is (u,v), recover
+
+```text
+x_U = u_U,
+x_P = v_P - B u_U,
+b   = -u_P,
+y_U = v_U - E_U x.
+```
+
+All coefficients are dyadic. The checker forms this inverse independently
+from the output equations and checks both product orders on all 224 data
+columns. This establishes invertibility of the content map. It does not
+price an inverse physical service.
+
+The literal forward replay checks all 640 input columns. It checks the
+frame of each scalar source and target, both frames of every native
+call, and all final frames. Every native recipe, frame list, and endpoint
+adapter is inherited byte for byte from an independently reviewed
+source. The new suffix uses only scalar operations at the common FULL
+cut. It introduces no new native phase operator.
+
+The selected targets are advanced before the code and the exchanges.
+The source code runs only after the complete retained native sweep.
+Thus the proof needs no early all-source FULL cut, old source read, or
+commutation of Q with the response.
+
+## Complete local invoices
+
+Both variants have the same scalar bill:
+
+```text
+retained native word scalar operations       6456
+FULL-X row code                              1760
+sixteen signed exchanges: 16*24               384
+total                                       8600
+```
+
+Their exact child and view invoices are:
+
+| Item | Initial I entry | Selected Q entry |
+| --- | ---: | ---: |
+| Native profile | 1392 H1 + 64 H2 + 48 H3 + 16 H9 | 1392 H1 + 64 H2 + 48 H3 + 16 H8 |
+| Native mass | 1808 | 1792 |
+| Native children | 1520 | 1520 |
+| Input monomial views | 112 | 128 |
+| Output monomial views | 96 | 96 |
+| Native side-map upper bound | 3008 | 3040 |
+| Extra owned or private fields | 0 | 0 |
+| Odd divisions | 0 | 0 |
+
+The sixteen direct F9 recipes have identity side maps. The H8 recipes
+retain both side maps. The invoice does not transfer the identity-map
+claim from F9 to H8.
+
+At the scalar and native operation boundaries, the maximum content row
+one-norm is 22. The additional binary denominator height is one. These
+are exact local content bounds. They do not include primitive internal
+roundoff, recursive child precision, or the complete caller.
+
+## Verification and limits
+
+Both providers and both entry variants pass normal and optimized Python
+with byte-identical payloads and receipts. The serialized payload is
+replayed in each run. A missing source-code ADD and a missing exchange
+ADD are both rejected in every complete word.
+
+Run either command with a new output directory:
+
+```text
+python3 emit_clean_exchange.py --out <new-directory>
+python3 -O emit_clean_exchange.py --out <another-new-directory>
+```
+
+The emitter refuses an existing output directory.
+
+The next productive source can use (Y_P,X_U), whose content is Cx.
+The other bank then contains (-b,(y+Ex)_U), with mixed physical phases.
+A routed next-entry proof must bind these actual roles and phases. This
+packet does not apply C^-1, identify the source with x, or assume that
+the same reader survives another service.
+
+The construction builds on the campaign's rank-sixteen response, row
+capture, direct-FULL formation, and line-entry reuse packets. AI agents
+prepared and checked this extension. Independent review is recorded in
+a separate packet.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json
new file mode 100644
index 0000000000..61b6a46fe6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "CLEAN-DUAL.md": "1515a8b82ecfcb32d7dc19a4a8bc0fcf0af870ac444bb1628443dfb378360cb9",
+    "dual-normal/CHECKS.json": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b",
+    "dual-normal/CLEAN-DUAL.json.gz": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660",
+    "dual-optimized/CHECKS.json": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b",
+    "dual-optimized/CLEAN-DUAL.json.gz": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660",
+    "emit_dual.py": "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+  "scope": "Four exact640-column local inverse-adjoint/conjugate words with unchanged physical phase records,8600 scalar,1792 native mass. The routed caller and complete supplier remain separate.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json
new file mode 100644
index 0000000000..8b54249651
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json
@@ -0,0 +1,26 @@
+{
+  "files": {
+    "CLEAN-LATE-EXCHANGE.md": "eb8e579b11d3d4ce8e77a2d6003b1a95135d84f79ce60d48ee2370194797569c",
+    "emit_clean_exchange.py": "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc",
+    "run-normal/CHECKS.json": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b",
+    "run-normal/CLEAN-LATE-EXCHANGE.json.gz": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d",
+    "run-optimized/CHECKS.json": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b",
+    "run-optimized/CLEAN-LATE-EXCHANGE.json.gz": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+  "scope": "Four complete local words, all640 input columns, arbitrary borrowed target state, and416 restored helpers. Routed next-entry and complete supplier costs remain separate.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING",
+  "variants": {
+    "I": {
+      "native_mass": 1808,
+      "role": "Initial clean centre formation",
+      "scalar": 8600
+    },
+    "Q": {
+      "native_mass": 1792,
+      "role": "Clean centre exchange with arbitrary selected line-frame input",
+      "scalar": 8600
+    }
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json
new file mode 100644
index 0000000000..bb9da0263e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json
@@ -0,0 +1,140 @@
+{
+  "actual_D_equals_negative_B_transpose": true,
+  "all_content_inverse_orders": true,
+  "native_phase_scope": "All native and endpoint spatial operators are unchanged unitary records from the reviewed Q-entry word. Each inverse-adjoint native operator equals itself.",
+  "negative_controls": "A wrong code or exchange ADD sign fails in all four words.",
+  "payload_decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+  "producer_sha256": "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8",
+  "reports": {
+    "base": {
+      "inverse_adjoint": {
+        "additional_content_binary_height": 2,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
+      },
+      "selected_swap_conjugate": {
+        "additional_content_binary_height": 2,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
+      }
+    },
+    "extra": {
+      "inverse_adjoint": {
+        "additional_content_binary_height": 2,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
+      },
+      "selected_swap_conjugate": {
+        "additional_content_binary_height": 2,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
+      }
+    }
+  },
+  "scope": "Complete local physical inverse-adjoint and selected-role conjugate. A routed caller and its full supplier bill remain separate.",
+  "status": "PASS_EXACT_CLEAN_INVERSE_ADJOINT_AND_SELECTED_CONJUGATE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz
new file mode 100644
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CHECKS.json
new file mode 100644
index 0000000000..bb9da0263e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CHECKS.json
@@ -0,0 +1,140 @@
+{
+  "actual_D_equals_negative_B_transpose": true,
+  "all_content_inverse_orders": true,
+  "native_phase_scope": "All native and endpoint spatial operators are unchanged unitary records from the reviewed Q-entry word. Each inverse-adjoint native operator equals itself.",
+  "negative_controls": "A wrong code or exchange ADD sign fails in all four words.",
+  "payload_decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+  "producer_sha256": "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8",
+  "reports": {
+    "base": {
+      "inverse_adjoint": {
+        "additional_content_binary_height": 2,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
+      },
+      "selected_swap_conjugate": {
+        "additional_content_binary_height": 2,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
+      }
+    },
+    "extra": {
+      "inverse_adjoint": {
+        "additional_content_binary_height": 2,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
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+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
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+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
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+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
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+      "selected_swap_conjugate": {
+        "additional_content_binary_height": 2,
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+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "extra_boundary_swap_instructions": 0,
+        "maximum_content_prefix_row_one_norm": "12",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_phase_records_unchanged": true,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
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+        },
+        "selected_input_and_output_adapter_symmetry": true,
+        "unchanged_arbitrary_helpers": 416
+      }
+    }
+  },
+  "scope": "Complete local physical inverse-adjoint and selected-role conjugate. A routed caller and its full supplier bill remain separate.",
+  "status": "PASS_EXACT_CLEAN_INVERSE_ADJOINT_AND_SELECTED_CONJUGATE"
+}
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_clean_exchange.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_clean_exchange.py
new file mode 100644
index 0000000000..f9a65bb73d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_clean_exchange.py
@@ -0,0 +1,242 @@
+#!/usr/bin/env python3
+"""Form clean centre rows by a late exchange with productive fields."""
+
+import argparse
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE = HERE.parent / "row-only-capture-20261020"
+LANES = HERE.parents[2]
+PINS = {
+    "helper": (SOURCE / "emit_capture.py",
+               "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f"),
+    "formation": (SOURCE / "direct-normal/DIRECT-FULL-CAPTURE.json.gz",
+                  "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c"),
+    "capture": (LANES / "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json",
+                "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"),
+    "phase_review": (LANES / "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json",
+                     "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"),
+    "line_prefix": (HERE.parent / "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz",
+                    "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e"),
+    "line_phase_review": (LANES / "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json",
+                          "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source " + name)
+    return raw
+
+
+read("helper")
+spec = importlib.util.spec_from_file_location("clean_exchange_base", PINS["helper"][0])
+base = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = base
+spec.loader.exec_module(base)
+n = base.n
+
+
+def expected_map(code, response, selected):
+    result = n.r.identity(640)
+    for p in range(112):
+        if p in selected:
+            result[p] = {112 + p: F(-1)}
+            result[112 + p] = dict(code[p])
+        else:
+            n.r.add(result[112 + p], response[p])
+    return result
+
+
+def inverse_content(code, response, selected):
+    x = n.r.identity(224)[:112]
+    for p in selected:
+        x[p] = {112 + p: F(1)}
+        for j, value in code[p].items():
+            if j != p:
+                n.r.add(x[p], {j: -value})
+    result = [dict(row) for row in x] + [{} for _ in range(112)]
+    for p in range(112):
+        if p in selected:
+            result[112 + p] = {p: F(-1)}
+        else:
+            result[112 + p] = {112 + p: F(1)}
+            for j, value in response[p].items():
+                n.r.add(result[112 + p], x[j], -value)
+    return result
+
+
+def verify(word, expected):
+    current = list(word["start"])
+    state = n.r.identity(640)
+    maximum, height = F(1), 0
+    for event in word["events"]:
+        if event[0] == "native":
+            _, field, old, new, rank, key = event
+            need(current[field] == old, "The exact native input frame")
+            need(len(n.basis(word["frames"][old] + word["frames"][new]))
+                 == len(word["frames"][new]), "The native frame is nested")
+            need(rank == len(word["frames"][new]) - len(word["frames"][old])
+                 == word["native_recipes"][key]["rank"], "The exact native rank")
+            current[field] = new
+        else:
+            need(event[0] == "scalar", "The complete event grammar")
+            gate, frame = event[1:]
+            op, target, source, raw = gate
+            coefficient = F(raw)
+            need(current[target] == frame, "The exact scalar target frame")
+            if op == "add":
+                need(source != target and current[source] == frame, "The exact source frame")
+                n.r.add(state[target], state[source], coefficient)
+            else:
+                need(op == "scale", "Only ADD and SCALE instructions")
+                state[target] = {j: coefficient * value for j, value in state[target].items()
+                                 if coefficient * value}
+            maximum = max(maximum, sum(abs(value) for value in state[target].values()))
+            for value in state[target].values():
+                d = value.denominator
+                need(d & (d - 1) == 0, "All content is dyadic")
+                height = max(height, d.bit_length() - 1)
+    need(state == expected, "All640 independent arbitrary input fields")
+    need(current == word["final"], "All640 complete final frames")
+    need(state[224:] == n.r.identity(640)[224:], "All416 arbitrary helpers are restored")
+    profile = Counter(event[4] for event in word["events"] if event[0] == "native")
+    direct_full = sum(event[0] == "native" and event[5] == "capture-full"
+                      for event in word["events"])
+    return {
+        "all_independent_input_fields": 640, "unchanged_arbitrary_helpers": 416,
+        "native_profile": dict(sorted(profile.items())), "native_children": sum(profile.values()),
+        "native_mass": sum(k * v for k, v in profile.items()),
+        "native_side_map_upper_bound": 2 * (sum(profile.values()) - direct_full),
+        "direct_full_identity_wrapper_children": direct_full,
+        "explicit_input_monomial_views": len(word["input_views"]),
+        "explicit_output_monomial_views": len(word["output_views"]),
+        "scalar_stage_prices": {stage: base.price(word["events"][start:end])
+                               for stage, (start, end) in word["stage_ranges"].items()},
+        "real_scalar_primitives": base.price(word["events"]),
+        "maximum_content_prefix_row_one_norm": str(maximum),
+        "additional_content_binary_height": height,
+        "owned_fields": 0, "private_fields": 0, "odd_divisions": 0,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    source = json.loads(read("formation"))
+    line_prefix = json.loads(read("line_prefix"))
+    capture = json.loads(read("capture"))
+    read("phase_review")
+    read("line_phase_review")
+    pivots = capture["pivots"]
+    selected = set(pivots)
+    code, response = n.rows(capture["code"]), n.rows(capture["response"])
+    need(pivots == source["selected_ports"] and code == n.rows(source["code"])
+         and response == n.rows(source["response"]), "The exact formation and row code")
+    for p in selected:
+        need(code[p].get(p) == 1 and set(code[p]) & selected == {p},
+             "Each normalized reader has its own pivot")
+    expected = expected_map(code, response, selected)
+    inverse = inverse_content(code, response, selected)
+    need(n.r.product(expected[:224], inverse) == n.r.product(inverse, expected[:224])
+         == n.r.identity(224), "Both exact content inverse orders")
+    providers, reports = {}, {}
+    for provider in source["providers"]:
+        providers[provider], reports[provider] = {}, {}
+        for entry, original in (
+                ("I", source["providers"][provider]), ("Q", line_prefix["providers"][provider])):
+            word = deepcopy(original)
+            core_start, core_end = original["stage_ranges"]["retained_core"]
+            progress = "selected_full_progress" if entry == "I" else "selected_line_progress"
+            full_start, full_end = original["stage_ranges"][progress]
+            word["events"] = deepcopy(original["events"][core_start:core_end]
+                                      + original["events"][full_start:full_end])
+            ranges = {"retained_core": [0, core_end - core_start],
+                      "selected_progress": [core_end - core_start, len(word["events"])]}
+            start = len(word["events"])
+            for op, target, source_index, coefficient in capture["scalar_word"]:
+                word["events"].append(["scalar", [op, target, source_index, coefficient], 1])
+            ranges["source_row_code"] = [start, len(word["events"])]
+            start = len(word["events"])
+            for p in pivots:
+                word["events"].extend([
+                    ["scalar", ["add", 112 + p, p, "1"], 1],
+                    ["scalar", ["add", p, 112 + p, "-1"], 1],
+                    ["scalar", ["add", 112 + p, p, "1"], 1],
+                ])
+            ranges["signed_selected_exchanges"] = [start, len(word["events"])]
+            word["stage_ranges"] = ranges
+            report = verify(word, expected)
+            rank = 9 if entry == "I" else 8
+            need(report["native_profile"] == {1: 1392, 2: 64, 3: 48, rank: 16}
+                 and report["native_mass"] == 1664 + 16 * rank, "The exact complete native profile")
+            need(report["scalar_stage_prices"] == {
+                "retained_core": 6456, "selected_progress": 0,
+                "source_row_code": 1760, "signed_selected_exchanges": 384},
+                "All code and exchange costs are explicit")
+            need(report["real_scalar_primitives"] == 8600, "The exact complete scalar invoice")
+            for stage in ("source_row_code", "signed_selected_exchanges"):
+                bad = deepcopy(word)
+                index = next(i for i in range(*ranges[stage]) if bad["events"][i][1][0] == "add")
+                del bad["events"][index]
+                try:
+                    verify(bad, expected)
+                except ValueError:
+                    pass
+                else:
+                    raise ValueError("An omitted " + stage + " ADD was accepted")
+            providers[provider][entry], reports[provider][entry] = word, report
+    payload = {
+        "schema": "clean-late-sixteen-centre-exchange-v1",
+        "source_pins": {name: {"path": str(path), "sha256": pin}
+                        for name, (path, pin) in PINS.items()},
+        "ports": source["ports"], "selected_ports": pivots, "code": capture["code"],
+        "response": capture["response"], "content_map": n.r.encoded(expected[:224]),
+        "inverse_content_map": n.r.encoded(inverse), "providers": providers,
+        "physical_contract": {
+            "input_I": "X=Qx; Y=y, with all640 fields independent and arbitrary.",
+            "input_Q": "X=Qx; Y_P=Q_P z; Y_U=y_U, with independent arbitrary z.",
+            "source_output_I": "X_P=-F9 y_P; X_U=F9 x_U.",
+            "source_output_Q": "X_P=-F9 z; X_U=F9 x_U.",
+            "target_output": "Y_P=F9 Lx; Y_U=F9 q_U (y+Ex)_U.",
+            "centre_baseline": "The selected centre rows contain no borrowed-Y contribution. The old selectedY baseline is retained with a minus sign on selectedX.",
+            "scope": "Complete local native formation by productive exchange. The actual routed next-entry and a complete caller are separate.",
+        },
+    }
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    for provider, entries in json.loads(raw)["providers"].items():
+        for entry, word in entries.items():
+            need(verify(word, expected) == reports[provider][entry], "The full serialized clean exchange")
+    (args.out / "CLEAN-LATE-EXCHANGE.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {"status": "PASS_EXACT_CLEAN_LATE_CENTRE_EXCHANGE",
+               "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "payload_decompressed_sha256": sha256(raw).hexdigest(),
+               "reports": reports, "content_inverse_both_orders": True,
+               "negative_controls": "Omitted source-code or signed-exchange ADD fails in all four complete words.",
+               "native_phase_scope": "Every native recipe, frame, and endpoint adapter is byte-exact inherited from the reviewed direct-FULL formation or line-entry prefix.",
+               "scope": payload["physical_contract"]["scope"]}
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py
new file mode 100644
index 0000000000..f0fa247738
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py
@@ -0,0 +1,229 @@
+#!/usr/bin/env python3
+"""Emit the inverse-adjoint clean word and its selected-role conjugate."""
+
+import argparse
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+PINS = {
+    "producer": (HERE / "emit_clean_exchange.py",
+                 "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc"),
+    "source": (HERE / "run-normal/CLEAN-LATE-EXCHANGE.json.gz",
+               "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083"),
+    "freeze": (HERE / "FREEZE.json",
+               "96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned clean source " + name)
+    return raw
+
+
+read("producer")
+spec = importlib.util.spec_from_file_location("clean_dual_base", PINS["producer"][0])
+base = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = base
+spec.loader.exec_module(base)
+n = base.n
+
+
+def conjugate(rows, permutation):
+    result = [{} for _ in rows]
+    for target, row in enumerate(rows):
+        result[permutation[target]] = {permutation[source]: value
+                                       for source, value in row.items()}
+    return result
+
+
+def expected_swap(code, response, selected):
+    result = n.r.identity(640)
+    for p in range(112):
+        if p in selected:
+            result[p] = {112 + j: value for j, value in code[p].items()}
+            result[112 + p] = {p: F(-1)}
+        else:
+            n.r.add(result[p], {112 + p: F(-1)})
+            for j in selected:
+                value = response[p].get(j, F(0))
+                if value:
+                    n.r.add(result[p], {112 + j: value})
+    return result
+
+
+def lower(original, permutation):
+    word = deepcopy(original)
+    events = []
+    for event in original["events"]:
+        new = deepcopy(event)
+        if event[0] == "native":
+            new[1] = permutation[event[1]]
+        else:
+            need(event[0] == "scalar", "The complete source event grammar")
+            op, target, source, raw = event[1]
+            coefficient = F(raw)
+            if op == "add":
+                new[1] = [op, permutation[source], permutation[target], str(-coefficient)]
+            else:
+                need(op == "scale" and coefficient, "An invertible real scale")
+                new[1] = [op, permutation[target], None, str(1 / coefficient)]
+        events.append(new)
+    word["events"] = events
+    for key in ("start", "final"):
+        word[key] = [original[key][permutation[p]] for p in range(640)]
+        need(word[key] == original[key], "Selected endpoint frame symmetry")
+    for record in word["input_views"]:
+        record["field"] = permutation[record["field"]]
+        record["role"] = "source" if record["field"] < 112 else "selected_target"
+    word["input_views"].sort(key=lambda record: record["field"])
+    input_by_field = {record["field"]: record for record in original["input_views"]}
+    physical_keys = ("frame", "left", "right", "rank", "port")
+    for record in word["input_views"]:
+        old = input_by_field[record["field"]]
+        need(all(record[key] == old[key] for key in physical_keys),
+             "The complete same-port input adapter is invariant")
+    for record in word["output_views"]:
+        need(permutation[112 + record["port"]] == 112 + record["port"],
+             "Every ordinary output adapter keeps its physical field")
+    need(word["native_recipes"] == original["native_recipes"]
+         and word["frames"] == original["frames"], "All native physical records are unchanged")
+    word["wire_permutation"] = {str(p): q for p, q in enumerate(permutation) if p != q}
+    word["scalar_rule"] = "Keep event order. Transpose each ADD and negate its coefficient. Invert each real SCALE."
+    return word
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    read("freeze")
+    source = json.loads(read("source"))
+    for name in ("phase_review", "line_phase_review"):
+        base.read(name)
+    selected = set(source["selected_ports"])
+    code, response = n.rows(source["code"]), n.rows(source["response"])
+    direct = n.rows(source["content_map"])
+    inverse = n.rows(source["inverse_content_map"])
+    need(n.r.product(direct, inverse) == n.r.product(inverse, direct) == n.r.identity(224),
+         "Both source content inverse orders")
+    for p in range(112):
+        if p in selected:
+            need(code[p].get(p) == 1 and set(code[p]) & selected == {p},
+                 "The exact normalized centre minor")
+            continue
+        row = {p: F(1)}
+        for j in selected:
+            d = response[p].get(j, F(0))
+            need(d == -code[j].get(p, F(0)), "The actual D=-B transpose identity")
+            n.r.add(row, code[j], d)
+        need(row == response[p], "The actual ordinary response is u+D(a+Bu)")
+    dual = n.r.transpose(inverse, 224)
+    dual_inverse = n.r.transpose(direct, 224)
+    need(n.r.product(dual, dual_inverse) == n.r.product(dual_inverse, dual) == n.r.identity(224),
+         "Both inverse-adjoint content inverse orders")
+    full_dual = dual + n.r.identity(640)[224:]
+    identity_permutation = list(range(640))
+    swap_permutation = list(identity_permutation)
+    for p in selected:
+        swap_permutation[p], swap_permutation[112 + p] = 112 + p, p
+    swap = conjugate(full_dual, swap_permutation)
+    need(swap == expected_swap(code, response, selected),
+         "The direct Bswapclean block formula")
+    swap_inverse = conjugate(dual_inverse, swap_permutation[:224])
+    need(n.r.product(swap[:224], swap_inverse) == n.r.product(swap_inverse, swap[:224])
+         == n.r.identity(224), "Both Bswapclean content inverse orders")
+    providers, reports = {}, {}
+    for provider, entries in source["providers"].items():
+        original = entries["Q"]
+        providers[provider], reports[provider] = {}, {}
+        for name, permutation, expected in (
+                ("inverse_adjoint", identity_permutation, full_dual),
+                ("selected_swap_conjugate", swap_permutation, swap)):
+            word = lower(original, permutation)
+            report = base.verify(word, expected)
+            need(report["real_scalar_primitives"] == 8600
+                 and report["native_mass"] == 1792
+                 and report["native_profile"] == {1: 1392, 2: 64, 3: 48, 8: 16},
+                 "The full dual invoice")
+            need(report["native_side_map_upper_bound"] == 3040
+                 and report["explicit_input_monomial_views"] == 128
+                 and report["explicit_output_monomial_views"] == 96,
+                 "All actual adapter and wrapper counts")
+            report["extra_boundary_swap_instructions"] = 0
+            report["native_phase_records_unchanged"] = True
+            report["selected_input_and_output_adapter_symmetry"] = True
+            for stage in ("source_row_code", "signed_selected_exchanges"):
+                bad = deepcopy(word)
+                index = next(i for i in range(*word["stage_ranges"][stage])
+                             if bad["events"][i][1][0] == "add")
+                bad["events"][index][1][3] = str(-F(bad["events"][index][1][3]))
+                try:
+                    base.verify(bad, expected)
+                except ValueError:
+                    pass
+                else:
+                    raise ValueError("A wrong dual ADD sign was accepted")
+            providers[provider][name], reports[provider][name] = word, report
+    payload = {
+        "schema": "clean-inverse-adjoint-selected-conjugate-v1",
+        "source_pins": {name: {"path": str(path), "sha256": pin}
+                        for name, (path, pin) in PINS.items()},
+        "ports": source["ports"], "selected_ports": source["selected_ports"],
+        "code": source["code"], "response": source["response"],
+        "content_maps": {"inverse_adjoint": n.r.encoded(dual),
+                         "selected_swap_conjugate": n.r.encoded(swap[:224])},
+        "inverse_content_maps": {"inverse_adjoint": n.r.encoded(dual_inverse),
+                                 "selected_swap_conjugate": n.r.encoded(swap_inverse)},
+        "providers": providers,
+        "physical_contract": {
+            "input": "X=Q(a,u); Y_P=Q_P z; Y_U=v.",
+            "inverse_adjoint_output_content": "X=(-z,u+D a-v); Y=(a+Bv,v).",
+            "selected_swap_conjugate_output_content": "X=(z+Bv,u+D z-v); Y=(-a,v).",
+            "output_frames": "All X and selected Y have F9; ordinary Y has F9 q_U.",
+            "operators": "B is the normalized reader off-pivot block; D=-B^T, with actual real dyadic coefficients.",
+            "scope": "Complete local physical inverse-adjoint and selected-role conjugate. A routed caller and its full supplier bill remain separate.",
+        },
+    }
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    for provider, words in saved["providers"].items():
+        for name, word in words.items():
+            expected = n.rows(saved["content_maps"][name]) + n.r.identity(640)[224:]
+            report = base.verify(word, expected)
+            need(all(value == reports[provider][name][key] for key, value in report.items()),
+                 "The complete serialized dual replay")
+    (args.out / "CLEAN-DUAL.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {
+        "status": "PASS_EXACT_CLEAN_INVERSE_ADJOINT_AND_SELECTED_CONJUGATE",
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_decompressed_sha256": sha256(raw).hexdigest(),
+        "reports": reports, "all_content_inverse_orders": True,
+        "actual_D_equals_negative_B_transpose": True,
+        "negative_controls": "A wrong code or exchange ADD sign fails in all four words.",
+        "native_phase_scope": "All native and endpoint spatial operators are unchanged unitary records from the reviewed Q-entry word. Each inverse-adjoint native operator equals itself.",
+        "scope": payload["physical_contract"]["scope"],
+    }
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True), flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json
new file mode 100644
index 0000000000..31337b060e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json
@@ -0,0 +1,127 @@
+{
+  "content_inverse_both_orders": true,
+  "native_phase_scope": "Every native recipe, frame, and endpoint adapter is byte-exact inherited from the reviewed direct-FULL formation or line-entry prefix.",
+  "negative_controls": "Omitted source-code or signed-exchange ADD fails in all four complete words.",
+  "payload_decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+  "producer_sha256": "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc",
+  "reports": {
+    "base": {
+      "I": {
+        "additional_content_binary_height": 1,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 16,
+        "explicit_input_monomial_views": 112,
+        "explicit_output_monomial_views": 96,
+        "maximum_content_prefix_row_one_norm": "22",
+        "native_children": 1520,
+        "native_mass": 1808,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "9": 16
+        },
+        "native_side_map_upper_bound": 3008,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_helpers": 416
+      },
+      "Q": {
+        "additional_content_binary_height": 1,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "maximum_content_prefix_row_one_norm": "22",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_helpers": 416
+      }
+    },
+    "extra": {
+      "I": {
+        "additional_content_binary_height": 1,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 16,
+        "explicit_input_monomial_views": 112,
+        "explicit_output_monomial_views": 96,
+        "maximum_content_prefix_row_one_norm": "22",
+        "native_children": 1520,
+        "native_mass": 1808,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "9": 16
+        },
+        "native_side_map_upper_bound": 3008,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_helpers": 416
+      },
+      "Q": {
+        "additional_content_binary_height": 1,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "maximum_content_prefix_row_one_norm": "22",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_helpers": 416
+      }
+    }
+  },
+  "scope": "Complete local native formation by productive exchange. The actual routed next-entry and a complete caller are separate.",
+  "status": "PASS_EXACT_CLEAN_LATE_CENTRE_EXCHANGE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-optimized/CHECKS.json
new file mode 100644
index 0000000000..31337b060e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-optimized/CHECKS.json
@@ -0,0 +1,127 @@
+{
+  "content_inverse_both_orders": true,
+  "native_phase_scope": "Every native recipe, frame, and endpoint adapter is byte-exact inherited from the reviewed direct-FULL formation or line-entry prefix.",
+  "negative_controls": "Omitted source-code or signed-exchange ADD fails in all four complete words.",
+  "payload_decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+  "producer_sha256": "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc",
+  "reports": {
+    "base": {
+      "I": {
+        "additional_content_binary_height": 1,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 16,
+        "explicit_input_monomial_views": 112,
+        "explicit_output_monomial_views": 96,
+        "maximum_content_prefix_row_one_norm": "22",
+        "native_children": 1520,
+        "native_mass": 1808,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "9": 16
+        },
+        "native_side_map_upper_bound": 3008,
+        "odd_divisions": 0,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_helpers": 416
+      },
+      "Q": {
+        "additional_content_binary_height": 1,
+        "all_independent_input_fields": 640,
+        "direct_full_identity_wrapper_children": 0,
+        "explicit_input_monomial_views": 128,
+        "explicit_output_monomial_views": 96,
+        "maximum_content_prefix_row_one_norm": "22",
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
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+        },
+        "unchanged_arbitrary_helpers": 416
+      }
+    },
+    "extra": {
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+        "direct_full_identity_wrapper_children": 16,
+        "explicit_input_monomial_views": 112,
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+        "native_children": 1520,
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+          "2": 64,
+          "3": 48,
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+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_map_upper_bound": 3040,
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+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
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+        "unchanged_arbitrary_helpers": 416
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+    }
+  },
+  "scope": "Complete local native formation by productive exchange. The actual routed next-entry and a complete caller are separate.",
+  "status": "PASS_EXACT_CLEAN_LATE_CENTRE_EXCHANGE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-optimized/CLEAN-LATE-EXCHANGE.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-optimized/CLEAN-LATE-EXCHANGE.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json
new file mode 100644
index 0000000000..327a949b0b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json
@@ -0,0 +1,430 @@
+{
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+  "exit_compiler_sha256": "cb8c0880051b24175d2b84080f51ad65a12e85755b6237e7439d12576ffe9bbf",
+  "exit_compiler_source_pins": {
+    "coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json": [
+      "plain",
+      "20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701"
+    ],
+    "oblique-native-20261017/matched-native-involution/FREEZE.json": [
+      "plain",
+      "b35eae3fb4b53f51cfbed6bec8968b950c70e65bfe777cbe0d15e86c36dd4ab5"
+    ],
+    "oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz": [
+      "decompressed",
+      "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025"
+    ]
+  },
+  "fresh_changed_exit_phases": 352,
+  "payload_decompressed_sha256": "7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d",
+  "producer_sha256": "3d6c9283a2217306bae8f998891439e5cff435a7b3d7575c9481c115f411a282",
+  "receipts": {
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+            "owned_fields": 0,
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+            },
+            "rank_nine_admission": "not needed",
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_coded_exits.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_coded_exits.py
new file mode 100644
index 0000000000..b627fe5c3b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_coded_exits.py
@@ -0,0 +1,140 @@
+#!/usr/bin/env python3
+"""Bind both frozen low-displacement words to exact left-coded exits."""
+
+import argparse
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+LIB = LANES / "oblique-native-20261017/matched-left-gauge/emit_left_gauge.py"
+LIB_PIN = "cb8c0880051b24175d2b84080f51ad65a12e85755b6237e7439d12576ffe9bbf"
+PINS = {
+    "native-normal-v2/NATIVE-PROGRAM.json.gz":
+        "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    "odd16-normal-v2/EXTENSION-PROGRAM.json.gz":
+        "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "run-normal/RESPONSE-PROGRAM.json":
+        "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c",
+}
+CYCLIC = LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json"
+CYCLIC_PIN = "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"
+if sha256(LIB.read_bytes()).hexdigest() != LIB_PIN:
+    raise ValueError("Frozen exit compiler pin")
+spec = importlib.util.spec_from_file_location("low_coded_exit", LIB)
+g = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = g
+spec.loader.exec_module(g)
+need = g.need
+
+
+def read(relative):
+    raw = (HERE / relative).read_bytes()
+    if relative.endswith(".gz"):
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == PINS[relative], "Frozen input " + relative)
+    return json.loads(raw)
+
+
+def translate(old, pairs):
+    word = dict(old)
+    events = []
+    for event in old["events"]:
+        if event[0] != "scalar":
+            need(event[0] == "native", "Raw input event type")
+            events.append(event)
+            continue
+        op, target, source, coefficient = event[1]
+        c = F(coefficient)
+        gate = ([op, target, c.numerator, c.denominator] if op == "scale"
+                else [op, target, source, c.numerator, c.denominator])
+        events.append(["scalar", gate, event[2]])
+    word["events"] = events
+    word["pair_codes"] = pairs
+    return word
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    native = read("native-normal-v2/NATIVE-PROGRAM.json.gz")
+    odd = read("odd16-normal-v2/EXTENSION-PROGRAM.json.gz")
+    model = read("run-normal/RESPONSE-PROGRAM.json")
+    cyclic_raw = CYCLIC.read_bytes()
+    need(sha256(cyclic_raw).hexdigest() == CYCLIC_PIN, "Pair geometry pin")
+    cyclic = json.loads(cyclic_raw)
+    gauge = g.read("coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json")
+    scalar_phase = g.u.compiler.diag(9, (1, 0, 0, 0, 0, 0, 0, 0, 0))
+    W = scalar_phase.then(g.u.compiler.cgate(9, 45)).then(scalar_phase)
+    need(json.loads(json.dumps(W.circuit)) == gauge["W"]["circuit"], "Exact pinned W circuit")
+    W_circuit = tuple(tuple(tuple(v) if isinstance(v, list) else v for v in event)
+                      for event in gauge["W"]["circuit"])
+    g.u.phase.equal(g.u.phase.recipe(gauge["W"]["native_recipe"]), W_circuit, "Pinned W phase")
+    large = set(model["large_ports"])
+    inputs = {"rank30": (native["providers"], native["response"]),
+              "rank16": (odd["providers"], odd["model"]["response"])}
+    programs, receipts = {}, {}
+    for name, (providers, response_strings) in inputs.items():
+        response = g.rational_rows(response_strings)
+        programs[name], receipts[name] = {}, {}
+        for family, coded in (("W48_I64", large), ("W112", set(range(112)))):
+            programs[name][family], receipts[name][family] = {}, {}
+            for provider, words in providers.items():
+                programs[name][family][provider], receipts[name][family][provider] = {}, {}
+                for direction, old in words.items():
+                    translated = translate(old, cyclic["pair_codes"])
+                    g.replay(translated, response, direction)
+                    word, receipt = g.build(translated, cyclic["ports"], coded, W, W_circuit,
+                                            response, direction)
+                    g.replay(word, response, direction)
+                    need(receipt["real_scalar_primitives"] == (5288 if name == "rank30" else 7384),
+                         "Unchanged complete scalar invoice")
+                    expected = {
+                        ("rank30", "W48_I64"): {1: 988, 2: 48, 4: 55, 5: 55, 6: 9, 7: 9},
+                        ("rank30", "W112"): {1: 988, 2: 48, 5: 55, 6: 55, 7: 9, 8: 9},
+                        ("rank16", "W48_I64"): {1: 1472, 2: 112},
+                        ("rank16", "W112"): {1: 1408, 2: 112, 3: 64},
+                    }[name, family]
+                    need(receipt["profile"] == expected, "Exact changed-exit profile")
+                    need(receipt["native_mass"] == (1696 if family == "W48_I64" else 1824),
+                         "Exact changed-exit native mass")
+                    need(receipt["all_input_columns"] == 640 and receipt["inline_monomial_maps"] == 48,
+                         "All columns and priced zero-rank exits")
+                    programs[name][family][provider][direction] = word
+                    receipts[name][family][provider][direction] = receipt
+            print(name, family, receipts[name][family]["base"]["forward"], flush=True)
+    payload = {"schema": "low-displacement-coded-exits-v1", "source_pins": PINS,
+               "responses": {"rank30": native["response"], "rank16": odd["model"]["response"]},
+               "providers_by_response_and_code": programs}
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    for name, families in saved["providers_by_response_and_code"].items():
+        response = g.rational_rows(saved["responses"][name])
+        for providers in families.values():
+            for words in providers.values():
+                for direction, word in words.items():
+                    g.replay(word, response, direction)
+    (args.out / "CODED-EXITS-PROGRAM.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    checks = {
+        "status": "PASS_LOW_DISPLACEMENT_CODED_EXITS", "source_pins": PINS,
+        "exit_compiler_sha256": LIB_PIN, "exit_compiler_source_pins": g.PINS,
+        "cyclic_geometry_sha256": CYCLIC_PIN,
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_decompressed_sha256": sha256(raw).hexdigest(),
+        "fresh_changed_exit_phases": len(g.PHASE_CACHE), "receipts": receipts,
+        "scope": "Exact changed output representations. No free decoder, stage transport, helper progress or complete supplier claim.",
+    }
+    (args.out / "CODED-EXITS-CHECKS.json").write_text(json.dumps(checks, indent=2, sort_keys=True) + "\n")
+    print(checks["status"], checks["payload_decompressed_sha256"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_followthrough.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_followthrough.py
new file mode 100644
index 0000000000..492b44bc91
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_followthrough.py
@@ -0,0 +1,227 @@
+#!/usr/bin/env python3
+"""Check two response extensions on the frozen cyclic native paths."""
+
+import argparse
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+EMITTER = HERE / "emit_native.py"
+EMITTER_PIN = "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745"
+SOURCE = HERE / "native-normal-v2/NATIVE-PROGRAM.json.gz"
+SOURCE_PIN = "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558"
+EIGHT_CLIQUES = [
+    [1, 5, 19, 54, 64, 73, 82, 83], [3, 4, 22, 50, 60, 69, 80, 84],
+    [6, 35, 38, 39, 40, 77, 85, 86], [8, 12, 45, 88, 103, 107, 108, 109],
+    [17, 29, 30, 56, 58, 67, 93, 95], [18, 32, 34, 49, 65, 68, 98, 101],
+    [24, 26, 28, 48, 66, 75, 96, 97], [23, 31, 33, 55, 59, 74, 100, 102],
+]
+if sha256(EMITTER.read_bytes()).hexdigest() != EMITTER_PIN:
+    raise ValueError("Frozen native emitter pin")
+spec = importlib.util.spec_from_file_location("low_native", EMITTER)
+n = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = n
+spec.loader.exec_module(n)
+r, need = n.r, n.need
+
+
+def make_model(old, cyclic, kind):
+    model = {key: old[key] for key in (
+        "ports", "large_ports", "small_ports", "selected_ports", "ordinary_ports",
+        "selected_block", "selected_inverse", "vertex_assignments", "small_cliques")}
+    large, small = old["large_ports"], old["small_ports"]
+    response, inverse = n.rows(old["response"]), n.rows(old["response_inverse"])
+    if kind == "reciprocal-large":
+        mt = r.transpose(n.rows(old["mode_inverse"]), 112)
+        et, eit = r.transpose(inverse, 112), r.transpose(response, 112)
+        model["mode_response"] = r.encoded(mt)
+        model["mode_inverse"] = r.encoded(r.transpose(n.rows(old["mode_response"]), 112))
+        for p in large:
+            response[p], inverse[p] = et[p], eit[p]
+        word_large = [gate for gate in old["common_frame_words"]["inverse_transpose_E"]
+                      if gate[1] in set(large)]
+        word_small = [gate for gate in old["common_frame_words"]["E"] if gate[1] in set(small)]
+        word = word_large + word_small
+        need(r.replay(word)[0] == response, "Partial reciprocal common-frame code")
+        model["common_frame_words"] = {
+            "E": word, "inverse_E": r.inverse_word(word),
+            "transpose_E": r.transpose_word(word),
+            "inverse_transpose_E": r.transpose_word(r.inverse_word(word)),
+        }
+        expected = {"E": response, "inverse_E": inverse,
+                    "transpose_E": r.transpose(response, 112),
+                    "inverse_transpose_E": r.transpose(inverse, 112)}
+        for name, gates in model["common_frame_words"].items():
+            need(r.replay(gates)[0] == expected[name] and r.price(gates) == 3210,
+                 "Complete reciprocal scalar code and invoice " + name)
+        model["extension_scope"] = "Raw backward gives the old E48 inverse, with the old C64 transpose."
+    else:
+        need(kind == "odd-grid-rank16", "Extension kind")
+        h = r.identity(112)
+        for pair in cyclic["pair_codes"]:
+            for i, p in enumerate(pair["ports"]):
+                h[p] = {q: F(pair["matrix"][i][j]) for j, q in enumerate(pair["ports"])}
+        hi = r.transpose(h, 112)
+        for p in large:
+            hi[p] = {q: c / 2 for q, c in hi[p].items()}
+        mode, mi = r.identity(112), r.identity(112)
+        u, v = [{} for _ in range(112)], []
+        for record in old["vertex_assignments"]:
+            group, signs = record["ordered_carriers_a_b_c"], record["signs"]
+            for i, p in enumerate(group):
+                mode[p] = {q: F(int(i == j) - signs[i] * signs[j])
+                           for j, q in enumerate(group) if i != j}
+                mi[p] = {q: F(int(i == j)) - F(signs[i] * signs[j], 5)
+                         for j, q in enumerate(group)}
+                u[p] = {len(v): F(-signs[i])}
+            v.append({q: F(signs[j]) for j, q in enumerate(group)})
+        response, inverse = r.product(hi, r.product(mode, h)), r.product(hi, r.product(mi, h))
+        u, v = r.product(hi, u), r.product(v, h)
+        need(sorted(p for group in EIGHT_CLIQUES for p in group) == sorted(small),
+             "Eight disjoint eight-cliques cover the actual64 ports")
+        for group in EIGHT_CLIQUES:
+            need(all((old["ports"][p] & old["ports"][q]).bit_count() % 2 == int(p == q)
+                     for p in group for q in group), "Actual orthonormal eight-clique")
+            for p in group:
+                response[p] = {q: F(-1) for q in group if q != p}
+                inverse[p] = {q: F(int(p == q)) - F(1, 7) for q in group}
+                u[p] = {len(v): F(-1)}
+            v.append({p: F(1) for p in group})
+        correction = [dict(row) for row in response]
+        for p in range(112):
+            r.add(correction[p], {p: F(-1)})
+        need(r.product(u, v) == correction and r.rank(u, 16) == r.rank(v, 112) == 16,
+             "Exact rank16 correction factor")
+        model.update(mode_response=r.encoded(mode), mode_inverse=r.encoded(mi),
+                     small_cliques=EIGHT_CLIQUES, correction_U=r.encoded(u), correction_V=r.encoded(v))
+        model["extension_scope"] = "Integer native response; inverse requires retained-grid denominators5 and7."
+    model["response"], model["response_inverse"] = r.encoded(response), r.encoded(inverse)
+    need(r.product(response, inverse) == r.product(inverse, response) == r.identity(112),
+         "Both full response inverse orders")
+    need(all(p not in row for p, row in enumerate(response)), "Physical zero diagonal")
+    correction = [dict(row) for row in response]
+    for p in range(112):
+        r.add(correction[p], {p: F(-1)})
+    model["correction_rank"] = r.rank(correction, 112)
+    model["full_determinant"] = str(r.determinant(response))
+    selected = old["selected_ports"]
+    selected_block = r.restrict(response, selected)
+    need(selected_block == n.rows(old["selected_block"]), "The selected block stays L")
+    model["selected_inverse_block"] = r.encoded(r.restrict(inverse, selected))
+    model["ordinary_determinant"] = str(r.determinant(r.restrict(response, old["ordinary_ports"])))
+    if kind == "odd-grid-rank16":
+        want = [{j: (F(4 if i == j else 0) + selected_block[i].get(j, F(0))) / 5
+                 for j in range(8) if i == j or selected_block[i].get(j)} for i in range(8)]
+        need(r.restrict(inverse, selected) == want, "The new inverse principal block is (4I+L)/5")
+        need(r.determinant(response) == 35 ** 8
+             and F(model["ordinary_determinant"]) == F(7 ** 8 * 31 ** 4, 16),
+             "Exact odd-grid principal determinants")
+        principal_inverse = [
+            {j: F(40 if i == j else 0, 31) - F(10, 31) * selected_block[i].get(j, F(0))
+             for j in range(8) if i == j or selected_block[i].get(j)}
+            for i in range(8)]
+    else:
+        principal_inverse = n.rows(old["selected_inverse"])
+    need(r.product(r.restrict(inverse, selected), principal_inverse) == r.identity(8),
+         "Inverse response selected principal inverse")
+    ordinary = old["ordinary_ports"]
+    p = [{j: inverse[row][s] for j, s in enumerate(selected) if inverse[row].get(s)}
+         for row in ordinary]
+    t = [{j: inverse[row][s] for j, s in enumerate(ordinary) if inverse[row].get(s)}
+         for row in selected]
+    ordinary_inverse = r.restrict(inverse, ordinary)
+    for row, correction in zip(ordinary_inverse, r.product(r.product(p, principal_inverse), t)):
+        r.add(row, correction, -1)
+    ordinary_response = r.restrict(response, ordinary)
+    need(r.product(ordinary_response, ordinary_inverse) == r.product(ordinary_inverse, ordinary_response)
+         == r.identity(104), "Both new ordinary principal inverse orders")
+    model["ordinary_inverse"] = r.encoded(ordinary_inverse)
+    return model
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--kind", choices=("reciprocal-large", "odd-grid-rank16"), required=True)
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    raw = gzip.decompress(SOURCE.read_bytes())
+    need(sha256(raw).hexdigest() == SOURCE_PIN, "Frozen native payload pin")
+    source = json.loads(raw)
+    old = json.loads(n.read("new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json"))
+    cyclic = json.loads(n.read("independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json"))
+    model = make_model(old, cyclic, args.kind)
+    words = {direction: n.make_word(cyclic, model, direction) for direction in ("forward", "backward")}
+    base = source["providers"]["base"]["forward"]
+    inherited = {}
+    for key, record in base["native_recipes"].items():
+        old_frame, new_frame = map(int, key.split(":"))
+        inherited[tuple(base["frames"][old_frame]), tuple(base["frames"][new_frame])] = record
+    frames = words["forward"]["frames"]
+    need(frames == words["backward"]["frames"], "Shared native paths")
+    edge_pairs = sorted({(event[2], event[3]) for word in words.values()
+                         for event in word["events"] if event[0] == "native"})
+    recipes, fresh, reused = {}, 0, 0
+    for old_frame, new_frame in edge_pairs:
+        pair = tuple(frames[old_frame]), tuple(frames[new_frame])
+        if pair in inherited:
+            record = inherited[pair]
+            reused += 1
+        else:
+            operation = n.compiler.canonical_frame(9, pair[0]).adjoint().then(
+                n.compiler.canonical_frame(9, pair[1]))
+            record, _ = n.compiler.lower_child(operation)
+            need(record["rank"] == len(pair[1]) - len(pair[0]), "Fresh extension native rank")
+            n.phase.equal(n.phase.recipe(record), n.phase.adjoint(n.phase.frame(pair[0], 9))
+                          + n.phase.frame(pair[1], 9), "Fresh extension native phase")
+            fresh += 1
+            if fresh % 100 == 0:
+                print("Fresh extension phases", fresh, flush=True)
+        recipes[str(old_frame) + ":" + str(new_frame)] = record
+    reports = {}
+    for direction, word in words.items():
+        word["native_recipes"] = recipes
+        word["endpoint_adapters"] = base["endpoint_adapters"]
+        need(word["start"] == base["start"] and word["final"] == base["final"],
+             "The inherited endpoint adapters have identical exact frames")
+        for i in set(word["start"] + word["final"]):
+            need(word["frames"][i] == base["frames"][i], "Exact endpoint frame basis")
+        reports[direction] = n.verify_word(word, n.rows(model["response"]), direction)
+    expected_profile = ({1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}
+                        if args.kind == "reciprocal-large" else {1: 1520, 2: 64, 3: 48})
+    expected_scalar = 5288 if args.kind == "reciprocal-large" else 7384
+    for report in reports.values():
+        need(report["native_profile"] == expected_profile and report["native_mass"] == 1792
+             and report["real_scalar_primitives"] == expected_scalar, "Complete extension invoice")
+    payload = {"schema": "low-displacement-native-extension-v1", "kind": args.kind,
+               "model": model, "providers": {provider: words for provider in source["providers"]}}
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    for provider, directions in saved["providers"].items():
+        for direction, word in directions.items():
+            need(n.verify_word(word, n.rows(saved["model"]["response"]), direction) == reports[direction],
+                 "Serialized extension replay " + provider)
+    (args.out / "EXTENSION-PROGRAM.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    checks = {"status": "PASS_" + args.kind.upper().replace("-", "_"),
+              "kind": args.kind, "source_native_decompressed_sha256": SOURCE_PIN,
+              "source_emitter_sha256": EMITTER_PIN,
+              "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+              "payload_decompressed_sha256": sha256(raw).hexdigest(),
+              "fresh_native_phases": fresh, "inherited_native_phases": reused,
+              "inherited_endpoint_phases": 224, "reports": reports,
+              "full_correction_rank": model["correction_rank"],
+              "full_determinant": model["full_determinant"],
+              "ordinary_determinant": model["ordinary_determinant"],
+              "scope": "Exact local data word. Odd-grid code admission, terminal, helper progress and recursive supplier duties are separate."}
+    (args.out / "EXTENSION-CHECKS.json").write_text(json.dumps(checks, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(checks, sort_keys=True), flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py
new file mode 100644
index 0000000000..532c8709eb
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py
@@ -0,0 +1,279 @@
+#!/usr/bin/env python3
+"""Emit and check the native rank-thirty response on the actual ports."""
+
+import argparse
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+PINS = {
+    "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json":
+        ("plain", "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"),
+    "new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json":
+        ("plain", "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c"),
+    "new-core-transfer-20261017/low-displacement-20261020/check_response.py":
+        ("plain", "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"),
+    "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz":
+        ("decompressed", "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa"),
+    "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py":
+        ("plain", "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"),
+    "interface-proof/verify_native_lift.py":
+        ("plain", "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(relative):
+    mode, pin = PINS[relative]
+    raw = (LANES / relative).read_bytes()
+    if mode == "decompressed":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Source pin " + relative)
+    return raw
+
+
+def load_module(name, relative):
+    read(relative)
+    spec = importlib.util.spec_from_file_location(name, LANES / relative)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+
+r = load_module("low_response", "new-core-transfer-20261017/low-displacement-20261020/check_response.py")
+compiler = load_module("low_compiler", "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py")
+phase = load_module("low_phase", "interface-proof/verify_native_lift.py")
+
+
+def basis(vectors):
+    rows = list(dict.fromkeys(vectors))
+    count = 0
+    for bit in range(8, -1, -1):
+        found = next((i for i in range(count, len(rows)) if rows[i] >> bit & 1), None)
+        if found is None:
+            continue
+        rows[count], rows[found] = rows[found], rows[count]
+        for i in range(len(rows)):
+            if i != count and rows[i] >> bit & 1:
+                rows[i] ^= rows[count]
+        count += 1
+    return tuple(rows[:count])
+
+
+def rows(value):
+    return [{int(p): F(c) for p, c in row.items()} for row in value]
+
+
+def verify_word(word, response, direction):
+    current = list(word["start"])
+    state = [{i: F(1)} for i in range(len(current))]
+    maximum = F(1)
+    scalar_word = []
+    for event in word["events"]:
+        if event[0] == "native":
+            _, field, old, new, rank, key = event
+            need(current[field] == old, "Literal native entry frame")
+            need(len(basis(word["frames"][old] + word["frames"][new])) == len(word["frames"][new]),
+                 "Literal nested native edge")
+            need(rank == len(word["frames"][new]) - len(word["frames"][old])
+                 == word["native_recipes"][key]["rank"], "Literal native rank")
+            current[field] = new
+        else:
+            need(event[0] == "scalar", "Literal event grammar")
+            gate, frame = event[1:]
+            op, target, origin, coefficient = gate
+            c = F(coefficient)
+            need(current[target] == frame, "Literal scalar target frame")
+            if op == "scale":
+                state[target] = {p: c * v for p, v in state[target].items() if c * v}
+            else:
+                need(op == "add" and target != origin and current[origin] == frame,
+                     "Literal scalar source frame")
+                r.add(state[target], state[origin], c)
+            maximum = max(maximum, sum(abs(v) for v in state[target].values()))
+            scalar_word.append(gate)
+    expected = [{i: F(1)} for i in range(len(current))]
+    for target, row in enumerate(response):
+        if direction == "forward":
+            r.add(expected[112 + target], row)
+        else:
+            for origin, coefficient in row.items():
+                r.add(expected[origin], {112 + target: -coefficient})
+    need(state == expected and current == word["final"], "All640 columns and final frames")
+    profile = Counter(event[4] for event in word["events"] if event[0] == "native")
+    return {"all_input_columns": len(current), "untouched_arbitrary_fields": len(current) - 224,
+            "owned_fields": 0, "private_fields": 0, "native_profile": dict(sorted(profile.items())),
+            "native_mass": sum(k * v for k, v in profile.items()), "native_children": sum(profile.values()),
+            "real_scalar_primitives": r.price(scalar_word), "prefix_row_l1_bound": str(maximum),
+            "native_side_map_bound": 2 * sum(profile.values()), "endpoint_maps": 224}
+
+
+def make_word(cyclic, model, direction):
+    frames = deepcopy(cyclic["frames"])
+    indices = {tuple(frame): i for i, frame in enumerate(frames)}
+    small = set(model["small_ports"])
+    current = list(cyclic["start"])
+    events = []
+    mode = rows(model["mode_response"])
+    by_parameter = {record["id"]: record for record in cyclic["parameters"]}
+    transfer_records = []
+    for event in cyclic["programs"][direction]:
+        kind = event[0]
+        if kind == "native":
+            _, field, old, new, rank = event
+            if field % 112 in small:
+                need(field < 224, "Only data fields receive native progress")
+                continue
+            need(current[field] == old, "Pinned cyclic native frame")
+            current[field] = new
+            events.append(["native", field, old, new, rank, str(old) + ":" + str(new)])
+        elif kind == "parameter_add":
+            _, target, origin, parameter, sign, frame = event
+            record = by_parameter[parameter]
+            carriers = cyclic["cyclic_carriers"][record["vertex"]]
+            c = sign * mode[carriers[record["row"]]].get(carriers[record["column"]], F(0))
+            if c:
+                transfer_records.append({"part": "large48", "event": len(events),
+                                         "coefficient": str(c), "parameter": parameter})
+                events.append(["scalar", ["add", target, origin, str(c)], frame])
+        else:
+            need(kind in ("add", "scale"), "Pinned cyclic scalar grammar")
+            _, target, origin, coefficient, frame = event
+            events.append(["scalar", [kind, target, origin, coefficient], frame])
+
+    def frame(vectors):
+        vectors = basis(vectors)
+        if vectors not in indices:
+            indices[vectors] = len(frames)
+            frames.append(list(vectors))
+        return indices[vectors]
+
+    def native(field, new):
+        old = current[field]
+        if old == new:
+            return
+        need(len(basis(frames[old] + frames[new])) == len(frames[new]), "Clique nested edge")
+        events.append(["native", field, old, new, len(frames[new]) - len(frames[old]),
+                       str(old) + ":" + str(new)])
+        current[field] = new
+
+    q = cyclic["ports"]
+    for group in model["small_cliques"]:
+        k = len(group)
+        for depth in range(1, k):
+            for i, p in enumerate(group):
+                native(p, frame(q[group[(i + j) % k]] for j in range(depth)))
+                native(112 + p, frame(q[group[(i - j) % k]] for j in range(1, depth + 1)))
+            for i, p in enumerate(group):
+                target_port = group[(i + depth) % k]
+                need(current[p] == current[112 + target_port], "Every clique transfer has equal frames")
+                target, origin, coefficient = ((112 + target_port, p, "-1") if direction == "forward"
+                                               else (p, 112 + target_port, "1"))
+                transfer_records.append({"part": "small64", "event": len(events),
+                                         "source_port": p, "target_port": target_port,
+                                         "coefficient": coefficient})
+                events.append(["scalar", ["add", target, origin, coefficient], current[p]])
+        for p in group:
+            native(p, cyclic["final"][p])
+            native(112 + p, cyclic["final"][112 + p])
+    need(current == cyclic["final"], "Full native frame completion")
+    return {"frames": frames, "start": cyclic["start"], "final": cyclic["final"],
+            "events": events, "transfer_records": transfer_records}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    cyclic = json.loads(read("independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json"))
+    model = json.loads(read("new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json"))
+    core = json.loads(read("new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz"))
+    for provider, data in core["providers"].items():
+        need(data["canonical"]["ports"] == cyclic["ports"], "Pinned provider directions " + provider)
+        need(len(data["canonical"]["start"]) == 632, "Pinned live-field count " + provider)
+    words = {direction: make_word(cyclic, model, direction) for direction in ("forward", "backward")}
+    need(words["forward"]["frames"] == words["backward"]["frames"], "Both directions use the same actual frames")
+    frames = words["forward"]["frames"]
+    edge_pairs = sorted({(event[2], event[3]) for word in words.values()
+                         for event in word["events"] if event[0] == "native"})
+    recipes = {}
+    for i, (old, new) in enumerate(edge_pairs):
+        operation = compiler.canonical_frame(9, tuple(frames[old])).adjoint().then(
+            compiler.canonical_frame(9, tuple(frames[new])))
+        record, _ = compiler.lower_child(operation)
+        need(record["rank"] == len(frames[new]) - len(frames[old]), "Fresh native rank")
+        phase.equal(phase.recipe(record), phase.adjoint(phase.frame(frames[old], 9))
+                    + phase.frame(frames[new], 9), "Fresh native phase " + str((old, new)))
+        recipes[str(old) + ":" + str(new)] = record
+        if (i + 1) % 100 == 0:
+            print("Native phases", i + 1, "/", len(edge_pairs), flush=True)
+    endpoints = []
+    for p, q in enumerate(cyclic["ports"]):
+        for role in ("source", "target"):
+            conventional = (compiler.cgate(9, q) if role == "source"
+                            else compiler.cgate(9, q, -1).then(compiler.fourier(9)))
+            circuit = (("C", q, 1),) if role == "source" else (("C", q, -1),) + phase.fourier(9)
+            frame = cyclic["start"][p] if role == "source" else cyclic["final"][112 + p]
+            operation = conventional.adjoint().then(compiler.canonical_frame(9, tuple(frames[frame])))
+            record, _ = compiler.lower_child(operation)
+            need(record["rank"] == 0, "Endpoint adapter is monomial")
+            phase.equal(phase.recipe(record), phase.adjoint(circuit) + phase.frame(frames[frame], 9),
+                        "Fresh conventional endpoint " + str((role, p)))
+            endpoints.append({"port": p, "role": role, "frame": frame, **record})
+    reports = {}
+    for direction, word in words.items():
+        word["native_recipes"] = recipes
+        word["endpoint_adapters"] = endpoints
+        reports[direction] = verify_word(word, rows(model["response"]), direction)
+    need(reports["forward"]["native_profile"] == {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9},
+         "Complete profile")
+    need(reports["forward"]["native_mass"] == 1792 and reports["forward"]["real_scalar_primitives"] == 5288,
+         "Complete local invoice")
+    # Deletion of one nonzero transfer must change the complete content map.
+    bad = deepcopy(words["forward"])
+    del bad["events"][bad["transfer_records"][0]["event"]]
+    try:
+        verify_word(bad, rows(model["response"]), "forward")
+    except ValueError:
+        pass
+    else:
+        raise ValueError("The missing transfer control was accepted")
+    payload = {"schema": "low-displacement-native-v1", "source_pins": PINS,
+               "response": model["response"], "common_frame_words": model["common_frame_words"],
+               "selected_ports": model["selected_ports"], "small_cliques": model["small_cliques"],
+               "providers": {provider: words for provider in core["providers"]}}
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    for provider, directions in saved["providers"].items():
+        for direction, word in directions.items():
+            need(verify_word(word, rows(saved["response"]), direction) == reports[direction],
+                 "Serialized provider replay " + provider + " " + direction)
+    (args.out / "NATIVE-PROGRAM.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {"status": "PASS_LOW_DISPLACEMENT_NATIVE", "source_pins": PINS,
+               "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "payload_decompressed_sha256": sha256(raw).hexdigest(),
+               "fresh_native_phase_checks": len(recipes), "fresh_endpoint_phase_checks": len(endpoints),
+               "reports": reports, "same_geometry_both_providers_checked": True,
+               "negative_control": "one nonzero transfer omitted and rejected",
+               "scope": "Complete local data shears and exact phases. Helpers are unchanged; their progress, recursive hosting, routed codes and terminal remain open."}
+    (args.out / "NATIVE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True), flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/CARRIER-PREFIX.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/CARRIER-PREFIX.md
new file mode 100644
index 0000000000..88709fb3e0
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/CARRIER-PREFIX.md
@@ -0,0 +1,40 @@
+# The complete carrier prefix
+
+This packet stops the independently reviewed local reuse word before its
+selected query. It supplies a concrete native prefix for a separate
+routed reader query.
+
+The input is \(X=Qx\), \(Y_U=y_U\), and \(Y_P=Q_Pz\), with arbitrary
+independent records \(z\). The output is
+
+\[
+X'=F_9x,\qquad
+Y'_U=F_9q_U(y+Ex)_U,\qquad
+Y'_P=F_9z.
+\]
+
+All 416 auxiliary fields are unchanged. The word has 2406 events:
+2390 retained-core events followed by sixteen line-to-FULL native
+calls. It has no selected query. Both providers pass all 640 independent
+columns and every exact read, write, and native frame check.
+
+The profile is \(1392H_1+64H_2+48H_3+16H_8\), with native mass 1792,
+1520 children, and 6456 scalar primitives. There are 128 input views,
+96 ordinary output views, and a native side-map upper bound of 3040.
+The content prefix row one-norm is 22; its additional binary denominator
+height is one. There is no extra owned or private field.
+
+Every physical recipe and adapter is copied from the pinned line-entry
+reuse packet, whose independent review is also pinned. The two output
+directories have byte-identical payloads and receipts under normal and
+optimized Python.
+
+This packet supplies only the native prefix. The global dispatcher,
+past-reader query, and their full invoices are separate. It does not
+replace a past reader with the current reader.
+
+Run `emit_prefix.py --out <new-directory>` with normal Python or
+optimized Python. The emitter rejects an existing output directory.
+
+AI agents prepared this extension of the reviewed productive row-capture
+and line-entry reuse constructions.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json
new file mode 100644
index 0000000000..bc2670414d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json
@@ -0,0 +1,12 @@
+{
+  "files": {
+    "CARRIER-PREFIX.md": "2ef1ff2371a01289310137570b0ce03b2739c85e74c1e7ba94ea434eedcff1b4",
+    "emit_prefix.py": "657afc180b397e851fbefa16f56ace98129072a6bd2faf5d84dbc2391720698e",
+    "prefix-normal/CARRIER-PREFIX.json.gz": "42b7d01235d86252c52d979bbc8dd8978cd08f57ef0f968124cbf18c7cb1a70c",
+    "prefix-normal/CHECKS.json": "82c8bb1dd1bc0c05d37cffe30697f7762627526ea012855f35d4b72ae537583d",
+    "prefix-optimized/CARRIER-PREFIX.json.gz": "42b7d01235d86252c52d979bbc8dd8978cd08f57ef0f968124cbf18c7cb1a70c",
+    "prefix-optimized/CHECKS.json": "82c8bb1dd1bc0c05d37cffe30697f7762627526ea012855f35d4b72ae537583d"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Exact carrier-only prefix. Global dispatcher and routed query are separate."
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json
new file mode 100644
index 0000000000..006f55295f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "ROUTED-QUERY.md": "2ee46160065120ca90477ebabebd833c8e0dc4678544fb33c267193cada5e7cd",
+    "emit_routed_query.py": "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900",
+    "query-normal/CHECKS.json": "55cb6d50b4a219ba3cea2ee59a3b15b03afa3c3c749dd13a72ee6148414845a2",
+    "query-normal/ROUTED-QUERY.json.gz": "b6a1031861db0b2293880af7c01919c5c628a8c23e7a293f73976a82e25011ac",
+    "query-optimized/CHECKS.json": "55cb6d50b4a219ba3cea2ee59a3b15b03afa3c3c749dd13a72ee6148414845a2",
+    "query-optimized/ROUTED-QUERY.json.gz": "b6a1031861db0b2293880af7c01919c5c628a8c23e7a293f73976a82e25011ac"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a",
+  "scope": "Literal global FULL reader query and exact native carrier prefix. Actual D25 dispatcher, recursive hosting and complete supplier are separate.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/ROUTED-QUERY.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/ROUTED-QUERY.md
new file mode 100644
index 0000000000..72d7769e03
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/ROUTED-QUERY.md
@@ -0,0 +1,152 @@
+# A literal query for a centre reader retained from an earlier stage
+
+This packet expands the bridge worker's fixed-reader construction into
+literal scalar and field-map instructions. It checks their composition
+with the complete native carrier prefix. It covers the actual D25 stage
+pairs \((s,t)=(0,1),(0,2),(1,2)\).
+
+The local carrier prefix and the query use different charts. The prefix
+has the exact local native charts. The query starts after the dispatcher
+has placed all X fields and the sixteen selected Y fields in the global
+FULL chart at level \(t\). The dispatcher is a separate binding. This
+packet does not assume that those charts are identical.
+
+## Required update
+
+Let \(P\) be the sixteen selected ports. Let \(J\) insert values at \(P\).
+The normalized reader and its unit row code at stage \(s\) are
+
+\[
+L_s=J^T+B_s,\qquad B_sJ=0,\qquad C_s=I+JB_s.
+\]
+
+All symbols include their actual ordered owner routes. The native
+response at stage \(t\) is \(E_t\). The query must add
+\(L_sE_tx\) to the selected record. It must restore every X field.
+
+The native prefix accepts arbitrary independent selected records \(z\).
+Before the query its contents are
+
+\[
+X=x,\qquad Y_P=z,\qquad Y_U=y_U+(E_tx)_U,
+\]
+
+with the prefix's stated physical output frames. After the query the
+selected content is \(z+L_sE_tx\). If \(z=L_sy\), it is exactly
+\(L_s(y+E_tx)\). The ordinary output content is already correct and is
+not accessed by the query.
+
+## Literal query order
+
+The source theorem gives
+
+\[
+L_sE_tC_t^{-1}
+=B_s-B_t+(L_sE_tJ)J^T.
+\]
+
+The emitted word executes:
+
+1. Add \(B_sX_U\) to \(Y_P\), through the actual past-stage FULL views.
+2. Add \(X_P\) to \(Y_P\).
+3. Apply \(C_t\) to X, through the current-stage FULL views.
+4. Subtract the current \(X_P\) from \(Y_P\).
+5. Add \((L_sE_tJ)X_P\) to \(Y_P\).
+6. Apply \(C_t^{-1}\) to X through the same current-stage views.
+
+Steps 2 and 4 account for \(-B_tX_U\). The X fields in step 5 contain
+the current reader \(L_tX\). Step 6 restores the original source bank.
+No inverse of \(E_t\) and no odd division is used.
+
+Every view is an explicit `map` event. Both the entry map and its inverse
+are present. For each term in step 5, the word maps the selected X
+source, adds its scalar multiple to the selected Y target, and restores
+the X source with the exact inverse map. A scale of a target is also
+explicit. No target baseline is assumed to be zero.
+
+## Exact owner paths and phases
+
+The verifier represents a coefficient by a pair consisting of its input
+field and a 25-dimensional orthogonal owner matrix. It multiplies the
+matrices in chronological operator order. Terms can cancel only when
+their complete ordered matrices agree. It does not identify the
+responses at stages \(s\) and \(t\).
+
+For each map with matrix \(R\), the packet records a translation
+\(\delta_R\), the inverse matrix, and the inverse translation. It
+checks orthogonality, both matrix inverse orders, and that every
+uncompleted axis is fixed. It verifies the complete Z4 phase identity
+
+\[
+F_{9+8t}P_RF_{9+8t}^{-1}=X_{\delta_R}P_R.
+\]
+
+This is a polynomial identity, including its quadratic and linear
+parts. It holds on the complete spatial domain; it is not a sample of
+spatial points. The phase checker is the pinned source implementation.
+An independent review of this integration must still check that
+dependency and the actual dispatcher.
+
+The actual payload contains 545 distinct FULL maps for each pair with
+reader stage zero, and 1616 for pair \((1,2)\). These counts include
+distinct inverse and view maps where required. The instruction count
+remains 2064 map calls in every pair.
+
+## Verification and price
+
+Both native providers are replayed on all 640 independent local input
+columns before the query. The global query is then replayed on all
+640 independent formal fields. The result matches the direct expression
+\(L_sE_t\), with all 3808 owner-path terms. All 112 X fields are restored.
+The 96 ordinary Y fields and all 416 helpers are unchanged by the query.
+
+The serialized payload is read and checked again. Controls that omit
+one middle source view or the final source-code restoration fail.
+Normal and optimized Python give byte-identical outputs.
+
+| Part | Scalar primitives | Explicit map calls |
+| --- | ---: | ---: |
+| Past-reader complement query | 1760 | 224 |
+| Two selected-field copies | 256 | 0 |
+| Current source code and its inverse | 3520 | 448 |
+| Middle selected-source query | 5632 | 1392 |
+| Query total | 11168 | 2064 |
+
+Adding the native prefix gives 17624 scalar primitives and native
+profile
+
+\[
+1392H_1+64H_2+48H_3+16H_8,
+\]
+
+with mass 1792. The query maps are additional to the prefix's 128 input
+views, 96 output views, and native side-map upper bound 3040. The actual
+global dispatcher must also be charged. There are no extra owned or
+private fields and no new native child in the query.
+
+The exact formal coefficient sweep gives prefix row one-norm 448 and
+binary denominator height two for every pair. This is an upper bound
+for the actual register norm. Distinct formal owner paths may have
+further dependencies in their action on arrays, so it is not a claim
+that the induced spatial operator norm is exactly 448. These bounds
+apply to the stated independent inputs at the query entrance. A
+recursive precision certificate must also account for how those inputs
+were formed and for each child implementation.
+
+Reproduce into new directories:
+
+```sh
+python3 emit_routed_query.py --out replay-normal
+python3 -O emit_routed_query.py --out replay-optimized
+```
+
+The result is a concrete query implementation and a checked native
+prefix, with the exact intended splice stated. A complete D25 service
+requires the separately pinned dispatcher that proves that splice.
+Recursive hosting and the complete supplier remain open. The local
+same-reader price 9880 is not the price of this past-reader service.
+
+This packet implements the fixed-reader theorem and source-view records
+from the bridge-access lane. It uses the reviewed productive row-capture
+and line-entry native family. AI agents prepared the code, proof, and
+checks.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICE-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICE-FREEZE.json
new file mode 100644
index 0000000000..886dfd1aca
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICE-FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "SERVICES.md": "f7038b6f8d507d741e01102589ca8d4341544c6abd47200510d53696fec4752a",
+    "emit_service.py": "03ae362f0ff697fe13718f2f0516bb09f640ad743fdf943038975aee9a0d35fd",
+    "service-normal/CHECKS.json": "82091780784cdf9ae9f388f2fa353bd64214d93e7517595890e7a22b18817eb5",
+    "service-normal/FIXED-READER-SERVICES.json.gz": "89a0e1d9621b58e54c8d51ea40b7404220dc0156fd4966e99b6f8664ab350ebe",
+    "service-optimized/CHECKS.json": "82091780784cdf9ae9f388f2fa353bd64214d93e7517595890e7a22b18817eb5",
+    "service-optimized/FIXED-READER-SERVICES.json.gz": "89a0e1d9621b58e54c8d51ea40b7404220dc0156fd4966e99b6f8664ab350ebe"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "88d25925705e6657656afb727430ce0d541c5e657426166363694d8b66180d13",
+  "scope": "Six exact data services on the regular D25 cover under the inherited416-helper host contract. Recursive hosting and complete supplier cost remain separate.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICES.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICES.md
new file mode 100644
index 0000000000..bb6a258dbd
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/SERVICES.md
@@ -0,0 +1,117 @@
+# Six complete data services that retain a past centre reader
+
+This packet joins the exact native carrier prefix, the actual D25 DATA
+dispatcher, and the literal global FULL query. It gives both native
+providers for each pair \((s,t)=(0,1),(0,2),(1,2)\). It uses the inherited
+416-field helper host contract. It does not construct or price that host.
+
+Let \(F_\ell\) act on the first \(9+8\ell\) coordinates. Let \(P\) be the
+sixteen fixed pivots and \(U\) their complement. Define
+\(G=\operatorname{diag}(I_P,q_U)\). The complete data interface is
+
+\[
+(F_{t-1}x,\ F_{t-1}Gw)
+\longmapsto
+(F_tx,\ F_tG(w+A_{s,t}x)),
+\]
+
+where
+
+\[
+(A_{s,t})_P=L_sE_t,\qquad (A_{s,t})_U=(E_t)_U.
+\]
+
+The contents of w, including all selected records, are independent and
+arbitrary. If \(w=C_sy\), then the selected output is
+\(L_s(y+E_tx)\), while the ordinary output is \((y+E_tx)_U\).
+Thus the service carries and updates the same reader from stage s.
+It does not replace it by the current reader.
+
+The physical input level is \(t-1\). In particular, pair \((0,2)\)
+requires a stage-zero reader that has already reached physical level
+one. It is not a direct jump from physical level zero to level two.
+
+## Exact schedule and binding
+
+The bundled service executes these blocks in order:
+
+1. Apply the 224 current DATA entry views.
+2. Apply the 128 local native input adapters.
+3. Execute all 2406 native-prefix events over the complete cover.
+4. Apply the 96 ordinary target output adapters.
+5. Apply the 224 current DATA exit views.
+6. Complete the cover barrier.
+7. Execute the literal past-reader query at global FULL.
+
+The selected target entry is an intrinsic positive line. The native
+prefix carries it to FULL with an H8 child. Its ordinary targets retain
+their hole paths. After the DATA exits, all source X fields and selected
+Y fields are in global FULL. The late query can then read them through
+the pinned past/current source maps. It does not read an ordinary Y
+field.
+
+`emit_service.py` checks all 896 DATA entry and exit phase equations for
+the two service stages, including the common exterior, translation
+order, intrinsic lines, and final hole or FULL type. It checks that the
+current query views equal the actual DATA exit views. It then replays
+all six complete content maps using those DATA route matrices.
+
+The native programs and every literal query instruction are included in
+one payload. The dispatcher, prefix, and query source pins remain in the
+payload. The local native phase proofs are inherited by exact byte
+identity from the independent line-entry review.
+
+For each field the owner route is an orthogonal bijection on the regular
+\(O(25,2)\) cover. Complete body calls restore their arbitrary helpers
+before those helpers are reused. The complete cover sweep is required
+before the query. The data route argument does not prove a new helper
+allocation or recursive child host.
+
+## Complete service invoice
+
+Every service has native profile
+
+\[
+1392H_1+64H_2+48H_3+16H_8,
+\]
+
+with mass 1792 and 1520 children. Its scalar cost is
+\(6456+11168=17624\). The explicit monomial call bound is:
+
+| Part | Calls |
+| --- | ---: |
+| DATA entry and exit | 448 |
+| Local endpoint adapters | 224 |
+| Native side-map upper bound | 3040 |
+| Past-reader query | 2064 |
+| Total | 5776 |
+
+The bound includes identity maps where the fixed instruction stock
+retains them. No extra owned or private field is used. There is no odd
+division. A map call still needs its finite implementation cost in a
+complete supplier.
+
+All 640 independent fields pass the local and ordered-owner content
+replays. Every source and all 416 helpers are restored as specified.
+The query formal coefficient bound is 448 with binary height two.
+The native-prefix bound is 22 with binary height one. These bounds do
+not replace the recursive precision proof.
+
+Normal and optimized Python produce byte-identical service payloads and
+receipts. Reproduce into new directories:
+
+```sh
+python3 emit_service.py --out replay-normal
+python3 -O emit_service.py --out replay-optimized
+```
+
+The result closes the data-chart splice for this forward reuse family.
+The inherited helper host, recursive parking, finite map costs, an
+outer caller, and the complete supplier invoice remain explicit
+obligations. No complete kappa improvement is claimed.
+
+This result combines the bridge-access dispatcher and fixed-reader
+theorem with the native carrier and literal query from this lane.
+The controller supplied the normalized row code. AI agents prepared
+the proof, implementation, and checks. Independent joined-service
+review is recorded separately.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_prefix.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_prefix.py
new file mode 100644
index 0000000000..0a3f7ddbc0
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_prefix.py
@@ -0,0 +1,97 @@
+#!/usr/bin/env python3
+"""Emit the checked native prefix before a routed reader query."""
+
+import argparse
+from copy import deepcopy
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE = HERE.parent / "row-only-capture-20261020"
+LANES = HERE.parents[2]
+PINS = {
+    "reuse": (SOURCE / "reuse-normal/LINE-ENTRY-REUSE.json.gz",
+              "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110"),
+    "checker": (SOURCE / "emit_capture.py",
+                "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f"),
+    "review": (LANES / "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json",
+               "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source " + name)
+    return raw
+
+
+read("checker")
+spec = importlib.util.spec_from_file_location("reuse_prefix_base", PINS["checker"][0])
+base = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = base
+spec.loader.exec_module(base)
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    source = json.loads(read("reuse"))
+    read("review")
+    response = base.n.rows(source["response"])
+    selected = set(source["selected_ports"])
+    providers, reports = {}, {}
+    for provider, original in source["providers"].items():
+        word = deepcopy(original)
+        end = original["stage_ranges"]["late_query"][0]
+        word["events"] = word["events"][:end]
+        del word["stage_ranges"]["late_query"]
+        report = base.verify(word, base.n.r.identity(112), response,
+                             [{} for _ in range(112)], selected)
+        need(report["real_scalar_primitives"] == 6456 and report["native_mass"] == 1792,
+             "The complete carrier-only invoice")
+        need(end == 2406 and len(word["events"]) == end, "The exact complete prefix cut")
+        providers[provider], reports[provider] = word, report
+    payload = {
+        "schema": "sixteen-record-carrier-prefix-v1",
+        "source_pins": {key: {"path": str(path), "sha256": pin}
+                        for key, (path, pin) in PINS.items()},
+        "ports": source["ports"], "selected_ports": source["selected_ports"],
+        "ordinary_ports": source["ordinary_ports"], "response": source["response"],
+        "providers": providers,
+        "physical_contract": {
+            "input": "X=Qx; Y_U=y_U; Y_P=Q_P z, with arbitrary independent z.",
+            "output": "Xout=F9x; Yout_U=F9q_U(y+Ex)_U; Yout_P=F9z.",
+            "scope": "The complete native prefix ends before any selected reader query.",
+        },
+    }
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    for provider, word in json.loads(raw)["providers"].items():
+        need(base.verify(word, base.n.r.identity(112), response,
+                         [{} for _ in range(112)], selected) == reports[provider],
+             "The serialized prefix passes")
+    (args.out / "CARRIER-PREFIX.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {"status": "PASS_EXACT_CARRIER_ONLY_PREFIX",
+               "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "payload_decompressed_sha256": sha256(raw).hexdigest(),
+               "reports": reports}
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_routed_query.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_routed_query.py
new file mode 100644
index 0000000000..ca0e863c35
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_routed_query.py
@@ -0,0 +1,330 @@
+#!/usr/bin/env python3
+"""Emit and replay the complete old-reader query after the native prefix."""
+
+import argparse
+from collections import defaultdict
+from fractions import Fraction as F
+from functools import cache
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[2]
+UNIT = tuple(1 << j for j in range(25))
+PINS = {
+    "prefix": (HERE / "prefix-normal/CARRIER-PREFIX.json.gz",
+               "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e"),
+    "prefix_checker": (HERE / "emit_prefix.py",
+                       "657afc180b397e851fbefa16f56ace98129072a6bd2faf5d84dbc2391720698e"),
+    "query": (LANES / "bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-PROGRAM.json",
+              "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b"),
+    "capture": (LANES / "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json",
+                "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"),
+    "phase": (LANES / "bridge-access-20261017/check_bridge_access.py",
+              "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source " + name)
+    return raw
+
+
+def module(name):
+    read(name)
+    spec = importlib.util.spec_from_file_location("routed_query_" + name, PINS[name][0])
+    result = importlib.util.module_from_spec(spec)
+    sys.modules[spec.name] = result
+    spec.loader.exec_module(result)
+    return result
+
+
+prefix_checker = module("prefix_checker")
+base = prefix_checker.base
+phase = module("phase")
+
+
+def act(columns, value):
+    result = 0
+    while value:
+        bit = value & -value
+        result ^= columns[bit.bit_length() - 1]
+        value ^= bit
+    return result
+
+
+@cache
+def compose(left, right):
+    return tuple(act(left, value) for value in right)
+
+
+def transpose(columns):
+    return tuple(sum(((columns[j] >> i) & 1) << j for j in range(25))
+                 for i in range(25))
+
+
+def add(target, source, coefficient=F(1)):
+    for key, value in source.items():
+        target[key] = target.get(key, F(0)) + coefficient * value
+        if not target[key]:
+            del target[key]
+
+
+def product(left, right):
+    result = []
+    for row in left:
+        out = {}
+        for (j, a), coefficient in row.items():
+            for (k, b), value in right[j].items():
+                add(out, {(k, compose(a, b)): coefficient * value})
+        result.append(out)
+    return result
+
+
+def routed(rows, ports, views):
+    rho = {view["port"]: tuple(view["route_columns"]) for view in views}
+    return [{(j, compose(rho[p], rho[j])): value for j, value in row.items()}
+            for p, row in zip(ports, rows)]
+
+
+def initial_prefix(response, selected):
+    state = [{(i, UNIT): F(1)} for i in range(640)]
+    for p in range(112):
+        if p not in selected:
+            add(state[112 + p], response[p])
+    return state
+
+
+def replay(events, maps, initial, selected):
+    state = [dict(row) for row in initial]
+    scalar_cost = 0
+    map_cost = 0
+    maximum = max(sum(abs(value) for value in row.values()) for row in state)
+    height = 0
+    for event in events:
+        if event[0] == "map":
+            _, field, index = event
+            need(field < 112 or field - 112 in selected, "A query map uses only FULL fields")
+            route = tuple(maps[index]["columns"])
+            state[field] = {(i, compose(route, a)): value
+                            for (i, a), value in state[field].items()}
+            map_cost += 1
+        else:
+            need(event[0] == "scalar", "The literal query event grammar")
+            _, op, target, source, raw = event
+            value = F(raw)
+            need(target < 112 or target - 112 in selected, "A scalar target is FULL")
+            if op == "add":
+                need(source < 112 or source - 112 in selected, "A scalar source is FULL")
+                need(target != source, "Distinct source and target arrays")
+                add(state[target], state[source], value)
+            else:
+                need(op == "scale", "Only ADD and SCALE instructions")
+                state[target] = {key: value * other for key, other in state[target].items()}
+            scalar_cost += base.n.r.price([[op, target, source, raw]])
+            maximum = max(maximum, sum(abs(other) for other in state[target].values()))
+            for other in state[target].values():
+                d = other.denominator
+                need(d & (d - 1) == 0, "Every query coefficient is dyadic")
+                height = max(height, d.bit_length() - 1)
+    return state, {"scalar_primitives": scalar_cost, "monomial_maps": map_cost,
+                   "exact_prefix_content_one_norm": str(maximum),
+                   "additional_binary_height": height}
+
+
+def make_query(pair, capture, pivots):
+    maps, indices, events, stages = [], {}, [], {}
+    full = phase.product([(v, 1) for v in UNIT[:9 + 8 * pair["service_stage"]]])
+
+    def register(columns, translation):
+        columns = tuple(columns)
+        key = columns, translation
+        if key in indices:
+            return indices[key]
+        inverse = transpose(columns)
+        need(compose(columns, inverse) == compose(inverse, columns) == UNIT,
+             "Each actual query route is orthogonal")
+        need(columns[9 + 8 * pair["service_stage"]:] == UNIT[9 + 8 * pair["service_stage"]:],
+             "Each query route fixes the uncompleted axes")
+        transformed = phase.product([(act(columns, v), 1)
+                                     for v in UNIT[:9 + 8 * pair["service_stage"]]])
+        need(phase.add_phase(transformed, phase.line(translation, 2)) == full,
+             "The complete Z4 phase of each FULL view")
+        indices[key] = len(maps)
+        maps.append({"columns": columns, "translation": translation,
+                     "inverse_columns": inverse, "inverse_translation": act(inverse, translation)})
+        return indices[key]
+
+    def view(field, record, inverse=False):
+        route = tuple(record["route_columns"])
+        delta = record["translation"]
+        if inverse:
+            route = transpose(route)
+            delta = act(route, delta)
+        events.append(["map", field, register(route, delta)])
+
+    def begin():
+        return len(events)
+
+    def end(name, start):
+        stages[name] = [start, len(events)]
+
+    old = {view["port"]: view for view in pair["old_reader_views"]}
+    current = {view["port"]: view for view in pair["current_code_views"]}
+    ordinary = sorted(set(range(112)) - set(pivots))
+    old_fields = [(p, p) for p in ordinary] + [(112 + p, p) for p in pivots]
+    start = begin()
+    for field, p in old_fields:
+        view(field, old[p])
+    for op, p, r, coefficient in capture["scalar_word"]:
+        events.append(["scalar", op, 112 + p, r, coefficient])
+    for field, p in reversed(old_fields):
+        view(field, old[p], True)
+    end("old_reader_complement", start)
+    start = begin()
+    for p in pivots:
+        events.append(["scalar", "add", 112 + p, p, "1"])
+    end("first_selected_copy", start)
+
+    def code_stage(name, word):
+        start = begin()
+        for p in range(112):
+            view(p, current[p])
+        for op, p, r, coefficient in word:
+            events.append(["scalar", op, p, r, coefficient])
+        for p in reversed(range(112)):
+            view(p, current[p], True)
+        end(name, start)
+
+    code_stage("current_code", capture["scalar_word"])
+    start = begin()
+    for p in pivots:
+        events.append(["scalar", "add", 112 + p, p, "-1"])
+    end("second_selected_copy", start)
+    start = begin()
+    for op, p, r, coefficient, route_index in pair["middle_query"]:
+        if op == "scale":
+            events.append(["scalar", "scale", 112 + p, None, coefficient])
+        else:
+            need(op == "mapped_add_restore", "The pinned middle-query grammar")
+            record = pair["middle_routes"][route_index]
+            forward = register(record["columns"], record["FULL_translation"])
+            backward = register(record["inverse_columns"], record["inverse_FULL_translation"])
+            need(tuple(maps[forward]["inverse_columns"]) == tuple(maps[backward]["columns"])
+                 and maps[forward]["inverse_translation"] == maps[backward]["translation"],
+                 "The literal source restoration map")
+            events.append(["map", r, forward])
+            events.append(["scalar", "add", 112 + p, r, coefficient])
+            events.append(["map", r, backward])
+    end("middle_query", start)
+    code_stage("current_inverse_code", capture["inverse_scalar_word"])
+    return events, maps, stages
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    prefix = json.loads(read("prefix"))
+    query = json.loads(read("query"))
+    capture = json.loads(read("capture"))
+    pivots = query["pivots"]
+    selected = set(pivots)
+    need(pivots == prefix["selected_ports"] == capture["pivots"], "One actual pivot set")
+    response = base.n.rows(prefix["response"])
+    reader = base.n.rows(capture["centre_reader"])
+    prefix_reports = {}
+    for provider, word in prefix["providers"].items():
+        prefix_reports[provider] = base.verify(
+            word, base.n.r.identity(112), response, [{} for _ in range(112)], selected)
+    reports, words = {}, {}
+    for pair in query["pairs"]:
+        key = str(pair["reader_stage"]) + ":" + str(pair["service_stage"])
+        et = routed(response, range(112), pair["current_code_views"])
+        ls = routed(reader, pivots, pair["old_reader_views"])
+        direct = product(ls, et)
+        need(sum(map(len, direct)) == 3808, "Every direct old-reader owner path")
+        initial = initial_prefix(et, selected)
+        expected = [dict(row) for row in initial]
+        for p, row in zip(pivots, direct):
+            add(expected[112 + p], row)
+        events, maps, stages = make_query(pair, capture, pivots)
+        actual, report = replay(events, maps, initial, selected)
+        need(actual == expected, "All640 complete arbitrary fields with exact ordered owner paths")
+        need(actual[:112] == initial[:112] and actual[224:] == initial[224:],
+             "Every source and arbitrary helper is restored")
+        need(report["scalar_primitives"] == 11168 and report["monomial_maps"] == 2064,
+             "The complete literal routed-query invoice")
+        query_initial = [{(i, UNIT): F(1)} for i in range(640)]
+        query_expected = [dict(row) for row in query_initial]
+        for p, row in zip(pivots, direct):
+            add(query_expected[112 + p], row)
+        query_actual, query_bound = replay(events, maps, query_initial, selected)
+        need(query_actual == query_expected, "The query is valid on every independent FULL input")
+        negative_index = next(i for i in range(*stages["middle_query"]) if events[i][0] == "map")
+        bad = events[:negative_index] + events[negative_index + 1:]
+        bad_state, _ = replay(bad, maps, initial, selected)
+        need(bad_state != expected, "An omitted middle source view is rejected")
+        bad = events[:stages["current_inverse_code"][0]]
+        bad_state, _ = replay(bad, maps, initial, selected)
+        need(bad_state != expected, "An omitted source-code restoration is rejected")
+        words[key] = {"reader_stage": pair["reader_stage"], "service_stage": pair["service_stage"],
+                      "events": events, "maps": maps, "stage_ranges": stages}
+        reports[key] = {**report, "exact_query_entry_unit_bound": query_bound,
+                        "complete_local_scalar": 6456 + report["scalar_primitives"],
+                        "native_mass": 1792, "native_profile": {"1": 1392, "2": 64, "3": 48, "8": 16},
+                        "restored_source_fields": 112, "unchanged_arbitrary_helpers": 416,
+                        "direct_owner_path_terms": 3808, "distinct_checked_full_maps": len(maps)}
+    payload = {
+        "schema": "fixed-reader-literal-global-query-v1",
+        "source_pins": {key: {"path": str(path), "sha256": pin}
+                        for key, (path, pin) in PINS.items()},
+        "pivots": pivots, "native_prefixes": prefix["providers"], "queries": words,
+        "physical_contract": {
+            "query_entrance": "All X and selected Y fields are in the actual completed global FULL frame.",
+            "query": "X is restored; selected Y gains L_s E_t X; ordinary Y and all helpers are unchanged.",
+            "complete_content": "The selected record z gains L_s E_t x after the checked native carrier prefix. If z=L_s y, it is L_s(y+E_t x).",
+            "scope": "The complete D25 entry/exit dispatcher that puts the local prefix into these global charts is a separate pinned binding.",
+        },
+    }
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    for key, word in saved["queries"].items():
+        pair = next(p for p in query["pairs"] if
+                    key == str(p["reader_stage"]) + ":" + str(p["service_stage"]))
+        et = routed(response, range(112), pair["current_code_views"])
+        actual, report = replay(word["events"], word["maps"], initial_prefix(et, selected), selected)
+        need(report["scalar_primitives"] == reports[key]["scalar_primitives"]
+             and report["monomial_maps"] == reports[key]["monomial_maps"],
+             "The serialized query invoice")
+        expected = initial_prefix(et, selected)
+        for p, row in zip(pivots, product(routed(reader, pivots, pair["old_reader_views"]), et)):
+            add(expected[112 + p], row)
+        need(actual == expected, "The serialized complete operator map")
+    (args.out / "ROUTED-QUERY.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {"status": "PASS_EXACT_LITERAL_ROUTED_QUERY_AND_NATIVE_PREFIX",
+               "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "payload_decompressed_sha256": sha256(raw).hexdigest(),
+               "prefix_reports": prefix_reports, "query_reports": reports,
+               "scope": "Exact local prefix and global FULL query. The actual D25 dispatcher is a separate binding; recursive hosting and the supplier remain open."}
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_service.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_service.py
new file mode 100644
index 0000000000..5c1510a9f0
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_service.py
@@ -0,0 +1,187 @@
+#!/usr/bin/env python3
+"""Bind the native prefix, DATA dispatcher, and routed reader query."""
+
+import argparse
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[2]
+PINS = {
+    "helper": (HERE / "emit_routed_query.py",
+               "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900"),
+    "query": (HERE / "query-normal/ROUTED-QUERY.json.gz",
+              "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a"),
+    "dispatcher": (LANES / "bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json",
+                   "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24"),
+    "dispatcher_freeze": (LANES / "bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json",
+                          "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source " + name)
+    return raw
+
+
+read("helper")
+spec = importlib.util.spec_from_file_location("fixed_reader_service_query", PINS["helper"][0])
+q = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = q
+spec.loader.exec_module(q)
+
+
+def verify(bundle):
+    prefix = json.loads(q.read("prefix"))
+    capture = json.loads(q.read("capture"))
+    old_query = json.loads(q.read("query"))
+    selected = set(bundle["selected_ports"])
+    need(bundle["native_prefixes"] == prefix["providers"], "The full native programs are unchanged")
+    response = q.base.n.rows(prefix["response"])
+    reader = q.base.n.rows(capture["centre_reader"])
+    phase_checks = 0
+    routed_stage_views = {}
+    for stage in bundle["stage_views"]:
+        t = stage["service_stage"]
+        need(stage["physical_input_level"] == t - 1
+             and stage["physical_output_level"] == t, "The adjacent physical level")
+        before = [(v, 1) for v in q.UNIT[:9 + 8 * (t - 1)]]
+        after = [(v, 1) for v in q.UNIT[:9 + 8 * t]]
+        exterior = [(v, 1) for v in stage["common_exterior_axes"]]
+        need(exterior == [(v, 1) for v in q.UNIT[9:9 + 8 * t]], "The complete common exterior")
+        entries = {item["field"]: item for item in stage["DATA_entry"]}
+        exits = {item["field"]: item for item in stage["DATA_exit"]}
+        need(set(entries) == set(exits) == set(range(224)), "All data boundary fields")
+        for field in range(224):
+            entry, out = entries[field], exits[field]
+            p = field % 112
+            rho = tuple(entry["route_columns"])
+            need(rho == tuple(out["route_columns"]), "The same owner partition at both ends")
+            need(q.compose(rho, rho) == q.UNIT
+                 and q.transpose(rho) == rho, "The orthogonal involutive DATA route")
+            line = prefix["ports"][p]
+            need(q.act(rho, line) == line, "The intrinsic line is fixed")
+            full = field < 112 or p in selected
+            physical_before = before + ([] if full else [(line, -1)])
+            actual = q.phase.add_phase(
+                q.phase.product([(q.act(rho, v), exponent) for v, exponent in physical_before]),
+                q.phase.line(entry["translation_after_route"], 2))
+            expected = q.phase.product(exterior + ([(line, 1)] if full else []))
+            need(actual == expected and entry["intrinsic_input"] == ("Q_p" if full else "I"),
+                 "The exact global-to-local input phase")
+            need(q.act(rho, entry["translation_before_route"]) == entry["translation_after_route"],
+                 "The exact translation order at entry")
+            physical_after = after + ([] if full else [(line, -1)])
+            actual = q.phase.add_phase(
+                q.phase.product([(q.act(rho, v), exponent) for v, exponent in physical_after]),
+                q.phase.line(out["translation_after_route"], 2))
+            need(actual == q.phase.product(physical_after)
+                 and out["global_output"] == ("FULL" if full else "FULL*q_p"),
+                 "The exact local-to-global output phase")
+            phase_checks += 2
+        routed_stage_views[t] = [
+            {"port": p, "route_columns": entries[p]["route_columns"],
+             "translation": exits[p]["translation_after_route"]} for p in range(112)]
+    prefix_reports = {}
+    for provider, word in bundle["native_prefixes"].items():
+        prefix_reports[provider] = q.base.verify(
+            word, q.base.n.r.identity(112), response, [{} for _ in range(112)], selected)
+    expected_pairs = {(provider, s, t) for provider in bundle["native_prefixes"]
+                      for s, t in ((0, 1), (0, 2), (1, 2))}
+    actual_pairs = set()
+    reports = []
+    for service in bundle["services"]:
+        provider, s, t = service["provider"], service["reader_stage"], service["service_stage"]
+        actual_pairs.add((provider, s, t))
+        key = f"{s}:{t}"
+        word = bundle["queries"][key]
+        pair = old_query["pairs"][service["query_pair_record"]]
+        need((pair["reader_stage"], pair["service_stage"]) == (s, t), "The exact retained reader")
+        need(pair["current_code_views"] == routed_stage_views[t],
+             "The query current chart is the actual DATA exit chart")
+        need(service["physical_input_level"] == t - 1
+             and service["physical_output_level"] == t, "The reader label is not the physical level")
+        need([part["op"] for part in service["ordered_blocks"]] == [
+            "DATA_entry", "native_input_adapters", "complete_native_carrier_cover_sweep",
+            "ordinary_output_adapters", "DATA_exit", "complete_cover_barrier",
+            "fixed_past_reader_query"], "The complete cover barrier precedes the query")
+        prefix_word = bundle["native_prefixes"][provider]
+        need(service["ordered_blocks"][2]["event_range"] == [0, len(prefix_word["events"])],
+             "No native event is omitted")
+        et = q.routed(response, range(112), routed_stage_views[t])
+        ls = q.routed(reader, bundle["selected_ports"], pair["old_reader_views"])
+        initial = q.initial_prefix(et, selected)
+        expected = [dict(row) for row in initial]
+        for p, row in zip(bundle["selected_ports"], q.product(ls, et)):
+            q.add(expected[112 + p], row)
+        actual, query_report = q.replay(word["events"], word["maps"], initial, selected)
+        need(actual == expected, "The complete service on all640 formal input fields")
+        scalar = prefix_reports[provider]["real_scalar_primitives"] + query_report["scalar_primitives"]
+        maps = service["map_call_bound"]
+        need(scalar == service["scalar_primitives"] == 17624
+             and maps == {"DATA": 448, "late_query": 2064, "local_endpoint_adapters": 224,
+                          "native_side_maps": 3040, "total": 5776},
+             "The complete service invoice")
+        reports.append({"provider": provider, "reader_stage": s, "service_stage": t,
+                        "native_mass": 1792, "scalar_primitives": scalar,
+                        "monomial_map_call_bound": maps["total"],
+                        "all_independent_input_fields": 640,
+                        "query_prefix_formal_one_norm": query_report["exact_prefix_content_one_norm"],
+                        "query_additional_binary_height": query_report["additional_binary_height"]})
+    need(actual_pairs == expected_pairs and len(bundle["services"]) == len(expected_pairs),
+         "Both providers and all three actual stage pairs")
+    return {"complete_services": reports, "data_boundary_phase_equations": phase_checks,
+            "prefix_reports": prefix_reports}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    query = json.loads(read("query"))
+    dispatcher = json.loads(read("dispatcher"))
+    read("dispatcher_freeze")
+    for name, (path, pin) in dispatcher["source_pins"].items():
+        raw = (LANES / path).read_bytes()
+        if path.endswith(".gz"):
+            raw = gzip.decompress(raw)
+        need(sha256(raw).hexdigest() == pin, "The complete dispatcher source pin " + name)
+    bundle = {
+        "schema": "six-fixed-reader-forward-services-v1",
+        "source_pins": {key: {"path": str(path), "sha256": pin}
+                        for key, (path, pin) in PINS.items()},
+        "selected_ports": dispatcher["selected_ports"], "contract": dispatcher["contract"],
+        "owner_contract": dispatcher["owner_contract"], "stage_views": dispatcher["stage_views"],
+        "native_prefixes": query["native_prefixes"], "queries": query["queries"],
+        "services": dispatcher["invocations"],
+        "scope": "Complete data interfaces on the regular D25 cover, under the inherited416-helper host contract. Recursive hosting and the complete supplier cost remain separate.",
+    }
+    report = verify(bundle)
+    raw = (json.dumps(bundle, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    need(verify(json.loads(raw)) == report, "The complete serialized service bundle")
+    (args.out / "FIXED-READER-SERVICES.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {"status": "PASS_EXACT_SIX_FIXED_READER_D25_SERVICES",
+               "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "payload_decompressed_sha256": sha256(raw).hexdigest(), **report,
+               "scope": bundle["scope"]}
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz
new file mode 100644
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CHECKS.json
new file mode 100644
index 0000000000..0a9cefe6a1
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CHECKS.json
@@ -0,0 +1,65 @@
+{
+  "payload_decompressed_sha256": "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e",
+  "producer_sha256": "657afc180b397e851fbefa16f56ace98129072a6bd2faf5d84dbc2391720698e",
+  "reports": {
+    "base": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "explicit_input_monomial_views": 128,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "22",
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 6456,
+      "scalar_stage_prices": {
+        "precode": 0,
+        "retained_core": 6456,
+        "selected_line_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    },
+    "extra": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "explicit_input_monomial_views": 128,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "22",
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 6456,
+      "scalar_stage_prices": {
+        "precode": 0,
+        "retained_core": 6456,
+        "selected_line_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    }
+  },
+  "status": "PASS_EXACT_CARRIER_ONLY_PREFIX"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-optimized/CARRIER-PREFIX.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-optimized/CARRIER-PREFIX.json.gz
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literal 0
HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-optimized/CHECKS.json
new file mode 100644
index 0000000000..0a9cefe6a1
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-optimized/CHECKS.json
@@ -0,0 +1,65 @@
+{
+  "payload_decompressed_sha256": "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e",
+  "producer_sha256": "657afc180b397e851fbefa16f56ace98129072a6bd2faf5d84dbc2391720698e",
+  "reports": {
+    "base": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "explicit_input_monomial_views": 128,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "22",
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 6456,
+      "scalar_stage_prices": {
+        "precode": 0,
+        "retained_core": 6456,
+        "selected_line_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    },
+    "extra": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "explicit_input_monomial_views": 128,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "22",
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 6456,
+      "scalar_stage_prices": {
+        "precode": 0,
+        "retained_core": 6456,
+        "selected_line_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    }
+  },
+  "status": "PASS_EXACT_CARRIER_ONLY_PREFIX"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/CHECKS.json
new file mode 100644
index 0000000000..424ae56de9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/CHECKS.json
@@ -0,0 +1,140 @@
+{
+  "payload_decompressed_sha256": "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a",
+  "prefix_reports": {
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+      "real_scalar_primitives": 6456,
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+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
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+  },
+  "producer_sha256": "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900",
+  "query_reports": {
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+      "complete_local_scalar": 17624,
+      "direct_owner_path_terms": 3808,
+      "distinct_checked_full_maps": 545,
+      "exact_prefix_content_one_norm": "448",
+      "exact_query_entry_unit_bound": {
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+        "exact_prefix_content_one_norm": "448",
+        "monomial_maps": 2064,
+        "scalar_primitives": 11168
+      },
+      "monomial_maps": 2064,
+      "native_mass": 1792,
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+        "3": 48,
+        "8": 16
+      },
+      "restored_source_fields": 112,
+      "scalar_primitives": 11168,
+      "unchanged_arbitrary_helpers": 416
+    },
+    "0:2": {
+      "additional_binary_height": 2,
+      "complete_local_scalar": 17624,
+      "direct_owner_path_terms": 3808,
+      "distinct_checked_full_maps": 545,
+      "exact_prefix_content_one_norm": "448",
+      "exact_query_entry_unit_bound": {
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+        "exact_prefix_content_one_norm": "448",
+        "monomial_maps": 2064,
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+      },
+      "monomial_maps": 2064,
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+      },
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+    },
+    "1:2": {
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+      "distinct_checked_full_maps": 1616,
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+      "exact_query_entry_unit_bound": {
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+      "monomial_maps": 2064,
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+      "restored_source_fields": 112,
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+      "unchanged_arbitrary_helpers": 416
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+  },
+  "scope": "Exact local prefix and global FULL query. The actual D25 dispatcher is a separate binding; recursive hosting and the supplier remain open.",
+  "status": "PASS_EXACT_LITERAL_ROUTED_QUERY_AND_NATIVE_PREFIX"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-optimized/CHECKS.json
new file mode 100644
index 0000000000..424ae56de9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-optimized/CHECKS.json
@@ -0,0 +1,140 @@
+{
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+      "native_mass": 1792,
+      "native_profile": {
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+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 6456,
+      "scalar_stage_prices": {
+        "precode": 0,
+        "retained_core": 6456,
+        "selected_line_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    },
+    "extra": {
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+      "arbitrary_input_columns": 640,
+      "explicit_input_monomial_views": 128,
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+        "exact_prefix_content_one_norm": "448",
+        "monomial_maps": 2064,
+        "scalar_primitives": 11168
+      },
+      "monomial_maps": 2064,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_source_fields": 112,
+      "scalar_primitives": 11168,
+      "unchanged_arbitrary_helpers": 416
+    },
+    "1:2": {
+      "additional_binary_height": 2,
+      "complete_local_scalar": 17624,
+      "direct_owner_path_terms": 3808,
+      "distinct_checked_full_maps": 1616,
+      "exact_prefix_content_one_norm": "448",
+      "exact_query_entry_unit_bound": {
+        "additional_binary_height": 2,
+        "exact_prefix_content_one_norm": "448",
+        "monomial_maps": 2064,
+        "scalar_primitives": 11168
+      },
+      "monomial_maps": 2064,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "restored_source_fields": 112,
+      "scalar_primitives": 11168,
+      "unchanged_arbitrary_helpers": 416
+    }
+  },
+  "scope": "Exact local prefix and global FULL query. The actual D25 dispatcher is a separate binding; recursive hosting and the supplier remain open.",
+  "status": "PASS_EXACT_LITERAL_ROUTED_QUERY_AND_NATIVE_PREFIX"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-optimized/ROUTED-QUERY.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-optimized/ROUTED-QUERY.json.gz
new file mode 100644
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-normal/CHECKS.json
new file mode 100644
index 0000000000..41691c9152
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-normal/CHECKS.json
@@ -0,0 +1,135 @@
+{
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+  "status": "PASS_EXACT_SIX_FIXED_READER_D25_SERVICES"
+}
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-optimized/CHECKS.json
new file mode 100644
index 0000000000..41691c9152
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-optimized/CHECKS.json
@@ -0,0 +1,135 @@
+{
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+    {
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+      "native_mass": 1792,
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+      "scalar_stage_prices": {
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+  "status": "PASS_EXACT_SIX_FIXED_READER_D25_SERVICES"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-optimized/FIXED-READER-SERVICES.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/service-optimized/FIXED-READER-SERVICES.json.gz
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literal 0
HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-CHECKS.json
new file mode 100644
index 0000000000..7e2639d365
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-CHECKS.json
@@ -0,0 +1,78 @@
+{
+  "fresh_endpoint_phase_checks": 224,
+  "fresh_native_phase_checks": 1141,
+  "negative_control": "one nonzero transfer omitted and rejected",
+  "payload_decompressed_sha256": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+  "producer_sha256": "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745",
+  "reports": {
+    "backward": {
+      "all_input_columns": 640,
+      "endpoint_maps": 224,
+      "native_children": 1212,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1036,
+        "3": 48,
+        "4": 55,
+        "5": 55,
+        "6": 9,
+        "7": 9
+      },
+      "native_side_map_bound": 2424,
+      "owned_fields": 0,
+      "prefix_row_l1_bound": "30",
+      "private_fields": 0,
+      "real_scalar_primitives": 5288,
+      "untouched_arbitrary_fields": 416
+    },
+    "forward": {
+      "all_input_columns": 640,
+      "endpoint_maps": 224,
+      "native_children": 1212,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1036,
+        "3": 48,
+        "4": 55,
+        "5": 55,
+        "6": 9,
+        "7": 9
+      },
+      "native_side_map_bound": 2424,
+      "owned_fields": 0,
+      "prefix_row_l1_bound": "46",
+      "private_fields": 0,
+      "real_scalar_primitives": 5288,
+      "untouched_arbitrary_fields": 416
+    }
+  },
+  "same_geometry_both_providers_checked": true,
+  "scope": "Complete local data shears and exact phases. Helpers are unchanged; their progress, recursive hosting, routed codes and terminal remain open.",
+  "source_pins": {
+    "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": [
+      "plain",
+      "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"
+    ],
+    "interface-proof/verify_native_lift.py": [
+      "plain",
+      "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b"
+    ],
+    "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz": [
+      "decompressed",
+      "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa"
+    ],
+    "new-core-transfer-20261017/low-displacement-20261020/check_response.py": [
+      "plain",
+      "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"
+    ],
+    "new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json": [
+      "plain",
+      "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c"
+    ],
+    "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py": [
+      "plain",
+      "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+    ]
+  },
+  "status": "PASS_LOW_DISPLACEMENT_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz
new file mode 100644
index 0000000000000000000000000000000000000000..725c71f7ea6f0cc0b316852deaf034ed3d87725f
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json
new file mode 100644
index 0000000000..15e7e1bdd9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json
@@ -0,0 +1,51 @@
+{
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+  "full_correction_rank": 16,
+  "full_determinant": "2251875390625",
+  "inherited_endpoint_phases": 224,
+  "inherited_native_phases": 685,
+  "kind": "odd-grid-rank16",
+  "ordinary_determinant": "5323914784321/16",
+  "payload_decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+  "producer_sha256": "b03568530696ab810070ba3243b59dd74740fb634fe7f26b2cbdb1d3283d045f",
+  "reports": {
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+      "endpoint_maps": 224,
+      "native_children": 1632,
+      "native_mass": 1792,
+      "native_profile": {
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+        "2": 64,
+        "3": 48
+      },
+      "native_side_map_bound": 3264,
+      "owned_fields": 0,
+      "prefix_row_l1_bound": "22",
+      "private_fields": 0,
+      "real_scalar_primitives": 7384,
+      "untouched_arbitrary_fields": 416
+    },
+    "forward": {
+      "all_input_columns": 640,
+      "endpoint_maps": 224,
+      "native_children": 1632,
+      "native_mass": 1792,
+      "native_profile": {
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+        "2": 64,
+        "3": 48
+      },
+      "native_side_map_bound": 3264,
+      "owned_fields": 0,
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+      "private_fields": 0,
+      "real_scalar_primitives": 7384,
+      "untouched_arbitrary_fields": 416
+    }
+  },
+  "scope": "Exact local data word. Odd-grid code admission, terminal, helper progress and recursive supplier duties are separate.",
+  "source_emitter_sha256": "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745",
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+  "status": "PASS_ODD_GRID_RANK16"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/reciprocal-normal-v2/EXTENSION-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/reciprocal-normal-v2/EXTENSION-CHECKS.json
new file mode 100644
index 0000000000..adebf6dabc
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/reciprocal-normal-v2/EXTENSION-CHECKS.json
@@ -0,0 +1,57 @@
+{
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+  "full_correction_rank": 30,
+  "full_determinant": "33554432",
+  "inherited_endpoint_phases": 224,
+  "inherited_native_phases": 1141,
+  "kind": "reciprocal-large",
+  "ordinary_determinant": "2097152",
+  "payload_decompressed_sha256": "e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416",
+  "producer_sha256": "b03568530696ab810070ba3243b59dd74740fb634fe7f26b2cbdb1d3283d045f",
+  "reports": {
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+      "endpoint_maps": 224,
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+      "native_mass": 1792,
+      "native_profile": {
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+      "native_side_map_bound": 2424,
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+      "untouched_arbitrary_fields": 416
+    },
+    "forward": {
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+      "endpoint_maps": 224,
+      "native_children": 1212,
+      "native_mass": 1792,
+      "native_profile": {
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+      "real_scalar_primitives": 5288,
+      "untouched_arbitrary_fields": 416
+    }
+  },
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+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json
new file mode 100644
index 0000000000..fb98041000
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "ROUTE32.md": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28",
+    "emit_model.py": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711",
+    "emit_native.py": "f961d989a708b40b26780860caa88bf73b86d451b603add3f254d0d0a7a709ff",
+    "model-normal/CHECKS.json": "69ee6905c99ab4d93f48d828c378f6c902d5e8a9844df68acbc8971158d76502",
+    "model-normal/ROUTE32-MODEL.json": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52",
+    "native-normal/CHECKS.json": "304b30eb8f9810ff36fcf0a4181bd630a0eb041a6fba89a53fbeea227860cae3",
+    "native-normal/ROUTE32-NATIVE.json.gz": "69342058ffb9128ecc743cf478772896fd037c7aeeac845326d65626d7f3b425"
+  },
+  "normal_optimized_byte_identical": true,
+  "scope": "Complete raw local native word and exact route-compatible in-place code. The common-root gauge and full productive caller remain separate.",
+  "status": "PASS_ROUTE32_RESPONSE_CAPTURE_AND_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md
new file mode 100644
index 0000000000..d50856ffc1
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md
@@ -0,0 +1,209 @@
+# A route-compatible response with a dyadic centre code
+
+The current shared-root route divides the 112 ports into three
+classes. The class label r_p is the first vector r in the ordered
+root space with q_p dot r=1. The order is
+
+```text
+0,30,45,51,75,85,102,120,384,414,429,435,459,469,486,504.
+```
+
+The actual classes have 64, 32, and 16 ports, with labels 30, 45,
+and 75. The 64 small ports split equally between classes 30 and 45.
+The 48 large ports split into 32 in class 30 and 16 in class 75.
+
+The rank-sixteen response does not preserve these classes. Each of
+its eight small cliques contains four ports from each of the two
+small classes. Each large six-mode block contains four modes in
+class 30 and two in class 75. A change of construction is required.
+
+## The response
+
+Every actual two-port pair code stays within a route class. Apply
+the same pair-code matrix H as in the rank-sixteen construction.
+At each large vertex, replace the six-mode block by two blocks:
+
+```text
+I_4 - d_4 d_4^T,      I_2 - d_2 d_2^T.
+```
+
+The groups are the four and two modes with the same route label.
+Retain their original signs. Split each small eight-clique into its
+two four-port route classes, and use I_4-11^T on each part.
+
+There are eight large four-mode blocks, eight large two-mode blocks,
+and sixteen small four-port blocks. These 32 blocks partition all
+112 mode labels. If M is their direct sum, set
+
+```text
+E = H^-1 M H.
+```
+
+The full physical E has zero diagonal. Each nonzero entry E_pt
+connects ports with r_p=r_t. Also,
+
+```text
+rank(E-I) = 32,
+det(E) = 3^24.
+```
+
+Each block inverse is I-dd^T/(k-1), where k is two or four.
+Thus the full response is a rational unit, and its only odd inverse
+denominator is three. The complete inverse is checked in both
+orders. The old selected-eight principal block is singular. This
+packet uses empty selection: the ordinary response is the entire
+112 by 112 unit.
+
+The source graph cannot keep rank sixteen by choosing another
+monochromatic eight-clique cover. All 64 maximal eight-cliques have
+four ports from each small route class. The largest monochromatic
+clique in the actual graph has size four. This is an exact check
+against the independently reviewed complete maximal-clique list.
+It is a restriction of this clique construction, not a lower bound
+for all possible native responses.
+
+## Two in-place centre codes
+
+Apply the actual H pair code. In each signed block choose its first
+mode as a pivot. The sum-and-difference code multiplies coordinates
+by their signs, subtracts the pivot from every other coordinate,
+multiplies the pivot by the block size, and adds all complement
+coordinates to it. The pivot then holds the old signed sum.
+
+This code C and its literal inverse each cost 1,870 old real scalar
+units. They use no owned field, no new field, no native child, and
+no odd division. The maximum prefix row one-norm is 8 forward and
+4 backward. The inverse needs at most three extra binary
+fractional bits.
+
+The exact diagonal form is
+
+```text
+C E C^-1 = diag(-3 I_24, -I_8, I_80),
+```
+
+with the diagonal entries placed at the actual pivot ports listed
+in the payload. The 32 centre coordinates occupy existing data
+fields. The other 80 fields retain independent complement data.
+
+A second code uses a rank-one reflection on each four-mode block.
+For its sign vector d, let p be the pivot and let
+
+```text
+s = d - 2 d_p e_p,
+S = I - s s^T/2.
+```
+
+Then S squared is I, rank(S-I)=1, and S d=2 d_p e_p.
+Thus S diagonalizes I-dd^T with centre multiplier -3.
+Its exact no-scratch word is
+
+```text
+x_i += d_i d_p x_p        for all i other than p
+x_p *= -2
+x_p += d_i d_p x_i        for all i other than p
+x_p /= 2
+x_i -= d_i d_p x_p        for all i other than p.
+```
+
+It costs 78 old units per four-mode block. The two-mode blocks use
+the preceding pivot code. Including H, this second complete code
+and its inverse each cost 2,486 units. They are dyadic and use no
+additional field or native child. Their forward and inverse prefix
+row one-norms are 8 and 4. Their maximum binary heights are one
+and two.
+
+The reflection code has a smaller block displacement rank. The
+pivot code has a smaller scalar invoice. No decoder advantage for
+the reflection code is claimed without its physical caller.
+
+## Route and phase scope
+
+Both complete physical codes preserve the route labels. Therefore
+they commute with every field-diagonal spatial operator of the
+form diag(A_(r_p)). This follows entry by entry: every nonzero
+scalar coefficient connects two copies of the same A_r.
+
+For the unshifted shared-root D11 stages, put e=511, v_p=e+r_p,
+and u_(s,p)=v_p+e_(8+s), for s=1,2. The actual route has columns
+
+```text
+kappa_(s,p)(e_j) = e_j + (u_(s,p))_j u_(s,p).
+```
+
+The advance is P_kappa inverse F9 P_kappa; stage zero is F9.
+If two route labels agree, their complete column lists, permutation
+operators, and ordered advance operators agree. This includes
+their phase, since they are the same ordered circuit. Thus the
+commutation applies to these actual unshifted advances, rather
+than to a nominal label alone. Added field-dependent address views
+or phase corrections still require their own checks. Route
+preservation does not permit Q to move through C.
+
+For either code the current entry word C Q^2 is literal: it has
+112 explicit input translations followed by the scalar code.
+The spatial interpreter retains the ordered translation labels.
+The formal transported code q C q, with q=Q^-1, has the same
+diagonal response because the centre multipliers are scalar.
+This fact does not supply a raw-output decoder or a free transition
+to a subsequent input code.
+
+The relative q-difference spaces have dimension one for the eight
+two-mode blocks and dimension three for the other 24 blocks.
+Only the eight two-mode spaces lie inside the common root space.
+Thus a common-root gauge cost cannot be inferred from route
+preservation. It requires the actual native and endpoint operators.
+
+## Complete raw native word
+
+The large sector uses the pinned cyclic pair flags. It changes only
+the scalar transfer coefficients. The small sector uses the exact
+sixteen four-cliques and their cyclic flags. Every nonzero ADD has
+equal source and target frames.
+
+The local map is
+
+```text
+F(x,y,h) = (x, y+E x, h),
+B(x,y,h) = (x-E^T y, y, h).
+```
+
+The input convention is X=Qx, Y=y. The output convention is
+X=F9 x' and Y=F9 Q^-1 y'. The native invoice in either direction is
+
+```text
+944 H1 + 48 H3 + 64 H5 + 64 H6,
+1120 native children, native mass 1792,
+4312 old real scalar primitives, 224 endpoint adapters.
+```
+
+The native prefix row one-norm is 14 in either direction.
+All 640 input columns are independent. The 416 fields outside
+the data banks remain unchanged. They receive no productive
+advance in this word.
+
+The emitter checks 297 fresh native operators, including their
+global phases. It reuses 752 operators only after exact ordered
+frame comparison with the frozen reviewed sources. The 224
+endpoint adapters have the same exact endpoint frames as those
+sources. Both complete provider words are serialized, read back,
+and replayed. Removal of a nonzero transfer is rejected.
+
+## Evidence
+
+`emit_model.py` pins the pair geometry, root space, clique list,
+and rank-sixteen predecessor. It checks the response and inverse,
+both capture codes, all 640 columns, literal inverse orders,
+route preservation, and the spatial entry code.
+
+`emit_native.py` binds the exact model hash and emits both complete
+native directions. Normal and optimized runs must give identical
+payloads and receipts. The model and native freezes are separate
+from a common-root gauge extension and independent review.
+
+The construction builds on the root's route-compatible split,
+the controller's common-root geometry, the independent cyclic
+flags, and the native rank-sixteen word. The four-mode reflection
+uses the root's rank-one capture formula. AI assistance was used.
+This packet does not claim a complete supplier or kappa bound.
+No publication is authorized.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_model.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_model.py
new file mode 100644
index 0000000000..b6dd94d986
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_model.py
@@ -0,0 +1,244 @@
+#!/usr/bin/env python3
+"""Build the route-compatible response and its exact in-place codes."""
+
+import argparse
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+PARENT = HERE.parent
+LANES = PARENT.parents[1]
+SOURCE = PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz"
+SOURCE_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+PINS = {
+    PARENT / "pivot-codes/emit_pivot_codes.py":
+        "af2f2ab1c5daba0bcd1a8878f2b81b2834e10a4f8ca1a2ef66779d52b30e64b4",
+    LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json":
+        "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    LANES / "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json":
+        "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd",
+    PARENT / "run-normal/RESPONSE-PROGRAM.json":
+        "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c",
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+for path, pin in PINS.items():
+    need(sha256(path.read_bytes()).hexdigest() == pin, "Source pin " + str(path))
+spec = importlib.util.spec_from_file_location("frozen_pivot", PARENT / "pivot-codes/emit_pivot_codes.py")
+pivot = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(pivot)
+r = pivot.r
+
+
+def binary_basis(vectors):
+    rows = list(dict.fromkeys(vectors))
+    used = 0
+    for bit in range(8, -1, -1):
+        found = next((i for i in range(used, len(rows)) if rows[i] >> bit & 1), None)
+        if found is None:
+            continue
+        rows[used], rows[found] = rows[found], rows[used]
+        for i in range(len(rows)):
+            if i != used and rows[i] >> bit & 1:
+                rows[i] ^= rows[used]
+        used += 1
+    return rows[:used]
+
+
+def pair_word(cyclic):
+    word, matrix = [], r.identity(112)
+    for pair in cyclic["pair_codes"]:
+        a, b = pair["ports"]
+        aa, ab = pair["matrix"][0]
+        ba, bb = pair["matrix"][1]
+        matrix[a], matrix[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)}
+        if aa != 1:
+            word.append(["scale", a, None, str(aa)])
+        word.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)],
+                     ["add", b, a, str(ba * aa)]])
+    need(pivot.replay(word)[0] == matrix, "Actual pair word")
+    return word, matrix
+
+
+def capture(groups, pair, reflection):
+    word = list(pair)
+    for group in groups:
+        ports, signs = group["ports"], group["signs"]
+        p, k = ports[0], len(ports)
+        if reflection and k == 4:
+            for t, sign in zip(ports[1:], signs[1:]):
+                word.append(["add", t, p, str(sign * signs[0])])
+            word.append(["scale", p, None, "-2"])
+            for t, sign in zip(ports[1:], signs[1:]):
+                word.append(["add", p, t, str(sign * signs[0])])
+            word.append(["scale", p, None, "1/2"])
+            for t, sign in zip(ports[1:], signs[1:]):
+                word.append(["add", t, p, str(-sign * signs[0])])
+        else:
+            for t, sign in zip(ports, signs):
+                if sign == -1:
+                    word.append(["scale", t, None, "-1"])
+            for t in ports[1:]:
+                word.append(["add", t, p, "-1"])
+            word.append(["scale", p, None, str(k)])
+            for t in ports[1:]:
+                word.append(["add", p, t, "1"])
+    return word
+
+
+def make_model(old, cyclic, geometry, rank30):
+    q = old["ports"]
+    root_space = geometry["common_even_isotropic_space"]
+    need(root_space == sorted(root_space), "The route enumeration uses numeric order")
+    need(q == geometry["q_labels"] == cyclic["ports"], "Actual route direction labels")
+    routes = [next(t for t in root_space if (q[p] & t).bit_count() % 2) for p in range(112)]
+    need(Counter(routes) == {30: 64, 45: 32, 75: 16}, "Exact route classes")
+    pair, h = pair_word(cyclic)
+    hi = pivot.replay(pivot.inverse(pair))[0]
+    need(all(routes[a] == routes[b] for data in cyclic["pair_codes"]
+             for a, b in [data["ports"]]), "Every pair code preserves the route")
+    groups = []
+    mode, mode_inverse = r.identity(112), r.identity(112)
+    mode_u, mode_v = [{} for _ in range(112)], []
+    for record in old["vertex_assignments"]:
+        ports, signs = record["ordered_carriers_a_b_c"], record["signs"]
+        for route in sorted({routes[p] for p in ports}):
+            entries = [(p, s) for p, s in zip(ports, signs) if routes[p] == route]
+            need(len(entries) == (4 if route == 30 else 2), "Large route split")
+            groups.append({"ports": [p for p, _ in entries], "signs": [s for _, s in entries],
+                           "route": route, "kind": "large", "vertex": record["vertex"]})
+    small = []
+    for clique in old["small_cliques"]:
+        for route in sorted({routes[p] for p in clique}):
+            ports = [p for p in clique if routes[p] == route]
+            need(len(ports) == 4, "Small route split")
+            need(all((q[p] & q[t]).bit_count() % 2 == int(p == t)
+                     for p in ports for t in ports), "Actual four-clique")
+            small.append(ports)
+            groups.append({"ports": ports, "signs": [1] * 4, "route": route, "kind": "small"})
+    need(sorted(p for group in groups for p in group["ports"]) == list(range(112)),
+         "All32 blocks partition the data modes")
+    for index, group in enumerate(groups):
+        ports, signs = group["ports"], group["signs"]
+        k = len(ports)
+        group["pivot"] = ports[0]
+        group["centre_multiplier"] = 1 - k
+        group["relative_q_basis"] = binary_basis([q[p] ^ q[ports[0]] for p in ports[1:]])
+        group["relative_q_rank"] = len(group["relative_q_basis"])
+        group["relative_q_in_common_root"] = all(t in root_space for t in group["relative_q_basis"])
+        for i, p in enumerate(ports):
+            mode[p] = {t: F(int(i == j) - signs[i] * signs[j])
+                       for j, t in enumerate(ports) if i != j}
+            mode_inverse[p] = {t: F(int(i == j)) - F(signs[i] * signs[j], k - 1)
+                               for j, t in enumerate(ports)}
+            mode_u[p] = {index: F(-signs[i])}
+        mode_v.append({p: F(sign) for p, sign in zip(ports, signs)})
+    response = r.product(hi, r.product(mode, h))
+    response_inverse = r.product(hi, r.product(mode_inverse, h))
+    u, v = r.product(hi, mode_u), r.product(mode_v, h)
+    delta = [dict(row) for row in response]
+    for p in range(112):
+        r.add(delta[p], {p: F(-1)})
+    need(r.product(u, v) == delta and r.rank(u, 32) == r.rank(v, 112) == 32,
+         "Actual rank32 response correction")
+    need(r.product(response, response_inverse) == r.product(response_inverse, response) == r.identity(112),
+         "Both complete response inverse orders")
+    need(all(p not in row for p, row in enumerate(response)), "Zero physical diagonal")
+    need(all(routes[p] == routes[t] for p, row in enumerate(response) for t in row),
+         "Every response coefficient preserves the actual route")
+    need(r.determinant(response) == 3 ** 24, "The whole ordinary response is a unit")
+    complete = rank30["maximal_small_cliques"]
+    need(Counter(tuple(sorted(Counter(routes[p] for p in clique).items()))
+                 for clique in complete if len(clique) == 8) == {((30, 4), (45, 4)): 64},
+         "No actual eight-clique stays inside one route")
+    need(max(max(Counter(routes[p] for p in clique).values()) for clique in complete) == 4,
+         "The actual monochromatic clique bound")
+    model = {
+        "ports": q, "large_ports": old["large_ports"], "small_ports": old["small_ports"],
+        "selected_ports": [], "ordinary_ports": list(range(112)),
+        "root_basis": geometry["common_even_isotropic_basis"], "root_space": root_space,
+        "port_routes": routes, "groups": groups, "small_cliques": small,
+        "mode_response": r.encoded(mode), "mode_inverse": r.encoded(mode_inverse),
+        "response": r.encoded(response), "response_inverse": r.encoded(response_inverse),
+        "correction_U": r.encoded(u), "correction_V": r.encoded(v),
+        "full_determinant": str(3 ** 24), "correction_rank": 32,
+        "old_selected_block": r.encoded(r.restrict(response, old["selected_ports"])),
+        "old_selected_determinant": str(r.determinant(r.restrict(response, old["selected_ports"]))),
+    }
+    diagonal = r.identity(112)
+    for group in groups:
+        diagonal[group["pivot"]] = {group["pivot"]: F(group["centre_multiplier"])}
+    codes, reports = {}, {}
+    for name, reflection in [("pivot", False), ("reflection", True)]:
+        word = capture(groups, pair, reflection)
+        inverse = pivot.inverse(word)
+        c, growth = pivot.replay(word)
+        ci, inverse_growth = pivot.replay(inverse)
+        need(r.product(c, r.product(response, ci)) == diagonal, "Exact diagonal centre action " + name)
+        need(pivot.replay(word + inverse)[0] == pivot.replay(inverse + word)[0] == r.identity(112),
+             "Literal code inverse orders " + name)
+        need(all(routes[p] == routes[t] for p, row in enumerate(c) for t in row),
+             "The full physical code preserves routes " + name)
+        entry = [["translate", p, None, str(qp)] for p, qp in enumerate(q)] + word
+        want = [{(p, q[p]): coefficient for p, coefficient in row.items()} for row in c]
+        need(pivot.replay(entry, spatial=True)[0] == want, "Exact input-square entry " + name)
+        need(pivot.replay(entry + pivot.inverse(entry), spatial=True)[0]
+             == [{(p, 0): F(1)} for p in range(112)], "Exact spatial inverse " + name)
+        codes[name] = {"word": word, "inverse_word": inverse, "entry_word": entry,
+                       "code": r.encoded(c), "inverse_code": r.encoded(ci)}
+        reports[name] = {"invoice": pivot.price(word), "inverse_invoice": pivot.price(inverse),
+                         "prefix": growth, "inverse_prefix": inverse_growth}
+    need(reports["pivot"]["invoice"]["old_real_scalar_units"] == 1870, "Complete pivot invoice")
+    need(reports["reflection"]["invoice"]["old_real_scalar_units"] == 2486,
+         "Complete reflection invoice")
+    model["diagonal_response"] = r.encoded(diagonal)
+    model["codes"] = codes
+    return model, reports
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    raw = gzip.decompress(SOURCE.read_bytes())
+    need(sha256(raw).hexdigest() == SOURCE_PIN, "Frozen rank16 source")
+    old = json.loads(raw)["model"]
+    inputs = {path.name: json.loads(path.read_bytes()) for path in PINS if path.suffix == ".json"}
+    model, reports = make_model(old, inputs["CYCLIC-FLAGS.json"], inputs["GEOMETRY.json"],
+                               inputs["RESPONSE-PROGRAM.json"])
+    data = (json.dumps(model, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    (args.out / "ROUTE32-MODEL.json").write_bytes(data)
+    checks = {
+        "status": "PASS_ROUTE32_RESPONSE_AND_CAPTURE",
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_sha256": sha256(data).hexdigest(),
+        "source_decompressed_sha256": SOURCE_PIN,
+        "reports": reports,
+        "correction_rank": 32,
+        "determinant": model["full_determinant"],
+        "old_selected_determinant": model["old_selected_determinant"],
+        "relative_q_rank_counts": dict(sorted(Counter(g["relative_q_rank"] for g in model["groups"]).items())),
+        "blocks_inside_common_root": sum(g["relative_q_in_common_root"] for g in model["groups"]),
+        "all_blocks": len(model["groups"]),
+        "arbitrary_inputs_checked": 640,
+        "old_small_monochromatic_maximum_clique_size": 4,
+        "scope": "Exact route-compatible unit and dyadic in-place centre codes. Native implementation and the physical moving-code caller have separate checks.",
+    }
+    (args.out / "CHECKS.json").write_text(json.dumps(checks, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(checks, sort_keys=True), flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_native.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_native.py
new file mode 100644
index 0000000000..33a8d8197a
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_native.py
@@ -0,0 +1,130 @@
+#!/usr/bin/env python3
+"""Emit the complete native data word for the route-compatible response."""
+
+import argparse
+from copy import deepcopy
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+PARENT = HERE.parent
+EMITTER = PARENT / "emit_native.py"
+EMITTER_PIN = "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745"
+MODEL = HERE / "model-normal/ROUTE32-MODEL.json"
+MODEL_PIN = "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52"
+SOURCES = {
+    PARENT / "native-normal-v2/NATIVE-PROGRAM.json.gz":
+        "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz":
+        "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+need(sha256(EMITTER.read_bytes()).hexdigest() == EMITTER_PIN, "Frozen native emitter")
+spec = importlib.util.spec_from_file_location("route32_native_helpers", EMITTER)
+n = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = n
+spec.loader.exec_module(n)
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    need(sha256(MODEL.read_bytes()).hexdigest() == MODEL_PIN, "Frozen route-compatible model")
+    model = json.loads(MODEL.read_bytes())
+    cyclic = json.loads(n.read("independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json"))
+    inherited = {}
+    source = None
+    for path, pin in SOURCES.items():
+        raw = gzip.decompress(path.read_bytes())
+        need(sha256(raw).hexdigest() == pin, "Native phase source pin")
+        source = json.loads(raw)
+        word = source["providers"]["base"]["forward"]
+        for key, recipe in word["native_recipes"].items():
+            old, new = map(int, key.split(":"))
+            pair = tuple(word["frames"][old]), tuple(word["frames"][new])
+            if pair in inherited:
+                need(inherited[pair] == recipe, "Repeated exact recipe agrees")
+            inherited[pair] = recipe
+    base = source["providers"]["base"]["forward"]
+    words = {direction: n.make_word(cyclic, model, direction) for direction in ("forward", "backward")}
+    frames = words["forward"]["frames"]
+    need(frames == words["backward"]["frames"], "Both orientations have identical actual frames")
+    pairs = sorted({(event[2], event[3]) for word in words.values()
+                    for event in word["events"] if event[0] == "native"})
+    recipes, fresh, reused = {}, 0, 0
+    for old, new in pairs:
+        pair = tuple(frames[old]), tuple(frames[new])
+        if pair in inherited:
+            recipe = inherited[pair]
+            reused += 1
+        else:
+            operation = n.compiler.canonical_frame(9, pair[0]).adjoint().then(
+                n.compiler.canonical_frame(9, pair[1]))
+            recipe, _ = n.compiler.lower_child(operation)
+            n.phase.equal(n.phase.recipe(recipe), n.phase.adjoint(n.phase.frame(pair[0], 9))
+                          + n.phase.frame(pair[1], 9), "Fresh route32 native phase")
+            fresh += 1
+            if fresh % 100 == 0:
+                print("Fresh route32 phases", fresh, flush=True)
+        need(recipe["rank"] == len(pair[1]) - len(pair[0]), "Exact new native rank")
+        recipes[str(old) + ":" + str(new)] = recipe
+    reports = {}
+    for direction, word in words.items():
+        word["native_recipes"] = recipes
+        word["endpoint_adapters"] = base["endpoint_adapters"]
+        need(word["start"] == base["start"] and word["final"] == base["final"],
+             "Identical inherited endpoint indices")
+        need(all(word["frames"][i] == base["frames"][i] for i in word["start"] + word["final"]),
+             "Identical inherited endpoint bases")
+        reports[direction] = n.verify_word(word, n.rows(model["response"]), direction)
+        need(reports[direction]["native_profile"] == {1: 944, 3: 48, 5: 64, 6: 64}
+             and reports[direction]["native_mass"] == 1792
+             and reports[direction]["real_scalar_primitives"] == 4312, "Complete native invoice")
+    bad = deepcopy(words["forward"])
+    del bad["events"][bad["transfer_records"][0]["event"]]
+    try:
+        n.verify_word(bad, n.rows(model["response"]), "forward")
+    except ValueError:
+        pass
+    else:
+        raise ValueError("The missing transfer control was accepted")
+    payload = {"schema": "route32-native-v1", "model": model,
+               "providers": {provider: words for provider in source["providers"]}}
+    data = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(data)
+    for provider, directions in saved["providers"].items():
+        for direction, word in directions.items():
+            need(n.verify_word(word, n.rows(saved["model"]["response"]), direction) == reports[direction],
+                 "Serialized complete native replay " + provider + " " + direction)
+    (args.out / "ROUTE32-NATIVE.json.gz").write_bytes(gzip.compress(data, mtime=0))
+    checks = {
+        "status": "PASS_ROUTE32_COMPLETE_NATIVE",
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "model_sha256": MODEL_PIN,
+        "payload_decompressed_sha256": sha256(data).hexdigest(),
+        "fresh_native_phases": fresh,
+        "inherited_native_phases": reused,
+        "inherited_endpoint_phases": 224,
+        "reports": reports,
+        "missing_transfer_rejected": True,
+        "scope": "Complete local native data word. The416 other fields are unchanged. Productive helper progress, common-root conjugation, moving-code transitions and recursive hosting are separate.",
+    }
+    (args.out / "CHECKS.json").write_text(json.dumps(checks, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(checks, sort_keys=True), flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/CHECKS.json
new file mode 100644
index 0000000000..43a6775d56
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/CHECKS.json
@@ -0,0 +1,76 @@
+{
+  "all_blocks": 32,
+  "arbitrary_inputs_checked": 640,
+  "blocks_inside_common_root": 8,
+  "correction_rank": 32,
+  "determinant": "282429536481",
+  "old_selected_determinant": "0",
+  "old_small_monochromatic_maximum_clique_size": 4,
+  "payload_sha256": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52",
+  "producer_sha256": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711",
+  "relative_q_rank_counts": {
+    "1": 8,
+    "3": 24
+  },
+  "reports": {
+    "pivot": {
+      "inverse_invoice": {
+        "explicit_translation_maps": 0,
+        "native_children": 0,
+        "old_real_scalar_units": 1870,
+        "owned_fields": 0,
+        "real_fixed_three_division_scans": 0,
+        "real_fixed_three_multiplication_scans": 0
+      },
+      "inverse_prefix": {
+        "additional_binary_height": 3,
+        "additional_odd_three_height": 0,
+        "maximum_prefix_row_one_norm": "4"
+      },
+      "invoice": {
+        "explicit_translation_maps": 0,
+        "native_children": 0,
+        "old_real_scalar_units": 1870,
+        "owned_fields": 0,
+        "real_fixed_three_division_scans": 0,
+        "real_fixed_three_multiplication_scans": 0
+      },
+      "prefix": {
+        "additional_binary_height": 0,
+        "additional_odd_three_height": 0,
+        "maximum_prefix_row_one_norm": "8"
+      }
+    },
+    "reflection": {
+      "inverse_invoice": {
+        "explicit_translation_maps": 0,
+        "native_children": 0,
+        "old_real_scalar_units": 2486,
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/native-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/native-normal/CHECKS.json
new file mode 100644
index 0000000000..adba4ddc3a
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/native-normal/CHECKS.json
@@ -0,0 +1,49 @@
+{
+  "fresh_native_phases": 297,
+  "inherited_endpoint_phases": 224,
+  "inherited_native_phases": 752,
+  "missing_transfer_rejected": true,
+  "model_sha256": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52",
+  "payload_decompressed_sha256": "2f037b4757c46efb849bcfd8ad6cc2919d8486c5a9001d6325152446caf0f3e5",
+  "producer_sha256": "f961d989a708b40b26780860caa88bf73b86d451b603add3f254d0d0a7a709ff",
+  "reports": {
+    "backward": {
+      "all_input_columns": 640,
+      "endpoint_maps": 224,
+      "native_children": 1120,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 944,
+        "3": 48,
+        "5": 64,
+        "6": 64
+      },
+      "native_side_map_bound": 2240,
+      "owned_fields": 0,
+      "prefix_row_l1_bound": "14",
+      "private_fields": 0,
+      "real_scalar_primitives": 4312,
+      "untouched_arbitrary_fields": 416
+    },
+    "forward": {
+      "all_input_columns": 640,
+      "endpoint_maps": 224,
+      "native_children": 1120,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 944,
+        "3": 48,
+        "5": 64,
+        "6": 64
+      },
+      "native_side_map_bound": 2240,
+      "owned_fields": 0,
+      "prefix_row_l1_bound": "14",
+      "private_fields": 0,
+      "real_scalar_primitives": 4312,
+      "untouched_arbitrary_fields": 416
+    }
+  },
+  "scope": "Complete local native data word. The416 other fields are unchanged. Productive helper progress, common-root conjugation, moving-code transitions and recursive hosting are separate.",
+  "status": "PASS_ROUTE32_COMPLETE_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/native-normal/ROUTE32-NATIVE.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/native-normal/ROUTE32-NATIVE.json.gz
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literal 0
HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/FREEZE.json
new file mode 100644
index 0000000000..5695a091f3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "ROW-INVOLUTION-NATIVE.md": "3cb445c5216f9a3371ad938da1f663408c6db6b8d3f66875d86d83e830bd7e86",
+    "emit_involution.py": "418137de0328111682a5232877196d59ed7f9246345f05ea7058749c75c909b5",
+    "run-normal-final/CHECKS.json": "fe908f18cdcb242551715a88365aaa110bc37814824dd63fafcf86d3ed0c8812",
+    "run-normal-final/ROW-INVOLUTION-NATIVE.json.gz": "b045fcc338dbb53bd686d5d332d7b51147c43fcc645279db0e8159d3ca8c80ee",
+    "run-optimized-final/CHECKS.json": "fe908f18cdcb242551715a88365aaa110bc37814824dd63fafcf86d3ed0c8812",
+    "run-optimized-final/ROW-INVOLUTION-NATIVE.json.gz": "b045fcc338dbb53bd686d5d332d7b51147c43fcc645279db0e8159d3ca8c80ee"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "aa5356c5cb618984ba3c76c40a255ebd26a66f0a88ac9f57792ab8f6677f9a30",
+  "scope": "Eight complete mixed-output native words for A and AT. Raw endpoint conversion, routed caller, recursive hosting and full supplier cost remain separate.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/ROW-INVOLUTION-NATIVE.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/ROW-INVOLUTION-NATIVE.md
new file mode 100644
index 0000000000..3eb42782be
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/ROW-INVOLUTION-NATIVE.md
@@ -0,0 +1,187 @@
+# Native services for a rank-sixteen involution and its transpose
+
+This packet emits eight complete native words. It covers two providers,
+two response matrices, and two shear directions. The matrices are the
+controller's frozen \(A\) and \(A^T\), with
+
+\[
+A^2=(A^T)^2=I,\qquad \operatorname{rank}(A-I)=16,\qquad \det A=1.
+\]
+
+Each word has sixteen selected FULL target outputs and 96 ordinary hole
+outputs. This change of output contract is part of the construction.
+
+## Exact physical operation
+
+Let \(M\) be \(A\) or \(A^T\). Let \(P\) be the selected set and \(U\) its
+complement. Put \(q_p=Q_p^{-1}\). All words accept
+\(X_p=Q_px_p\) and \(Y_p=y_p\). All 640 input fields are independent and
+arbitrary. The forward word gives
+
+\[
+ X_{\rm out}=F_9x,\qquad
+ (Y_{\rm out})_P=F_9(y+Mx)_P,\qquad
+ (Y_{\rm out})_U=F_9q_U(y+Mx)_U.
+\]
+
+The backward word gives
+
+\[
+ X_{\rm out}=F_9(x-M^Ty),\qquad
+ (Y_{\rm out})_P=F_9y_P,\qquad
+ (Y_{\rm out})_U=F_9q_Uy_U.
+\]
+
+Every one of the 416 auxiliary fields is unchanged. There is no extra
+owned field, private field, zero-input assumption, or odd division.
+
+The selected physical ports, in the pinned order, are
+
+```text
+0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23.
+```
+
+The first eight ports are four complete physical pair blocks. The pair
+code therefore does not mix selected and ordinary fields.
+
+## Actual transfer slots
+
+In each signed mode block of size \(k=6\) or \(8\), the old response is
+\(E_k=I-dd^T\). The new response is
+
+\[
+A_k=I+\bigl((k-2)e_p-d\bigr)d^T,\qquad d_p=1.
+\]
+
+Only the pivot row changes. Its diagonal coefficient is \(k-2\), and its
+other coefficients are \((k-3)d_j\). The transpose changes only the pivot
+column. For an ordinary row, its old pivot-column coefficient is
+multiplied by \(-(k-3)\). Thus the off-diagonal support stays inside the
+actual cyclic or clique transfer slots. All new mode coefficients are
+integers.
+
+The emitter uses the source transfer record for each slot. It divides the
+recorded coefficient by its old mode coefficient to obtain the exact
+orientation sign, checks that the sign is \(1\) or \(-1\), and multiplies
+that sign by the new mode coefficient. This is done in both native
+directions. It does not infer a backward circuit from a matrix transpose.
+
+The source stores the small-clique map separately from the large mode
+matrix. The emitter inserts those pinned small physical rows before it
+computes the coefficient ratios. The small component has no pair code.
+
+For a forward word, remove every event that writes a selected Y field.
+The pair closure makes this removal complete. No retained event reads a
+selected Y field. For a backward word, also remove every transfer that
+reads a selected Y field. All source-X progress and ordinary-Y progress
+remain in place.
+
+After the entire retained sweep, all 112 X fields are FULL, all ordinary
+Y fields have completed their hole paths, and every selected Y field is
+still in I. Apply sixteen explicit rank-nine FULL children to the
+selected Y fields. Then:
+
+- Forward: add \(M[P,*]X\) to \(Y_P\).
+- Backward: subtract \(M[P,*]^TY_P\) from X.
+
+All these late operations have the exact common FULL chart. In the
+backward word, the ordinary contributions were made during the retained
+sweep and the selected contributions are made by the late scatter. Their
+sum is exactly \(-M^Ty\).
+
+## The backward scatter
+
+The forward selected-row query is a shear with arbitrary Y baselines.
+Take the inverse transpose of each elementary gate in chronological
+order. A gate `Y += c X` becomes `X -= c Y`; a scale of a selected Y by
+\(a\) becomes a scale of that Y by \(a^{-1}\). The resulting word is the
+inverse transpose of the complete forward query. It is precisely the
+required negative transpose scatter.
+
+The temporary selected-Y scales are undone. They do not consume a
+record or require a zero baseline. This implementation has the same
+scalar price as the forward query. A direct grouping by X targets also
+passed, but costs 112 more scalar primitives. Its prototype and outputs
+are retained separately; the final packet uses the cheaper exact word.
+
+## Complete local invoice
+
+The two providers have the same invoice. Each of the eight words has
+
+\[
+1392H_1+64H_2+48H_3+16H_9.
+\]
+
+This is 1520 native children and native mass 1808. The sixteen new FULL
+children use the previously reviewed rank-nine recipe with identity
+left and right wrappers. The remaining native side-map upper bound is
+3008. Each word has 112 explicit input monomial views and 96 explicit
+output monomial views.
+
+| Response | Direction | Retained scalar cost | Late query | Total scalar cost | Content prefix norm |
+| --- | --- | ---: | ---: | ---: | ---: |
+| \(A\) | Forward | 6456 | 2960 | 9416 | 70 |
+| \(A\) | Backward | 6456 | 2960 | 9416 | 22 |
+| \(A^T\) | Forward | 6952 | 1984 | 8936 | 30 |
+| \(A^T\) | Backward | 6952 | 1984 | 8936 | 62 |
+
+The content bounds are exact maxima of row one-norms at scalar/native
+boundaries in the literal word. The additional binary denominator height
+is one. These are not bounds for the internal implementation of a
+recursive child.
+
+## Phase and verification
+
+The emitter pins the full native source, the matrix/query packet, the
+cyclic flags, the direct-FULL formation packet, and its independent
+review. Every used native recipe, ordered frame array, input view, and
+output view matches that reviewed formation packet byte-for-byte. No
+new spatial operator is introduced. Only the scalar coefficients and
+their chronology change. The direct FULL children include their global
+phase.
+
+The verifier executes every literal event on all 640 independent input
+columns. It checks the entry and exit frame of every native call and the
+exact common frame of every scalar read and write. It checks all output
+content, all final frames, all helpers, all scalar costs, all native
+ranks, and the prefix bounds. It then reads the serialized payload and
+repeats the complete checks. In each word, deletion of a retained ADD or
+a late-query ADD is rejected.
+
+Normal Python and optimized Python produce byte-identical final
+payloads and receipts. Reproduce into new directories:
+
+```sh
+python3 emit_involution.py --out replay-normal
+python3 -O emit_involution.py --out replay-optimized
+```
+
+The first two development runs stopped at source-schema checks before
+they emitted a payload. The earlier grouped-scatter normal and optimized
+runs passed and are kept as development evidence. The files named in
+`FREEZE.json` are the final result.
+
+## What this enables
+
+The native family now contains a dyadic involution with displacement
+rank sixteen, together with both actual shear directions for it and its
+transpose. The old odd centre eigenvalues are absent. The construction
+permits sixteen nonzero diagonal entries by giving those targets a
+complete FULL path and a late query. Thus a zero-diagonal restriction of
+the old native transfer grammar no longer forces the response family.
+
+For example, the backward word with response \(A^T\) has content update
+\(x\mapsto x-Ay\), while the forward word with response \(A\) has content
+update \(y\mapsto y+Ax\). Their content responses are reciprocal because
+\(A^{-1}=A\). Their physical outputs still have the stated mixed frames.
+No interstage Q commutation, free conversion to all-hole outputs, or
+complete caller follows from this content identity.
+
+This packet supplies no complete supplier or kappa improvement. A caller
+must account for the actual routed responses, selected-field phase
+transitions, recursive children, and final output contract.
+
+This work uses the controller's row-completion theorem, the cyclic native
+family, and the productive row-capture construction from the coordinated
+centre-information campaign. AI agents prepared the proof, code, and
+checks. Independent review of this new complete family is separate.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/emit_involution.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/emit_involution.py
new file mode 100644
index 0000000000..f4e0603534
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/emit_involution.py
@@ -0,0 +1,323 @@
+#!/usr/bin/env python3
+"""Emit both native orientations of the sixteen-row involution."""
+
+import argparse
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+PARENT = HERE.parent
+LANES = PARENT.parents[1]
+PINS = {
+    "helper": (
+        PARENT / "row-only-capture-20261020/emit_capture.py",
+        "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f",
+    ),
+    "native": (
+        PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+        "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    ),
+    "involution": (
+        LANES / "controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json",
+        "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b",
+    ),
+    "formation": (
+        PARENT / "row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz",
+        "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c",
+    ),
+    "formation_review": (
+        LANES / "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json",
+        "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532",
+    ),
+    "cyclic": (
+        LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json",
+        "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    ),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source " + name)
+    return raw
+
+
+read("helper")
+spec = importlib.util.spec_from_file_location("involution_native_base", PINS["helper"][0])
+base = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = base
+spec.loader.exec_module(base)
+n = base.n
+
+
+def verify(word, response, direction, selected):
+    current = list(word["start"])
+    state = [{i: F(1)} for i in range(640)]
+    maximum, height = F(1), 0
+    for event in word["events"]:
+        if event[0] == "native":
+            _, field, old, new, rank, key = event
+            need(current[field] == old, "The exact native input frame")
+            need(len(n.basis(word["frames"][old] + word["frames"][new]))
+                 == len(word["frames"][new]), "A nested native edge")
+            need(rank == len(word["frames"][new]) - len(word["frames"][old])
+                 == word["native_recipes"][key]["rank"], "The exact native rank")
+            current[field] = new
+        else:
+            need(event[0] == "scalar", "The literal event grammar")
+            gate, frame = event[1:]
+            op, target, source, raw = gate
+            coefficient = F(raw)
+            need(current[target] == frame, "The exact scalar target frame")
+            if op == "add":
+                need(target != source and current[source] == frame,
+                     "The exact scalar source frame")
+                n.r.add(state[target], state[source], coefficient)
+            else:
+                need(op == "scale", "Only ADD and SCALE instructions")
+                state[target] = {i: coefficient * value
+                                 for i, value in state[target].items() if coefficient * value}
+            maximum = max(maximum, sum(abs(value) for value in state[target].values()))
+            for value in state[target].values():
+                d = value.denominator
+                need(d & (d - 1) == 0, "Every content coefficient is dyadic")
+                height = max(height, d.bit_length() - 1)
+    expected = [{i: F(1)} for i in range(640)]
+    for p, row in enumerate(response):
+        if direction == "forward":
+            n.r.add(expected[112 + p], row)
+        else:
+            for j, coefficient in row.items():
+                n.r.add(expected[j], {112 + p: -coefficient})
+    need(state == expected, "All640 independent input columns")
+    need(current == word["final"], "All640 final frames")
+    need(state[224:] == [{i: F(1)} for i in range(224, 640)],
+         "All416 arbitrary helpers are unchanged")
+    need(all(current[p] == 1 for p in range(112)), "All X outputs are FULL")
+    need(all(current[112 + p] == 1 for p in selected), "All selected Y outputs are FULL")
+    profile = Counter(event[4] for event in word["events"] if event[0] == "native")
+    children = sum(profile.values())
+    return {
+        "arbitrary_input_columns": 640, "unchanged_arbitrary_helper_fields": 416,
+        "native_profile": dict(sorted(profile.items())), "native_children": children,
+        "native_mass": sum(k * v for k, v in profile.items()),
+        "native_side_map_upper_bound": 2 * (children - len(selected)),
+        "direct_full_identity_wrapper_children": len(selected),
+        "explicit_input_monomial_views": len(word["input_views"]),
+        "explicit_output_monomial_views": len(word["output_views"]),
+        "real_scalar_primitives": base.price(word["events"]),
+        "scalar_stage_prices": {stage: base.price(word["events"][start:stop])
+                               for stage, (start, stop) in word["stage_ranges"].items()},
+        "maximum_content_prefix_row_one_norm": str(maximum),
+        "additional_content_binary_height": height,
+        "owned_fields": 0, "private_fields": 0, "fixed_odd_scans": 0,
+    }
+
+
+def retune(original, old_mode, mode, cyclic):
+    events = deepcopy(original["events"])
+    parameters = {record["id"]: record for record in cyclic["parameters"]}
+    changes = []
+    for record in original["transfer_records"]:
+        index = record["event"]
+        if record["part"] == "large48":
+            parameter = parameters[record["parameter"]]
+            carriers = cyclic["cyclic_carriers"][parameter["vertex"]]
+            row, column = carriers[parameter["row"]], carriers[parameter["column"]]
+        else:
+            need(record["part"] == "small64", "The actual transfer family")
+            row, column = record["target_port"], record["source_port"]
+        old = old_mode[row][column]
+        new = mode[row][column]
+        event = events[index]
+        need(event[0] == "scalar" and event[1][0] == "add", "A literal transfer slot")
+        sign = F(event[1][3]) / old
+        need(sign in (1, -1), "The pinned transfer orientation")
+        need(new and new.denominator == 1, "The new integer transfer has the old support")
+        event[1][3] = str(sign * new)
+        if new != old:
+            changes.append({"original_event": index, "mode_row": row, "mode_column": column,
+                            "old_coefficient": str(sign * old), "new_coefficient": str(sign * new)})
+    return events, changes
+
+
+def backward_query(forward_word):
+    word = []
+    for op, target, source, coefficient in forward_word:
+        if op == "add":
+            word.append(["scalar", ["add", source - 112, 112 + target, str(-F(coefficient))], 1])
+        else:
+            need(op == "scale", "Only ADD and SCALE instructions in the pinned query")
+            word.append(["scalar", ["scale", 112 + target, None, str(1 / F(coefficient))], 1])
+    return word
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    source = json.loads(read("native"))
+    involution = json.loads(read("involution"))
+    formation = json.loads(read("formation"))
+    cyclic = json.loads(read("cyclic"))
+    read("formation_review")
+    pivots = involution["pivots"]
+    selected = set(pivots)
+    selected_y = {112 + p for p in selected}
+    need(pivots == formation["selected_ports"], "The exact physical selected set")
+    old_mode = n.rows(source["model"]["mode_response"])
+    old_response = n.rows(source["model"]["response"])
+    for p in source["model"]["small_ports"]:
+        need(old_mode[p] == {p: F(1)}, "The source stores the small clique map separately")
+        old_mode[p] = old_response[p]
+    responses = {name: n.rows(involution[key]) for name, key in
+                 (("A", "response"), ("AT", "response_transpose"))}
+    modes = {name: n.rows(involution[key]) for name, key in
+             (("A", "mode_response"), ("AT", "mode_response_transpose"))}
+    need(responses["AT"] == n.r.transpose(responses["A"], 112), "The physical transpose")
+    need(all(n.r.product(response, response) == n.r.identity(112)
+             for response in responses.values()), "Both response involutions")
+    for pair in cyclic["pair_codes"]:
+        ports = set(pair["ports"])
+        need(not ports & selected or ports <= selected, "The selected pair closure")
+    reports, providers, ledgers = {}, {}, {}
+    for provider, directions in source["providers"].items():
+        providers[provider], reports[provider], ledgers[provider] = {}, {}, {}
+        reference = formation["providers"][provider]
+        for name, response in responses.items():
+            providers[provider][name], reports[provider][name], ledgers[provider][name] = {}, {}, {}
+            for direction, original in directions.items():
+                events, changed_weights = retune(original, old_mode, modes[name], cyclic)
+                kept, deleted, indices = [], [], []
+                for index, event in enumerate(events):
+                    target = event[1] if event[0] == "native" else event[1][1]
+                    reads_selected = (event[0] == "scalar" and event[1][0] == "add"
+                                      and event[1][2] in selected_y)
+                    if target in selected_y or (direction == "backward" and reads_selected):
+                        deleted.append(event)
+                    else:
+                        need(not reads_selected, "No retained event reads a selected Y")
+                        kept.append(event)
+                        indices.append(index)
+                events = list(kept)
+                ranges = {"retained_core": [0, len(events)]}
+                current = list(original["start"])
+                for event in kept:
+                    if event[0] == "native":
+                        need(current[event[1]] == event[2], "The retained native path")
+                        current[event[1]] = event[3]
+                need(all(current[p] == 1 for p in range(112)), "The completed X query cut")
+                need(all(current[field] == 0 for field in selected_y), "All selected Y are still in I")
+                start_full = len(events)
+                for p in pivots:
+                    events.append(["native", 112 + p, 0, 1, 9, "capture-full"])
+                ranges["selected_full_progress"] = [start_full, len(events)]
+                start_query = len(events)
+                if direction == "forward":
+                    for op, target, origin, coefficient in involution["final_query_words"][name]:
+                        need(target in selected and (op != "add" or 112 <= origin < 224),
+                             "The pinned selected-row query")
+                        events.append(["scalar", [op, 112 + target,
+                                                  None if origin is None else origin - 112,
+                                                  coefficient], 1])
+                else:
+                    events.extend(backward_query(involution["final_query_words"][name]))
+                ranges["late_query"] = [start_query, len(events)]
+                used = {event[5] for event in kept if event[0] == "native"}
+                recipes = {key: original["native_recipes"][key] for key in sorted(used)}
+                for key, recipe in recipes.items():
+                    need(recipe == reference["native_recipes"][key],
+                         "Every retained native recipe is in the reviewed formation word")
+                recipes["capture-full"] = reference["native_recipes"]["capture-full"]
+                need(original["frames"] == reference["frames"]
+                     and original["start"] == reference["start"], "The exact inherited frame arrays")
+                final = list(original["final"])
+                for p in pivots:
+                    final[112 + p] = 1
+                need(final == reference["final"], "The exact inherited mixed output frames")
+                word = {"events": events, "frames": original["frames"],
+                        "start": original["start"], "final": final, "native_recipes": recipes,
+                        "input_views": reference["input_views"], "output_views": reference["output_views"],
+                        "stage_ranges": ranges, "retained_original_event_indices": indices}
+                report = verify(word, response, direction, selected)
+                need(report["native_profile"] == {1: 1392, 2: 64, 3: 48, 9: 16}
+                     and report["native_mass"] == 1808, "The complete hybrid native profile")
+                need(report["explicit_input_monomial_views"] == 112
+                     and report["explicit_output_monomial_views"] == 96, "Every boundary view is charged")
+                for stage in ("retained_core", "late_query"):
+                    bad = deepcopy(word)
+                    index = next(i for i in range(*ranges[stage])
+                                 if bad["events"][i][0] == "scalar"
+                                 and bad["events"][i][1][0] == "add")
+                    del bad["events"][index]
+                    try:
+                        verify(bad, response, direction, selected)
+                    except ValueError:
+                        pass
+                    else:
+                        raise ValueError("An omitted " + stage + " ADD was accepted")
+                providers[provider][name][direction] = word
+                reports[provider][name][direction] = report
+                ledgers[provider][name][direction] = {
+                    "changed_original_transfer_weights": changed_weights,
+                    "removed_events": len(deleted),
+                    "removed_native_profile": dict(sorted(Counter(
+                        event[4] for event in deleted if event[0] == "native").items())),
+                    "removed_scalar_primitives_after_retuning": base.price(deleted),
+                    "no_retained_selected_Y_read": True,
+                }
+    payload = {
+        "schema": "sixteen-row-involution-mixed-native-v1",
+        "source_pins": {name: {"path": str(path), "sha256": pin}
+                        for name, (path, pin) in PINS.items()},
+        "ports": source["model"]["ports"], "selected_ports": pivots,
+        "responses": {name: n.r.encoded(response) for name, response in responses.items()},
+        "providers": providers, "transfer_ledgers": ledgers,
+        "physical_contract": {
+            "input": "X=Qx; Y=y; all640 input fields are independent and arbitrary.",
+            "forward": "Xout=F9x; Yout_P=F9(y+Mx)_P; Yout_U=F9q_U(y+Mx)_U.",
+            "backward": "Xout=F9(x-M^T y); Yout_P=F9y_P; Yout_U=F9q_U y_U.",
+            "scope": "M is A or AT. These are mixed output contracts. A^2=I does not supply a routed caller or a raw all-hole interface.",
+        },
+    }
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    for provider, families in saved["providers"].items():
+        for name, directions in families.items():
+            for direction, word in directions.items():
+                need(verify(word, responses[name], direction, selected) == reports[provider][name][direction],
+                     "Every serialized complete word passes")
+    (args.out / "ROW-INVOLUTION-NATIVE.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {
+        "status": "PASS_EXACT_EIGHT_MIXED_ROW_INVOLUTION_WORDS",
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_decompressed_sha256": sha256(raw).hexdigest(),
+        "reports": reports, "transfer_ledgers": ledgers,
+        "native_phase_scope": "All complete native operators, exact ordered frame arrays, and physical endpoint views bind byte-for-byte to the independently reviewed formation packet.",
+        "negative_controls": "One omitted retained ADD and one omitted late-query ADD fail in each of eight complete words.",
+        "scope": "Complete local hybrid F/B family only. Raw endpoint conversion, routed caller composition, recursive hosting, and the full supplier cost remain separate.",
+    }
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps({"status": receipt["status"], "payload_decompressed_sha256": sha256(raw).hexdigest(),
+                      "reports": reports}, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-normal-final/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-normal-final/CHECKS.json
new file mode 100644
index 0000000000..932960f38d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-normal-final/CHECKS.json
@@ -0,0 +1,5708 @@
+{
+  "native_phase_scope": "All complete native operators, exact ordered frame arrays, and physical endpoint views bind byte-for-byte to the independently reviewed formation packet.",
+  "negative_controls": "One omitted retained ADD and one omitted late-query ADD fail in each of eight complete words.",
+  "payload_decompressed_sha256": "aa5356c5cb618984ba3c76c40a255ebd26a66f0a88ac9f57792ab8f6677f9a30",
+  "producer_sha256": "418137de0328111682a5232877196d59ed7f9246345f05ea7058749c75c909b5",
+  "reports": {
+    "base": {
+      "A": {
+        "backward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "22",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "scalar_stage_prices": {
+            "late_query": 2960,
+            "retained_core": 6456,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        },
+        "forward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "70",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "scalar_stage_prices": {
+            "late_query": 2960,
+            "retained_core": 6456,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        }
+      },
+      "AT": {
+        "backward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "62",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "scalar_stage_prices": {
+            "late_query": 1984,
+            "retained_core": 6952,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        },
+        "forward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "30",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "scalar_stage_prices": {
+            "late_query": 1984,
+            "retained_core": 6952,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        }
+      }
+    },
+    "extra": {
+      "A": {
+        "backward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "22",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "scalar_stage_prices": {
+            "late_query": 2960,
+            "retained_core": 6456,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        },
+        "forward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "70",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "scalar_stage_prices": {
+            "late_query": 2960,
+            "retained_core": 6456,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        }
+      },
+      "AT": {
+        "backward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "62",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "scalar_stage_prices": {
+            "late_query": 1984,
+            "retained_core": 6952,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        },
+        "forward": {
+          "additional_content_binary_height": 1,
+          "arbitrary_input_columns": 640,
+          "direct_full_identity_wrapper_children": 16,
+          "explicit_input_monomial_views": 112,
+          "explicit_output_monomial_views": 96,
+          "fixed_odd_scans": 0,
+          "maximum_content_prefix_row_one_norm": "30",
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_map_upper_bound": 3008,
+          "owned_fields": 0,
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "scalar_stage_prices": {
+            "late_query": 1984,
+            "retained_core": 6952,
+            "selected_full_progress": 0
+          },
+          "unchanged_arbitrary_helper_fields": 416
+        }
+      }
+    }
+  },
+  "scope": "Complete local hybrid F/B family only. Raw endpoint conversion, routed caller composition, recursive hosting, and the full supplier cost remain separate.",
+  "status": "PASS_EXACT_EIGHT_MIXED_ROW_INVOLUTION_WORDS",
+  "transfer_ledgers": {
+    "base": {
+      "A": {
+        "backward": {
+          "changed_original_transfer_weights": [
+            {
+              "mode_column": 76,
+              "mode_row": 0,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 309
+            },
+            {
+              "mode_column": 81,
+              "mode_row": 27,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 315
+            },
+            {
+              "mode_column": 21,
+              "mode_row": 36,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 318
+            },
+            {
+              "mode_column": 51,
+              "mode_row": 111,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 323
+            },
+            {
+              "mode_column": 16,
+              "mode_row": 20,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 329
+            },
+            {
+              "mode_column": 92,
+              "mode_row": 7,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 339
+            },
+            {
+              "mode_column": 87,
+              "mode_row": 57,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 345
+            },
+            {
+              "mode_column": 52,
+              "mode_row": 46,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 347
+            },
+            {
+              "mode_column": 72,
+              "mode_row": 0,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 452
+            },
+            {
+              "mode_column": 78,
+              "mode_row": 27,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 458
+            },
+            {
+              "mode_column": 53,
+              "mode_row": 36,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 461
+            },
+            {
+              "mode_column": 9,
+              "mode_row": 111,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 466
+            },
+            {
+              "mode_column": 25,
+              "mode_row": 20,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 472
+            },
+            {
+              "mode_column": 94,
+              "mode_row": 7,
+              "new_coefficient": "3",
+              "old_coefficient": "-1",
+              "original_event": 482
+            },
+            {
+              "mode_column": 104,
+              "mode_row": 57,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 488
+            },
+            {
+              "mode_column": 62,
+              "mode_row": 46,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 490
+            },
+            {
+              "mode_column": 71,
+              "mode_row": 0,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 595
+            },
+            {
+              "mode_column": 15,
+              "mode_row": 27,
+              "new_coefficient": "3",
+              "old_coefficient": "-1",
+              "original_event": 601
+            },
+            {
+              "mode_column": 11,
+              "mode_row": 36,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 604
+            },
+            {
+              "mode_column": 89,
+              "mode_row": 111,
+              "new_coefficient": "3",
+              "old_coefficient": "-1",
+              "original_event": 615
+            },
+            {
+              "mode_column": 79,
+              "mode_row": 20,
+              "new_coefficient": "-3",
+              "old_coefficient": "1",
+              "original_event": 621
+            },
+            {
+              "mode_column": 63,
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-optimized-final/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-optimized-final/CHECKS.json
new file mode 100644
index 0000000000..932960f38d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-optimized-final/CHECKS.json
@@ -0,0 +1,5708 @@
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL-FREEZE.json
new file mode 100644
index 0000000000..b92af328c6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL-FREEZE.json
@@ -0,0 +1,15 @@
+{
+  "files": {
+    "DIRECT-FULL.md": "905d4ae107dcc014e28bb01a0e6090d02ad075ed219e4e1b921fe50a86ba032c",
+    "direct-normal/CHECKS.json": "267b3b0cfff10073d0edc497d5f1ee3290e789124eca7e9e3c63a7e2fc3605f3",
+    "direct-normal/DIRECT-FULL-CAPTURE.json.gz": "b1bade79c227366b9c283acfbbb4cbdc5dbf3f6a1764bac0e69abd2493e38487",
+    "direct-optimized/CHECKS.json": "267b3b0cfff10073d0edc497d5f1ee3290e789124eca7e9e3c63a7e2fc3605f3",
+    "direct-optimized/DIRECT-FULL-CAPTURE.json.gz": "b1bade79c227366b9c283acfbbb4cbdc5dbf3f6a1764bac0e69abd2493e38487",
+    "emit_direct_full.py": "fbe845f577874795b83de0f7733e90c904aabebb7d33bf1a8874d10c6e0fa574"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c",
+  "scope": "Only sixteen FULL child recipes change; all exact interface contracts remain unchanged.",
+  "source_decompressed_sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL.md
new file mode 100644
index 0000000000..322074d021
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL.md
@@ -0,0 +1,20 @@
+# Direct FULL recipe
+
+The native rank-nine kernel is, by its exact recipe definition, the
+nine positive coordinate line gates. The canonical FULL frame is
+the same circuit. Thus each of the sixteen new FULL calls can use
+identity left and right maps.
+
+The original generic compiler produced two nontrivial wrappers for
+each such call. They compose with the native kernel to the same
+operator. The new checker compares the two complete operators,
+including global phase, and replays every complete bank word.
+The selected, ordinary, source, and helper contracts do not change.
+
+This separate refinement removes 32 nontrivial native side maps.
+The complete side-map upper bound is now 3,008. The profile,
+mass 1,808, scalar price 11,640, and 208 explicit boundary views
+remain unchanged. The earlier frozen packet is preserved.
+
+The native-review lane identified this direct-kernel refinement.
+AI assistance was used.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/FREEZE.json
new file mode 100644
index 0000000000..352c37ada2
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "PRODUCTIVE-CAPTURE.md": "de842ef7745cc86ab21a7e05472bc99ef47e7d0c75185b70cfe40219715aee66",
+    "emit_capture.py": "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f",
+    "run-normal/CHECKS.json": "8f769610ac2a5bd905a89566dde512bfa7ab47a46770b76897deb0536f004c2d",
+    "run-normal/PRODUCTIVE-CAPTURE.json.gz": "943b23d9d41801ffced2e19e765f097eecf2e5ecc5e83079fd63af4b907fa788",
+    "run-optimized/CHECKS.json": "8f769610ac2a5bd905a89566dde512bfa7ab47a46770b76897deb0536f004c2d",
+    "run-optimized/PRODUCTIVE-CAPTURE.json.gz": "943b23d9d41801ffced2e19e765f097eecf2e5ecc5e83079fd63af4b907fa788"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2",
+  "scope": "Exact local productive centre-row formation, including arbitrary target baselines. Selected targets finish in FULL. No next-stage I-frame, recursive hosting or final supplier claim.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json
new file mode 100644
index 0000000000..d0d58ab7c0
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "LINE-ENTRY-REUSE.md": "f2ceaf4ba246a20226aec105145d29c2442bd58681256487439b04064815aa2c",
+    "emit_line_entry_reuse.py": "c8a799f29b6244190e2880b44206a240b8cd16427661c3cc7aff9f1905bdec62",
+    "reuse-normal/CHECKS.json": "cfb3da51fb929a1ffa35b6a1cb973426431d98acba355cf2d6b606bf32450048",
+    "reuse-normal/LINE-ENTRY-REUSE.json.gz": "b3cc486c4ecf0574a8a9a6a94ba62a068340ed30525a3dcf889dd19cf7d84047",
+    "reuse-optimized/CHECKS.json": "cfb3da51fb929a1ffa35b6a1cb973426431d98acba355cf2d6b606bf32450048",
+    "reuse-optimized/LINE-ENTRY-REUSE.json.gz": "b3cc486c4ecf0574a8a9a6a94ba62a068340ed30525a3dcf889dd19cf7d84047"
+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110",
+  "scope": "The arbitrary-record local line-entry interface uses the same local reader. Routed past-reader access, caller composition, and recursive hosting remain separate.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE.md
new file mode 100644
index 0000000000..3d74e03659
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE.md
@@ -0,0 +1,86 @@
+# A local line-entry interface for sixteen stored centre rows
+
+This packet changes the input contract of the frozen productive row capture.
+It accepts sixteen independent records with their positive line phases. It
+does not form or decode those records.
+
+Let \(P\) be the fixed sixteen-port set in `PRODUCTIVE-CAPTURE.md`. Let
+\(q_p=Q_p^{-1}\), let \(F_9\) be the exact full transform, and let \(C\) and
+\(E\) be the pinned row code and native response. The physical inputs are
+
+\[
+ X_p=Q_px_p,\qquad
+ Y_p=y_p\ (p\notin P),\qquad
+ Y_p=Q_pz_p\ (p\in P).
+\]
+
+The records \(z_p\), all other data, and all 416 helper fields are arbitrary
+and independent. The emitted outputs are
+
+\[
+ X_p=F_9x_p,\qquad
+ Y_p=F_9q_p(y+Ex)_p\ (p\notin P),\qquad
+ Y_p=F_9[z_p+(CEx)_p]\ (p\in P).
+\]
+
+The entry has no row precode. The word keeps the 96 ordinary target paths
+from the formation packet. No retained event reads a selected target.
+Each selected target starts in its exact canonical line chart and advances
+to FULL with one rank-eight child. The word then executes the same pinned
+FULL-source query as the formation packet. Thus the independent record is
+preserved as an additive baseline. No assumption that a record is zero is
+used.
+
+The input adapter for each selected target is the pinned source adapter
+for the same physical port, bound to the selected target field. The 16
+new rank-eight recipes are derived from the exact ordered operation
+\(\Gamma_{\rm FULL}\Gamma_{\rm line}^{-1}\). Both providers pass the
+independent phase interpreter, including the global phase. The output
+adapters and every retained native recipe are byte-exact inherited data.
+
+For each provider the complete local invoice is:
+
+| Item | Count |
+| --- | ---: |
+| Native profile | \(1392H_1+64H_2+48H_3+16H_8\) |
+| Native mass | 1792 |
+| Native children | 1520 |
+| Scalar primitives | 9880 |
+| Retained-core scalar primitives | 6456 |
+| Late-query scalar primitives | 3424 |
+| Input monomial views | 128 |
+| Output monomial views | 96 |
+| Native side-map upper bound | 3040 |
+| Owned or private fields | 0 |
+| Fixed odd-division scans | 0 |
+
+The literal scalar/native boundary sweep has maximum content row one-norm
+112 and binary denominator height one. This is a bound on register content
+at those boundaries. It is not a bound for the internal implementation of
+a recursive child.
+
+`emit_line_entry_reuse.py` verifies every one of the 640 independent input
+columns, the exact frame of every read and write, all final frames, and
+the identity on all 416 helpers. It verifies the serialized output again.
+A control that changes a selected input frame from its line to I fails.
+Normal Python and optimized Python produce byte-identical payloads and
+receipts.
+
+Reproduce into new output directories:
+
+```sh
+python3 emit_line_entry_reuse.py --out replay-normal
+python3 -O emit_line_entry_reuse.py --out replay-optimized
+```
+
+This is a local reuse interface with the same local reader \(C_P\). For a
+reader retained from an earlier routed stage, the late query is
+\(L_sE_t\), with its actual ordered source views. That query has a separate
+word and invoice. In particular, the 9880 figure here is not its price.
+The caller must also supply the stated positive line input on each stored
+record and accept the stated FULL output. No complete supplier, recursive
+hosting, or kappa improvement is claimed.
+
+This result uses the controller's frozen row-code packet, the cyclic
+native family, and the reviewed formation packet. The proof, emitter, and
+checks were prepared with AI assistance.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/PRODUCTIVE-CAPTURE.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/PRODUCTIVE-CAPTURE.md
new file mode 100644
index 0000000000..af407f2546
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/PRODUCTIVE-CAPTURE.md
@@ -0,0 +1,212 @@
+# Sixteen centre rows in productive output fields
+
+This packet forms the 16 centre rows of the actual rank16 response
+in 16 existing target fields. It uses no owned field, private field,
+or odd-division scan. The other 96 targets retain their original
+output values and phases. The 112 source fields and all 416 arbitrary
+helpers retain the original source contract.
+
+The complete local profile is
+
+```
+1392 H1 + 64 H2 + 48 H3 + 16 H9.
+```
+
+It has 1,520 children and native mass 1,808. The scalar cost is
+11,640 real primitives. There are 112 explicit input monomial views,
+96 explicit output monomial views, and at most 3,040 native side
+maps. These prices apply to each of the two actual providers.
+
+This is an implemented local capture. It does not close the caller
+or establish a kappa improvement. A selected FULL target has a
+different phase at the next stage from an ordinary hole target.
+That phase must be consumed or paid for.
+
+## Reader and row code
+
+Use the frozen rank16 response `E=I+UV`. Its centre factor is
+
+```
+VU = diag(-6 I8,-8 I8).
+```
+
+The selected physical ports, in centre order, are
+
+```
+P = [0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23].
+```
+
+The first eight ports form four complete physical pair-code
+blocks: `(0,27)`, `(36,111)`, `(20,46)`, and `(7,57)`.
+The other eight ports are in the small cliques. Put
+
+```
+L = V_P^-1 V,
+H_c = diag(-5 I8,-7 I8).
+```
+
+The pinned row-capture algebra proves that `L_P=I16` and
+`L E=H_c L`. Define the full row code `C` by
+
+```
+(Cz)_P = Lz,       (Cz)_U = z_U.
+```
+
+The matrix `C` is a dyadic shear. Its inverse changes the sign of
+the off-pivot terms. Its precode and inverse each cost 1,760 scalar
+primitives. It needs no clean input or scratch field.
+
+The eight large rows of `L` have 21 nonzero coefficients: one
+pivot coefficient 1 and 20 coefficients in `{1/2,-1/2}`.
+The eight small rows have eight unit coefficients. The complete
+output code is invertible, so using selected fields to carry the
+centre rows does not discard their arbitrary input values.
+
+## Complete physical contract
+
+Let `F9` be the actual full spatial frame, and let `q_p=Q_p^-1`.
+The input is
+
+```
+X_p = Q_p x_p,       Y_p = y_p.
+```
+
+All helper fields are arbitrary. The output is
+
+```
+X_p = F9 x_p                         for every p;
+Y_p = F9 q_p (y+E x)_p               for p outside P;
+Y_p = F9 [C(y+E x)]_p                for p in P.
+```
+
+The selected rows therefore contain
+`F9(Ly+H_c Lx)`. Their borrowed baseline `Ly` is part of the
+specified output. It is not assumed to vanish.
+
+## Literal construction
+
+First apply the pinned scalar shear `C` to the current target
+bank in frame I. It writes only the 16 selected targets and reads
+only ordinary target fields. The ordinary target inputs therefore
+remain unchanged.
+
+Next execute the original forward native word with all operations
+whose target is a selected Y field removed. Both providers have
+the same exact deletion ledger:
+
+```
+250 removed events = 128 H1 events + 122 scalar events.
+```
+
+The removed scalar events cost 928. No retained operation reads a
+selected Y field. No source operation reads Y. The selected large
+ports contain complete pair-code blocks, so this deletion does not
+split an input or output pair transform. The retained word thus
+gives the original 96 ordinary outputs and the original 112 source
+outputs. The selected targets still contain `Ly` in frame I.
+
+The final common-FULL query cut is after the entire retained sweep.
+It is not before the target pair-code inverses. In the original
+event list, event 2638 gives the last source its FULL frame, and
+event 2639 completes the final other target. The emitter checks
+that all 112 sources are FULL before it starts the late query.
+
+At that cut, advance each selected target from I to FULL with one
+explicit H9 call. Then add `(CE)_P x=H_c Lx` from the completed
+FULL source bank into the selected FULL targets. Every ADD has
+equal actual source and target frames.
+
+For a large selected row, the query first doubles its current
+target. It then adds the integer coefficients of twice the required
+row, and finally divides the target by two. This retains any
+arbitrary baseline exactly. The coefficients are in
+`{5,-5,10,-10}`. The small rows use `{7,-7}` directly. These are
+ordinary dyadic ADD instructions under the pinned scalar tariff.
+There is no division by 5 or 7.
+
+The full scalar bill is
+
+```
+precode C                  1760
+retained original word     6456
+selected FULL progress        0
+late selected query        3424
+total                     11640.
+```
+
+The original native mass was 1,792. The deletion removes 128 H1
+calls and the replacement adds 16 H9 calls. Hence the new mass is
+`1792-128+16*9=1808`. This mass difference does not by itself price
+the complete recurrence: the 16 high-rank calls must be included
+with their exact sizes.
+
+## Boundary phases and verification
+
+The 112 source input views are the exact pinned rank-zero maps
+from physical `Q_p` to the source's canonical line frame.
+The emitter compiles the 96 ordinary output views in the actual
+outgoing direction, from the canonical hole to `F9 q_p`.
+The selected FULL frame is checked to equal the actual `F9`,
+including phase. No ordinary `q_p` is inserted on a selected
+output. There is no implicit commutation of `Q` with `C` or `E`.
+
+For each provider the new full-frame call, the FULL identity,
+and all 96 ordinary output views receive exact Pauli and Gaussian
+state checks. These are 196 fresh checks across the two providers.
+All retained native recipes and the source entry views are exact
+records from the pinned, independently reviewed rank16 source.
+
+The full literal replay checks all 640 input columns, every source
+and target frame at each ADD, every endpoint, and all 416 unchanged
+helpers. It checks the serialized payload again. Omitting a precode
+ADD is rejected by the borrowed-baseline columns. Omitting a late
+query ADD is rejected by the source columns.
+
+The maximum content prefix row one-norm is 132 and the additional
+content binary height is one. This row-norm bound applies to the
+linear content ledger at the completed primitive cuts. Under the
+unitary native charts it is also a bound in the per-field Hilbert
+norm. It does not replace an internal recursive-child guard or a
+complete numerical precision invoice.
+
+## General row replacement
+
+The construction uses a property of the forward word, not a
+special clean-input identity. Suppose a forward word has the
+following properties:
+
+1. Source progress is independent of the target bank and ends in
+   one common frame.
+2. A selected set of target fields is closed under all target
+   pair transforms, and no retained operation reads those fields.
+3. The selected row code is a unit that changes only selected
+   rows and can be applied at the initial common target frame.
+
+Delete the selected target paths, apply the row code to their
+initial values, advance them to the final source frame, and add the
+selected coded response rows there. The ordinary target outputs
+stay unchanged. The selected targets carry the coded complete
+output, including arbitrary target baselines. The complete cost
+is the retained word plus the row code, the selected frame
+advances, the late queries, and all boundary maps.
+
+This gives a concrete family in which centre information can be
+formed inside productive fields. It does not require a separate
+centre bank. To reuse these fields, a caller must maintain the
+reader and the exact phase of each selected field. The present
+packet proves the formation step only.
+
+## Credit and replay
+
+The response and cyclic native paths come from the pinned
+rank16 extension and the cyclic pair-flag work. The controller lane
+supplied the normalized row code, its centre identity, and the two
+scalar words. The bridge-access lane checked the deletion cut and
+the physical pair closure. The native-review lane independently
+checked the scalar rows and corrected a preliminary manual price
+before this packet was frozen. This lane emits the complete native
+capture and the outgoing views. AI assistance was used.
+
+Normal and optimized Python runs use new output directories. They
+must produce byte-identical payloads and receipts. The independent
+native review is separate from these producer checks.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/CHECKS.json
new file mode 100644
index 0000000000..bd9ff46c28
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/CHECKS.json
@@ -0,0 +1,71 @@
+{
+  "payload_decompressed_sha256": "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c",
+  "producer_sha256": "fbe845f577874795b83de0f7733e90c904aabebb7d33bf1a8874d10c6e0fa574",
+  "reports": {
+    "base": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "direct_full_nontrivial_side_maps": 0,
+      "explicit_input_monomial_views": 112,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "132",
+      "native_children": 1520,
+      "native_mass": 1808,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "9": 16
+      },
+      "native_side_map_upper_bound": 3008,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 11640,
+      "scalar_stage_prices": {
+        "late_query": 3424,
+        "precode": 1760,
+        "retained_core": 6456,
+        "selected_full_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    },
+    "extra": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "direct_full_nontrivial_side_maps": 0,
+      "explicit_input_monomial_views": 112,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "132",
+      "native_children": 1520,
+      "native_mass": 1808,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "9": 16
+      },
+      "native_side_map_upper_bound": 3008,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 11640,
+      "scalar_stage_prices": {
+        "late_query": 3424,
+        "precode": 1760,
+        "retained_core": 6456,
+        "selected_full_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    }
+  },
+  "scope": "Only the sixteen FULL recipe wrappers change. All exact source, target and arbitrary-baseline contracts are unchanged.",
+  "source_decompressed_sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2",
+  "status": "PASS_DIRECT_FULL_REFINEMENT"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-optimized/CHECKS.json
new file mode 100644
index 0000000000..bd9ff46c28
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-optimized/CHECKS.json
@@ -0,0 +1,71 @@
+{
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+      "native_profile": {
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+        "3": 48,
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+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 11640,
+      "scalar_stage_prices": {
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+        "retained_core": 6456,
+        "selected_full_progress": 0
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+      "selected_full_targets": 16,
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HcmV?d00001

diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_capture.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_capture.py
new file mode 100644
index 0000000000..3ff37bc7c6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_capture.py
@@ -0,0 +1,291 @@
+#!/usr/bin/env python3
+"""Emit sixteen productive centre rows at the exact full frame."""
+
+import argparse
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+PARENT = HERE.parent
+LANES = PARENT.parents[1]
+PINS = {
+    "native": (
+        PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz",
+        "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    ),
+    "capture": (
+        LANES / "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json",
+        "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7",
+    ),
+    "helper": (
+        PARENT / "emit_native.py",
+        "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745",
+    ),
+    "cyclic": (
+        LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json",
+        "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585",
+    ),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source " + name)
+    return raw
+
+
+read("helper")
+spec = importlib.util.spec_from_file_location("row_capture_native", PINS["helper"][0])
+n = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = n
+spec.loader.exec_module(n)
+
+
+def price(events):
+    return n.r.price([event[1] for event in events if event[0] == "scalar"])
+
+
+def verify(word, code, response, captured_response, selected):
+    current = list(word["start"])
+    state = [{p: F(1)} for p in range(640)]
+    maximum = F(1)
+    height = 0
+    for event in word["events"]:
+        if event[0] == "native":
+            _, field, old, new, rank, key = event
+            need(current[field] == old, "The exact native entry frame")
+            need(len(n.basis(word["frames"][old] + word["frames"][new]))
+                 == len(word["frames"][new]), "A nested native frame")
+            need(rank == len(word["frames"][new]) - len(word["frames"][old])
+                 == word["native_recipes"][key]["rank"], "The exact native rank")
+            current[field] = new
+        else:
+            need(event[0] == "scalar", "The event grammar")
+            gate, frame = event[1:]
+            op, target, source, coefficient = gate
+            coefficient = F(coefficient)
+            need(current[target] == frame, "The exact scalar target frame")
+            if op == "add":
+                need(source != target and current[source] == frame, "The exact current source frame")
+                n.r.add(state[target], state[source], coefficient)
+            else:
+                need(op == "scale", "Only dyadic scalar instructions")
+                state[target] = {p: coefficient * value for p, value in state[target].items()}
+            maximum = max(maximum, sum(abs(value) for value in state[target].values()))
+            for value in state[target].values():
+                denominator = value.denominator
+                need(denominator & (denominator - 1) == 0, "No odd denominator")
+                height = max(height, denominator.bit_length() - 1)
+    expected = [{p: F(1)} for p in range(640)]
+    for p in range(112):
+        if p in selected:
+            expected[112 + p] = {112 + j: value for j, value in code[p].items()}
+            n.r.add(expected[112 + p], captured_response[p])
+        else:
+            n.r.add(expected[112 + p], response[p])
+    need(state == expected, "All640 independent arbitrary input columns")
+    need(current == word["final"], "All complete output frames")
+    need(state[224:] == [{p: F(1)} for p in range(224, 640)], "All416 helpers are unchanged")
+    profile = Counter(event[4] for event in word["events"] if event[0] == "native")
+    return {
+        "arbitrary_input_columns": 640, "unchanged_source_fields": 112,
+        "unchanged_arbitrary_helper_fields": 416, "selected_full_targets": len(selected),
+        "ordinary_hole_targets": 112 - len(selected), "native_profile": dict(sorted(profile.items())),
+        "native_children": sum(profile.values()), "native_mass": sum(k * v for k, v in profile.items()),
+        "native_side_map_upper_bound": 2 * sum(profile.values()),
+        "explicit_input_monomial_views": len(word["input_views"]),
+        "explicit_output_monomial_views": len(word["output_views"]),
+        "real_scalar_primitives": price(word["events"]),
+        "scalar_stage_prices": {stage: price(word["events"][start:stop])
+                               for stage, (start, stop) in word["stage_ranges"].items()},
+        "maximum_content_prefix_row_one_norm": str(maximum),
+        "additional_content_binary_height": height,
+        "owned_fields": 0, "private_fields": 0, "fixed_odd_scans": 0,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    source = json.loads(read("native"))
+    capture = json.loads(read("capture"))
+    cyclic = json.loads(read("cyclic"))
+    selected_list = capture["pivots"]
+    selected = set(selected_list)
+    need(selected_list == [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23],
+         "The fixed physical pivot set")
+    code, inverse_code = n.rows(capture["code"]), n.rows(capture["code_inverse"])
+    response, captured = n.rows(capture["response"]), n.rows(capture["selected_capture_response"])
+    need(response == n.rows(source["model"]["response"]), "The exact native response")
+    need(n.r.product(code, response) == captured, "The ordered captured response C E")
+    need(n.r.product(code, inverse_code) == n.r.product(inverse_code, code) == n.r.identity(112),
+         "Both row-code inverse orders")
+    for p in range(112):
+        if p in selected:
+            need(code[p].get(p) == 1 and set(code[p]) & selected == {p}, "Normalized row shear")
+            multiplier = F(-5 if selected_list.index(p) < 8 else -7)
+            need(captured[p] == {j: multiplier * value for j, value in code[p].items()},
+                 "The actual centre left eigenvector")
+        else:
+            need(code[p] == {p: F(1)} and captured[p] == response[p], "The ordinary rows stay unchanged")
+    for pair in cyclic["pair_codes"]:
+        ports = set(pair["ports"])
+        need(not ports & selected or ports <= selected, "No selected physical pair is split")
+    fresh_phases = 0
+    words, reports, removals = {}, {}, {}
+    for provider, directions in source["providers"].items():
+        original = directions["forward"]
+        frames = original["frames"]
+        need(frames[0] == [] and len(frames[1]) == 9, "The exact I and FULL frames")
+        full = n.compiler.canonical_frame(9, tuple(frames[1]))
+        full_recipe, _ = n.compiler.lower_child(full)
+        need(full_recipe["rank"] == 9, "An explicit full rank-nine child")
+        n.phase.equal(n.phase.recipe(full_recipe), n.phase.frame(frames[1], 9),
+                      "Exact new full-frame child " + provider)
+        n.phase.equal(n.phase.frame(frames[1], 9), n.phase.fourier(9),
+                      "The selected FULL exit has the exact F9 phase " + provider)
+        fresh_phases += 2
+        selected_fields = {112 + p for p in selected}
+        kept, deleted, retained_indices = [], [], []
+        for index, event in enumerate(original["events"]):
+            target = event[1] if event[0] == "native" else event[1][1]
+            if target in selected_fields:
+                deleted.append(event)
+            else:
+                if event[0] == "scalar" and event[1][0] == "add":
+                    need(event[1][2] not in selected_fields, "No retained read of a selected target")
+                kept.append(event)
+                retained_indices.append(index)
+        pre = []
+        for op, target, source_index, coefficient in capture["scalar_word"]:
+            need(target in selected and (op != "add" or source_index not in selected),
+                 "The precode uses only current ordinary Y sources")
+            pre.append(["scalar", [op, 112 + target, None if source_index is None
+                                   else 112 + source_index, coefficient], 0])
+        events = pre + deepcopy(kept)
+        ranges = {"precode": [0, len(pre)], "retained_core": [len(pre), len(events)]}
+        current = list(original["start"])
+        for event in kept:
+            if event[0] == "native":
+                need(current[event[1]] == event[2], "The retained frame path is continuous")
+                current[event[1]] = event[3]
+        need(all(current[p] == 1 for p in range(112)), "All112 sources are FULL at the query cut")
+        need(all(current[112 + p] == 0 for p in selected), "The selected target baselines remain in I")
+        start_full = len(events)
+        for p in selected_list:
+            events.append(["native", 112 + p, 0, 1, 9, "capture-full"])
+        ranges["selected_full_progress"] = [start_full, len(events)]
+        start_query = len(events)
+        for op, target, source_index, coefficient in capture["final_query_word"]:
+            need(op in ("add", "scale") and target in selected, "The fully dyadic final query")
+            if op == "add":
+                need(112 <= source_index < 224, "The final query reads a completed X source")
+            events.append(["scalar", [op, 112 + target, None if source_index is None
+                                      else source_index - 112, coefficient], 1])
+        ranges["late_query"] = [start_query, len(events)]
+        used = {event[5] for event in kept if event[0] == "native"}
+        recipes = {key: original["native_recipes"][key] for key in sorted(used)}
+        recipes["capture-full"] = full_recipe
+        input_views, output_views = [], []
+        for record in original["endpoint_adapters"]:
+            p = record["port"]
+            if record["role"] == "source":
+                need(record["frame"] == original["start"][p] and record["rank"] == 0,
+                     "The pinned physical input adapter")
+                input_views.append(record)
+            elif p not in selected:
+                conventional = n.compiler.cgate(9, source["model"]["ports"][p], -1).then(
+                    n.compiler.fourier(9))
+                canonical = n.compiler.canonical_frame(9, tuple(frames[record["frame"]]))
+                operation = canonical.adjoint().then(conventional)
+                recipe, _ = n.compiler.lower_child(operation)
+                need(recipe["rank"] == 0, "An explicit ordinary physical output view")
+                circuit = n.phase.adjoint(n.phase.frame(frames[record["frame"]], 9)) \
+                    + (("C", source["model"]["ports"][p], -1),) + n.phase.fourier(9)
+                n.phase.equal(n.phase.recipe(recipe), circuit, "Exact ordinary output view")
+                fresh_phases += 1
+                output_views.append({"port": p, "frame": record["frame"], "recipe": recipe,
+                                     "circuit": circuit})
+        final = list(original["final"])
+        for p in selected:
+            final[112 + p] = 1
+        word = {"start": original["start"], "final": final, "frames": frames, "events": events,
+                "native_recipes": recipes, "input_views": input_views, "output_views": output_views,
+                "stage_ranges": ranges, "retained_original_event_indices": retained_indices,
+                "new_full_recipe_circuit": n.phase.frame(frames[1], 9)}
+        report = verify(word, code, response, captured, selected)
+        need(report["native_profile"] == {1: 1392, 2: 64, 3: 48, 9: 16}, "The full native invoice")
+        need(report["scalar_stage_prices"] == {"precode": 1760, "retained_core": 6456,
+                                              "selected_full_progress": 0, "late_query": 3424},
+             "The full literal scalar invoice")
+        need(report["real_scalar_primitives"] == 11640 and report["native_mass"] == 1808,
+             "The complete local prices")
+        need(len(input_views) == 112 and len(output_views) == 96, "All actual boundary views")
+        words[provider], reports[provider] = word, report
+        removals[provider] = {"events": len(deleted), "native_profile": dict(Counter(
+            event[4] for event in deleted if event[0] == "native")),
+            "scalar_primitives": price(deleted), "no_retained_selected_target_read": True}
+        for stage in ("precode", "late_query"):
+            bad = deepcopy(word)
+            index = next(i for i in range(*ranges[stage]) if bad["events"][i][0] == "scalar"
+                         and bad["events"][i][1][0] == "add")
+            del bad["events"][index]
+            try:
+                verify(bad, code, response, captured, selected)
+            except ValueError:
+                pass
+            else:
+                raise ValueError("An omitted " + stage + " term was accepted")
+    payload = {
+        "schema": "productive-sixteen-full-capture-v1",
+        "source_pins": {name: {"path": str(path), "sha256": pin} for name, (path, pin) in PINS.items()},
+        "ports": source["model"]["ports"], "selected_ports": selected_list,
+        "ordinary_ports": sorted(set(range(112)) - selected), "code": capture["code"],
+        "inverse_code": capture["code_inverse"], "response": capture["response"],
+        "captured_response": capture["selected_capture_response"], "providers": words,
+        "physical_contract": {
+            "input": "X_p=Q_p x_p; Y_p=y_p; all416 helpers arbitrary",
+            "source_output": "X_p=F9 x_p for all112 ports",
+            "ordinary_target_output": "Y_p=F9 q_p (y+E x)_p for p outside P",
+            "selected_target_output": "Y_p=F9 [C(y+E x)]_p for p in P",
+            "helpers": "All416 unchanged; no owned or private field",
+        },
+    }
+    data = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(data)
+    for provider, word in saved["providers"].items():
+        need(verify(word, code, response, captured, selected) == reports[provider],
+             "The complete serialized replay")
+    (args.out / "PRODUCTIVE-CAPTURE.json.gz").write_bytes(gzip.compress(data, mtime=0))
+    receipt = {
+        "status": "PASS_COMPLETE_PRODUCTIVE_FULL_CAPTURE",
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_decompressed_sha256": sha256(data).hexdigest(),
+        "source_pins": payload["source_pins"], "reports": reports, "removed_events": removals,
+        "fresh_phase_checks": fresh_phases, "negative_controls": ["omitted precode ADD", "omitted late-query ADD"],
+        "scope": "Complete local arbitrary-baseline capture with exact changed output phases. No next-stage I-frame claim, recursive hosting or final supplier improvement.",
+    }
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True), flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_direct_full.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_direct_full.py
new file mode 100644
index 0000000000..268e42c112
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_direct_full.py
@@ -0,0 +1,79 @@
+#!/usr/bin/env python3
+"""Remove the two identity-composite wrappers of the direct FULL child."""
+
+import argparse
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE = HERE / "run-normal/PRODUCTIVE-CAPTURE.json.gz"
+SOURCE_PIN = "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2"
+HELPER = HERE / "emit_capture.py"
+HELPER_PIN = "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f"
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+need(sha256(HELPER.read_bytes()).hexdigest() == HELPER_PIN, "Frozen full-capture checker")
+spec = importlib.util.spec_from_file_location("frozen_productive_capture", HELPER)
+base = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = base
+spec.loader.exec_module(base)
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    raw = gzip.decompress(SOURCE.read_bytes())
+    need(sha256(raw).hexdigest() == SOURCE_PIN, "Exact complete capture source")
+    source = json.loads(raw)
+    identity = {"linear_Z4": [0] * 9, "matrix_rows": [1 << j for j in range(9)],
+                "offset": 0, "phase": 0, "quadratic_rows": [0] * 9}
+    recipe = {"left": identity, "rank": 9, "right": identity}
+    base.n.phase.equal(base.n.phase.recipe(recipe), base.n.phase.fourier(9),
+                       "The native FULL kernel has identity wrappers")
+    code = base.n.rows(source["code"])
+    response = base.n.rows(source["response"])
+    captured = base.n.rows(source["captured_response"])
+    selected = set(source["selected_ports"])
+    reports = {}
+    for provider, word in source["providers"].items():
+        old = word["native_recipes"]["capture-full"]
+        base.n.phase.equal(base.n.phase.recipe(recipe), base.n.phase.recipe(old),
+                           "The exact old and direct FULL operators")
+        word["native_recipes"]["capture-full"] = recipe
+        report = base.verify(word, code, response, captured, selected)
+        count = sum(event[0] == "native" and event[5] == "capture-full" for event in word["events"])
+        need(count == 16, "All sixteen direct FULL calls")
+        report["native_side_map_upper_bound"] -= 2 * count
+        report["direct_full_nontrivial_side_maps"] = 0
+        need(report["native_side_map_upper_bound"] == 3008, "The complete refined side-map bound")
+        reports[provider] = report
+    source["schema"] = "productive-sixteen-direct-full-capture-v1"
+    source["refinement_source_decompressed_sha256"] = SOURCE_PIN
+    data = (json.dumps(source, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    (args.out / "DIRECT-FULL-CAPTURE.json.gz").write_bytes(gzip.compress(data, mtime=0))
+    receipt = {
+        "status": "PASS_DIRECT_FULL_REFINEMENT",
+        "source_decompressed_sha256": SOURCE_PIN,
+        "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+        "payload_decompressed_sha256": sha256(data).hexdigest(),
+        "reports": reports,
+        "scope": "Only the sixteen FULL recipe wrappers change. All exact source, target and arbitrary-baseline contracts are unchanged.",
+    }
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_line_entry_reuse.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_line_entry_reuse.py
new file mode 100644
index 0000000000..d89e113296
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_line_entry_reuse.py
@@ -0,0 +1,132 @@
+#!/usr/bin/env python3
+"""Emit the local line-entry interface for arbitrary centre records."""
+
+import argparse
+from copy import deepcopy
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE = HERE / "run-normal/PRODUCTIVE-CAPTURE.json.gz"
+SOURCE_PIN = "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2"
+HELPER = HERE / "emit_capture.py"
+HELPER_PIN = "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f"
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+need(sha256(HELPER.read_bytes()).hexdigest() == HELPER_PIN, "The pinned formation checker")
+spec = importlib.util.spec_from_file_location("line_entry_base", HELPER)
+base = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = base
+spec.loader.exec_module(base)
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    raw = gzip.decompress(SOURCE.read_bytes())
+    need(sha256(raw).hexdigest() == SOURCE_PIN, "Exact complete formation source")
+    source = json.loads(raw)
+    selected = set(source["selected_ports"])
+    response = base.n.rows(source["response"])
+    captured = base.n.rows(source["captured_response"])
+    identity = base.n.r.identity(112)
+    reports, words = {}, {}
+    fresh = 0
+    for provider, original in source["providers"].items():
+        word = deepcopy(original)
+        start_core, end_core = original["stage_ranges"]["retained_core"]
+        start_query, end_query = original["stage_ranges"]["late_query"]
+        kept = deepcopy(original["events"][start_core:end_core])
+        query = deepcopy(original["events"][start_query:end_query])
+        events = list(kept)
+        word["native_recipes"].pop("capture-full")
+        source_views = {view["port"]: view for view in original["input_views"]}
+        input_views = [{**view, "field": view["port"]} for view in original["input_views"]]
+        for p in source["selected_ports"]:
+            line = original["start"][p]
+            word["start"][112 + p] = line
+            old = base.n.compiler.canonical_frame(9, tuple(word["frames"][line]))
+            full = base.n.compiler.canonical_frame(9, tuple(word["frames"][1]))
+            operation = old.adjoint().then(full)
+            recipe, _ = base.n.compiler.lower_child(operation)
+            need(recipe["rank"] == 8, "The exact line-to-FULL rank")
+            circuit = base.n.phase.adjoint(base.n.phase.frame(word["frames"][line], 9)) \
+                + base.n.phase.frame(word["frames"][1], 9)
+            base.n.phase.equal(base.n.phase.recipe(recipe), circuit,
+                               "Exact selected line-entry advance")
+            fresh += 1
+            key = "capture-line:" + str(p)
+            word["native_recipes"][key] = recipe
+            events.append(["native", 112 + p, line, 1, 8, key])
+            input_views.append({**source_views[p], "role": "selected_target",
+                                "field": 112 + p, "source_entry_port": p})
+        query_start = len(events)
+        events.extend(query)
+        word["events"] = events
+        word["input_views"] = input_views
+        word.pop("new_full_recipe_circuit")
+        word["stage_ranges"] = {"precode": [0, 0], "retained_core": [0, len(kept)],
+                                "selected_line_progress": [len(kept), query_start],
+                                "late_query": [query_start, len(events)]}
+        report = base.verify(word, identity, response, captured, selected)
+        need(report["native_profile"] == {1: 1392, 2: 64, 3: 48, 8: 16},
+             "The complete reuse profile")
+        need(report["native_mass"] == 1792 and report["real_scalar_primitives"] == 9880,
+             "The complete current-reader local invoice")
+        need(len(input_views) == 128 and len(word["output_views"]) == 96,
+             "All source and selected target input views are charged")
+        reports[provider], words[provider] = report, word
+        bad = deepcopy(word)
+        bad["start"][112 + source["selected_ports"][0]] = 0
+        try:
+            base.verify(bad, identity, response, captured, selected)
+        except ValueError:
+            pass
+        else:
+            raise ValueError("The wrong selected I-frame input was accepted")
+    payload = {
+        "schema": "productive-sixteen-line-entry-reuse-v1",
+        "source_decompressed_sha256": SOURCE_PIN,
+        "ports": source["ports"], "selected_ports": source["selected_ports"],
+        "ordinary_ports": source["ordinary_ports"], "response": source["response"],
+        "selected_query_response": source["captured_response"], "providers": words,
+        "physical_contract": {
+            "input": "X_p=Q_p x_p; Y_p=y_p outside P; Y_p=Q_p z_p on P",
+            "source_output": "X_p=F9 x_p for every p",
+            "ordinary_target_output": "Y_p=F9 q_p (y+E x)_p outside P",
+            "selected_target_output": "Y_p=F9 [z_p+(C E x)_p] on P",
+            "baseline": "All16 records z and all other data/helper fields are independent and arbitrary.",
+            "reader_scope": "The late query uses the same local reader C_P. A routed past-reader query is a separate word and invoice.",
+        },
+    }
+    data = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(data)
+    for provider, word in saved["providers"].items():
+        need(base.verify(word, identity, response, captured, selected) == reports[provider],
+             "The complete serialized line-entry replay")
+    (args.out / "LINE-ENTRY-REUSE.json.gz").write_bytes(gzip.compress(data, mtime=0))
+    receipt = {"status": "PASS_EXACT_LOCAL_LINE_ENTRY_REUSE",
+               "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "source_decompressed_sha256": SOURCE_PIN,
+               "payload_decompressed_sha256": sha256(data).hexdigest(),
+               "reports": reports, "fresh_phase_checks": fresh,
+               "negative_control": "A selected I-frame input is rejected.",
+               "scope": "Exact arbitrary-record local interface only. The actual past/current routed reader product, its access maps, and the complete supplier remain separate."}
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/CHECKS.json
new file mode 100644
index 0000000000..86ddadbe7b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/CHECKS.json
@@ -0,0 +1,71 @@
+{
+  "fresh_phase_checks": 32,
+  "negative_control": "A selected I-frame input is rejected.",
+  "payload_decompressed_sha256": "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110",
+  "producer_sha256": "c8a799f29b6244190e2880b44206a240b8cd16427661c3cc7aff9f1905bdec62",
+  "reports": {
+    "base": {
+      "additional_content_binary_height": 1,
+      "arbitrary_input_columns": 640,
+      "explicit_input_monomial_views": 128,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "112",
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 9880,
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-optimized/CHECKS.json
new file mode 100644
index 0000000000..86ddadbe7b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-optimized/CHECKS.json
@@ -0,0 +1,71 @@
+{
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+  "negative_control": "A selected I-frame input is rejected.",
+  "payload_decompressed_sha256": "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110",
+  "producer_sha256": "c8a799f29b6244190e2880b44206a240b8cd16427661c3cc7aff9f1905bdec62",
+  "reports": {
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+      "explicit_input_monomial_views": 128,
+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "112",
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
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+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
+      "owned_fields": 0,
+      "private_fields": 0,
+      "real_scalar_primitives": 9880,
+      "scalar_stage_prices": {
+        "late_query": 3424,
+        "precode": 0,
+        "retained_core": 6456,
+        "selected_line_progress": 0
+      },
+      "selected_full_targets": 16,
+      "unchanged_arbitrary_helper_fields": 416,
+      "unchanged_source_fields": 112
+    },
+    "extra": {
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+      "arbitrary_input_columns": 640,
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+      "explicit_output_monomial_views": 96,
+      "fixed_odd_scans": 0,
+      "maximum_content_prefix_row_one_norm": "112",
+      "native_children": 1520,
+      "native_mass": 1792,
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+        "3": 48,
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+      "native_side_map_upper_bound": 3040,
+      "ordinary_hole_targets": 96,
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+      "real_scalar_primitives": 9880,
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+      },
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+      "unchanged_arbitrary_helper_fields": 416,
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+    }
+  },
+  "scope": "Exact arbitrary-record local interface only. The actual past/current routed reader product, its access maps, and the complete supplier remain separate.",
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+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-optimized/LINE-ENTRY-REUSE.json.gz b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-optimized/LINE-ENTRY-REUSE.json.gz
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-CHECKS.json
new file mode 100644
index 0000000000..f3f8854e73
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-CHECKS.json
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+  "correction_rank_small64": 14,
+  "full_determinant": "33554432",
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+  "payload_sha256": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c",
+  "scope": "Exact port matrices, principal units, scalar codes and geometry. Native phases and terminal access are separate.",
+  "selected_determinant": "1/16",
+  "small_clique_sizes": {
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+    "5": 11
+  },
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+  },
+  "status": "PASS_LOW_DISPLACEMENT_RESPONSE"
+}
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new file mode 100644
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/FREEZE.json
new file mode 100644
index 0000000000..f296bee1e1
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+  },
+  "normal_optimized_byte_identical": true,
+  "payload_decompressed_sha256": "1bdddb7955d0ada6dabcf150fce0a568cd336a846f51be3324c081f10dd374c7",
+  "scope": "Direct Fsimple and selected-conjugate inverse-adjoint Bcustom. Both640-column local words have2912 scalar,96H1+128H8+96H9,mass1984. All209 exact physical kernel phases pass. No complete caller or recursive host claim.",
+  "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/SIMPLE-CLEAN-NATIVE.md b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/SIMPLE-CLEAN-NATIVE.md
new file mode 100644
index 0000000000..ce3ab25577
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/SIMPLE-CLEAN-NATIVE.md
@@ -0,0 +1,172 @@
+# Direct native self-transfer with clean selected centres
+
+This packet gives two complete local words. The first has the content
+map
+
+```text
+Fsimple(a,u,z,v) = (-z, u, a+Bu, v+u).
+```
+
+The second has the content map
+
+```text
+Bcustom(a,u,z,v) = (z, u-B^Tz-v, -a, v).
+```
+
+Here P is the same set of 16 selected ports as in the frozen clean
+exchange. U contains the other 96 ports. The exact row code is
+C(a,u)=(a+Bu,u). Both words use the physical types
+
+```text
+input:    X=Q(a,u),       Y_P=Q_P z,       Y_U=v;
+output:   X in F9,       Y_P in F9,       Y_U in F9 q_U.
+```
+
+The invoice for either complete word is
+
+```text
+native profile                96 H1 + 128 H8 + 96 H9
+native mass                   1984
+native children               320
+real scalar primitives        2912
+native side-map upper bound   448
+boundary adapters             0
+extra owned or private fields 0
+odd divisions                 0
+```
+
+This is a direct local implementation. It does not give a closed routed
+caller, a new recursive host, or a complete supplier bound.
+
+## Physical construction
+
+Write q_p=Q_p^-1. All 112 source fields have physical value Q_p x_p.
+Apply the exact native operator F9 q_p to each source. Each operator has
+rank eight and gives F9 x_p. Apply the same operator to each of the 16
+selected target fields. These fields now contain F9 z_p.
+
+Apply F9 to each of the 96 ordinary target fields. This has rank nine.
+Both fields at each ordinary port now have the same FULL type. Execute
+the literal scalar ADD
+
+```text
+Y_p += X_p.
+```
+
+Then apply q_p to that ordinary target. The complete physical result is
+F9 q_p(v_p+u_p). This use of q_p is valid because Q_p and F9 commute.
+The checker verifies the complete operator and its global phase at
+every actual port. It does not infer the identity from a frame name.
+
+All source fields still have the same FULL type. Execute the pinned
+1,760-unit code C on X. At each selected port execute
+
+```text
+Y_p += X_p;
+X_p -= Y_p;
+Y_p += X_p.
+```
+
+The three ADDs send (L_p x,z_p) to (-z_p,L_p x), where L=[I,B].
+They cost 24 real scalar primitives per port. The ordinary source
+fields do not change. This proves the stated Fsimple endpoint.
+
+The full rank-nine kernel has identity left and right wrappers. It is
+the nine positive coordinate C gates that define F9. The rank-eight and
+rank-one kernels retain both emitted wrappers in the invoice.
+
+## Literal inverse-adjoint
+
+Let M denote the real content matrix of Fsimple. The physical word is
+
+```text
+W = A_out M A_in^-1,
+```
+
+where A_in and A_out are the unitary block diagonal input and output
+operators listed above. Thus
+
+```text
+W^-* = A_out M^-T A_in^-1.
+```
+
+To emit this operation, keep the original chronological instruction
+order. Keep every native operator unchanged, with its exact phase.
+For every scalar ADD, exchange source and target and negate the
+coefficient. Replace a scalar scale by its reciprocal.
+
+Let S exchange X_p with Y_p at each selected port. The selected input
+types are Q_p on both banks. The selected output types are FULL on both
+banks. Thus S commutes with both boundary operators. Replace every
+selected field label in the inverse-adjoint word by its partner label.
+This emits S W^-* S. It requires no extra runtime exchanges.
+
+Direct block inversion gives
+
+```text
+S M^-T S (a,u,z,v) = (z, u-B^T z-v, -a, v).
+```
+
+The checker executes the complete changed word. It checks both orders
+of the content inverse identity. It does not treat the desired block
+formula as a substitute for the native instruction sequence.
+
+## Verification and tensor scope
+
+The direct source uses the common port list and row code of the two
+pinned providers. It replaces their old native paths. Thus there is one
+common direct word, rather than two copies of the same word.
+
+Each complete word passes all 640 independent input columns. The 416
+auxiliary fields are arbitrary and unchanged. The checker verifies
+every native edge, every scalar operand type, every final type, and
+every scalar cost. It replays the serialized payload. It rejects a
+missing ordinary self-response ADD and a missing reader ADD in both
+words.
+
+There are 209 exact physical kernel checks: one full kernel, 112
+line-to-FULL kernels, and 96 negative-line exit kernels. The check uses
+the exact Pauli action and one complete 512-entry Gaussian state. The
+Pauli action determines the Clifford up to scalar phase. The state
+comparison determines that scalar phase.
+
+These one-alphabet operator equalities lift to every tensor width f.
+Each native kernel is replaced by its tensor power. Each scalar ADD
+uses two fields in the same current physical type. The number of
+emitted scalar instructions and native calls is independent of f.
+No polynomial expansion of a tensor-power line operator is used.
+
+At scalar instruction boundaries, the content row one-norm reaches
+22 for Fsimple and four for Bcustom. The additional binary denominator
+height is one in both words. These are local content bounds. The
+internal precision of a recursive child remains separate.
+
+Run the two checks in new output directories:
+
+```text
+python3 emit_simple.py --out <new-directory>
+python3 -O emit_simple.py --out <another-new-directory>
+```
+
+The normal and optimized payloads and receipts are byte-identical.
+
+## Cost consequence and source credit
+
+The direct ordinary self-transfer adds two native ranks per ordinary
+port relative to the frozen clean word. The full mass is therefore
+1,984 instead of 1,792. The 320 larger children also have a different
+recursive moment from the 1,520 children of the clean word. A full
+budget comparison must use the complete profile above.
+
+This packet uses the row code from the controller's frozen row-capture
+packet and the clean selected exchange from this lane. It also uses
+the direct-FULL kernel established in the row-capture refinement and
+its independent review. The source hashes and paths are in the
+payload. The compiler and exact phase interpreter have separate
+pinned source records.
+
+The construction removes the ordinary D(a+Bu) response by a different
+native word. It does not claim that one can remove a final Bv ADD from
+the old clean dual. Independent review of this new direct word is a
+separate step. AI assistance was used for the construction, code,
+proof, and checks.
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/emit_simple.py b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/emit_simple.py
new file mode 100644
index 0000000000..f242f34532
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/emit_simple.py
@@ -0,0 +1,264 @@
+#!/usr/bin/env python3
+"""Emit the direct clean self-response and its selected dual."""
+
+import argparse
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import sys
+
+
+HERE = Path(__file__).resolve().parent
+PREVIOUS = HERE.parent / "clean-late-exchange-20261020"
+PINS = {
+    "helper": (PREVIOUS / "emit_clean_exchange.py",
+               "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc"),
+    "source": (PREVIOUS / "run-normal/CLEAN-LATE-EXCHANGE.json.gz",
+               "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083"),
+}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(name):
+    path, pin = PINS[name]
+    raw = path.read_bytes()
+    if path.suffix == ".gz":
+        raw = gzip.decompress(raw)
+    need(sha256(raw).hexdigest() == pin, "Pinned source " + name)
+    return raw
+
+
+read("helper")
+spec = importlib.util.spec_from_file_location("simple_clean_base", PINS["helper"][0])
+base = importlib.util.module_from_spec(spec)
+sys.modules[spec.name] = base
+spec.loader.exec_module(base)
+n = base.n
+
+
+def dual(word, permutation):
+    result = deepcopy(word)
+    for event in result["events"]:
+        if event[0] == "native":
+            event[1] = permutation[event[1]]
+        else:
+            op, target, source, coefficient = event[1]
+            if op == "add":
+                event[1] = [op, permutation[source], permutation[target], str(-F(coefficient))]
+            else:
+                need(op == "scale", "The scalar grammar")
+                event[1] = [op, permutation[target], None, str(1 / F(coefficient))]
+    for key in ("start", "final"):
+        result[key] = [word[key][permutation[p]] for p in range(640)]
+        need(result[key] == word[key], "The selected physical types agree")
+    result["wire_permutation"] = {str(p): q for p, q in enumerate(permutation) if p != q}
+    return result
+
+
+def replay(word, expected, kernels):
+    current = list(word["start"])
+    state = n.r.identity(640)
+    maximum, height = F(1), 0
+    for event in word["events"]:
+        if event[0] == "native":
+            _, field, old, new, rank, key = event
+            need(current[field] == old, "The exact native input type")
+            need(kernels[key]["rank"] == rank
+                 and kernels[key]["edge"] == [old, new], "The exact physical native edge")
+            current[field] = new
+            continue
+        need(event[0] == "scalar", "Every event is priced")
+        gate, frame = event[1:]
+        op, target, source, coefficient = gate
+        coefficient = F(coefficient)
+        need(current[target] == frame, "The exact scalar target type")
+        if op == "add":
+            need(target != source and current[source] == frame, "The exact scalar source type")
+            n.r.add(state[target], state[source], coefficient)
+        else:
+            need(op == "scale" and coefficient, "An invertible real scale")
+            state[target] = {j: value * coefficient for j, value in state[target].items()
+                             if value * coefficient}
+        maximum = max(maximum, sum(abs(value) for value in state[target].values()))
+        for value in state[target].values():
+            d = value.denominator
+            need(d & (d - 1) == 0, "Dyadic content")
+            height = max(height, d.bit_length() - 1)
+    need(state == expected, "All640 independent input columns")
+    need(state[224:] == n.r.identity(640)[224:], "All416 helpers remain unchanged")
+    need(current == word["final"], "Every final physical type")
+    profile = Counter(event[4] for event in word["events"] if event[0] == "native")
+    prices = {name: base.base.price(word["events"][a:b])
+              for name, (a, b) in word["stage_ranges"].items()}
+    return {
+        "all_independent_input_columns": 640, "unchanged_arbitrary_helpers": 416,
+        "native_profile": dict(sorted(profile.items())), "native_children": sum(profile.values()),
+        "native_mass": sum(rank * count for rank, count in profile.items()),
+        "real_scalar_primitives": sum(prices.values()), "scalar_stage_prices": prices,
+        "native_side_map_upper_bound": 2 * (sum(profile.values()) - profile[9]),
+        "boundary_adapter_calls": 0, "extra_owned_fields": 0, "extra_private_fields": 0,
+        "odd_divisions": 0, "content_prefix_row_one_norm": str(maximum),
+        "additional_content_binary_height": height,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--out", type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=False)
+    source = json.loads(read("source"))
+    capture = json.loads(base.read("capture"))
+    ports, pivots = source["ports"], source["selected_ports"]
+    selected, ordinary = set(pivots), sorted(set(range(112)) - set(pivots))
+    code = n.rows(source["code"])
+    need(code == n.rows(capture["code"]), "The actual FULL row code")
+    frames = [(), n.phase.fourier(9)]
+    frames += [(("C", q, 1),) for q in ports]
+    frames += [(("C", q, -1),) + n.phase.fourier(9) for q in ports]
+    kernels = {}
+    full = n.compiler.fourier(9)
+    full_recipe = source["providers"]["base"]["I"]["native_recipes"]["capture-full"]
+    need(full_recipe == source["providers"]["extra"]["I"]["native_recipes"]["capture-full"],
+         "The same exact direct FULL kernel")
+    kernels["full"] = {"rank": 9, "edge": [0, 1], "recipe": full_recipe}
+    n.phase.equal(n.phase.recipe(full_recipe), frames[1], "Exact direct FULL phase")
+    for p, q in enumerate(ports):
+        operation = n.compiler.cgate(9, q, -1).then(full)
+        recipe, _ = n.compiler.lower_child(operation)
+        need(recipe["rank"] == 8, "The direct source rank is eight")
+        edge = [2 + p, 1]
+        n.phase.equal(n.phase.recipe(recipe), n.phase.adjoint(frames[edge[0]]) + frames[edge[1]],
+                      "Exact direct line-to-FULL phase " + str(p))
+        kernels["advance:" + str(p)] = {"rank": 8, "edge": edge, "recipe": recipe}
+        if p in ordinary:
+            recipe, _ = n.compiler.lower_child(n.compiler.cgate(9, q, -1))
+            need(recipe["rank"] == 1, "The exact negative line rank")
+            edge = [1, 114 + p]
+            n.phase.equal(n.phase.recipe(recipe),
+                          n.phase.adjoint(frames[edge[0]]) + frames[edge[1]],
+                          "Exact ordinary exit and FULL commutation " + str(p))
+            kernels["exit:" + str(p)] = {"rank": 1, "edge": edge, "recipe": recipe}
+        if (p + 1) % 16 == 0:
+            print("Exact port kernels", p + 1, "/112", flush=True)
+    start, final = [0] * 640, [0] * 640
+    for p in range(112):
+        start[p], final[p] = 2 + p, 1
+        start[112 + p] = 2 + p if p in selected else 0
+        final[112 + p] = 1 if p in selected else 114 + p
+    events, ranges = [], {}
+
+    def stage(name, records):
+        a = len(events)
+        events.extend(records)
+        ranges[name] = [a, len(events)]
+
+    stage("source_progress", [["native", p, 2 + p, 1, 8, "advance:" + str(p)]
+                              for p in range(112)])
+    stage("selected_progress", [["native", 112 + p, 2 + p, 1, 8, "advance:" + str(p)]
+                                for p in pivots])
+    stage("ordinary_full_progress", [["native", 112 + p, 0, 1, 9, "full"] for p in ordinary])
+    stage("ordinary_self_adds", [["scalar", ["add", 112 + p, p, "1"], 1] for p in ordinary])
+    stage("ordinary_negative_lines", [["native", 112 + p, 1, 114 + p, 1, "exit:" + str(p)]
+                                     for p in ordinary])
+    stage("source_row_code", [["scalar", gate, 1] for gate in capture["scalar_word"]])
+    rotations = []
+    for p in pivots:
+        rotations.extend([["scalar", ["add", 112 + p, p, "1"], 1],
+                          ["scalar", ["add", p, 112 + p, "-1"], 1],
+                          ["scalar", ["add", 112 + p, p, "1"], 1]])
+    stage("signed_selected_exchanges", rotations)
+    forward = {"start": start, "final": final, "events": events, "stage_ranges": ranges}
+    expected_forward = n.r.identity(640)
+    expected_custom = n.r.identity(640)
+    for p in range(112):
+        if p in selected:
+            expected_forward[p] = {112 + p: F(-1)}
+            expected_forward[112 + p] = dict(code[p])
+            expected_custom[p] = {112 + p: F(1)}
+            expected_custom[112 + p] = {p: F(-1)}
+        else:
+            n.r.add(expected_forward[112 + p], {p: F(1)})
+            n.r.add(expected_custom[p], {112 + p: F(-1)})
+            for j in pivots:
+                n.r.add(expected_custom[p], {112 + j: -code[j].get(p, F(0))})
+    permutation = list(range(640))
+    for p in pivots:
+        permutation[p], permutation[112 + p] = 112 + p, p
+    custom = dual(forward, permutation)
+    words = {"Fsimple": forward, "Bcustom": custom}
+    expected = {"Fsimple": expected_forward, "Bcustom": expected_custom}
+    reports = {}
+    for name, word in words.items():
+        report = replay(word, expected[name], kernels)
+        need(report["native_profile"] == {1: 96, 8: 128, 9: 96}
+             and report["native_mass"] == 1984 and report["native_children"] == 320,
+             "The full native profile")
+        need(report["real_scalar_primitives"] == 2912
+             and report["scalar_stage_prices"]["ordinary_self_adds"] == 768
+             and report["scalar_stage_prices"]["source_row_code"] == 1760
+             and report["scalar_stage_prices"]["signed_selected_exchanges"] == 384,
+             "Every scalar instruction is priced")
+        for stage_name in ("ordinary_self_adds", "source_row_code"):
+            bad = deepcopy(word)
+            i = next(i for i in range(*ranges[stage_name]) if bad["events"][i][1][0] == "add")
+            del bad["events"][i]
+            try:
+                replay(bad, expected[name], kernels)
+            except ValueError:
+                pass
+            else:
+                raise ValueError("A missing " + stage_name + " ADD was accepted")
+        reports[name] = report
+    transpose_custom = n.r.transpose(expected_custom[:224], 224)
+    swapped_transpose = [{} for _ in range(224)]
+    for target, row in enumerate(transpose_custom):
+        swapped_transpose[permutation[target]] = {permutation[j]: v for j, v in row.items()}
+    need(n.r.product(expected_forward[:224], swapped_transpose)
+         == n.r.product(swapped_transpose, expected_forward[:224]) == n.r.identity(224),
+         "Both exact selected-conjugate inverse-adjoint identities")
+    payload = {
+        "schema": "direct-simple-clean-native-v1",
+        "source_pins": {name: {"path": str(path), "sha256": pin}
+                        for name, (path, pin) in PINS.items()},
+        "native_dependency_pins": n.PINS, "ports": ports, "selected_ports": pivots,
+        "code": source["code"], "physical_frame_circuits": frames, "native_kernels": kernels,
+        "words": words, "content_maps": {name: n.r.encoded(rows[:224]) for name, rows in expected.items()},
+        "provider_scope": "The same complete direct word applies to both pinned providers; their common ports and row code are used.",
+        "physical_contract": {
+            "input": "X=Q(a,u), selectedY=Q_P z, ordinaryY=v.",
+            "Fsimple": "Output content (-z,u,a+Bu,v+u).",
+            "Bcustom": "Output content (z,u-B^Tz-v,-a,v).",
+            "output": "X and selectedY have F9; ordinaryY has F9 q_U.",
+            "scope": "Direct physical local words. No caller, recursive host or complete supplier bound.",
+        },
+    }
+    raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode()
+    saved = json.loads(raw)
+    for name, word in saved["words"].items():
+        need(replay(word, expected[name], saved["native_kernels"]) == reports[name],
+             "The complete serialized direct word")
+    (args.out / "SIMPLE-CLEAN-NATIVE.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    receipt = {"status": "PASS_DIRECT_SIMPLE_CLEAN_NATIVE",
+               "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(),
+               "payload_decompressed_sha256": sha256(raw).hexdigest(), "reports": reports,
+               "fresh_exact_native_phase_checks": len(kernels),
+               "phase_method": "Exact Pauli action and one complete512-entry Gaussian state determine each Clifford including global phase.",
+               "both_content_inverse_orders": True,
+               "negative_controls": "An omitted self-response or reader ADD is rejected in both words.",
+               "scope": payload["physical_contract"]["scope"]}
+    (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n")
+    print(json.dumps(receipt, sort_keys=True), flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-normal/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-normal/CHECKS.json
new file mode 100644
index 0000000000..cbd2e03c5f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-normal/CHECKS.json
@@ -0,0 +1,68 @@
+{
+  "both_content_inverse_orders": true,
+  "fresh_exact_native_phase_checks": 209,
+  "negative_controls": "An omitted self-response or reader ADD is rejected in both words.",
+  "payload_decompressed_sha256": "1bdddb7955d0ada6dabcf150fce0a568cd336a846f51be3324c081f10dd374c7",
+  "phase_method": "Exact Pauli action and one complete512-entry Gaussian state determine each Clifford including global phase.",
+  "producer_sha256": "6a4bacced0962b4f29d5b29743c6f07382ba98f850c57bb4dd828f9e98b1ea0b",
+  "reports": {
+    "Bcustom": {
+      "additional_content_binary_height": 1,
+      "all_independent_input_columns": 640,
+      "boundary_adapter_calls": 0,
+      "content_prefix_row_one_norm": "4",
+      "extra_owned_fields": 0,
+      "extra_private_fields": 0,
+      "native_children": 320,
+      "native_mass": 1984,
+      "native_profile": {
+        "1": 96,
+        "8": 128,
+        "9": 96
+      },
+      "native_side_map_upper_bound": 448,
+      "odd_divisions": 0,
+      "real_scalar_primitives": 2912,
+      "scalar_stage_prices": {
+        "ordinary_full_progress": 0,
+        "ordinary_negative_lines": 0,
+        "ordinary_self_adds": 768,
+        "selected_progress": 0,
+        "signed_selected_exchanges": 384,
+        "source_progress": 0,
+        "source_row_code": 1760
+      },
+      "unchanged_arbitrary_helpers": 416
+    },
+    "Fsimple": {
+      "additional_content_binary_height": 1,
+      "all_independent_input_columns": 640,
+      "boundary_adapter_calls": 0,
+      "content_prefix_row_one_norm": "22",
+      "extra_owned_fields": 0,
+      "extra_private_fields": 0,
+      "native_children": 320,
+      "native_mass": 1984,
+      "native_profile": {
+        "1": 96,
+        "8": 128,
+        "9": 96
+      },
+      "native_side_map_upper_bound": 448,
+      "odd_divisions": 0,
+      "real_scalar_primitives": 2912,
+      "scalar_stage_prices": {
+        "ordinary_full_progress": 0,
+        "ordinary_negative_lines": 0,
+        "ordinary_self_adds": 768,
+        "selected_progress": 0,
+        "signed_selected_exchanges": 384,
+        "source_progress": 0,
+        "source_row_code": 1760
+      },
+      "unchanged_arbitrary_helpers": 416
+    }
+  },
+  "scope": "Direct physical local words. No caller, recursive host or complete supplier bound.",
+  "status": "PASS_DIRECT_SIMPLE_CLEAN_NATIVE"
+}
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diff --git a/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-optimized/CHECKS.json b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-optimized/CHECKS.json
new file mode 100644
index 0000000000..cbd2e03c5f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-optimized/CHECKS.json
@@ -0,0 +1,68 @@
+{
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+      "boundary_adapter_calls": 0,
+      "content_prefix_row_one_norm": "4",
+      "extra_owned_fields": 0,
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+}
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diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md
new file mode 100644
index 0000000000..a1fc7101cb
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md
@@ -0,0 +1,140 @@
+# Native recipes for the new centre-deleted core
+
+This lane checks the native operators for both PR3133 provider words.
+The words are the byte-equal copies in PR3148. It uses the new frame and
+warp data. It does not use the earlier T74 frame data.
+
+Fresh generation passed for both providers. Each run checked 1130 frames,
+3036 directed child edges, 224 endpoint adapters, 180 signed physical warp
+classes, 72 logical warp operators, and 56 residual wrapper classes. The
+residual classes include 32 proper terminal pairs, of which 24 are cold.
+Each source run rejected 25 wrapper mutations and 13 warp mutations.
+
+The fresh child and residual recipe files have the same hashes as the
+authenticated PR3133 native receipt. Both literal dual runs also passed:
+each checked all 180 signed classes on all 512 columns. In each provider,
+172 literal dual recipes differ from the forward recipes. All literal
+dual recipes have rank zero. Thus the choice of logical warp orientation
+does affect the phase tables, but it does not add native children.
+
+The independent interpreter review is a separate calculation. The scalar
+map, stock, controller, precision, and complete kappa calculation are also
+separate checks. `RESULT.json` gives the generation result; `FREEZE.json`
+pins its inputs, scripts, proofs, and outputs.
+
+## Exact operator test
+
+For a binary subspace U, let T_U be the canonical Clifford frame in the
+pinned source. A child from U to V must implement T_V T_U^{-1}. The
+generator derives its recipe from this product. It checks the full Pauli
+table and the exact Gaussian dyadic image of the zero basis vector. These
+two checks include the global phase.
+
+To see this, let A and B be unitary operators with the same action on all
+Pauli generators. Then B^{-1} A commutes with every X and Z generator. An
+operator that commutes with every Z generator is diagonal in the standard
+basis. If it also commutes with every X generator, all diagonal entries
+are equal. Thus A is a scalar multiple of B. Equality on the zero basis
+vector fixes that scalar as one. The argument applies to each generated
+Clifford product. It also proves equality of all positive tensor powers.
+
+Each child recipe has the form L C_[r] R, with R applied first. The
+serialized L and R are monomial Clifford operators. For a nested frame
+change, the checked r is the difference of the frame dimensions. The
+physical warp product is T_V K_G^{sign} T_U^{-1}. Its checked r is zero.
+The separate Gaussian matrix implementation checks every one of its 512
+columns.
+
+A helper that enters at E and leaves at V has residual T_V T_E^{-1}.
+The recipes include the proper terminal subspaces of the new words. They
+also include the cold pairs with E equal to zero. The exact wrapper test
+checks R^{-1}, then the residual, then L^{-1}; the result is C_[r]. It does
+not replace a proper terminal frame by FULL.
+
+## Literal dual warps
+
+The backward scalar proof uses the inverse transpose of each logical
+warp. For a unitary warp K this is the entrywise conjugate of K. The
+source emitter stores the same signed warp labels for both orientations.
+The orientation must therefore select a physical implementation.
+
+There are two valid routes. The free-operator proof can establish the
+endpoint identity for an arbitrary consistent choice of invertible warp
+generators. The physical implementation can then use the forward K in
+both orientations. Alternatively, the literal dual implementation can
+use conjugate(K) in the backward orientation. This lane supplies exact
+recipes for the second route as well.
+
+The literal dual route has a general rank-zero closure property. Let K
+be a monomial Clifford operator whose nonzero entries are fourth roots of
+unity. Every source K_G has this property. In a standard basis, K is an affine
+permutation with a phase of the form
+
+    i^(c + alpha.x + 2 q(x)),
+
+where q is a binary quadratic form. Conjugation changes this phase by
+2(c + alpha.x) modulo 4. The quadratic term vanishes. After the affine
+permutation, this phase is a signed Z Pauli. Thus
+
+    conjugate(K) K^{-1} = P
+
+for a Pauli P. Suppose the accepted physical warp is
+
+    W = T_V K T_U^{-1}
+
+and W is monomial. Then its literal dual counterpart is
+
+    T_V conjugate(K) T_U^{-1} = (T_V P T_V^{-1}) W.
+
+A Clifford frame maps a Pauli to a Pauli. A Pauli is monomial. Hence the
+literal dual counterpart is monomial and needs no native child. Apply the
+same argument to K^{-1} for a negative signed occurrence. This proof does
+not require U and V to be FULL, or require the Pauli to be diagonal after
+frame conjugation.
+
+`generate_dual_warps.py` also checks this conclusion directly for each
+signed class of each new provider. It uses the physical product
+T_V conjugate(K_G)^{sign} T_U^{-1}. A separate Gaussian matrix calculation
+compares all 512 columns. A wrong global phase must fail.
+
+## Source and credit
+
+The core comes from
+[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), at
+commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. The byte-equal provider
+words are in
+[PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), at
+commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`:
+
+- [Base word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz).
+- [Extra word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz).
+
+The unchanged recipe sources come from
+[PR2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), at
+commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`:
+
+- [Phase compiler](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_phases.py).
+- [Residual wrappers](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_adapters.py).
+- [Gaussian matrix implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_gauss.py).
+- [Serialized warp checker](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_check_recipes.py).
+- [Exact Clifford implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py).
+
+The source files retain their original author and AI-assistance notices.
+The wrapper source credits the PR458 construction. The warp source credits
+Cinna Davis and PR2226. OpenAI Codex assisted this lane's driver, literal
+dual calculation, proof, and local checks. The independent review is a
+separate agent calculation. It is not a maintainer review.
+
+## Reproduction
+
+Use one process and the workspace Python that has NumPy:
+
+    work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_recipes.py
+    OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_dual_warps.py
+    python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/freeze_results.py
+
+The first command checks every source and input pin before generation.
+It runs the wrapper, phase, and serialized warp checks for each provider.
+The second command checks the source and first-stage output pins before
+it generates the literal dual recipes. The scripts write results only
+inside this lane. No PR, push, or publication commit is part of this work.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json
new file mode 100644
index 0000000000..c3df9a69e7
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json
@@ -0,0 +1,10 @@
+{
+  "source_commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb",
+  "source_sha256": {
+    "bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce",
+    "bw_check_recipes.py": "d600b959a0ac462dc28deb8c0d5d8f9e0c76d7f7d7b6f92a296c5ef9e0a1de19",
+    "bw_gauss.py": "0884b14d6d77cde419a3c773ad9b21d0d18de1e6e20e6b6d5add458ed32ba4cb",
+    "bw_phases.py": "9d1a620e26715f4c42fd0347ecc14ef5a4a9031867869b64e8bae4d8526a821e",
+    "vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/DERIVATION.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/DERIVATION.md
new file mode 100644
index 0000000000..e9e79ba207
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/DERIVATION.md
@@ -0,0 +1,101 @@
+# A clean record from an arbitrary target baseline
+
+This note gives an independent algebraic derivation. `REVIEW.md`
+states the accepted native packet and its exact scope.
+
+Let \(P,R\) partition the data ports. Suppose an admitted native prefix
+reaches the exact cut
+\[
+ X=x,\qquad Y_P=y_P,\qquad Y_R=y_R+E_Rx
+\]
+in content coordinates. The physical fields \(X\) and \(Y_P\) must have
+the same FULL frame. The ordinary \(Y_R\) fields can retain their
+declared hole frames.
+
+Let \(L=[I,B]\) in \(P,R\) order, and let
+\[
+ C=\begin{pmatrix}I&B\\0&I\end{pmatrix}.
+\]
+Apply \(C\) to the FULL X bank. Each selected pair now has values
+\((a,b)=((Lx)_p,y_p)\). Apply the following three scalar ADDs:
+\[
+ b\leftarrow b+a,\qquad
+ a\leftarrow a-b,\qquad
+ b\leftarrow b+a.
+\]
+Their successive pair values are
+\[
+ (a,b+a),\qquad (-b,b+a),\qquad (-b,a),
+\]
+where the last two displays use the original \(a,b\).
+Thus the final content is
+\[
+ X_P=-y_P,\quad X_R=x_R,\quad
+ Y_P=Lx,\quad Y_R=y_R+E_Rx.
+\]
+Every selected target baseline is arbitrary. No clean input field is
+used. The minus sign is part of the three-ADD rotation and needs no
+extra scale.
+
+Under the pinned old scalar tariff, a unit complex ADD costs eight
+real scalar units. The rotation costs 24 per selected port. For the
+sixteen-port code with cost 1760 and a retained core cost of 6456,
+the scalar total is
+\[
+ 6456+1760+16\cdot24=8600.
+\]
+The independent native replay confirms the cut, exact event order,
+frames, retained phase records, and invoice.
+
+Define the next source bank by the same-port role assignment
+\[
+ Z=(Y_P,X_R),\qquad V=(X_P,Y_R).
+\]
+Then \(Z=Cx\) has only source input. The complementary bank is
+\[
+ V_P=-y_P,\qquad V_R=y_R+E_Rx.
+\]
+This is an invertible map for arbitrary input. Its inverse is
+\[
+ x=C^{-1}Z,\qquad
+ y_P=-V_P,\qquad
+ y_R=V_R-E_R C^{-1}Z.
+\]
+The inverse formula keeps operator order. It does not require any
+commutation of \(C\), \(E\), or spatial frame operators.
+
+The role assignment itself does not establish a legal next-stage
+entry. That claim needs the actual owner paths and endpoint phases.
+With the expected native endpoint, the physical Z fields are all
+FULL, while V is FULL on P and a hole on R. The next entry must
+therefore admit both resulting types. It must retain the arbitrary
+V baseline and the encoded source \(Cx\).
+
+For line-entry reuse, replace the arbitrary selected input \(y_P\)
+by a record \(z\) with physical frame \(Q_P\). The accepted H8 prefix
+takes this input to FULL \(z\). The same proof gives
+\(X_P=-z,\ Y_P=Lx\). Its scalar bill is unchanged; its sixteen
+progress children have rank eight instead of rank nine.
+
+## Closure of the source-code family
+
+Let the entries of \(B\) belong to any associative operator ring.
+Set \(N_B=e_PB\), where \(B\) has zero columns on P and takes its
+input only from R. Then \(N_{B_2}N_{B_1}=0\), even when the entries
+of \(B_1\) and \(B_2\) do not commute. Consequently,
+\[
+ (I+N_{B_2})(I+N_{B_1})=I+N_{B_1+B_2},\qquad
+ (I+N_B)^{-1}=I-N_B.
+\]
+For an invertible block diagonal route
+\(T=\operatorname{diag}(T_P,T_R)\),
+\[
+ T(I+N_B)T^{-1}
+ =I+e_P(T_PBT_R^{-1}).
+\]
+Thus a route that preserves the P/R partition preserves this family.
+Repeated clean exchanges can accumulate such source codes without
+products of two reader corrections. This is a structural algebraic
+statement. It does not price the routed reader, admit the role
+dispatcher, or prove that an outer caller performs the required
+supplier computation.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..ad60187505
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json
@@ -0,0 +1,15 @@
+{
+  "files": {
+    "DERIVATION.md": "d8e77e0c3537a007a3674d03611dd8d6458589b8256cc2bc9bdb5c86d52124a9",
+    "REPRODUCTION.json": "65193ab9f017a3d9b49c46cf64bc93fc7dbc1b38789f692f8bbea11148186bce",
+    "REVIEW.md": "2a290ee65bb86a0a9c9acfb36b44735d98134350360b60a831c968a8c9c3ccd0",
+    "check.py": "e6564514a878cfa2411a41990a3d9c012f97a464c1b8361fb358fa741968f35c",
+    "normal/INPUTS.json": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763",
+    "normal/REVIEW.json": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5",
+    "optimized/INPUTS.json": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763",
+    "optimized/REVIEW.json": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "Four complete local clean-record words, exact frame and phase inheritance, arbitrary baseline and helper restoration, content inverse, and local invoice. The same-port role partition does not admit or price a routed dispatcher.",
+  "status": "PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..1d8353c9ee
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "INPUTS.json": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763",
+    "REVIEW.json": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "source_files_rechecked": 32,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..aeaa9fa11b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/REVIEW.md
@@ -0,0 +1,166 @@
+# Independent review of the clean centre exchange
+
+All four frozen local words pass. Each word forms a clean selected
+centre record from arbitrary input and keeps the previous selected
+baseline on the complementary data field. No clean field is required.
+There is no material defect in the local word.
+
+## Pinned packet
+
+The producer directory is
+`new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/`.
+Its freeze has SHA256
+`96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc`.
+The decompressed payload has SHA256
+`b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083`.
+The proof has SHA256
+`eb8e579b11d3d4ce8e77a2d6003b1a95135d84f79ce60d48ee2370194797569c`.
+
+The packet has separate I-entry and Q-entry words for both providers.
+The checker does not import the producer. It uses the earlier
+independent exact matrix, column, row, and scalar-tariff tools.
+`normal/INPUTS.json` gives every consumed source pin.
+
+## Exact operation
+
+Use the actual sixteen pivots P and let R be the other 96 ports.
+Let \(L=V_P^{-1}V=[I,B]\) and
+\[
+ C=\begin{pmatrix}I&B\\0&I\end{pmatrix}.
+\]
+The independent checker reconstructs this reader from the pinned
+response factors and signed pivot Gram matrix. It checks both
+inverse orders of C and its literal 1760-unit scalar code.
+
+The retained native core advances all X paths and the 96 ordinary
+Y paths. It removes exactly 250 selected-target events, including
+128 H1 calls. There is no retained read of a removed selected target.
+The selected target then advances to FULL: by H9 in I-entry formation,
+or by the accepted H8 line-to-FULL recipe in Q-entry reuse.
+
+At this common-FULL cut, apply C to X. Apply three unit ADDs on
+each selected pair \((a,b)=(X_p,Y_p)\):
+\[
+ b\leftarrow b+a,\qquad a\leftarrow a-b,\qquad b\leftarrow b+a.
+\]
+This is the signed exchange \((a,b)\mapsto(-b,a)\). It costs 24
+real scalar units per pair. A separate sign scale is not required.
+`DERIVATION.md` gives the complete algebra and inverse.
+
+The exact physical input is
+\[
+ X=Qx,\quad Y_R=y_R,\quad
+ Y_P=
+ \begin{cases}
+ y_P&\text{in I-entry formation},\\
+ Q_Pz&\text{in Q-entry reuse}.
+ \end{cases}
+\]
+Write \(b=y_P\) in the first case and \(b=z\) in the second.
+The exact physical output is
+\[
+ X_P=-F_9b,\qquad X_R=F_9x_R,\qquad
+ Y_P=F_9Lx,\qquad
+ Y_R=F_9q_R(y+Ex)_R.
+\]
+Only \(y_R\) is used in the last expression. The selected input b is
+arbitrary and independent. No commutation of Q with C or E is used.
+
+The checker verifies every one of the 640 input columns by a reverse
+pass. A separate forward row pass gives the same complete map.
+All 416 outside roles remain unchanged for arbitrary values.
+The independent formula for the inverse passes both 224-field
+matrix product orders. This inverse is an algebraic identity; this
+packet does not emit or price an inverse native service.
+
+## Physical frames and phases
+
+Every event is reconstructed from the exact old native core, the
+accepted selected progress children, the scalar source code, and
+the three-ADD exchanges. Every scalar source and target has the
+declared common frame. Every native occurrence has the accepted
+ordered input/output frame pair, rank, and phase record.
+
+The I-entry recipes and endpoint maps are byte equal to the accepted
+direct-FULL formation packet. Its independent freeze is
+`488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532`.
+The Q-entry recipes and endpoint maps are byte equal to the accepted
+line-entry packet. Its independent freeze is
+`cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c`.
+
+There are zero new phase operators. This review inherits those exact
+phase checks and verifies every new occurrence binding. The sixteen
+H9 calls have identity side maps. The sixteen H8 calls retain both
+accepted side maps; no identity-wrapper assumption is made for H8.
+
+The checker rejects a missing source code, missing exchanges, and a
+wrong exchange sign. Each mutation changes the map on arbitrary input.
+
+## Invoice
+
+Both providers have the following scalar bill in either entry variant:
+
+| Part | Real scalar units |
+|---|---:|
+| Retained core | 6456 |
+| C on FULL X | 1760 |
+| Sixteen signed exchanges | 384 |
+| Total | 8600 |
+
+The native and view bills are:
+
+| Entry | Child profile | Children | Native mass | Input views | Output views | Native side-map upper bound |
+|---|---|---:|---:|---:|---:|---:|
+| I | 1392 H1 + 64 H2 + 48 H3 + 16 H9 | 1520 | 1808 | 112 | 96 | 3008 |
+| Q | 1392 H1 + 64 H2 + 48 H3 + 16 H8 | 1520 | 1792 | 128 | 96 | 3040 |
+
+There is no added field, private field, or odd division.
+The maximum scalar-content row one-norm is exactly 22. The scalar
+word adds at most one binary denominator level at operation
+boundaries. These bounds do not cover primitive internals, recursive
+children, or roundoff propagation.
+
+## Role and composition scope
+
+The same-port role partition
+\[
+ Z=(Y_P,X_R),\qquad V=(X_P,Y_R)
+\]
+uses all 224 data fields exactly once. The checker verifies this
+partition and the clean source \(Z=F_9Cx\). It also verifies the
+arbitrary complementary baseline \(V_P=-F_9b\).
+
+This role partition is not by itself an implementation of a routed
+dispatcher. The actual owner paths, endpoint phases, field selectors,
+and their costs require a separate binding. A physical bank
+permutation must be priced if the caller uses one. The local result
+does not assume a free global bank conversion.
+
+`DERIVATION.md` also proves the source-code closure over a general
+operator ring: products of P-from-R corrections are zero, so these
+unit shears compose by addition. Block diagonal routes preserve the
+family. The proof permits noncommuting spatial operators. It does
+not supply the routed access cost or a complete coupled controller.
+
+Child hosting, the caller's encoded source, a final decoder, recursive
+precision, and the complete supplier cost remain open dependencies.
+
+## Reproduction and credit
+
+Run from the workspace root:
+
+```sh
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized
+```
+
+Both runs print `PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE`.
+`REPRODUCTION.json` records the byte comparison and final source
+hash check.
+
+The root and controller lanes proposed the clean coupled interface.
+The new-core-transfer lane emitted both native variants. This lane
+gave the independent complete replay, the three-ADD cost reduction,
+and the line-entry reuse check. The earlier formation and line-entry
+reviews provide the unchanged phase evidence. This work used AI
+assistance. No PR, push, commit, or publication was made.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py
new file mode 100644
index 0000000000..d14f21c3c9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py
@@ -0,0 +1,211 @@
+#!/usr/bin/env python3
+"""Check a clean centre exchange on all arbitrary input fields."""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+ACCEPTED = HERE.parent/'row-capture-native-review-20261020'
+HELPER = ACCEPTED/'check.py'
+PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84'
+if sha256(HELPER.read_bytes()).hexdigest() != PIN:
+    raise ValueError('Independent helper pin')
+spec = importlib.util.spec_from_file_location('independent_capture_review', HELPER)
+q = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(q)
+q.read(HELPER, PIN)
+need, P = q.need, q.P
+
+
+def endpoint(response, code):
+    result = q.unit(640)
+    for p in range(112):
+        if p in P:
+            result[p] = {112+p: F(-1)}
+            result[112+p] = dict(code[p])
+        else:
+            q.add(result[112+p], response[p])
+    return result
+
+
+def inverse_endpoint(response, code_inverse):
+    z = [{112+p if p in P else p: F(1)} for p in range(112)]
+    original_x = q.mul(code_inverse, z)
+    result = original_x+[{} for _ in range(112)]
+    for p in range(112):
+        if p in P:
+            result[112+p] = {p: F(-1)}
+        else:
+            result[112+p] = {112+p: F(1)}
+            for j, value in response[p].items():
+                q.add(result[112+p], original_x[j], -value)
+    return result
+
+
+def check_word(word, old, reference, code, response, c, entry):
+    selected = {112+p for p in P}
+    indices, removed = q.select_raw(old, selected)
+    need(word['retained_original_event_indices'] == indices, 'Exact retained index ledger')
+    kept = [old['events'][i] for i in indices]
+    need(len(removed) == 250 and
+         Counter(old['events'][i][4] for i in removed if old['events'][i][0] == 'native') == {1: 128},
+         'Exact selected-path deletion')
+    progress_name = 'selected_full_progress' if entry == 'I' else 'selected_line_progress'
+    progress = reference['events'][slice(*reference['stage_ranges'][progress_name])]
+    expected_rank = 9 if entry == 'I' else 8
+    need(len(progress) == 16, 'Every selected progress child')
+    for p, event in zip(P, progress):
+        before = 0 if entry == 'I' else reference['start'][112+p]
+        key = 'capture-full' if entry == 'I' else 'capture-line:'+str(p)
+        need(event == ['native', 112+p, before, 1, expected_rank, key], 'Accepted progress binding')
+    encode = [['scalar', list(gate), 1] for gate in code['scalar_word']]
+    rotate = []
+    for p in P:
+        rotate += [
+            ['scalar', ['add', 112+p, p, '1'], 1],
+            ['scalar', ['add', p, 112+p, '-1'], 1],
+            ['scalar', ['add', 112+p, p, '1'], 1],
+        ]
+    need(word['events'] == kept+progress+encode+rotate, 'Complete literal chronology')
+    stages = [('retained_core', kept), ('selected_progress', progress),
+              ('source_row_code', encode), ('signed_selected_exchanges', rotate)]
+    ranges, cursor = {}, 0
+    for name, events in stages:
+        ranges[name] = [cursor, cursor+len(events)]
+        cursor += len(events)
+    need(word['stage_ranges'] == ranges, 'Exact stage cut ledger')
+    for key in ('frames', 'start', 'final', 'input_views', 'output_views', 'native_recipes'):
+        need(word[key] == reference[key], 'Accepted physical records: '+key)
+    if entry == 'I':
+        need(word['new_full_recipe_circuit'] == reference['new_full_recipe_circuit'],
+             'Exact positive FULL circuit')
+    current = list(word['start'])
+    count, used = Counter(), set()
+    for i, event in enumerate(word['events']):
+        if i == ranges['source_row_code'][0]:
+            need(all(current[p] == 1 for p in range(112)) and
+                 all(current[p] == 1 for p in selected), 'Complete common-FULL exchange cut')
+        if event[0] == 'native':
+            _, field, before, after, rank, key = event
+            need(0 <= field < 224 and current[field] == before, 'Actual native field and input frame')
+            need(word['native_recipes'][key]['rank'] == rank, 'Actual native rank')
+            if key == 'capture-full' or key.startswith('capture-line:'):
+                need(event in progress, 'Exact accepted selected progress occurrence')
+            else:
+                need(key == str(before)+':'+str(after), 'Accepted ordered native pair')
+            current[field] = after
+            count[rank] += 1
+            used.add(key)
+        else:
+            need(event[0] == 'scalar', 'Complete event grammar')
+            _, gate, frame = event
+            op, target, origin, _ = gate
+            need(0 <= target < 224 and current[target] == frame, 'Scalar target frame')
+            if op == 'add':
+                need(0 <= origin < 224 and origin != target and current[origin] == frame,
+                     'Scalar source frame')
+            else:
+                need(op == 'scale' and origin is None, 'Exact scalar scale grammar')
+    need(current == word['final'] and used == set(word['native_recipes']), 'Final frame and recipe ledger')
+    need(count == {1: 1392, 2: 64, 3: 48, expected_rank: 16}, 'Complete native profile')
+    scalars = [e[1] for e in word['events'] if e[0] == 'scalar']
+    expected = endpoint(response, c)
+    need(q.reverse(scalars, 640) == q.transpose(expected, 640), 'All640 reverse input columns')
+    rows, growth = q.prefix(scalars, 640)
+    need(rows == expected and rows[224:] == q.unit(640)[224:], 'Separate forward rows and416 arbitrary roles')
+    source_fields = [112+p if p in P else p for p in range(112)]
+    other_fields = [p if p in P else 112+p for p in range(112)]
+    need(sorted(source_fields+other_fields) == list(range(224)), 'Exact same-port bank partition')
+    need([rows[field] for field in source_fields] == c, 'Clean encoded source on all112 ports')
+    need(all(rows[112+p] == c[p] and rows[p] == {112+p: F(-1)} for p in P),
+         'Every arbitrary baseline is retained with its sign')
+    bills = {name: q.price([e[1] for e in events if e[0] == 'scalar']) for name, events in stages}
+    need(bills == {'retained_core': 6456, 'selected_progress': 0,
+                   'source_row_code': 1760, 'signed_selected_exchanges': 384}, 'Exact stage bills')
+    need(q.price(scalars) == 8600, 'Complete scalar bill')
+    need(growth == {'row_one_norm': '22', 'binary_height': 1}, 'Exact content prefix bound')
+    for omitted in (encode, rotate):
+        bad = kept+progress+(encode if omitted is rotate else [])+(rotate if omitted is encode else [])
+        need(q.reverse([e[1] for e in bad if e[0] == 'scalar'], 640) != q.transpose(expected, 640),
+             'Missing code or exchange control')
+    wrong_rotation = [list(e[1]) for e in rotate]
+    wrong_rotation[1][3] = '1'
+    need(q.reverse([e[1] for e in kept+progress+encode if e[0] == 'scalar']+wrong_rotation, 640)
+         != q.transpose(expected, 640), 'Wrong signed rotation control')
+    return {
+        'input_columns': 640, 'unchanged_arbitrary_roles': 416,
+        'native_profile': dict(sorted(count.items())), 'native_children': sum(count.values()),
+        'native_mass': sum(r*n for r, n in count.items()), 'real_scalar_primitives': 8600,
+        'stage_prices': bills, 'input_views': 112 if entry == 'I' else 128, 'output_views': 96,
+        'native_side_maps_upper_bound': 3008 if entry == 'I' else 3040,
+        'new_fields': 0, 'private_fields': 0,
+        'odd_scans': 0, 'growth': growth, 'source_fields': source_fields,
+        'complementary_fields': other_fields,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    source = q.RAW/'clean-late-exchange-20261020'
+    line_review = HERE.parent/'line-entry-reuse-review-20261020'
+    q.frozen(ACCEPTED, 'FREEZE.json', '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532')
+    q.frozen(line_review, 'FREEZE.json', 'cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c')
+    q.frozen(source, 'FREEZE.json', '96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc')
+    q.frozen(q.ALG, 'FREEZE.json', '0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf')
+    raw = json.loads(q.read(q.RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz',
+                            'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True))
+    code = json.loads(q.read(q.ALG/'run-normal/ROW-CAPTURE.json',
+                             '4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7'))
+    refs = {
+        'I': json.loads(q.read(q.NATIVE/'direct-normal/DIRECT-FULL-CAPTURE.json.gz',
+                               'fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c', True)),
+        'Q': json.loads(q.read(q.NATIVE/'reuse-normal/LINE-ENTRY-REUSE.json.gz',
+                               'efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110', True)),
+    }
+    payload = json.loads(q.read(source/'run-normal/CLEAN-LATE-EXCHANGE.json.gz',
+                                'b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083', True))
+    response, c, _, algebra = q.algebra(raw, code)
+    ci = q.rows(code['code_inverse'])
+    expected, inverse = endpoint(response, c), inverse_endpoint(response, ci)
+    need(q.mul(expected[:224], inverse) == q.unit(224) and
+         q.mul(inverse, expected[:224]) == q.unit(224), 'Both complete content inverse orders')
+    need(q.rows(payload['content_map']) == expected[:224] and
+         q.rows(payload['inverse_content_map']) == inverse, 'Exact payload content maps')
+    need(payload['selected_ports'] == P and payload['ports'] == raw['model']['ports'],
+         'Exact ordered ports')
+    need(q.rows(payload['code']) == c and q.rows(payload['response']) == response, 'Exact matrix source binding')
+    need(set(payload['providers']) == {'base', 'extra'}, 'Both actual providers')
+    reports = {}
+    for provider, entries in payload['providers'].items():
+        need(set(entries) == {'I', 'Q'}, 'Both entry contracts')
+        reports[provider] = {}
+        for entry, word in entries.items():
+            reports[provider][entry] = check_word(
+                word, raw['providers'][provider]['forward'],
+                refs[entry]['providers'][provider], code, response, c, entry)
+    report = {
+        'status': 'PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE',
+        'algebra': algebra, 'content_inverse_both_orders': True, 'literal_words': reports,
+        'new_phase_operators': 0,
+        'phase_sources': {
+            'I': '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532',
+            'Q': 'cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c',
+        },
+        'negative_controls': ['missing source code', 'missing signed exchanges', 'wrong rotation sign'],
+        'scope': 'Four complete local clean-record words, exact physical contracts, arbitrary baseline preservation, and local invoice. The same-port role partition does not by itself admit or price a routed caller.',
+    }
+    args.out.mkdir(parents=True, exist_ok=True)
+    for name, value in [('REVIEW.json', report), ('INPUTS.json', q.INPUTS)]:
+        (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print(report['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..0ce6538a59
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/INPUTS.json
@@ -0,0 +1,102 @@
+{
+  "controller-followthrough-20261017/row-capture-20261020/FREEZE.json": {
+    "sha256": "0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/ROW-CAPTURE.md": {
+    "sha256": "0caea104839f0e9726c892ab2b21c2c3501deb818ab0c844e4fa5234cb870eee"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/check_row_capture.py": {
+    "sha256": "ccf661107a790c3d858a3f2bd4d8adc5269f588bfd989bd2e2029e26cbb14081"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/run-normal/CHECKS.json": {
+    "sha256": "7054fe6350d900561111b81f2ce46057edb62aef1f5581c4adac66f1c1742081"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json": {
+    "sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md": {
+    "sha256": "eb8e579b11d3d4ce8e77a2d6003b1a95135d84f79ce60d48ee2370194797569c"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json": {
+    "sha256": "96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_clean_exchange.py": {
+    "sha256": "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json": {
+    "sha256": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz": {
+    "decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+    "sha256": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-optimized/CHECKS.json": {
+    "sha256": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-optimized/CLEAN-LATE-EXCHANGE.json.gz": {
+    "sha256": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": {
+    "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz": {
+    "decompressed_sha256": "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c",
+    "sha256": "b1bade79c227366b9c283acfbbb4cbdc5dbf3f6a1764bac0e69abd2493e38487"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz": {
+    "decompressed_sha256": "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110",
+    "sha256": "b3cc486c4ecf0574a8a9a6a94ba62a068340ed30525a3dcf889dd19cf7d84047"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json": {
+    "sha256": "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json": {
+    "sha256": "5fe7900ca1791738790a663c882ea411d8e3f41cdb9f9b7f5d23f06deffbf939"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md": {
+    "sha256": "f6ddd5a2581319ac5b07d402384c4847bce88f10505cca926c9287e838e1760f"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py": {
+    "sha256": "c2a8f93e2c1cf23f8fc279e6dc87d6bd923e60c438531fe1770b0992d1dfdb7d"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json": {
+    "sha256": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/REVIEW.json": {
+    "sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/INPUTS.json": {
+    "sha256": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/REVIEW.json": {
+    "sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md": {
+    "sha256": "74bfa14362b8a704d409cb3995fe645173e99205653528bcf6b47f62de7455a1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json": {
+    "sha256": "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json": {
+    "sha256": "9525e5e1871d60a01c8acd222944abe6edab71f9d5448410265859dcece6901f"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md": {
+    "sha256": "39cb0df65e81f92854d0238d9023eaa092205bdce8e3b81724c2e4d19a3ef4f1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/check.py": {
+    "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json": {
+    "sha256": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/normal/REVIEW.json": {
+    "sha256": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/optimized/INPUTS.json": {
+    "sha256": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/optimized/REVIEW.json": {
+    "sha256": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/REVIEW.json
new file mode 100644
index 0000000000..c77114708c
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/REVIEW.json
@@ -0,0 +1,1064 @@
+{
+  "algebra": {
+    "code_prefix": {
+      "binary_height": 1,
+      "row_one_norm": "22"
+    },
+    "code_price": 1760,
+    "displacement_rank": 16,
+    "extra_fields": 0,
+    "odd_scans": 0,
+    "query_prefix_on_independent_inputs": {
+      "binary_height": 1,
+      "row_one_norm": "112"
+    },
+    "query_price": 3424
+  },
+  "content_inverse_both_orders": true,
+  "literal_words": {
+    "base": {
+      "I": {
+        "complementary_fields": [
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+        ],
+        "growth": {
+          "binary_height": 1,
+          "row_one_norm": "22"
+        },
+        "input_columns": 640,
+        "input_views": 112,
+        "native_children": 1520,
+        "native_mass": 1808,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "9": 16
+        },
+        "native_side_maps_upper_bound": 3008,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "source_fields": [
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+        "stage_prices": {
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+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      },
+      "Q": {
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+        "growth": {
+          "binary_height": 1,
+          "row_one_norm": "22"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "source_fields": [
+          112,
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+        "stage_prices": {
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+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    },
+    "extra": {
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diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/INPUTS.json
new file mode 100644
index 0000000000..0ce6538a59
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/INPUTS.json
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diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/REVIEW.json
new file mode 100644
index 0000000000..c77114708c
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/REVIEW.json
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+        "stage_prices": {
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+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    }
+  },
+  "negative_controls": [
+    "missing source code",
+    "missing signed exchanges",
+    "wrong rotation sign"
+  ],
+  "new_phase_operators": 0,
+  "phase_sources": {
+    "I": "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532",
+    "Q": "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"
+  },
+  "scope": "Four complete local clean-record words, exact physical contracts, arbitrary baseline preservation, and local invoice. The same-port role partition does not by itself admit or price a routed caller.",
+  "status": "PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..fc9256916b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "REPRODUCTION.json": "b8e3c2cf2d3022dde7243006c12fe02f2429906e6f4395d64111eb659f4b68b5",
+    "REVIEW.md": "f3df32e605bb5a0d9ac3b0eeb0c2262274be5d15c69e7497d64f4e8d5074e613",
+    "check.py": "3d805eb48a5e9d5a2048531e1ea6f5aad04624026e2c9bc57d7dcc166cc734ab",
+    "normal/INPUTS.json": "415de3009c15fda19dae77b3c2fafed5c3396c4e5aee3cf685cecb12a26cd34e",
+    "normal/REVIEW.json": "c9abd280df35e3fa2270c8853a5e5f32d380e3d87a5ca0337e99e7bc400fcda2",
+    "optimized/INPUTS.json": "415de3009c15fda19dae77b3c2fafed5c3396c4e5aee3cf685cecb12a26cd34e",
+    "optimized/REVIEW.json": "c9abd280df35e3fa2270c8853a5e5f32d380e3d87a5ca0337e99e7bc400fcda2"
+  },
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "Four complete local physical inverse-adjoint words, exact selected-field phase symmetry, both content inverse orders, and complete unchanged local invoice. Routed two-call computation and full supplier remain separate.",
+  "status": "PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..df42e8e088
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "INPUTS.json": "415de3009c15fda19dae77b3c2fafed5c3396c4e5aee3cf685cecb12a26cd34e",
+    "REVIEW.json": "c9abd280df35e3fa2270c8853a5e5f32d380e3d87a5ca0337e99e7bc400fcda2"
+  },
+  "source_files_rechecked": 18,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..6e586f95d5
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/REVIEW.md
@@ -0,0 +1,198 @@
+# Independent review of the clean inverse-adjoint pair
+
+All four complete local words pass: two providers, with the
+inverse-adjoint and its selected-field conjugate. Both operations
+cost 8600 real scalar units and have native mass 1792. No extra
+physical swap is required. There is no material local defect.
+
+## Sources and independent method
+
+The producer directory is
+`new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/`.
+The dual freeze has SHA256
+`fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43`.
+The decompressed dual payload has SHA256
+`6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c`.
+The producer proof has SHA256
+`1515a8b82ecfcb32d7dc19a4a8bc0fcf0af870ac444bb1628443dfb378360cb9`.
+
+The accepted clean source review has freeze SHA256
+`6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d`.
+The new checker imports that independent review code and no producer
+module. It reconstructs the response blocks, derives the complete
+inverse from the clean endpoint, and checks the dual word with a
+reverse input-column interpreter and a separate forward row pass.
+`normal/INPUTS.json` gives every consumed hash.
+
+## Independent block calculation
+
+Use selected ports P and ordinary ports R. Write the normalized
+reader as \(L=[I,B]\), and put \(D=E_{RP}\). The checker verifies
+the following identities on the actual source:
+\[
+ E=E^T,\qquad E_{PP}=0,\qquad E_{PR}=-B,\qquad
+ D=-B^T,\qquad E_R=[D,I+DB].
+\]
+The relation \(D=-B^T\) is thus a checked source identity, not a
+premise for an arbitrary reader.
+
+For inputs \((a,u,z,v)=(X_P,X_R,Y_P,Y_R)\), the clean content map is
+\[
+ M(a,u,z,v)=(-z,\ u,\ a+Bu,\ v+u+D(a+Bu)).
+\]
+Its inverse at \((A,U,Z,V)\) is
+\[
+ (Z-BU,\ U,\ -A,\ V-U-DZ).
+\]
+This gives
+\[
+ M^{-T}(a,u,z,v)=(-z,\ u+Da-v,\ a+Bv,\ v).
+\]
+Let S exchange only the selected X and Y coordinates. Then
+\[
+ S M^{-T} S(a,u,z,v)
+ =(z+Bv,\ u+Dz-v,\ -a,\ v).
+\]
+The checker derives the first dual from the full inverse matrix and
+the second by row and column permutation. Separate block formulas
+give the same matrices. Both inverse product orders pass for each.
+The formulas use no inverse of E and no odd division.
+
+For general operator-valued B and D, the selected conjugate is
+\[
+ (z-D^*v,\ u-B^*z-v,\ -a,\ v).
+\]
+The shorter formula with \(+B\) and \(+D\) requires \(D=-B^*\).
+This review proves that relation for the local real source. A routed
+operator substitution needs its own adjoint and access proof.
+
+## Why the physical inverse-adjoint uses the same native phases
+
+The physical entry and exit operators are
+\[
+ A_{\rm in}=\operatorname{diag}(Q_X,Q_P,I_R),\qquad
+ A_{\rm out}=\operatorname{diag}(F_{9,X},F_{9,P},F_9q_R).
+\]
+They are unitary. The accepted physical clean map is
+\(W=A_{\rm out}M A_{\rm in}^{-1}\). Therefore
+\[
+ W^{-*}=A_{\rm out}M^{-T}A_{\rm in}^{-1}.
+\]
+No frame operator is commuted through M in this identity.
+
+For chronological gates \(G_1,\ldots,G_n\), the complete operator is
+\(G_n\cdots G_1\), and its inverse-adjoint is
+\[
+ G_n^{-*}\cdots G_1^{-*}.
+\]
+Thus the chronological gate order stays fixed. Each exact native
+operator and boundary monomial is unitary, so \(U^{-*}=U\), including
+its global phase. This follows for the accepted kernels from their
+unitary positive line factors and unitary monomial side maps. The
+exact previously reviewed phase records are therefore retained.
+
+For a real scalar ADD, the inverse-adjoint transposes source and
+target and negates the coefficient. For a real SCALE, it inverts
+the coefficient. The checker compares every emitted event with this
+rule, at its original chronological position. Each new scalar
+source and target is still in the same declared frame.
+
+This is a statement about the exact mathematical child interface.
+It does not assert that a rounded numerical implementation is
+exactly unitary. Recursive precision and error propagation remain
+separate.
+
+## Exact selected-field conjugation
+
+On each selected port, both entry fields have the same intrinsic Q
+operator. Both exit fields have the same FULL operator. The checker
+verifies the equal input frame, port, rank, and complete left/right
+monomial records at each of the 32 selected physical input fields.
+It also verifies the FULL/FULL output symmetry. Hence S commutes
+with both \(A_{\rm in}\) and \(A_{\rm out}\).
+
+The circuit identity
+\[
+ S W^{-*}S
+ =(S G_n^{-*}S)\cdots(S G_1^{-*}S)
+\]
+allows every internal pair \(SS\) to cancel. Each remaining
+conjugated gate is implemented on the permuted physical field
+indices. The checker verifies that explicit permutation for every
+native event, scalar target, scalar source, and input adapter.
+The actual input adapter operator at each physical field is
+unchanged. The 96 ordinary output adapters keep their fields.
+
+The instruction list has the same length as the clean source.
+There are no runtime boundary swaps and no unpaid gate. This is
+an explicitly emitted circuit, not an assumption that an arbitrary
+caller can relabel live banks for free.
+
+The Q-entry physical contract for the selected conjugate is
+\[
+ \begin{aligned}
+ X&=Q(a,u),& Y_P&=Q_Pz,&Y_R&=v,\\
+ X'_P&=F_9(z+Bv),&
+ X'_R&=F_9(u+Dz-v),&
+ Y'_P&=-F_9a,\qquad Y'_R=F_9q_Rv.
+ \end{aligned}
+\]
+For the unpermuted dual, the content is
+\((-z,u+Da-v,a+Bv,v)\), with the same physical exit frames.
+
+## Complete verification and invoice
+
+All 640 arbitrary input columns pass in all four words. The
+separate forward replay agrees and preserves all 416 outside roles.
+The complete native frame ledger and every used recipe agree with
+the accepted clean source. There are zero new phase operators;
+this review inherits the exact spatial phase sweep rather than
+claiming another run of it. Reversing the scalar chronology changes
+the map, as the negative control requires.
+
+Every word has:
+
+| Item | Exact count |
+|---|---:|
+| Retained-core scalar units | 6456 |
+| Inverse-transposed source code | 1760 |
+| Inverse-transposed exchanges | 384 |
+| Total scalar units | 8600 |
+| Native profile | 1392 H1 + 64 H2 + 48 H3 + 16 H8 |
+| Native children | 1520 |
+| Native mass | 1792 |
+| Input views | 128 |
+| Output views | 96 |
+| Native side-map upper bound | 3040 |
+| Runtime boundary swaps | 0 |
+| New or private fields | 0 |
+| Odd scans | 0 |
+
+The H8 side maps stay charged. The exact content row one-norm
+maximum is 12, and the maximum additional binary denominator
+height is two. These bounds apply at scalar operation boundaries.
+They do not cover primitive internals or recursive child errors.
+
+The routed two-call computation, field dispatcher, helper host,
+terminal decoder, and full supplier cost are not established here.
+
+## Reproduction and credit
+
+Run from the workspace root:
+
+```sh
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-dual-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-dual-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/clean-dual-review-20261020/optimized
+```
+
+Both print `PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE`.
+The reproduction receipt records the output comparison and final
+source hash check.
+
+The cover-algebra lane supplied the useful selected-bank form.
+The new-core-transfer lane supplied the literal dual circuit. This
+lane independently derived the block formula and the field
+conjugation rule, and checked the complete native word. The earlier
+clean, line-entry, and formation reviews supply the retained phase
+evidence. AI assistance was used. No PR, push, commit, or publication
+was made.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/check.py
new file mode 100644
index 0000000000..0e97ceb645
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/check.py
@@ -0,0 +1,217 @@
+#!/usr/bin/env python3
+"""Check the physical inverse-adjoint and selected-field conjugate."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+ACCEPTED = HERE.parent/'clean-centre-exchange-review-20261020'
+HELPER = ACCEPTED/'check.py'
+PIN = 'e6564514a878cfa2411a41990a3d9c012f97a464c1b8361fb358fa741968f35c'
+if sha256(HELPER.read_bytes()).hexdigest() != PIN:
+    raise ValueError('Independent helper pin')
+spec = importlib.util.spec_from_file_location('independent_clean_review', HELPER)
+clean = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(clean)
+q = clean.q
+q.read(HELPER, PIN)
+need, P = q.need, q.P
+
+
+def matrices(source):
+    c, e = q.rows(source['code']), q.rows(source['response'])
+    need(e == q.transpose(e, 112), 'Actual self-adjoint response')
+    ci = q.unit(112)
+    for p in P:
+        need(c[p].get(p) == 1 and set(c[p]).intersection(P) == {p}, 'Normalized selected pivot')
+        need(not set(e[p]).intersection(P), 'Actual E_PP is zero')
+        for r in range(112):
+            if r not in P:
+                need(e[p].get(r, F(0)) == -c[p].get(r, F(0)), 'Actual E_PR equals negative B')
+                q.add(ci[p], {r: c[p].get(r, F(0))}, F(-1))
+    need(q.mul(c, ci) == q.unit(112) and q.mul(ci, c) == q.unit(112), 'Exact code inverse orders')
+    for r in range(112):
+        if r not in P:
+            expected = {r: F(1)}
+            for p in P:
+                d = e[r].get(p, F(0))
+                need(d == -c[p].get(r, F(0)), 'Actual D equals negative transpose of B')
+                q.add(expected, c[p], d)
+            need(e[r] == expected, 'Actual E_R equals [D,I+DB]')
+    original = clean.endpoint(e, c)[:224]
+    inverse = clean.inverse_endpoint(e, ci)
+    need(q.mul(original, inverse) == q.unit(224) and q.mul(inverse, original) == q.unit(224),
+         'Independent complete clean inverse orders')
+    dual = q.transpose(inverse, 224)
+    dual_inverse = q.transpose(original, 224)
+    direct = q.unit(224)
+    for p in range(112):
+        if p in P:
+            direct[p] = {112+p: F(-1)}
+            direct[112+p] = {p: F(1)}
+            for r, value in c[p].items():
+                if r not in P:
+                    q.add(direct[112+p], {112+r: value})
+        else:
+            q.add(direct[p], {112+p: F(-1)})
+            for r in P:
+                q.add(direct[p], {r: e[p].get(r, F(0))})
+    need(dual == direct, 'Separate unpermuted block formula')
+    return c, e, dual, dual_inverse
+
+
+def conjugate(matrix, permutation):
+    return [{permutation[j]: value for j, value in matrix[permutation[i]].items()}
+            for i in range(len(matrix))]
+
+
+def block_swap(c, e):
+    matrix = q.unit(224)
+    for p in range(112):
+        if p in P:
+            matrix[p] = {112+r: value for r, value in c[p].items()}
+            matrix[112+p] = {p: F(-1)}
+        else:
+            q.add(matrix[p], {112+p: F(-1)})
+            for r in P:
+                q.add(matrix[p], {112+r: e[p].get(r, F(0))})
+    return matrix
+
+
+def check_word(word, source, permutation, expected):
+    need(len(word['events']) == len(source['events']), 'No added boundary operations')
+    need(word['stage_ranges'] == source['stage_ranges'], 'Exact stage chronology')
+    need(word['wire_permutation'] ==
+         {str(p): t for p, t in enumerate(permutation) if p != t}, 'Exact stored field permutation')
+    need(all(permutation[permutation[p]] == p for p in range(640)), 'Involutive field permutation')
+    for key in ('frames', 'native_recipes', 'start', 'final', 'output_views'):
+        need(word[key] == source[key], 'Exact accepted physical record: '+key)
+    need(all(source[key][p] == source[key][permutation[p]] for key in ('start', 'final')
+             for p in range(640)), 'Selected endpoint frame invariance')
+    input_source = {r['field']: r for r in source['input_views']}
+    inputs = {r['field']: r for r in word['input_views']}
+    need(len(inputs) == len(word['input_views']) == 128 and set(inputs) == set(input_source),
+         'Every input adapter has one explicit physical field')
+    physical_keys = ('port', 'frame', 'rank', 'left', 'right')
+    for field, record in inputs.items():
+        need(record['role'] == ('source' if field < 112 else 'selected_target'), 'Actual adapter role')
+        need(all(record[k] == input_source[field][k] for k in physical_keys),
+             'Same operator at each physical input')
+        expected_record = deepcopy(input_source[permutation[field]])
+        expected_record['field'], expected_record['role'] = field, record['role']
+        need(record == expected_record, 'Exact adapter provenance and target rebind')
+    for p in P:
+        need(all(input_source[p][k] == input_source[112+p][k] for k in physical_keys),
+             'Complete selected Q/Q input phase symmetry')
+        need(source['final'][p] == source['final'][112+p] == 1, 'Complete FULL/FULL output symmetry')
+    need(all(r['port'] not in P for r in word['output_views']), 'All ordinary output fields remain fixed')
+    current = list(word['start'])
+    count, used = Counter(), set()
+    for event, old in zip(word['events'], source['events']):
+        if old[0] == 'native':
+            expected_event = deepcopy(old)
+            expected_event[1] = permutation[old[1]]
+            need(event == expected_event, 'Every unchanged unitary native occurrence is explicitly rebound')
+            _, field, before, after, rank, key = event
+            need(0 <= field < 224 and current[field] == before, 'Exact native input frame')
+            need(word['native_recipes'][key]['rank'] == rank, 'Exact accepted child rank')
+            current[field] = after
+            count[rank] += 1
+            used.add(key)
+        else:
+            need(old[0] == event[0] == 'scalar', 'Complete scalar grammar')
+            op, target, origin, value = old[1]
+            value = F(value)
+            if op == 'add':
+                expected_gate = ['add', permutation[origin], permutation[target], str(-value)]
+            else:
+                need(op == 'scale' and origin is None and value != 0, 'Invertible real scale')
+                expected_gate = ['scale', permutation[target], None, str(1/value)]
+            need(event == ['scalar', expected_gate, old[2]], 'Chronological inverse-adjoint scalar rule')
+            op, target, origin, _ = event[1]
+            need(0 <= target < 224 and current[target] == event[2], 'Actual scalar target frame')
+            if op == 'add':
+                need(0 <= origin < 224 and target != origin and current[origin] == event[2],
+                     'Actual scalar source frame')
+    need(current == word['final'] and used == set(word['native_recipes']), 'Complete final frame and recipe ledger')
+    need(count == {1: 1392, 2: 64, 3: 48, 8: 16}, 'Complete native profile')
+    scalars = [e[1] for e in word['events'] if e[0] == 'scalar']
+    target = expected+q.unit(640)[224:]
+    need(q.reverse(scalars, 640) == q.transpose(target, 640), 'All640 independent reverse columns')
+    rows, growth = q.prefix(scalars, 640)
+    need(rows == target and rows[224:] == q.unit(640)[224:], 'Separate forward rows and416 arbitrary roles')
+    prices = {name: q.price([e[1] for e in word['events'][start:end] if e[0] == 'scalar'])
+              for name, (start, end) in word['stage_ranges'].items()}
+    need(prices == {'retained_core': 6456, 'selected_progress': 0,
+                    'source_row_code': 1760, 'signed_selected_exchanges': 384}, 'Complete stage prices')
+    need(q.price(scalars) == 8600, 'Exact full scalar price')
+    need(growth == {'row_one_norm': '12', 'binary_height': 2}, 'Exact dual content prefix bound')
+    need(q.reverse(list(reversed(scalars)), 640) != q.transpose(target, 640),
+         'Wrong reversed scalar chronology control')
+    return {
+        'input_columns': 640, 'unchanged_arbitrary_roles': 416,
+        'native_profile': dict(sorted(count.items())), 'native_children': sum(count.values()),
+        'native_mass': sum(r*n for r, n in count.items()), 'real_scalar_primitives': 8600,
+        'scalar_stage_prices': prices, 'input_views': 128, 'output_views': 96,
+        'native_side_maps_upper_bound': 3040, 'runtime_boundary_swaps': 0,
+        'new_fields': 0, 'private_fields': 0, 'odd_scans': 0, 'growth': growth,
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    source_dir = q.RAW/'clean-late-exchange-20261020'
+    q.frozen(ACCEPTED, 'FREEZE.json', '6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d')
+    q.frozen(source_dir, 'DUAL-FREEZE.json', 'fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43')
+    source = json.loads(q.read(source_dir/'run-normal/CLEAN-LATE-EXCHANGE.json.gz',
+                               'b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083', True))
+    payload = json.loads(q.read(source_dir/'dual-normal/CLEAN-DUAL.json.gz',
+                                '6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c', True))
+    need(payload['selected_ports'] == source['selected_ports'] == P and
+         payload['ports'] == source['ports'] and payload['code'] == source['code'] and
+         payload['response'] == source['response'], 'Exact source matrix and port binding')
+    c, e, dual, dual_inverse = matrices(source)
+    identity = list(range(640))
+    swap = [112+p if p in P else p-112 if p-112 in P else p for p in range(640)]
+    maps = {'inverse_adjoint': dual, 'selected_swap_conjugate': conjugate(dual, swap[:224])}
+    inverses = {'inverse_adjoint': dual_inverse,
+                'selected_swap_conjugate': conjugate(dual_inverse, swap[:224])}
+    need(maps['selected_swap_conjugate'] == block_swap(c, e), 'Separate selected-swap block formula')
+    for name, matrix in maps.items():
+        need(q.mul(matrix, inverses[name]) == q.unit(224) and
+             q.mul(inverses[name], matrix) == q.unit(224), 'Both dual content inverse orders: '+name)
+        need(q.rows(payload['content_maps'][name]) == matrix and
+             q.rows(payload['inverse_content_maps'][name]) == inverses[name], 'Exact serialized matrix: '+name)
+    need(set(payload['providers']) == {'base', 'extra'}, 'Both actual providers')
+    reports = {}
+    for provider, words in payload['providers'].items():
+        need(set(words) == set(maps), 'Both complete dual variants')
+        reports[provider] = {}
+        for name, word in words.items():
+            reports[provider][name] = check_word(
+                word, source['providers'][provider]['Q'],
+                identity if name == 'inverse_adjoint' else swap, maps[name])
+    report = {
+        'status': 'PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE',
+        'literal_words': reports, 'actual_D_equals_negative_B_transpose': True,
+        'actual_E_PP_zero': True, 'actual_E_self_adjoint': True,
+        'all_content_inverse_orders': True, 'new_phase_operators': 0,
+        'phase_source_review': '6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d',
+        'negative_control': 'Reversing scalar chronology changes the complete map.',
+        'scope': 'Four complete local physical inverse-adjoint words, exact target-field phase symmetry, and unchanged local invoice. No routed two-call computation, helper host, or full supplier claim.',
+    }
+    args.out.mkdir(parents=True, exist_ok=True)
+    for name, value in [('REVIEW.json', report), ('INPUTS.json', q.INPUTS)]:
+        (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print(report['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..9b2058ac59
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal/INPUTS.json
@@ -0,0 +1,58 @@
+{
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md": {
+    "sha256": "1515a8b82ecfcb32d7dc19a4a8bc0fcf0af870ac444bb1628443dfb378360cb9"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json": {
+    "sha256": "fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json": {
+    "sha256": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz": {
+    "decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+    "sha256": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CHECKS.json": {
+    "sha256": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CLEAN-DUAL.json.gz": {
+    "sha256": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py": {
+    "sha256": "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz": {
+    "decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+    "sha256": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/DERIVATION.md": {
+    "sha256": "d8e77e0c3537a007a3674d03611dd8d6458589b8256cc2bc9bdb5c86d52124a9"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json": {
+    "sha256": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/REPRODUCTION.json": {
+    "sha256": "65193ab9f017a3d9b49c46cf64bc93fc7dbc1b38789f692f8bbea11148186bce"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/REVIEW.md": {
+    "sha256": "2a290ee65bb86a0a9c9acfb36b44735d98134350360b60a831c968a8c9c3ccd0"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py": {
+    "sha256": "e6564514a878cfa2411a41990a3d9c012f97a464c1b8361fb358fa741968f35c"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/INPUTS.json": {
+    "sha256": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/REVIEW.json": {
+    "sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/INPUTS.json": {
+    "sha256": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/REVIEW.json": {
+    "sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/check.py": {
+    "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal/REVIEW.json
new file mode 100644
index 0000000000..e12fcb18af
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/normal/REVIEW.json
@@ -0,0 +1,137 @@
+{
+  "actual_D_equals_negative_B_transpose": true,
+  "actual_E_PP_zero": true,
+  "actual_E_self_adjoint": true,
+  "all_content_inverse_orders": true,
+  "literal_words": {
+    "base": {
+      "inverse_adjoint": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      },
+      "selected_swap_conjugate": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    },
+    "extra": {
+      "inverse_adjoint": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      },
+      "selected_swap_conjugate": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    }
+  },
+  "negative_control": "Reversing scalar chronology changes the complete map.",
+  "new_phase_operators": 0,
+  "phase_source_review": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d",
+  "scope": "Four complete local physical inverse-adjoint words, exact target-field phase symmetry, and unchanged local invoice. No routed two-call computation, helper host, or full supplier claim.",
+  "status": "PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/optimized/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/optimized/INPUTS.json
new file mode 100644
index 0000000000..9b2058ac59
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/optimized/INPUTS.json
@@ -0,0 +1,58 @@
+{
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md": {
+    "sha256": "1515a8b82ecfcb32d7dc19a4a8bc0fcf0af870ac444bb1628443dfb378360cb9"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json": {
+    "sha256": "fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json": {
+    "sha256": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz": {
+    "decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+    "sha256": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CHECKS.json": {
+    "sha256": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CLEAN-DUAL.json.gz": {
+    "sha256": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py": {
+    "sha256": "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz": {
+    "decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+    "sha256": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/DERIVATION.md": {
+    "sha256": "d8e77e0c3537a007a3674d03611dd8d6458589b8256cc2bc9bdb5c86d52124a9"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json": {
+    "sha256": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/REPRODUCTION.json": {
+    "sha256": "65193ab9f017a3d9b49c46cf64bc93fc7dbc1b38789f692f8bbea11148186bce"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/REVIEW.md": {
+    "sha256": "2a290ee65bb86a0a9c9acfb36b44735d98134350360b60a831c968a8c9c3ccd0"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py": {
+    "sha256": "e6564514a878cfa2411a41990a3d9c012f97a464c1b8361fb358fa741968f35c"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/INPUTS.json": {
+    "sha256": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/REVIEW.json": {
+    "sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/INPUTS.json": {
+    "sha256": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/REVIEW.json": {
+    "sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/check.py": {
+    "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/optimized/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/optimized/REVIEW.json
new file mode 100644
index 0000000000..e12fcb18af
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/clean-dual-review-20261020/optimized/REVIEW.json
@@ -0,0 +1,137 @@
+{
+  "actual_D_equals_negative_B_transpose": true,
+  "actual_E_PP_zero": true,
+  "actual_E_self_adjoint": true,
+  "all_content_inverse_orders": true,
+  "literal_words": {
+    "base": {
+      "inverse_adjoint": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      },
+      "selected_swap_conjugate": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    },
+    "extra": {
+      "inverse_adjoint": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      },
+      "selected_swap_conjugate": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    }
+  },
+  "negative_control": "Reversing scalar chronology changes the complete map.",
+  "new_phase_operators": 0,
+  "phase_source_review": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d",
+  "scope": "Four complete local physical inverse-adjoint words, exact target-field phase symmetry, and unchanged local invoice. No routed two-call computation, helper host, or full supplier claim.",
+  "status": "PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..9a83c5cdfd
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "REPRODUCTION.json": "ef586d8c873c60c3e05b912a7c2d212475204ff5b807051f77b042f25d5275c8",
+    "REVIEW.md": "613fc0bc8d4d2470d05e2d1325a647f6da35d3a785e2ae834b1829094cf81fb1",
+    "check.py": "363b69d3b32ea8d5b1b9511c72224a5a32ada7dffc552dae16abf1b0b8387489",
+    "normal/INPUTS.json": "56112f8b986929079ad0e89ddec068e482230d6e967bde1db40c4b1bb55ca880",
+    "normal/REVIEW-CHECKS.json": "6107e7fe7f9e7821774a80cab51961147cbfaa81d325f95d4644fc57d4c4d80d",
+    "optimized/INPUTS.json": "56112f8b986929079ad0e89ddec068e482230d6e967bde1db40c4b1bb55ca880",
+    "optimized/REVIEW-CHECKS.json": "6107e7fe7f9e7821774a80cab51961147cbfaa81d325f95d4644fc57d4c4d80d"
+  },
+  "producer_freeze_sha256": "09ad251a968be73fe95eefb05f57b842eb9f55e43822f029505256705120c811",
+  "schema": "independent-complete-routed-reader-dual-review-v1",
+  "scope": "Six complete typed inverse-adjoint data services. No new recursive helper host, finite map implementation cost, closed caller, or complete supplier claim."
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..8ccff8175e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/REPRODUCTION.json
@@ -0,0 +1,9 @@
+{
+  "local_source_links_checked": true,
+  "normal_optimized_files": [
+    "REVIEW-CHECKS.json",
+    "INPUTS.json"
+  ],
+  "status": "PASS_NORMAL_OPTIMIZED_AND_PINS",
+  "unchanged_input_files": 34
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..633ca364df
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/REVIEW.md
@@ -0,0 +1,291 @@
+# Independent review of the complete routed reader dual
+
+The complete inverse-adjoint service passes for both providers and
+all three D25 reader/service pairs. The review found no material
+defect. It checks the native prefix and late query as one complete
+word, with the actual owner paths and physical boundary types.
+
+Each service costs 14896 real scalar primitives and native mass
+1792. The monomial map-call upper bound is 4384. All 640 input
+fields are arbitrary, and all 416 outside fields remain unchanged.
+The result does not construct a new helper host, price the finite
+map implementation, or close a full supplier.
+
+## Frozen sources and independent method
+
+The producer is
+[COMPLETE-DUAL.md](../../bridge-access-20261017/involution-reader-dual-20261020/COMPLETE-DUAL.md).
+Its freeze has SHA-256
+`09ad251a968be73fe95eefb05f57b842eb9f55e43822f029505256705120c811`.
+The decompressed complete payload has SHA-256
+`f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be`.
+
+The forward packet has freeze
+`3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6`
+and decompressed payload
+`35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091`.
+Its independent
+[routed involution-reader review](../../bridge-review-20261017/involution-reader-review-20261020/REVIEW.md)
+has freeze
+`b4770cbd56bc8b115728529ab218d60ca2bd1a385896ba78cfdf374f04370c97`.
+That review already accepts the forward service and the separate
+late dual. It does not accept the complete dual splice by itself.
+
+The unchanged native phase identities come from the independent
+[line-entry review](../line-entry-reuse-review-20261020/REVIEW.md),
+freeze
+`cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c`.
+This review verifies exact record equality before it uses that
+phase result. It does not claim a second spatial native phase sweep.
+
+The new checker imports only the pinned independent scalar-arithmetic
+helper. It imports no producer module or producer route engine.
+Its main new check is a reverse coefficient-column replay of the
+entire routed prefix and query. A separate forward-row replay checks
+the same endpoint and all emitted-boundary coefficient bounds.
+The DATA and late-map phases are checked with a separate Boolean
+Z4 coefficient expansion.
+
+## The exact typed endpoint
+
+Let P be the pinned sixteen selected ports and R its 96-port
+complement. Put
+
+\[
+G_R=\operatorname{diag}(I_P,q_R).
+\]
+
+Let \(F_\ell\) be the productive transform on the first \(9+8\ell\)
+axes. For reader stage s and service stage t, define
+
+\[
+(D_{s,t})_P=L_sA_t,\qquad
+(D_{s,t})_R=(A_t)_R.
+\]
+
+The verified pairs are \((0,1),(0,2),(1,2)\). The service is
+
+\[
+(F_{t-1}x,\ F_{t-1}G_Rw)
+\longmapsto
+(F_t(x-D_{s,t}^{*}w),\ F_tG_Rw).
+\]
+
+The physical input level is \(t-1\), not s. Pair \((0,2)\) therefore
+starts at physical level one. The selected and ordinary components
+of w are arbitrary independent values.
+
+The star includes matrix transpose, coefficient conjugation, and
+inverse owner route. The coefficients in this packet are real.
+No reader is moved through a response, a hole operator, or a
+productive transform.
+
+## Why the same chronological maps implement the dual
+
+For a complete physical map \(W=OMA^{-1}\), with unitary input
+frame A and output frame O,
+
+\[
+W^{-*}=OM^{-*}A^{-1}.
+\]
+
+Thus the inverse-adjoint keeps the direction of physical stage
+progress. It does not exchange the DATA entry and exit views.
+
+For a chronological gate list \(g_1,\ldots,g_n\), the physical
+operator is \(g_n\cdots g_1\). The inverse-adjoint is
+\(g_n^{-*}\cdots g_1^{-*}\). Its chronological list therefore
+has the same order. A unitary native child or physical monomial
+map stays unchanged, including its scalar phase. A real ADD
+becomes its negative transpose. A real nonzero scale becomes
+its reciprocal.
+
+The checker compares every event against this transformation of
+the frozen forward word. Every native event, phase key, ordered
+frame table, input adapter, and output adapter is unchanged.
+It checks all 3150 stored monomial side-map and endpoint records
+per provider for an invertible address map and a complete
+unit-modulus phase. The accepted native phase equations therefore
+remain applicable.
+
+The new scalar targets and sources are checked against the live
+physical frame ledger. Each ADD still has equal operand types.
+The new complete native prefix has content
+
+\[
+x\longmapsto x-(A_t)_R^*w_R,\qquad w\longmapsto w.
+\]
+
+Its local inverse-adjoint is checked on all 640 independent columns,
+not only on the original source inputs. The first 224 fields are
+the data fields. Every explicit top-level event stays within them.
+The other 416 fields are untouched by each such event.
+
+## DATA phases and actual owner order
+
+For a binary vector v, the parity on the Boolean cube satisfies
+
+\[
+v\cdot x\bmod2
+\equiv\sum_jv_jx_j-2\sum_{j<k}v_jv_kx_jx_k\pmod4.
+\]
+
+The checker uses this formula to expand each intrinsic phase
+factor. It adds the exact translation phase \(2\delta\cdot x\).
+Equality of all linear coefficients modulo four and all quadratic
+coefficients modulo two proves the full Z4 identity. The constant
+term is fixed at zero by the literal operators.
+
+The check reconstructs all 448 DATA entry and 448 DATA exit
+equations, including the common exterior. It verifies the actual
+orthogonal routes, the fixed intrinsic line, the translation before
+or after the route, and the selected FULL versus ordinary-hole type.
+Every DATA field occurs exactly once at each boundary.
+
+The owner relation is \(h=d\rho_{t,p}\). A body scalar gate from
+field j to field i therefore has global input-owner path
+
+\[
+\rho_{t,i}^{-1}\rho_{t,j}.
+\]
+
+The checker lifts every scalar event in the native prefix by this
+formula before it joins the late word. It does not first replace
+the prefix by its desired endpoint. This gives an independent
+chronological replay of the complete composition.
+
+For a fixed physical field, \(d\mapsto d\rho_{t,p}\) is a
+bijection on the regular cover. Thus body invocations have
+disjoint data records for that field. The complete cover sweep
+can be represented by the lifted scalar events above. This
+data partition does not construct a recursive helper host.
+
+## The literal late word and complete reverse replay
+
+All 672 late map events stay on the same physical fields, in
+the same chronological positions, with the same map records.
+Only scalar ADDs and scales change. A scalar source exchange
+must not move its surrounding physical view to another field.
+The checker verifies this distinction event by event.
+
+Each late route is orthogonal, has the declared inverse, fixes
+the uncompleted axes, and has the exact FULL conjugation phase.
+Each inverse translation is checked. All late operations use
+X or selected Y fields, which are FULL after the complete-cover
+barrier. Ordinary Y hole fields do not enter the late query.
+
+The checker independently builds \(A_t\) and \(L_s\) from the
+pinned matrices and actual routes. It then multiplies their
+ordered owner paths. Each selected product \(L_sA_t\) has 3824
+distinct field/path terms. The expected complete dual is formed
+by transposing these terms and inverting each full path.
+
+The reverse replay starts with independent output columns. At a
+physical map, it composes the existing owner path on the right
+by the map route. At an ADD, it propagates the target column to
+the source with the exact coefficient. This differs from the
+producer's forward-row execution. The separate forward pass
+composes map routes on the left.
+
+Both passes give the same complete upper shear for all six
+provider/pair cases. The late query alone is not equal to that
+complete service. Its missing ordinary native-prefix response
+is detected by a negative check. A changed transferred ADD sign
+also fails.
+
+The full late subtraction is
+\[
+X\mathrel{-}=(L_sA_t)^*w_P.
+\]
+Together with the replayed native-prefix subtraction, it gives
+\(X\mathrel{-}=D_{s,t}^*w\). Both products of the resulting complete
+operator with the forward adjoint are the identity on all 640
+fields. Every target baseline and every outside field is preserved.
+
+## Complete dispatcher and invoice
+
+Every invocation resolves to a checked provider and query pair.
+The serialized order is exactly:
+
+```text
+DATA entry
+128 local input adapters
+complete native carrier cover sweep
+96 ordinary output adapters
+DATA exit
+complete-cover barrier
+late inverse-adjoint reader query
+```
+
+The native event range is unchanged. The current physical stage,
+old reader label, DATA record index, query key, and literal query
+source are checked for all six invocations.
+
+| Part | Real scalar primitives | Monomial map calls |
+| --- | ---: | ---: |
+| Native prefix | 6456 | 224 endpoint adapters |
+| Late query | 8440 | 672 |
+| DATA entry and exit | 0 | 448 |
+| Native child side maps | 0 | at most 3040 |
+| Total | 14896 | at most 4384 |
+
+The native profile is
+\(1392H_1+64H_2+48H_3+16H_8\), with 1520 children and mass 1792.
+No new field, private zero field, or odd division is introduced.
+The scale reciprocals remain signed powers of two and keep the
+same scalar tariff.
+
+The exact content row-sum peaks are 12 in the native prefix,
+30 in the late dual on independent input fields, and 40 in
+the complete emitted word. The binary denominator heights are
+one, two, and two, respectively. These bounds concern the ideal
+content at emitted boundaries. They do not bound primitive
+arithmetic interiors, recursive child interiors, or roundoff.
+
+The map total is a call count. It does not price an all-size
+map implementation. The recursive helper supply, parking,
+precision, raw outer endpoint, and closed caller remain open.
+The untouched top-level outside fields do not establish those
+additional obligations.
+
+## Reusable consequence
+
+This check supplies the missing complete backward service for
+the fixed-reader interface. The transformation applies more
+generally to a finite word of unitary field maps and invertible
+linear scalar gates, provided that its exact physical types
+and arbitrary borrowed-field contract are retained.
+
+A lower shear with reader D becomes an upper shear with
+reader \(-D^*\). This conclusion does not require D to be
+invertible. It is not a construction of \(D^{-1}\), and it does
+not identify readers or responses at different stages.
+
+To compose such services, the complete physical boundary types
+must match. The local adjoint rule does not remove an entrance
+or exit conversion that a caller still requires.
+
+## Reproduction and credit
+
+From this review directory run:
+
+```text
+python3 -B check.py --out normal
+python3 -O -B check.py --out optimized
+```
+
+Both runs must print
+`PASS_INDEPENDENT_COMPLETE_READER_DUAL`.
+The receipts and input manifests must be byte equal. The
+reproduction record checks every consumed file hash again.
+
+The bridge-access lane supplied the complete dual. The controller
+lane supplied the row involution. The native lane supplied the
+carrier prefix. The bridge-review lane supplied the independent
+forward service and late-dual review. This lane supplied the
+earlier exact native phase review and the new complete physical
+splice review. AI agents prepared these local research records.
+
+No PR, push, commit, or publication is authorized. Before any
+future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/check.py
new file mode 100644
index 0000000000..0873ad4e39
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/check.py
@@ -0,0 +1,450 @@
+#!/usr/bin/env python3
+"""Check the complete routed inverse-adjoint service."""
+from collections import Counter
+from fractions import Fraction as F
+from functools import lru_cache
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import importlib.util
+import json
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+HELPER = HERE.parent/'row-capture-native-review-20261020/check.py'
+PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84'
+if sha256(HELPER.read_bytes()).hexdigest() != PIN:
+    raise ValueError('Independent arithmetic helper pin')
+spec = importlib.util.spec_from_file_location('independent_row_tools', HELPER)
+q = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(q)
+q.read(HELPER, PIN)
+need = q.need
+UNIT = tuple(1 << j for j in range(25))
+SOURCE = LANES/'bridge-access-20261017/involution-reader-dual-20261020'
+FORWARD = LANES/'bridge-access-20261017/involution-reader-20261020'
+
+
+def act(columns, vector):
+    result = 0
+    for j, column in enumerate(columns):
+        if vector >> j & 1:
+            result ^= column
+    return result
+
+
+@lru_cache(maxsize=8192)
+def compose(left, right):
+    return tuple(act(left, column) for column in right)
+
+
+def transpose(columns):
+    return tuple(sum(((v >> i) & 1) << j for j, v in enumerate(columns)) for i in range(len(columns)))
+
+
+def binary_rank(rows):
+    pivots = {}
+    for row in rows:
+        while row:
+            j = row.bit_length()-1
+            if j not in pivots:
+                pivots[j] = row
+                break
+            row ^= pivots[j]
+    return len(pivots)
+
+
+def phase(factors, translation=0):
+    """Expand each parity over the Boolean cube modulo four."""
+    linear = [2*((translation >> j) & 1) for j in range(25)]
+    quadratic = [0]*25
+    for vector, power in factors:
+        for j in range(25):
+            if vector >> j & 1:
+                linear[j] = (linear[j]+power) % 4
+                if power % 2:
+                    quadratic[j] ^= vector & ~((1 << (j+1))-1)
+    return tuple(linear), tuple(quadratic)
+
+
+def orthogonal(columns):
+    need(len(columns) == 25 and all(0 <= c < 1 << 25 for c in columns), 'Actual25-axis route')
+    need(compose(columns, transpose(columns)) == compose(transpose(columns), columns) == UNIT,
+         'Exact orthogonal inverse')
+
+
+def phase_bindings(bundle, records):
+    counts = Counter()
+    selected = set(bundle['pivots'])
+    need(len(bundle['stage_views']) == 2, 'Both physical adjacent stages')
+    for stage in bundle['stage_views']:
+        t = stage['service_stage']
+        need(t in (1, 2) and stage['physical_input_level'] == t-1 and
+             stage['physical_output_level'] == t, 'Adjacent stage levels')
+        before = [(v, 1) for v in UNIT[:9+8*(t-1)]]
+        after = [(v, 1) for v in UNIT[:9+8*t]]
+        exterior = [(v, 1) for v in UNIT[9:9+8*t]]
+        need(stage['common_exterior_axes'] == list(UNIT[9:9+8*t]), 'Complete common exterior')
+        for label in ('DATA_entry', 'DATA_exit'):
+            fields = set()
+            for view in stage[label]:
+                p, side, field = view['port'], view['side'], view['field']
+                need(side in ('X', 'Y') and field == p+(112 if side == 'Y' else 0) and
+                     field not in fields, 'Exact physical DATA field')
+                fields.add(field)
+                original = records[t, p]
+                rho = tuple(view['route_columns'])
+                orthogonal(rho)
+                need(view['route_columns'] == original['route_columns'] and
+                     view['owner_from_body'] == 'h=d*rho' and
+                     act(rho, original['q']) == original['q'], 'Actual owner route and intrinsic line')
+                full = side == 'X' or p in selected
+                align = original['literal_stage_alignment']
+                if label == 'DATA_entry':
+                    need(view['intrinsic_input'] == ('Q_p' if full else 'I'), 'Exact input type')
+                    delta = act(rho, align['entry_'+side])
+                    need(view['translation_before_route'] == align['entry_'+side] and
+                         view['translation_after_route'] == delta, 'Entry translation order')
+                    source = before+([] if full else [(original['q'], -1)])
+                    target = exterior+([(original['q'], 1)] if full else [])
+                else:
+                    key = 'exit_X' if full else 'exit_Y'
+                    delta = align[key]
+                    need(view['literal_translation_key'] == key and
+                         view['translation_after_route'] == delta and
+                         view['global_output'] == ('FULL' if full else 'FULL*q_p'), 'Exact exit type')
+                    source = target = after+([] if full else [(original['q'], -1)])
+                need(phase([(act(rho, v), n) for v, n in source], delta) == phase(target),
+                     'All Boolean Z4 phase coefficients')
+                counts[label] += 1
+            need(fields == set(range(224)), 'Every DATA field exactly once')
+    need(counts == {'DATA_entry': 448, 'DATA_exit': 448}, 'All896 DATA equations')
+    return dict(counts)
+
+
+def unitary_records(word):
+    records = []
+    for recipe in word['native_recipes'].values():
+        need(1 <= recipe['rank'] <= 9, 'Unitary native child')
+        records.extend(recipe[key] for key in ('left', 'right') if recipe[key] is not None)
+    for view in word['input_views']:
+        need(view['rank'] == 0 and view['right'] is None, 'Monomial input adapter')
+        records.append(view['left'])
+    for view in word['output_views']:
+        recipe = view['recipe']
+        need(recipe['rank'] == 0 and recipe['right'] is None, 'Monomial output adapter')
+        records.append(recipe['left'])
+    for record in records:
+        need(len(record['matrix_rows']) == 9 and binary_rank(record['matrix_rows']) == 9,
+             'Unitary nine-axis address map')
+        need(all(0 <= r < 512 for r in record['matrix_rows']) and
+             0 <= record['offset'] < 512 and 0 <= record['phase'] < 4, 'Exact monomial domain')
+        need(len(record['linear_Z4']) == len(record['quadratic_rows']) == 9 and
+             all(0 <= x < 4 for x in record['linear_Z4']) and
+             all(0 <= x < 512 for x in record['quadratic_rows']), 'Unit-modulus complete phase')
+    return len(records)
+
+
+def scalar_dual(gate):
+    op, target, source, coefficient = gate
+    c = F(coefficient)
+    if op == 'add':
+        return ['add', source, target, str(-c)]
+    need(op == 'scale' and c, 'Invertible scalar gate')
+    return ['scale', target, None, str(1/c)]
+
+
+def native_prefix(word, original, a, pivots):
+    need(set(word) == set(original), 'Complete native record keys')
+    for key in original:
+        if key != 'events':
+            need(word[key] == original[key], 'Exact unchanged native metadata: '+key)
+    need(len(word['events']) == len(original['events']) == 2406, 'Complete native event count')
+    current, profile = list(word['start']), Counter()
+    for new, old in zip(word['events'], original['events']):
+        if old[0] == 'native':
+            need(new == old, 'Every native occurrence and phase key is unchanged')
+            _, field, before, after, rank, key = new
+            need(0 <= field < 224 and current[field] == before and
+                 word['native_recipes'][key]['rank'] == rank, 'Typed native occurrence')
+            current[field] = after
+            profile[rank] += 1
+        else:
+            need(new == ['scalar', scalar_dual(old[1]), old[2]], 'Same-order scalar inverse-adjoint')
+            (op, target, source, _), frame = new[1:]
+            need(0 <= target < 224 and current[target] == frame, 'Exact new scalar target frame')
+            if op == 'add':
+                need(0 <= source < 224 and source != target and current[source] == frame,
+                     'Exact new scalar source frame')
+    need(current == word['final'], 'All640 final frames')
+    expected = q.unit(640)
+    for p, row in enumerate(a):
+        if p not in pivots:
+            for j, c in row.items():
+                q.add(expected[j], {112+p: -c})
+    scalars = [e[1] for e in word['events'] if e[0] == 'scalar']
+    need(q.reverse(scalars, 640) == q.transpose(expected, 640), 'All640 native reverse columns')
+    rows, growth = q.prefix(scalars, 640)
+    need(rows == expected and growth == {'row_one_norm': '12', 'binary_height': 1},
+         'Native forward rows and exact prefixes')
+    need(q.price(scalars) == 6456 and profile == {1: 1392, 2: 64, 3: 48, 8: 16},
+         'Exact native scalar and child invoice')
+    count = unitary_records(word)
+    need(count == 3150, 'All stored unitary side-map and endpoint records')
+    return scalars, {'columns': 640, 'unchanged_arbitrary_fields': 416, 'scalar': 6456,
+                     'profile': dict(profile), 'native_children': 1520, 'native_mass': 1792,
+                     'unitary_monomial_records': count, 'growth': growth}
+
+
+def query_operations(word, original, pivots):
+    need(set(word) == set(original), 'Complete query record keys')
+    for key in original:
+        if key != 'events':
+            need(word[key] == original[key], 'Exact unchanged query metadata: '+key)
+    need(len(word['events']) == len(original['events']), 'Complete query chronology')
+    level = word['service_stage']
+    full = [(v, 1) for v in UNIT[:9+8*level]]
+    for record in word['maps']:
+        route, inverse = tuple(record['columns']), tuple(record['inverse_columns'])
+        orthogonal(route)
+        need(inverse == transpose(route) and route[9+8*level:] == UNIT[9+8*level:],
+             'Exact map inverse and future axes')
+        need(record['inverse_translation'] == act(inverse, record['translation']), 'Inverse phase translation')
+        need(phase([(act(route, v), 1) for v, _ in full], record['translation']) == phase(full),
+             'Complete late FULL phase')
+    operations, scalars, maps = [], [], 0
+    for new, old in zip(word['events'], original['events']):
+        if old[0] == 'map':
+            need(new == old, 'Map stays on the same physical field at the same position')
+            _, field, index = new
+            need(field < 112 or field-112 in pivots, 'Map uses a FULL field')
+            operations.append(('map', field, None, F(1), tuple(word['maps'][index]['columns'])))
+            maps += 1
+        else:
+            need(old[0] == 'scalar' and new == ['scalar']+scalar_dual(old[1:]), 'Literal late scalar dual')
+            op, target, source, coefficient = new[1:]
+            need(target < 112 or target-112 in pivots, 'Late scalar target is FULL')
+            need(source is None or source < 112 or source-112 in pivots, 'Late scalar source is FULL')
+            operations.append((op, target, source, F(coefficient), UNIT))
+            scalars.append(new[1:])
+    need(maps == 672 and q.price(scalars) == 8440, 'Exact late query bill')
+    need(len({(lo, hi) for lo, hi in word['stage_ranges'].values()}) == 4, 'Four query intervals')
+    last = 0
+    for name in ('apply_current_involution', 'old_reader_complement',
+                 'selected_reader_copy', 'restore_current_involution'):
+        lo, hi = word['stage_ranges'][name]
+        need(lo == last and lo <= hi <= len(operations), 'No gap in the late query')
+        last = hi
+    need(last == len(operations), 'Every late operation is inside the query')
+    return operations
+
+
+def routed_unit():
+    return [{(i, UNIT): F(1)} for i in range(640)]
+
+
+def route_row(row, route, left=True):
+    return {(field, compose(route, old) if left else compose(old, route)): value
+            for (field, old), value in row.items()}
+
+
+def forward_rows(operations, initial=None):
+    rows = routed_unit() if initial is None else [dict(row) for row in initial]
+    maximum = max(sum(map(abs, row.values()), F(0)) for row in rows)
+    height = 0
+    for op, target, source, coefficient, route in operations:
+        if op == 'map':
+            rows[target] = route_row(rows[target], route)
+        elif op == 'scale':
+            rows[target] = {key: coefficient*x for key, x in rows[target].items()}
+        else:
+            need(op == 'add' and source != target, 'Distinct routed ADD')
+            q.add(rows[target], route_row(rows[source], route), coefficient)
+        maximum = max(maximum, sum(map(abs, rows[target].values()), F(0)))
+        for value in rows[target].values():
+            d = value.denominator
+            need(d & (d-1) == 0, 'Dyadic complete content')
+            height = max(height, d.bit_length()-1)
+    return rows, {'row_one_norm': str(maximum), 'binary_height': height}
+
+
+def reverse_columns(operations):
+    columns = routed_unit()
+    for op, target, source, coefficient, route in reversed(operations):
+        if op == 'map':
+            columns[target] = route_row(columns[target], route, left=False)
+        elif op == 'scale':
+            columns[target] = {key: coefficient*x for key, x in columns[target].items()}
+        else:
+            q.add(columns[source], route_row(columns[target], route, left=False), coefficient)
+    rows = [{} for _ in range(640)]
+    for source, column in enumerate(columns):
+        for (target, route), value in column.items():
+            q.add(rows[target], {(source, route): value})
+    return rows
+
+
+def routed_product(left, right):
+    result = []
+    for row in left:
+        target = {}
+        for (j, a), c in row.items():
+            for (k, b), d in right[j].items():
+                q.add(target, {(k, compose(a, b)): c*d})
+        result.append(target)
+    return result
+
+
+def route_matrix(matrix, ports, stage, routes):
+    return [{(j, compose(transpose(routes[stage, p]), routes[stage, j])): c for j, c in row.items()}
+            for p, row in zip(ports, matrix)]
+
+
+def complete_response(a, reader, pivots, s, t, routes):
+    at = route_matrix(a, range(112), t, routes)
+    ls = route_matrix(reader, pivots, s, routes)
+    direct = routed_product(ls, at)
+    need(sum(map(len, direct)) == 3824, 'Actual ordered selected response terms')
+    response = [dict(row) for row in at]
+    for p, row in zip(pivots, direct):
+        response[p] = row
+    return response, direct
+
+
+def upper_negative_adjoint(response, ports):
+    result = routed_unit()
+    for p, row in zip(ports, response):
+        for (j, route), c in row.items():
+            q.add(result[j], {(112+p, transpose(route)): -c})
+    return result
+
+
+def lower(response):
+    result = routed_unit()
+    for p, row in enumerate(response):
+        q.add(result[112+p], row)
+    return result
+
+
+def adjoint(rows):
+    result = [{} for _ in rows]
+    for i, row in enumerate(rows):
+        for (j, route), c in row.items():
+            q.add(result[j], {(i, transpose(route)): c})
+    return result
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    q.frozen(SOURCE, 'FREEZE.json', '09ad251a968be73fe95eefb05f57b842eb9f55e43822f029505256705120c811')
+    q.frozen(FORWARD, 'FREEZE.json', '3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6')
+    q.frozen(LANES/'bridge-review-20261017/involution-reader-review-20261020', 'FREEZE.json',
+             'b4770cbd56bc8b115728529ab218d60ca2bd1a385896ba78cfdf374f04370c97')
+    q.frozen(HERE.parent/'line-entry-reuse-review-20261020', 'FREEZE.json',
+             'cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c')
+    payload = json.loads(q.read(SOURCE/'final-normal/COMPLETE-DUAL.json.gz',
+                                'f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be', True))
+    original = json.loads(q.read(FORWARD/'final-normal/INVOLUTION-READER.json.gz',
+                                 '35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091', True))
+    capture = json.loads(q.read(q.ALG/'run-normal/ROW-CAPTURE.json',
+                                '4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7'))
+    algebra = json.loads(q.read(LANES/'controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json',
+                                'a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b'))
+    views = json.loads(q.read(LANES/'bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json',
+                              '125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473'))
+    need(payload['pivots'] == original['pivots'] == q.P and
+         payload['response'] == original['response'] == algebra['response'], 'Actual response and pivot binding')
+    need(payload['stage_views'] == original['stage_views'] and
+         payload['helper_hosting'] == original['helper_hosting'], 'Exact retained DATA and helper contracts')
+    a, reader = q.rows(algebra['response']), q.rows(capture['centre_reader'])
+    need(q.mul(a, a) == q.unit(112) and
+         q.mul(reader, a) == [{j: -c for j, c in row.items()} for row in reader], 'Actual involution and reader')
+    records = {(v['stage'], v['port']): v for v in views['entries']}
+    need(len(records) == 336, 'Complete actual stage-port source')
+    routes = {key: tuple(v['route_columns']) for key, v in records.items()}
+    for route in routes.values():
+        orthogonal(route)
+    phase_report = phase_bindings(payload, records)
+    selected = set(q.P)
+    prefix_scalars, prefix_reports = {}, {}
+    need(set(payload['native_prefixes']) == {'base', 'extra'}, 'Both native providers')
+    for provider, word in payload['native_prefixes'].items():
+        prefix_scalars[provider], prefix_reports[provider] = native_prefix(
+            word, original['native_prefixes'][provider], a, selected)
+    need(set(payload['queries']) == {'0:1', '0:2', '1:2'}, 'All three reader/service pairs')
+    reports, late_reports = {}, {}
+    for key, word in payload['queries'].items():
+        s, t = word['reader_stage'], word['service_stage']
+        need(key == str(s)+':'+str(t), 'Actual pair labels')
+        late = query_operations(word, original['queries'][key], selected)
+        response, direct = complete_response(a, reader, q.P, s, t, routes)
+        expected = upper_negative_adjoint(response, range(112))
+        expected_late = upper_negative_adjoint(direct, q.P)
+        late_rows, late_growth = forward_rows(late)
+        need(late_rows == reverse_columns(late) == expected_late and
+             late_growth == {'row_one_norm': '30', 'binary_height': 2}, 'Independent complete late dual')
+        late_reports[key] = {'columns': 640, 'scalar': 8440, 'maps': 672,
+                             'phase_records': len(word['maps']), 'growth': late_growth}
+        for provider, scalars in prefix_scalars.items():
+            operations = []
+            for op, target, source, coefficient in scalars:
+                route = (UNIT if source is None else
+                         compose(transpose(routes[t, target % 112]), routes[t, source % 112]))
+                operations.append((op, target, source, F(coefficient), route))
+            complete = operations+late
+            actual = reverse_columns(complete)
+            forward, growth = forward_rows(complete)
+            need(actual == forward == expected, 'All640 columns of the complete physical splice')
+            need(growth == {'row_one_norm': '40', 'binary_height': 2}, 'Complete emitted-boundary content peak')
+            need(actual[112:] == routed_unit()[112:] and
+                 all(j < 224 for row in actual[:112] for j, _ in row), 'All target baselines and416 outside fields')
+            forward_star = adjoint(lower(response))
+            need(routed_product(actual, forward_star) == routed_product(forward_star, actual) == routed_unit(),
+                 'Both full operator inverse-adjoint products')
+            without_prefix = reverse_columns(late)
+            need(without_prefix != expected, 'A late dual alone is not the full service')
+            wrong = list(complete)
+            index = next(i for i, (op, _, source, _, route) in enumerate(wrong)
+                         if op == 'add' and source >= 112 and route != UNIT)
+            op, target, source, coefficient, route = wrong[index]
+            wrong[index] = op, target, source, -coefficient, route
+            need(reverse_columns(wrong) != expected, 'A wrong transferred sign fails')
+            reports[key+':'+provider] = {'input_columns': 640, 'unchanged_arbitrary_fields': 416,
+                'scalar_primitives': 14896, 'native_mass': 1792, 'native_children': 1520,
+                'map_call_bound': 4384, 'growth': growth, 'both_inverse_products': True}
+        print('Independent complete pair', key, flush=True)
+    need(len(payload['invocations']) == len(original['invocations']) == 6, 'All six invocations')
+    seen = set()
+    for call, old in zip(payload['invocations'], original['invocations']):
+        wanted = json.loads(json.dumps(old))
+        wanted['ordered_blocks'][-1]['op'] = 'inverse_adjoint_fixed_past_reader_query'
+        need(call == wanted, 'Exact complete dispatcher and changed query binding')
+        s, t, provider = call['reader_stage'], call['service_stage'], call['provider']
+        key = str(s)+':'+str(t)
+        need(key+':'+provider in reports and (key, provider) not in seen, 'Unique complete resolved call')
+        seen.add((key, provider))
+        need(call['physical_input_level'] == t-1 and call['physical_output_level'] == t and
+             call['stage_view_record'] == t-1 and call['query_key'] == key, 'Actual adjacent physical level')
+        need([b['op'] for b in call['ordered_blocks']] == [
+            'DATA_entry', 'native_input_adapters', 'complete_native_carrier_cover_sweep',
+            'ordinary_output_adapters', 'DATA_exit', 'complete_cover_barrier',
+            'inverse_adjoint_fixed_past_reader_query'], 'Exact physical order and whole-cover barrier')
+        need(call['map_call_bound'] == {'DATA': 448, 'local_endpoint_adapters': 224,
+                                       'native_side_maps': 3040, 'late_query': 672, 'total': 4384}
+             and call['scalar_primitives'] == 14896, 'Full invocation bill')
+    report = {'status': 'PASS_INDEPENDENT_COMPLETE_READER_DUAL',
+        'native_prefixes': prefix_reports, 'late_queries': late_reports, 'services': reports,
+        'DATA_phase_equations': phase_report, 'new_native_phase_operators': 0,
+        'method': 'Independent full reverse coefficient columns, forward prefixes, and Boolean Z4 phase coefficients.',
+        'scope': 'Six complete typed data services. No new recursive helper host, finite map cost, closed caller, or supplier claim.'}
+    args.out.mkdir(parents=True, exist_ok=True)
+    for name, value in [('REVIEW-CHECKS.json', report), ('INPUTS.json', q.INPUTS)]:
+        (args.out/name).write_text(json.dumps(value, sort_keys=True, indent=2)+'\n')
+    print(report['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..3a47d697ad
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/normal/INPUTS.json
@@ -0,0 +1,106 @@
+{
+  "bridge-access-20261017/involution-reader-20261020/FREEZE.json": {
+    "sha256": "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6"
+  },
+  "bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md": {
+    "sha256": "718829c1842c856d5694abbcd6ebd509cafbb8901b4225be218f45abd2844dab"
+  },
+  "bridge-access-20261017/involution-reader-20261020/emit_query.py": {
+    "sha256": "29afc86c918f428d9562b02e2017a1eebc38b1cf2dcae2b2d6bf53c5473be14b"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json": {
+    "sha256": "fe484b746a1a3f3c7d54e40afeb3f3f9e3493fd7fc7ff350ac91920a8ab38c6f"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-normal/INVOLUTION-READER.json.gz": {
+    "decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091",
+    "sha256": "6fd5d6df96582aeaeef9a3295289d239586de3a1420ae7f8e99679e9ef96b810"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-optimized/CHECKS.json": {
+    "sha256": "fe484b746a1a3f3c7d54e40afeb3f3f9e3493fd7fc7ff350ac91920a8ab38c6f"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-optimized/INVOLUTION-READER.json.gz": {
+    "sha256": "6fd5d6df96582aeaeef9a3295289d239586de3a1420ae7f8e99679e9ef96b810"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/COMPLETE-DUAL.md": {
+    "sha256": "37a3a187acf93cad2048f9147457bf8925cf53ce61836b5e899dd13bc4239c5e"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json": {
+    "sha256": "09ad251a968be73fe95eefb05f57b842eb9f55e43822f029505256705120c811"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py": {
+    "sha256": "4c10ca91f788052bc3e1da43f63d6dde0a84d4b8b1c34e8f64f3912e47a86a32"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json": {
+    "sha256": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-normal/COMPLETE-DUAL.json.gz": {
+    "decompressed_sha256": "f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be",
+    "sha256": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-optimized/CHECKS.json": {
+    "sha256": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-optimized/COMPLETE-DUAL.json.gz": {
+    "sha256": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1"
+  },
+  "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json": {
+    "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/FREEZE.json": {
+    "sha256": "b4770cbd56bc8b115728529ab218d60ca2bd1a385896ba78cfdf374f04370c97"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md": {
+    "sha256": "cc96ab14ce744b4acf30bc5e8088a35807611a497abc673b11eab225d9bf7993"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md": {
+    "sha256": "653372564d82ea8b7c8f7b2b1a76de4cf97f97879864dcd9479f09ca6ceaf86e"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json": {
+    "sha256": "cbf5cf14b663c1c78f27f4f41ff18dc77eaa99619bf2d5f58373a574dc12a802"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/REVIEW.md": {
+    "sha256": "e8862531740470b3bb4f45b421c0ab100c07f00bed71271b398ee7bdb89d834d"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/check_review.py": {
+    "sha256": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json": {
+    "sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/optimized/REVIEW-CHECKS.json": {
+    "sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json": {
+    "sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json": {
+    "sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json": {
+    "sha256": "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json": {
+    "sha256": "5fe7900ca1791738790a663c882ea411d8e3f41cdb9f9b7f5d23f06deffbf939"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md": {
+    "sha256": "f6ddd5a2581319ac5b07d402384c4847bce88f10505cca926c9287e838e1760f"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py": {
+    "sha256": "c2a8f93e2c1cf23f8fc279e6dc87d6bd923e60c438531fe1770b0992d1dfdb7d"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json": {
+    "sha256": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/REVIEW.json": {
+    "sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/INPUTS.json": {
+    "sha256": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/REVIEW.json": {
+    "sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/check.py": {
+    "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/normal/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/normal/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..f9e73b56fd
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/normal/REVIEW-CHECKS.json
@@ -0,0 +1,160 @@
+{
+  "DATA_phase_equations": {
+    "DATA_entry": 448,
+    "DATA_exit": 448
+  },
+  "late_queries": {
+    "0:1": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 113,
+      "scalar": 8440
+    },
+    "0:2": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 113,
+      "scalar": 8440
+    },
+    "1:2": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 224,
+      "scalar": 8440
+    }
+  },
+  "method": "Independent full reverse coefficient columns, forward prefixes, and Boolean Z4 phase coefficients.",
+  "native_prefixes": {
+    "base": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "12"
+      },
+      "native_children": 1520,
+      "native_mass": 1792,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar": 6456,
+      "unchanged_arbitrary_fields": 416,
+      "unitary_monomial_records": 3150
+    },
+    "extra": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "12"
+      },
+      "native_children": 1520,
+      "native_mass": 1792,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar": 6456,
+      "unchanged_arbitrary_fields": 416,
+      "unitary_monomial_records": 3150
+    }
+  },
+  "new_native_phase_operators": 0,
+  "scope": "Six complete typed data services. No new recursive helper host, finite map cost, closed caller, or supplier claim.",
+  "services": {
+    "0:1:base": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "0:1:extra": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "0:2:base": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "0:2:extra": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "1:2:base": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "1:2:extra": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    }
+  },
+  "status": "PASS_INDEPENDENT_COMPLETE_READER_DUAL"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/optimized/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/optimized/INPUTS.json
new file mode 100644
index 0000000000..3a47d697ad
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/optimized/INPUTS.json
@@ -0,0 +1,106 @@
+{
+  "bridge-access-20261017/involution-reader-20261020/FREEZE.json": {
+    "sha256": "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6"
+  },
+  "bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md": {
+    "sha256": "718829c1842c856d5694abbcd6ebd509cafbb8901b4225be218f45abd2844dab"
+  },
+  "bridge-access-20261017/involution-reader-20261020/emit_query.py": {
+    "sha256": "29afc86c918f428d9562b02e2017a1eebc38b1cf2dcae2b2d6bf53c5473be14b"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json": {
+    "sha256": "fe484b746a1a3f3c7d54e40afeb3f3f9e3493fd7fc7ff350ac91920a8ab38c6f"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-normal/INVOLUTION-READER.json.gz": {
+    "decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091",
+    "sha256": "6fd5d6df96582aeaeef9a3295289d239586de3a1420ae7f8e99679e9ef96b810"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-optimized/CHECKS.json": {
+    "sha256": "fe484b746a1a3f3c7d54e40afeb3f3f9e3493fd7fc7ff350ac91920a8ab38c6f"
+  },
+  "bridge-access-20261017/involution-reader-20261020/final-optimized/INVOLUTION-READER.json.gz": {
+    "sha256": "6fd5d6df96582aeaeef9a3295289d239586de3a1420ae7f8e99679e9ef96b810"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/COMPLETE-DUAL.md": {
+    "sha256": "37a3a187acf93cad2048f9147457bf8925cf53ce61836b5e899dd13bc4239c5e"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json": {
+    "sha256": "09ad251a968be73fe95eefb05f57b842eb9f55e43822f029505256705120c811"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py": {
+    "sha256": "4c10ca91f788052bc3e1da43f63d6dde0a84d4b8b1c34e8f64f3912e47a86a32"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json": {
+    "sha256": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-normal/COMPLETE-DUAL.json.gz": {
+    "decompressed_sha256": "f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be",
+    "sha256": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-optimized/CHECKS.json": {
+    "sha256": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84"
+  },
+  "bridge-access-20261017/involution-reader-dual-20261020/final-optimized/COMPLETE-DUAL.json.gz": {
+    "sha256": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1"
+  },
+  "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json": {
+    "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/FREEZE.json": {
+    "sha256": "b4770cbd56bc8b115728529ab218d60ca2bd1a385896ba78cfdf374f04370c97"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md": {
+    "sha256": "cc96ab14ce744b4acf30bc5e8088a35807611a497abc673b11eab225d9bf7993"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md": {
+    "sha256": "653372564d82ea8b7c8f7b2b1a76de4cf97f97879864dcd9479f09ca6ceaf86e"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json": {
+    "sha256": "cbf5cf14b663c1c78f27f4f41ff18dc77eaa99619bf2d5f58373a574dc12a802"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/REVIEW.md": {
+    "sha256": "e8862531740470b3bb4f45b421c0ab100c07f00bed71271b398ee7bdb89d834d"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/check_review.py": {
+    "sha256": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json": {
+    "sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830"
+  },
+  "bridge-review-20261017/involution-reader-review-20261020/optimized/REVIEW-CHECKS.json": {
+    "sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json": {
+    "sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json": {
+    "sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json": {
+    "sha256": "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json": {
+    "sha256": "5fe7900ca1791738790a663c882ea411d8e3f41cdb9f9b7f5d23f06deffbf939"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md": {
+    "sha256": "f6ddd5a2581319ac5b07d402384c4847bce88f10505cca926c9287e838e1760f"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py": {
+    "sha256": "c2a8f93e2c1cf23f8fc279e6dc87d6bd923e60c438531fe1770b0992d1dfdb7d"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json": {
+    "sha256": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/REVIEW.json": {
+    "sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/INPUTS.json": {
+    "sha256": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5"
+  },
+  "new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/REVIEW.json": {
+    "sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/check.py": {
+    "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/optimized/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/optimized/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..f9e73b56fd
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/complete-reader-dual-review-20261020/optimized/REVIEW-CHECKS.json
@@ -0,0 +1,160 @@
+{
+  "DATA_phase_equations": {
+    "DATA_entry": 448,
+    "DATA_exit": 448
+  },
+  "late_queries": {
+    "0:1": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 113,
+      "scalar": 8440
+    },
+    "0:2": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 113,
+      "scalar": 8440
+    },
+    "1:2": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 224,
+      "scalar": 8440
+    }
+  },
+  "method": "Independent full reverse coefficient columns, forward prefixes, and Boolean Z4 phase coefficients.",
+  "native_prefixes": {
+    "base": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "12"
+      },
+      "native_children": 1520,
+      "native_mass": 1792,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar": 6456,
+      "unchanged_arbitrary_fields": 416,
+      "unitary_monomial_records": 3150
+    },
+    "extra": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "12"
+      },
+      "native_children": 1520,
+      "native_mass": 1792,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar": 6456,
+      "unchanged_arbitrary_fields": 416,
+      "unitary_monomial_records": 3150
+    }
+  },
+  "new_native_phase_operators": 0,
+  "scope": "Six complete typed data services. No new recursive helper host, finite map cost, closed caller, or supplier claim.",
+  "services": {
+    "0:1:base": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "0:1:extra": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "0:2:base": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "0:2:extra": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "1:2:base": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    },
+    "1:2:extra": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
+      "map_call_bound": 4384,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "scalar_primitives": 14896,
+      "unchanged_arbitrary_fields": 416
+    }
+  },
+  "status": "PASS_INDEPENDENT_COMPLETE_READER_DUAL"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/isotropic-pair-review-20261018/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/isotropic-pair-review-20261018/check.py
new file mode 100644
index 0000000000..3baaa8e3f3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/isotropic-pair-review-20261018/check.py
@@ -0,0 +1,593 @@
+#!/usr/bin/env python3
+"""Check the common port gauge with exact sparse Gaussian columns."""
+from collections import Counter
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+SOURCE = LANES / 'coherent-port/isotropic-pair-gauge-20261018'
+H6 = LANES / 'oblique-native-20261017/radical-centre-carry'
+PINS = {
+    'GAUGE.md': '17f7fcb6d67499f2d0280d1c49b0c0d01076ec839b620d0a82b8ce6de3e3395b',
+    'check_isotropic_gauge.py': 'fdab75d06215e6dc1215d8aaf6737443be0c5b4fe3ad8088ff95c5d9221c730d',
+    'GAUGE-PROGRAMS.json': '20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701',
+    'CHECKS.json': '4ef0a622416d46a2ccab39d6f87a2e67be82fdbbe0e6d7cc0e0e0bac5e0ad0c3',
+}
+INPUTS = {}
+
+
+def need(value, label):
+    if not value:
+        raise ValueError(label)
+
+
+def read(path, expected=None, compressed=False):
+    raw = path.read_bytes()
+    digest = sha256(raw).hexdigest()
+    content = gzip.decompress(raw) if compressed else raw
+    need(expected is None or sha256(content).hexdigest() == expected, 'Input pin: '+str(path))
+    INPUTS[str(path.relative_to(LANES))] = {'sha256': digest}
+    if compressed:
+        INPUTS[str(path.relative_to(LANES))]['decompressed_sha256'] = sha256(content).hexdigest()
+    return content
+
+
+def frozen(path, pin):
+    record = json.loads(read(path/'FREEZE.json', pin))
+    for name, digest in record['files'].items():
+        read(path/name, digest)
+    return record
+
+
+def rotate(r, i, power):
+    return ((r, i), (-i, r), (-r, -i), (i, -r))[power % 4]
+
+
+def phase_at(rows, linear, x):
+    exponent = sum(value for j, value in enumerate(linear) if x & (1 << j))
+    for j, row in enumerate(rows):
+        if x & (1 << j):
+            exponent += 2*((row & x) >> (j+1)).bit_count()
+    return exponent % 4
+
+
+def compile_circuit(circuit, n=9):
+    """Combine adjacent address and phase tables, without a Clifford tableau."""
+    size = 1 << n
+    mapping, phases = list(range(size)), [0]*size
+    output = []
+
+    def flush():
+        nonlocal mapping, phases
+        if mapping != list(range(size)) or any(phases):
+            output.append(('M', tuple(mapping), tuple(phases)))
+        mapping, phases = list(range(size)), [0]*size
+
+    for event in circuit:
+        kind = event[0]
+        if kind == 'C':
+            flush()
+            need(0 <= event[1] < size and event[2] in (-1, 1), 'Literal C gate')
+            output.append(tuple(event))
+            continue
+        if kind == 'P':
+            rows = event[1]
+            need(len(rows) == n and all(0 <= r < size for r in rows), 'Address matrix')
+            image = [sum(((r & x).bit_count() % 2) << j for j, r in enumerate(rows))
+                     for x in range(size)]
+            need(sorted(image) == list(range(size)), 'Address matrix is a permutation')
+            mapping = [image[x] for x in mapping]
+        elif kind == 'X':
+            mapping = [x ^ event[1] for x in mapping]
+        elif kind in ('D', 'phase'):
+            powers = ([event[1] % 4]*size if kind == 'phase' else
+                      [phase_at(event[1], event[2], x) for x in range(size)])
+            phases = [(p+powers[x]) % 4 for p, x in zip(phases, mapping)]
+        else:
+            raise ValueError(event)
+    flush()
+    return output
+
+
+def inverse(compiled):
+    result = []
+    for event in reversed(compiled):
+        if event[0] == 'C':
+            result.append(('C', event[1], -event[2]))
+        else:
+            image, phase = event[1:]
+            back, powers = [0]*len(image), [0]*len(image)
+            for x, y in enumerate(image):
+                back[y], powers[y] = x, -phase[x] % 4
+            result.append(('M', tuple(back), tuple(powers)))
+    return result
+
+
+def normalized(state, denominator):
+    state = {x: value for x, value in state.items() if value != (0, 0)}
+    if not state:
+        return {}, 0
+    bits = 0
+    for real, imag in state.values():
+        bits |= abs(real) | abs(imag)
+    shift = min(denominator, (bits & -bits).bit_length()-1)
+    return ({x: (real >> shift, imag >> shift) for x, (real, imag) in state.items()},
+            denominator-shift)
+
+
+def run(compiled, column):
+    state, denominator = {column: (1, 0)}, 0
+    for event in compiled:
+        if event[0] == 'M':
+            image, phases = event[1:]
+            state = {image[x]: rotate(real, imag, phases[x])
+                     for x, (real, imag) in state.items()}
+        else:
+            _, v, sign = event
+            moved = {}
+            for x, (real, imag) in state.items():
+                for y, value in ((x, (real-sign*imag, imag+sign*real)),
+                                 (x ^ v, (real+sign*imag, imag-sign*real))):
+                    old = moved.get(y, (0, 0))
+                    moved[y] = (old[0]+value[0], old[1]+value[1])
+            state = {x: value for x, value in moved.items() if value != (0, 0)}
+            denominator += 1
+    return normalized(state, denominator)
+
+
+def monomial(record):
+    need(set(record) == {'matrix_rows', 'quadratic_rows', 'linear_Z4', 'offset', 'phase'},
+         'Complete monomial record')
+    return [['D', record['quadratic_rows'], record['linear_Z4']],
+            ['P', record['matrix_rows']], ['X', record['offset']], ['phase', record['phase']]]
+
+
+def recipe(record):
+    rank = record['rank']
+    need(0 <= rank <= 9, 'Native rank')
+    before = [] if record['right'] is None else monomial(record['right'])
+    return compile_circuit(before + [['C', 1 << j, 1] for j in range(rank)]
+                           + monomial(record['left']))
+
+
+def compare(left, right, label, support=None):
+    digest = sha256()
+    coefficients = 0
+    for x in range(512):
+        actual, expected = run(left, x), run(right, x)
+        need(actual == expected, label+' column '+str(x))
+        if support is not None:
+            need(len(actual[0]) == support, label+' support')
+        coefficients += len(actual[0])
+        digest.update(json.dumps([x, actual[1], sorted(actual[0].items())], separators=(',', ':')).encode())
+    return {'spatial_columns': 512, 'nonzero_coefficients': coefficients, 'digest': digest.hexdigest()}
+
+
+def gauge(n, a, b):
+    size = 1 << n
+    phase = ('M', tuple(range(size)), tuple((b & x).bit_count() % 2 for x in range(size)))
+    return [phase, ('C', a, 1), phase]
+
+
+def span(vectors):
+    values = {0}
+    for vector in vectors:
+        values |= {x ^ vector for x in values}
+    return values
+
+
+def canonical(vectors, n=9):
+    """Build the declared chart from a truth-table inverse of its address map."""
+    rank, size = len(vectors), 1 << n
+    need(len(span(vectors)) == 1 << rank, 'Independent declared frame basis')
+    if rank == n:
+        return [('C', 1 << j, 1) for j in range(n)]
+    if not rank:
+        return []
+    columns = list(vectors)
+    for vector in (1 << j for j in range(n)):
+        if vector not in span(columns):
+            columns.append(vector)
+    need(len(columns) == n, 'Complete chart basis')
+    image = []
+    for x in range(size):
+        y = 0
+        for j, column in enumerate(columns):
+            if x & (1 << j):
+                y ^= column
+        image.append(y)
+    back = [0]*size
+    for x, y in enumerate(image):
+        back[y] = x
+    inverse_columns = [back[1 << j] for j in range(n)]
+    quadratic = [(1 << j) ^ sum(((v & w).bit_count() % 2) << k
+                                for k, w in enumerate(inverse_columns))
+                 for j, v in enumerate(inverse_columns)]
+    linear = [(row >> j) & 1 for j, row in enumerate(quadratic)]
+    K = [('M', tuple(image), tuple(phase_at(quadratic, linear, y) for y in image))]
+    return inverse(K)+[('C', 1 << j, 1) for j in range(rank)]+K
+
+
+def formula(n, a, b, q, x):
+    t, u = (b & q).bit_count() % 2, (b & x).bit_count() % 2
+    q0 = q ^ (a if t else 0)
+    return {x ^ (q0 if u else 0): rotate(1, 0, (2*t-1)*u)}, 0
+
+
+def general_checks():
+    counts = {}
+    for n in range(1, 5):
+        total = 0
+        for a in range(1, 1 << n):
+            for b in range(1, 1 << n):
+                if (a & b).bit_count() % 2 != 1:
+                    continue
+                w = gauge(n, a, b)
+                for q in range(1 << n):
+                    circuit = inverse(w)+[('C', q ^ a, -1), ('C', q, 1)]+w
+                    for x in range(1 << n):
+                        need(run(circuit, x) == formula(n, a, b, q, x), 'General pair formula')
+                        total += 1
+        counts[n] = total
+    w = gauge(9, 45, 1)
+    for q in range(512):
+        circuit = inverse(w)+[('C', q ^ 45, -1), ('C', q, 1)]+w
+        for x in range(512):
+            need(run(circuit, x) == formula(9, 45, 1, q, x), 'Every local direction')
+    for x in range(512):
+        need(run(w+w, x) == ({x: (0, 1)}, 0), 'Exact square phase')
+    for v in range(512):
+        need((run(w+[('C', v, 1)], 0) == run([('C', v, 1)]+w, 0)) == (v & 1 == 0),
+             'Exact pure-C continuation criterion')
+    # This shear is not orthogonal. Covectors use the inverse transpose.
+    chart = compile_circuit([['P', [3, 2]]], 2)
+    transported = inverse(chart)+gauge(2, 1, 1)+chart
+    dual_action = gauge(2, 1, 3)
+    for x in range(4):
+        need(run(transported, x) == run(dual_action, x), 'General chart dual action')
+    need(any(run(transported, x) != run(gauge(2, 1, 1), x) for x in range(4)),
+         'Naive covector action rejects for a non-orthogonal chart')
+    # Two two-bit columns check the tensor phase separately.
+    for q in range(4):
+        tensor = []
+        wg = []
+        for shift in (0, 2):
+            local = gauge(4, 3 << shift, 1 << shift)
+            tensor += inverse(local)+[('C', (q ^ 3) << shift, -1), ('C', q << shift, 1)]+local
+            wg += local
+        for x in range(16):
+            y, phase = 0, 0
+            for shift in (0, 2):
+                value = (x >> shift) & 3
+                t, u = q & 1, value & 1
+                y |= (value ^ ((q ^ (3 if t else 0)) if u else 0)) << shift
+                phase += (2*t-1)*u
+            need(run(tensor, x) == ({y: rotate(1, 0, phase)}, 0), 'Tensor pair phase')
+            need(run(wg+wg, x) == ({x: (-1, 0)}, 0), 'Tensor square phase i squared')
+    print('general formula and tensor phases PASS', flush=True)
+    return {'all_parameters_dimensions_1_to_4': counts, 'all_nine_bit_q_columns': 512*512,
+            'tensor_width_two_columns': 64, 'pure_C_continuation_directions': 512,
+            'nonorthogonal_chart_columns': 4}
+
+
+def transition_checks():
+    counts = {}
+    for n in range(1, 5):
+        parameters = [(a, b) for a in range(1, 1 << n) for b in range(1, 1 << n)
+                      if (a & b).bit_count() % 2]
+        gauges = {(a, b): gauge(n, a, b) for a, b in parameters}
+        total = 0
+        for a1, b1 in parameters:
+            for a2, b2 in parameters:
+                op = inverse(gauges[a1, b1])+gauges[a2, b2]
+                for x in (range(1 << n) if n <= 3 else (0,)):
+                    u1, u2 = (b1 & x).bit_count() % 2, (b2 & x).bit_count() % 2
+                    if a1 == a2:
+                        delta = u1 ^ u2
+                        expected = ({x ^ (a1 if delta else 0): ((-1)**(u1*delta), 0)}, 0)
+                    else:
+                        cross = (b2 & a1).bit_count() % 2
+                        expected = ({x: ((-1)**(u1+u2), 0),
+                                     x ^ a2: ((-1)**u1, 0),
+                                     x ^ a1: ((-1)**(u2+cross), 0),
+                                     x ^ a1 ^ a2: (1, 0)}, 1)
+                    need(run(op, x) == expected, 'Exact transition formula and global phase')
+                    need(len(expected[0]) == (1 if a1 == a2 else 4), 'Transition support criterion')
+                    total += 1
+        counts[n] = total
+    print('general transition formula and rank obstruction PASS', flush=True)
+    return {'dimensions_1_to_3_all_columns_and_dimension_4_zero_column': counts,
+            'same_radical_rank': 0, 'distinct_radicals_rank': 2}
+
+
+def source_binding(packet, h6, signed, core, geometry):
+    labels = next(iter(core['providers'].values()))['canonical']['ports']
+    need(all(p['canonical']['ports'] == labels for p in core['providers'].values()), 'Provider labels')
+    large = signed['large_ports']
+    need(sorted(row['port'] for row in packet['monomials']) == sorted(large), 'All actual centre ports')
+    need([p for p, q in enumerate(labels) if (q & 45).bit_count() % 2 == 0] == sorted(large),
+         'Exactly the actual radical-perpendicular ports')
+    need(sorted(tuple(row['ports']) for row in packet['left_coded_pair_plane_tails']) ==
+         sorted(tuple(row['ports']) for row in geometry['pair_edges']), 'Actual pair planes')
+    source_rows = packet['left_coded_source_tails']
+    target_rows = {row['port']: row for row in packet['left_coded_tails']}
+    routes = {}
+    for provider, record in h6['providers'].items():
+        for direction, word in record.items():
+            need(word['frames'][word['carry_frame']] == [45], 'Actual canonical carry frame')
+            need(len(word['centre_frames']) == 8, 'Eight source frames')
+            for j, frame in enumerate(word['centre_frames']):
+                need(span(word['frames'][frame]) == span(source_rows[j]['frame_basis']),
+                     'Actual centre subspace binding')
+            flags = [False]*640
+            changed = Counter()
+            endpoint = {(r['role'], r['port']): r for r in word['endpoint_adapters']}
+            checks = []
+            for event in word['events']:
+                if event[0] == 'native':
+                    _, field, before, after, rank, key = event
+                    need(not flags[field], 'No later native call on a coded source')
+                    if field in large and after == 1:
+                        j = word['centre_frames'].index(before)
+                        need(rank == 2, 'Old source exit rank')
+                        flags[field] = True
+                        changed['source_2_to_1'] += 1
+                    elif 112 <= field < 224 and field-112 in large and before == word['carry_frame']:
+                        p = field-112
+                        need(after == endpoint['target', p]['frame'] and rank == 7,
+                             'Old target exit and endpoint adapter')
+                        flags[field] = True
+                        changed['target_7_to_6'] += 1
+                        checks.append((p, word['native_recipes'][key], endpoint['target', p]))
+                elif event[0] == 'scalar':
+                    op = event[1]
+                    if op[0] in ('add', 'copy'):
+                        need(flags[op[1]] == flags[op[2]], 'Common W commutes with remaining scalar graph')
+                    elif op[0] == 'clear':
+                        need(not flags[op[1]], 'No coded field is cleared')
+                    else:
+                        need(op[0] == 'scale', 'Known scalar operation')
+                elif event[0] == 'set_empty_frame':
+                    need(not flags[event[1]], 'No coded frame reset')
+                else:
+                    raise ValueError(event)
+            need(changed == {'source_2_to_1': 48, 'target_7_to_6': 48}, 'All changed exits')
+            need({i for i, flag in enumerate(flags) if flag} == set(large) | {112+p for p in large},
+                 'Exactly two coded centre banks, with helpers unchanged')
+            routes[provider+'/'+direction] = {'changed_exits': dict(changed), 'coded_fields': 96,
+                                              'coded_borrowed_fields': 0,
+                                              'literal_source_basis_equal': [word['frames'][f] == source_rows[j]['frame_basis']
+                                                                             for j, f in enumerate(word['centre_frames'])]}
+            if provider == 'base' and direction == 'forward':
+                routes['_target_checks'] = checks
+                routes['_carry_recipe'] = word['native_recipes']['0:'+str(word['carry_frame'])]
+                routes['_source_old'] = [word['native_recipes'][str(frame)+':1']
+                                         for frame in word['centre_frames']]
+    return labels, routes
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('output', type=Path)
+    args = parser.parse_args()
+    args.output.mkdir(parents=True, exist_ok=False)
+    for name, pin in PINS.items():
+        read(SOURCE/name, pin)
+    read(SOURCE/'FREEZE.json', '3c1669513029238abf181d4137b7a25efd4113c951ac78301a9da2c7e9df6ec1')
+    packet = json.loads(read(SOURCE/'GAUGE-PROGRAMS.json', PINS['GAUGE-PROGRAMS.json']))
+    receipt = json.loads(read(SOURCE/'CHECKS.json', PINS['CHECKS.json']))
+    need(receipt['program_sha256'] == PINS['GAUGE-PROGRAMS.json'], 'Receipt packet binding')
+    dependencies = {}
+    for name, (kind, pin) in packet['pins'].items():
+        raw = read(LANES/name, pin, kind == 'gzip')
+        if name.endswith(('.json', '.gz')):
+            dependencies[name] = json.loads(raw)
+    frozen(H6, 'a1b0ec7bbead298e1484199b15896e2b5b688d53b3f2f5d9e0d73c29bea04a80')
+    h6 = json.loads(read(H6/'RADICAL-CENTRE-PROGRAM.json.gz',
+                        '25ddd47640a98e61b5edf5f36e2aad9867eab00e072545322bb36e4d63c561ea', True))
+    h6_binding_pins = {
+        'H6-SOURCE-PROGRAMS.json': '4eb739a9191aaba6b8c15a2c10868ceba80c4596000eca50c8f68f29c527e569',
+        'bind_h6_sources.py': '150453ca6e3bd75bdfab1805def824c44c34e83037b6996ff355d493de26686b',
+        'H6-SOURCE-CHECKS.json': 'cb5a9d3b4f83b4718ec70bdd5473d55cc25d3c3078d696f6f6504862c6443e7e',
+        'H6-SOURCE-BINDING.md': '7a3a9313f6c8b01dc5a2dc2aa156abb109ad624d25cf92f9aa0dc0b57d11d783',
+    }
+    for name, pin in h6_binding_pins.items():
+        read(SOURCE/name, pin)
+    actual_sources = json.loads(read(SOURCE/'H6-SOURCE-PROGRAMS.json', h6_binding_pins['H6-SOURCE-PROGRAMS.json']))
+    read(SOURCE/'H6-SOURCE-FREEZE.json', 'cf436b1016f7d9c5b933eb818098ff0339436fec20d0ed497045fc992e6ee0b5')
+    matching_freeze = json.loads(read(SOURCE/'MATCHING-EXITS-FREEZE.json',
+                                      '9d5e63259b861bf69ac5e00b2ec9ad3158aec3edac4ce54e08fcf33249f137be'))
+    for name, pin in matching_freeze['pins'].items():
+        read(SOURCE/name, pin)
+    matching = json.loads(read(SOURCE/'MATCHING-EXITS-PROGRAMS.json',
+                               '89ce6c4b426498e2fb9e7dfce9a4a192e3183644fef457c5b357baf63b9c6276'))
+    signed = dependencies['controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz']
+    core = dependencies['new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz']
+    geometry = dependencies['controller-followthrough-20261017/partial-orthogonal/SYMMETRIC-FAMILY.json']
+    labels, routes = source_binding(packet, h6, signed, core, geometry)
+    results = {'general': general_checks(), 'transitions': transition_checks()}
+    W, Z = compile_circuit(packet['W']['circuit']), compile_circuit(packet['canonical_Z'])
+    need(Z == canonical([45]), 'Independent construction of the exact canonical Z')
+    FULL = [('C', 1 << j, 1) for j in range(9)]
+    need(packet['n'] == 9 and packet['a'] == 45 and packet['b'] == 1, 'Actual gauge parameters')
+    results['W'] = compare(W, gauge(9, 45, 1), 'Literal W', 2)
+    need(packet['W']['native_recipe']['rank'] == 1, 'Native W rank')
+    results['W_recipe'] = compare(recipe(packet['W']['native_recipe']), W, 'W native recipe', 2)
+    results['canonical_carry_binding'] = compare(recipe(routes.pop('_carry_recipe')), Z, 'Actual canonical Z', 2)
+    results['alignments'] = {}
+    for name, intended in [('W_Z_inverse', inverse(Z)+W), ('Z_inverse_W', W+inverse(Z))]:
+        row = packet['alignments'][name]
+        actual = compile_circuit(monomial(row['record']))
+        need(actual == compile_circuit(row['circuit']), 'Serialized alignment circuit')
+        results['alignments'][name] = compare(actual, intended, name, 1)
+    results['pairs'] = []
+    for row in packet['monomials']:
+        p, q = row['port'], row['q']
+        need(q == labels[p] and row['q_partner'] == q ^ 45, 'Actual pair labels')
+        t, q0 = q & 1, q ^ (45 if q & 1 else 0)
+        need(row['q0'] == q0 and row['phase_coefficient'] == 2*t-1, 'Formula fields')
+        need(row['matrix_rows'] == [(1 << j) ^ (1 if q0 >> j & 1 else 0) for j in range(9)],
+             'Formula address matrix')
+        canonical_pair = inverse(Z)+[('C', q ^ 45, -1), ('C', q, 1)]+Z
+        results['pairs'].append({'port': p, **compare(compile_circuit(monomial(row['canonical_record'])),
+                                                    canonical_pair, 'Canonical pair '+str(p), 1)})
+    print('canonical gauge and all actual pairs PASS', flush=True)
+    results['target_tails'] = []
+    old_targets = {p: (old, adapter) for p, old, adapter in routes.pop('_target_checks')}
+    for row in packet['left_coded_tails']:
+        p, q = row['port'], row['q']
+        need(q == labels[p] and row['recipe']['rank'] == row['left_coded_rank'] == 6 and
+             row['right_coded_rank'] == 8, 'Target rank declarations')
+        expected = inverse(Z)+[('C', q, -1)]+FULL+W
+        actual = recipe(row['recipe'])
+        need(actual == compile_circuit(row['circuit']), 'Native target serialization')
+        entry = {'port': p, **compare(actual, expected, 'Left target '+str(p), 64)}
+        right = inverse(Z)+W+[('C', q, -1)]+FULL
+        for x in range(512):
+            need(len(run(right, x)[0]) == 256, 'Right-coded rank eight on every column')
+        old, adapter = old_targets[p]
+        intended_old = inverse(Z)+[('C', q, -1)]+FULL
+        entry['old_endpoint_binding'] = compare(recipe(old)+inverse(recipe(adapter)), intended_old,
+                                                'Actual old target exit '+str(p), 128)
+        need(run(actual, 0) != run(right, 0), 'Wrong W order rejects')
+        need(run(actual+[('M', tuple(range(512)), (2,)*512)], 0) != run(expected, 0),
+             'Wrong global sign rejects')
+        results['target_tails'].append(entry)
+        if len(results['target_tails']) % 8 == 0:
+            print('target tails', len(results['target_tails']), 'PASS', flush=True)
+    results['source_tails'] = []
+    old_sources = routes.pop('_source_old')
+    for row, old in zip(packet['left_coded_source_tails'], old_sources):
+        source = compile_circuit(row['source_frame'])
+        need(source == canonical(row['frame_basis']), 'Source frame and exact ordered basis')
+        need(row['recipe']['rank'] == row['new_rank'] == 1 and row['old_rank'] == 2,
+             'Source rank declarations')
+        need(recipe(row['recipe']) == compile_circuit(row['circuit']), 'Native source serialization')
+        entry = {'vertex': row['vertex'], **compare(recipe(row['recipe']), inverse(source)+FULL+W,
+                                                   'Source tail '+str(row['vertex']), 2)}
+        actual_old, claimed_old = recipe(old), inverse(source)+FULL
+        mismatches = []
+        for x in range(512):
+            if run(actual_old, x) != run(claimed_old, x):
+                mismatches.append(x)
+            need(len(run(actual_old+W, x)[0]) == 2, 'Actual coded H6 source rank one')
+        entry['h6_operator_binding'] = {'equal_columns': 512-len(mismatches),
+                                       'first_mismatch': next(iter(mismatches), None),
+                                       'actual_W_completed_support': 2}
+        results['source_tails'].append(entry)
+    results['pair_plane_tails'] = []
+    for row in packet['left_coded_pair_plane_tails']:
+        p, r = row['ports']
+        need(labels[p] ^ labels[r] == 45 and row['recipe']['rank'] == row['new_rank'] == 6 and
+             row['old_rank'] == 7, 'Actual pair plane and ranks')
+        source = compile_circuit(row['source_frame'])
+        need(source == canonical(row['frame_basis']), 'Pair plane and exact ordered basis')
+        need(recipe(row['recipe']) == compile_circuit(row['circuit']), 'Native plane serialization')
+        entry = {'ports': [p, r], **compare(recipe(row['recipe']), inverse(source)+FULL+W,
+                                          'Pair plane '+str(p), 64)}
+        for x in range(512):
+            need(len(run(inverse(source)+FULL, x)[0]) == 128, 'Old pair-plane rank seven')
+        results['pair_plane_tails'].append(entry)
+    print('source tails and pair planes PASS', flush=True)
+    results['actual_h6_sources'] = []
+    need(len(actual_sources['recipes']) == 16, 'Both actual providers and eight source vertices')
+    seen = set()
+    for row in actual_sources['recipes']:
+        provider, j = row['provider'], row['vertex']
+        need((provider, j) not in seen, 'Unique actual source recipe')
+        seen.add((provider, j))
+        word = h6['providers'][provider]['forward']
+        frame = word['centre_frames'][j]
+        need(row['frame_id'] == frame and row['frame_basis'] == word['frames'][frame],
+             'Exact actual H6 frame')
+        need(compile_circuit(row['frame_circuit']) == canonical(row['frame_basis']),
+             'Independent actual source canonical frame')
+        need(row['recipe']['rank'] == 1 and recipe(row['recipe']) == compile_circuit(row['circuit']),
+             'Actual one-child source recipe')
+        for direction in ('forward', 'backward'):
+            other = h6['providers'][provider][direction]
+            need(other['frames'][other['centre_frames'][j]] == row['frame_basis'] and
+                 other['native_recipes'][str(frame)+':1'] == word['native_recipes'][str(frame)+':1'],
+                 'Both orientation source records are identical')
+        old = recipe(word['native_recipes'][str(frame)+':1'])
+        results['actual_h6_sources'].append({'provider': provider, 'vertex': j,
+                                             **compare(recipe(row['recipe']), old+W, 'Actual source binding', 2)})
+    print('actual H6 source binding PASS', flush=True)
+    need(matching['gauge_freeze_sha256'] == '3c1669513029238abf181d4137b7a25efd4113c951ac78301a9da2c7e9df6ec1',
+         'Matching gauge dependency')
+    need(matching['source_pins'] == packet['pins'], 'Same matching source pins')
+    results['matching_targets'] = []
+    need(len(matching['target_exits']) == 48, 'All matching target exits')
+    for row in matching['target_exits']:
+        p, pair = row['port'], row['pair']
+        need(p in pair and tuple(pair) in {tuple(e['ports']) for e in geometry['pair_edges']},
+             'Actual matching pair and target')
+        perpendicular = {x for x in range(512) if all((x & labels[z]).bit_count() % 2 == 0 for z in pair)}
+        need(span(row['input_frame_basis']) == perpendicular and len(row['input_frame_basis']) == 7,
+             'Exact pair-perpendicular subspace')
+        source = compile_circuit(row['input_frame'])
+        need(source == canonical(row['input_frame_basis']), 'Literal matching input frame')
+        expected = inverse(source)+[('C', labels[p], -1)]+FULL+W
+        actual = compile_circuit(monomial(row['record']))
+        need(actual == compile_circuit(row['circuit']) and row['new_rank'] == 0 and row['old_rank'] == 1,
+             'Matching monomial record')
+        results['matching_targets'].append({'port': p, **compare(actual, expected, 'Matching target', 1)})
+        need(len(run(expected+inverse(W), 0)[0]) == 2, 'Old matching target rank one')
+    orders = [[] for _ in range(8)]
+    for edge in geometry['pair_edges']:
+        for vertex, port in zip(edge['vertices'], edge['ports']):
+            orders[vertex].append(port)
+    need(all(len(order) == 6 for order in orders), 'Actual six-carrier cyclic orders')
+    results['cyclic_sources'] = []
+    need(len(matching['cyclic_source_exits']) == 48, 'All cyclic source exits')
+    for row in matching['cyclic_source_exits']:
+        vertex, p = row['vertex'], row['carrier']
+        order = orders[vertex]
+        index = order.index(p)
+        five = [order[(index+j) % 6] for j in range(5)]
+        need(row['cyclic_order'] == order and row['five_ports'] == five, 'Exact cyclic source order')
+        need(span(row['input_frame_basis']) == span([45]+[labels[q] for q in five]) and
+             len(row['input_frame_basis']) == 6, 'Actual cyclic source subspace')
+        source = compile_circuit(row['input_frame'])
+        need(source == canonical(row['input_frame_basis']), 'Literal cyclic input frame')
+        actual = recipe(row['recipe'])
+        need(actual == compile_circuit(row['circuit']) and row['new_rank'] == row['recipe']['rank'] == 2 and
+             row['old_rank'] == 3, 'Cyclic native record')
+        results['cyclic_sources'].append({'vertex': vertex, 'carrier': p,
+                                         **compare(actual, inverse(source)+FULL+W, 'Cyclic source', 4)})
+        need(len(run(inverse(source)+FULL, 0)[0]) == 8, 'Old cyclic source rank three')
+    print('matching and cyclic exit phases PASS', flush=True)
+    control = receipt['width_two_control']
+    q, chars = control['q'], control['characters']
+    need(len(chars) == 2 and all((45 & x).bit_count() % 2 == 1 for x in chars), 'Width-two characters')
+    exponent = sum(((q & x).bit_count() % 2)-(((q ^ 45) & x).bit_count() % 2) for x in chars) % 4
+    need(exponent == 2 and sum((45 & x).bit_count() % 2 for x in chars) % 2 == 0,
+         'Simultaneous translation shortcut rejects')
+    old_profile = Counter()
+    for event in h6['providers']['base']['forward']['events']:
+        if event[0] == 'native':
+            old_profile[event[4]] += 1
+    new_profile = old_profile.copy()
+    new_profile[2] -= 48; new_profile[1] += 48
+    new_profile[7] -= 48; new_profile[6] += 48
+    results.update(status='PASS', routes=routes, source_pins=PINS,
+                   h6_route_delta={'old_profile': dict(sorted(old_profile.items())),
+                                   'new_profile': {k:v for k,v in sorted(new_profile.items()) if v},
+                                   'old_mass': sum(k*v for k,v in old_profile.items()),
+                                   'new_mass': sum(k*v for k,v in new_profile.items()),
+                                   'children': sum(new_profile.values()), 'scalar_graph_delta': 0,
+                                   'scope': 'The target replacement and corrected source recipes are bound to H6. Replace each selected target native exit together with its inverse endpoint adapter. The structural replacement gives W on 96 centre-bank outputs. Native side-map execution and complete supplier costs remain open.'},
+                   negative_controls={'wrong_W_order':48, 'wrong_global_sign':48,
+                                      'tensor_simultaneous_translation':1},
+                   phase_method='Sparse exact Gaussian columns; no producer or Clifford compiler import.')
+    for name, value in [('REVIEW.json', results), ('INPUTS.json', INPUTS)]:
+        (args.output/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print('PASS_ISOTROPIC_PAIR_INDEPENDENT_REVIEW', flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..786ab73ff4
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "REPRODUCTION.json": "5fe7900ca1791738790a663c882ea411d8e3f41cdb9f9b7f5d23f06deffbf939",
+    "REVIEW.md": "f6ddd5a2581319ac5b07d402384c4847bce88f10505cca926c9287e838e1760f",
+    "check.py": "c2a8f93e2c1cf23f8fc279e6dc87d6bd923e60c438531fe1770b0992d1dfdb7d",
+    "normal/INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5",
+    "normal/REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f",
+    "optimized/INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5",
+    "optimized/REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "Both local arbitrary-record provider words, exact phases, same-reader restriction, and complete local invoice. No routed past-reader query or complete supplier claim.",
+  "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..e94c51f785
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5",
+    "REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f"
+  },
+  "source_files_rechecked": 35,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..5a1315e905
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md
@@ -0,0 +1,199 @@
+# Independent review of the local line-entry reuse interface
+
+The frozen word accepts sixteen arbitrary independent records in
+positive line frames and preserves them as additive baselines.
+Both providers pass the complete local map, frame, phase, and
+invoice checks. No material defect was found.
+
+This is local reuse with the same reader. It is separate from the
+query for a reader kept from an earlier routed stage.
+
+## Frozen inputs and method
+
+The producer
+[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json)
+has SHA256
+`a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60`.
+The decompressed payload SHA256 is
+`efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110`.
+
+The accepted formation
+[review](../row-capture-native-review-20261020/FREEZE.json)
+has SHA256
+`488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532`.
+Its exact source payload has decompressed SHA256
+`7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2`.
+
+The checker imports only the pinned independent review helper and
+its integer Gaussian phase interpreter. It imports no producer
+code. It checks the new word by reverse output-column propagation
+and a separate forward prefix-row pass. It compares exact spatial
+columns for every new native recipe.
+
+## Exact arbitrary-record contract
+
+Keep the fixed selected set P and the actual response E from the
+formation packet. Put \(W=V_P^{-1}V\), and let C have rows W on P
+and identity rows elsewhere. For independent inputs x, ordinary
+target values \(y_R\), and selected records \(z_P\), the physical
+input is
+
+\[
+X_p=Q_px_p,\qquad
+Y_p=y_p\quad(p\in R),\qquad
+Y_p=Q_pz_p\quad(p\in P).
+\]
+
+The physical output is
+
+\[
+X'_p=F_9x_p,\qquad
+Y'_p=F_9q_p(y+Ex)_p\quad(p\in R),\qquad
+Y'_p=F_9[z_p+(CEx)_p]\quad(p\in P).
+\]
+
+The ordinary formula uses only \(y_R\); no selected baseline y is
+needed there. All sixteen z records are independent of each other,
+of x, and of every other field. The word does not form or decode z.
+
+## Literal order and field checks
+
+The word contains no row precode. Its event list is exactly:
+
+1. The 2390 retained core events from the accepted formation word.
+2. Sixteen selected line-to-FULL native calls.
+3. The 248 events in the accepted late-query word.
+
+Every retained event has its original bytes and order. No retained
+event reads or writes a selected target. The selected records
+therefore remain unchanged until their line-to-FULL calls.
+
+The new input frame on each selected target is exactly the source
+line frame for that port. Its input adapter is the accepted source
+adapter for that same port, with an explicit binding to the target
+field. All 128 input view fields are distinct.
+
+Every source and selected target is FULL before the late query.
+Every scalar addition has the same actual source and target frame.
+The final declarations are identical to those of the formation
+word. A selected input declared as I is rejected.
+
+Both providers pass all 640 arbitrary input columns. The column
+for each selected record is exactly the unit column for that
+record's output. All 416 fields outside the two data banks retain
+their arbitrary values. No event accesses those fields, and no
+new or owned field is introduced.
+
+The forward row pass agrees with the reverse-column result. An
+omitted late query is rejected.
+
+## Exact phases
+
+All 1447 retained native recipes are byte equal to the accepted
+formation records. The 112 source input adapters and the 96
+outgoing ordinary adapters are also exact inherited records.
+The sixteen additional input adapters use the accepted source
+records with their explicit new field bindings.
+
+For each selected port p, the new recipe must satisfy
+
+\[
+N_p\Gamma_{\mathrm{line}(p)}=F_9.
+\]
+
+The independent interpreter checks this exact identity on all
+512 spatial input columns. There are sixteen new recipes, hence
+8192 complete spatial columns and 4194304 nonzero coefficients.
+The checks include global phase. A wrong global phase is rejected.
+
+Combining this identity with the accepted input-adapter identity
+gives the physical operation \(Q_pz_p\mapsto F_9z_p\).
+No Q operator is moved through the reader or the response.
+The exact spatial identities tensor to all widths admitted by
+the retained native primitive contract.
+
+These H8 recipes retain their two generic monomial maps. The
+identity-map refinement for a complete F9 call does not apply here.
+
+## Local invoice and precision scope
+
+Each provider has the exact profile
+
+```text
+1392 H1 + 64 H2 + 48 H3 + 16 H8.
+```
+
+The complete local counts are:
+
+| Item | Count |
+| --- | ---: |
+| Native children | 1520 |
+| Native mass | 1792 |
+| Old real scalar units | 9880 |
+| Retained-core scalar units | 6456 |
+| Late-query scalar units | 3424 |
+| Input monomial views | 128 |
+| Output monomial views | 96 |
+| Native side-map upper bound | 3040 |
+| New or private fields | 0 |
+| Odd-arithmetic scans | 0 |
+
+The exact content row one-norm at emitted operation boundaries
+is at most 112. The additional content binary denominator height
+is one. These bounds include the full retained word and query.
+They do not bound primitive internals, recursive-child numerical
+guards, or accumulated roundoff.
+
+The sixteen calls remain rank-eight calls. Their exact recursive
+sizes, the owner-view work, and the complete caller must be priced
+before any complete supplier cost can be claimed.
+
+## The reader condition is necessary
+
+If z stores \(Wy\), the selected output stores \(W(y+Ex)\).
+Thus the local update preserves that same reader.
+
+For a different stored reader L, the required update is \(LEx\).
+The emitted update \(WEx\) is equal to it on all source inputs if
+and only if
+
+\[
+(L-W)E=0.
+\]
+
+The checker verifies both exact inverse orders for this actual E.
+Therefore that condition is equivalent to \(L=W\). More generally,
+the same implication holds for ordered operators when E has an
+inverse. It does not require any commutation of L, W, or E.
+
+Consequently, a reader from an earlier routed stage needs its
+actual ordered query \(L_sE_t\), unless equality of the transported
+reader with the current local reader has been proved. The separate
+bridge-access construction supplies such queries under its own
+premises and invoice. The 9880 local figure is not that invoice.
+
+This review proves the local line-entry interface. It does not
+prove a complete routed reuse, a final decoder, a recursive host,
+a complete supplier, or a kappa improvement.
+
+## Reproduction and credit
+
+Run from the workspace root:
+
+```text
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized
+```
+
+The required final line is
+`PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE`.
+The reproduction receipt records the final byte comparison and
+source hash checks.
+Both runs completed with the required result. Their result and
+input receipts are byte identical. All 35 consumed source files
+were rechecked and are unchanged.
+
+The producer proof retains the controller, cyclic-family, and
+formation-work credit. AI assistance was used. No PR, push, commit,
+or publication is authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py
new file mode 100644
index 0000000000..0419f9c41f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py
@@ -0,0 +1,200 @@
+#!/usr/bin/env python3
+"""Check the exact local interface for arbitrary line-encoded records."""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+PREVIOUS = HERE.parent/'row-capture-native-review-20261020'
+HELPER = PREVIOUS/'check.py'
+HELPER_PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84'
+if sha256(HELPER.read_bytes()).hexdigest() != HELPER_PIN:
+    raise ValueError('Independent review helper pin')
+spec = importlib.util.spec_from_file_location('independent_row_review', HELPER)
+review = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(review)
+review.read(HELPER, HELPER_PIN)
+need, read, frozen = review.need, review.read, review.frozen
+P = review.P
+SOURCE = review.NATIVE
+
+
+def trace(word):
+    current = list(word['start'])
+    profile, used = Counter(), set()
+    for i, event in enumerate(word['events']):
+        if i == word['stage_ranges']['late_query'][0]:
+            need(all(current[p] == 1 for p in range(112)) and
+                 all(current[112+p] == 1 for p in P), 'Complete common-FULL query cut')
+        if event[0] == 'native':
+            _, field, before, after, rank, key = event
+            need(0 <= field < 224 and current[field] == before, 'Native field and input frame')
+            need(word['native_recipes'][key]['rank'] == rank, 'Native occurrence rank')
+            current[field] = after
+            profile[rank] += 1
+            used.add(key)
+        else:
+            need(event[0] == 'scalar', 'Event opcode')
+            _, scalar, frame = event
+            op, target, origin, _ = scalar
+            need(0 <= target < 224 and current[target] == frame, 'Scalar target frame')
+            if op == 'add':
+                need(0 <= origin < 224 and current[origin] == frame and target != origin,
+                     'Scalar source frame')
+            else:
+                need(op == 'scale' and origin is None, 'Scale grammar')
+    need(current == word['final'], 'Exact complete final frames')
+    need(used == set(word['native_recipes']), 'Every stored native recipe is used')
+    return profile
+
+
+def check_word(word, old, e, ce):
+    need(word['frames'] == old['frames'] and word['final'] == old['final'],
+         'Exact inherited frame geometry and output declarations')
+    expected_start = list(old['start'])
+    for p in P:
+        expected_start[112+p] = old['start'][p]
+        need(len(word['frames'][expected_start[112+p]]) == 1,
+             'Selected canonical line frame')
+    need(word['start'] == expected_start, 'Only selected input frames change')
+    start, end = old['stage_ranges']['retained_core']
+    kept = old['events'][start:end]
+    start, end = old['stage_ranges']['late_query']
+    query = old['events'][start:end]
+    progress = [['native', 112+p, old['start'][p], 1, 8, 'capture-line:'+str(p)] for p in P]
+    need(word['events'] == kept+progress+query, 'Exact complete local reuse order')
+    need(word['retained_original_event_indices'] == old['retained_original_event_indices'],
+         'Same retained raw events')
+    need(word['stage_ranges'] == {
+        'precode': [0, 0], 'retained_core': [0, 2390],
+        'selected_line_progress': [2390, 2406], 'late_query': [2406, 2654]},
+        'Exact reuse stage boundaries')
+    selected = {112+p for p in P}
+    for event in kept:
+        if event[0] == 'scalar':
+            need(event[1][1] not in selected and
+                 (event[1][0] != 'add' or event[1][2] not in selected),
+                 'Retained core does not access selected records')
+        else:
+            need(event[1] not in selected, 'Retained native core does not access selected records')
+    inherited = set(old['native_recipes'])-{'capture-full'}
+    fresh = {'capture-line:'+str(p) for p in P}
+    need(set(word['native_recipes']) == inherited|fresh, 'Exact native recipe set')
+    for key in inherited:
+        need(word['native_recipes'][key] == old['native_recipes'][key],
+             'Byte-equal inherited native recipe')
+    need(word['output_views'] == old['output_views'], 'All96 exact outgoing views')
+    source_views = {r['port']: r for r in old['input_views']}
+    inputs = [{**r, 'field': r['port']} for r in old['input_views']]
+    inputs += [{**source_views[p], 'role': 'selected_target', 'field': 112+p,
+                'source_entry_port': p} for p in P]
+    need(word['input_views'] == inputs, 'Copied source adapters bound to actual target fields')
+    need(len({r['field'] for r in inputs}) == 128, 'Distinct charged input view fields')
+    count = trace(word)
+    need(count == {1: 1392, 2: 64, 3: 48, 8: 16}, 'Complete reuse native profile')
+    scalars = [event[1] for event in word['events'] if event[0] == 'scalar']
+    expected = review.unit(640)
+    for p in range(112):
+        review.add(expected[112+p], ce[p] if p in P else e[p])
+    columns = review.reverse(scalars, 640)
+    need(columns == review.transpose(expected, 640), 'All640 arbitrary input columns')
+    for p in P:
+        need(columns[112+p] == {112+p: F(1)}, 'Independent selected record preserved exactly')
+    actual, bound = review.prefix(scalars, 640)
+    need(actual == expected and actual[224:] == review.unit(640)[224:],
+         'Separate forward map and arbitrary outside fields')
+    need(bound == {'row_one_norm': '112', 'binary_height': 1}, 'Complete local content bounds')
+    need(review.price(scalars) == 9880, 'Complete reuse scalar invoice')
+    need(review.price([e[1] for e in kept if e[0] == 'scalar']) == 6456 and
+         review.price([e[1] for e in query if e[0] == 'scalar']) == 3424, 'Both scalar stages')
+    bad = dict(word)
+    bad['start'] = list(word['start'])
+    bad['start'][112+P[0]] = 0
+    try:
+        trace(bad)
+    except ValueError:
+        pass
+    else:
+        raise ValueError('Wrong selected I-frame control')
+    need(review.reverse([e[1] for e in kept if e[0] == 'scalar'], 640) != columns,
+         'Omitted late-query control')
+    return {
+        'input_columns': 640, 'arbitrary_selected_records': 16, 'unchanged_arbitrary_roles': 416,
+        'events': len(word['events']), 'native_profile': dict(sorted(count.items())),
+        'native_children': sum(count.values()), 'native_mass': sum(k*v for k, v in count.items()),
+        'real_scalar_primitives': 9880, 'retained_scalar_primitives': 6456,
+        'late_query_scalar_primitives': 3424, 'input_views': 128, 'output_views': 96,
+        'native_side_maps_upper_bound': 3040, 'new_fields': 0, 'private_fields': 0,
+        'odd_scans': 0, 'growth': bound, 'inherited_distinct_recipes': len(inherited),
+        'fresh_distinct_recipes': len(fresh),
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', required=True, type=Path)
+    args = parser.parse_args()
+    frozen(PREVIOUS, 'FREEZE.json',
+           '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532')
+    frozen(SOURCE, 'LINE-ENTRY-REUSE-FREEZE.json',
+           'a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60')
+    original = json.loads(read(SOURCE/'run-normal/PRODUCTIVE-CAPTURE.json.gz',
+                               '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', True))
+    payload = json.loads(read(SOURCE/'reuse-normal/LINE-ENTRY-REUSE.json.gz',
+                              'efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110', True))
+    need(payload['source_decompressed_sha256'] ==
+         '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2',
+         'Exact formation source')
+    need(payload['schema'] == 'productive-sixteen-line-entry-reuse-v1', 'Reuse schema')
+    need(payload['selected_ports'] == P and payload['ports'] == original['ports'] and
+         payload['ordinary_ports'] == original['ordinary_ports'], 'Actual ordered ports')
+    need(payload['response'] == original['response'] and
+         payload['selected_query_response'] == original['captured_response'],
+         'Same local reader response')
+    need(set(payload['providers']) == {'base', 'extra'} and
+         payload['providers']['base'] == payload['providers']['extra'], 'Both exact providers')
+    e, ce = review.rows(payload['response']), review.rows(payload['selected_query_response'])
+    reports = {name: check_word(word, original['providers'][name], e, ce)
+               for name, word in payload['providers'].items()}
+    phase = review.inherit()
+    word = payload['providers']['base']
+    full = [('C', 1 << j, 1) for j in range(9)]
+    checks = []
+    for p in P:
+        frame = word['start'][112+p]
+        native = phase.recipe(word['native_recipes']['capture-line:'+str(p)])
+        result = phase.compare(phase.canonical(word['frames'][frame])+native,
+                               full, 'Exact selected line progress '+str(p), 512)
+        checks.append({'port': p, 'frame': frame, **result})
+    first = P[0]
+    frame = word['start'][112+first]
+    bad = phase.canonical(word['frames'][frame])+phase.recipe(
+        word['native_recipes']['capture-line:'+str(first)])+phase.compile_circuit([['phase', 1]])
+    need(phase.run(bad, 0) != phase.run(full, 0), 'Wrong global phase control')
+    raw = json.loads(read(review.RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz',
+                          'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True))
+    inverse = review.rows(raw['model']['response_inverse'])
+    need(review.mul(e, inverse) == review.unit(112) and
+         review.mul(inverse, e) == review.unit(112), 'Actual invertible response')
+    report = {
+        'status': 'PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE',
+        'literal_words': reports, 'fresh_phase_checks': checks,
+        'exact_response_inverse_orders': True,
+        'negative_controls': ['wrong selected I input frame', 'omitted late query', 'wrong global phase'],
+        'reader_scope': 'The required update for a stored reader L is L E. Since E is invertible, equality with W E on all inputs requires L=W. No routed reader change is priced here.',
+        'scope': 'Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.',
+    }
+    args.out.mkdir(parents=True, exist_ok=True)
+    for name, value in [('REVIEW.json', report), ('INPUTS.json', review.INPUTS)]:
+        (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print(report['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..668725b9d5
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json
@@ -0,0 +1,110 @@
+{
+  "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": {
+    "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json": {
+    "sha256": "a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE.md": {
+    "sha256": "f2ceaf4ba246a20226aec105145d29c2442bd58681256487439b04064815aa2c"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_line_entry_reuse.py": {
+    "sha256": "c8a799f29b6244190e2880b44206a240b8cd16427661c3cc7aff9f1905bdec62"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/CHECKS.json": {
+    "sha256": "cfb3da51fb929a1ffa35b6a1cb973426431d98acba355cf2d6b606bf32450048"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz": {
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+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/INPUTS.json": {
+    "sha256": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/REVIEW.json": {
+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md": {
+    "sha256": "74bfa14362b8a704d409cb3995fe645173e99205653528bcf6b47f62de7455a1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json": {
+    "sha256": "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json": {
+    "sha256": "9525e5e1871d60a01c8acd222944abe6edab71f9d5448410265859dcece6901f"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md": {
+    "sha256": "39cb0df65e81f92854d0238d9023eaa092205bdce8e3b81724c2e4d19a3ef4f1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/check.py": {
+    "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json": {
+    "sha256": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/normal/REVIEW.json": {
+    "sha256": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/optimized/INPUTS.json": {
+    "sha256": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/optimized/REVIEW.json": {
+    "sha256": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/REVIEW.json
new file mode 100644
index 0000000000..9d50305f8d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized/REVIEW.json
@@ -0,0 +1,185 @@
+{
+  "exact_response_inverse_orders": true,
+  "fresh_phase_checks": [
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 2,
+      "nonzero_coefficients": 262144,
+      "port": 0,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 29,
+      "nonzero_coefficients": 262144,
+      "port": 27,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 38,
+      "nonzero_coefficients": 262144,
+      "port": 36,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 113,
+      "nonzero_coefficients": 262144,
+      "port": 111,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 22,
+      "nonzero_coefficients": 262144,
+      "port": 20,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 9,
+      "nonzero_coefficients": 262144,
+      "port": 7,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 59,
+      "nonzero_coefficients": 262144,
+      "port": 57,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 48,
+      "nonzero_coefficients": 262144,
+      "port": 46,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 3,
+      "nonzero_coefficients": 262144,
+      "port": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 5,
+      "nonzero_coefficients": 262144,
+      "port": 3,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 8,
+      "nonzero_coefficients": 262144,
+      "port": 6,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 10,
+      "nonzero_coefficients": 262144,
+      "port": 8,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 19,
+      "nonzero_coefficients": 262144,
+      "port": 17,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 20,
+      "nonzero_coefficients": 262144,
+      "port": 18,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 26,
+      "nonzero_coefficients": 262144,
+      "port": 24,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 25,
+      "nonzero_coefficients": 262144,
+      "port": 23,
+      "spatial_columns": 512
+    }
+  ],
+  "literal_words": {
+    "base": {
+      "arbitrary_selected_records": 16,
+      "events": 2654,
+      "fresh_distinct_recipes": 16,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "112"
+      },
+      "inherited_distinct_recipes": 1447,
+      "input_columns": 640,
+      "input_views": 128,
+      "late_query_scalar_primitives": 3424,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_maps_upper_bound": 3040,
+      "new_fields": 0,
+      "odd_scans": 0,
+      "output_views": 96,
+      "private_fields": 0,
+      "real_scalar_primitives": 9880,
+      "retained_scalar_primitives": 6456,
+      "unchanged_arbitrary_roles": 416
+    },
+    "extra": {
+      "arbitrary_selected_records": 16,
+      "events": 2654,
+      "fresh_distinct_recipes": 16,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "112"
+      },
+      "inherited_distinct_recipes": 1447,
+      "input_columns": 640,
+      "input_views": 128,
+      "late_query_scalar_primitives": 3424,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_maps_upper_bound": 3040,
+      "new_fields": 0,
+      "odd_scans": 0,
+      "output_views": 96,
+      "private_fields": 0,
+      "real_scalar_primitives": 9880,
+      "retained_scalar_primitives": 6456,
+      "unchanged_arbitrary_roles": 416
+    }
+  },
+  "negative_controls": [
+    "wrong selected I input frame",
+    "omitted late query",
+    "wrong global phase"
+  ],
+  "reader_scope": "The required update for a stored reader L is L E. Since E is invertible, equality with W E on all inputs requires L=W. No routed reader change is priced here.",
+  "scope": "Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.",
+  "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json
new file mode 100644
index 0000000000..1781475f6e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "EXTENSIONS-INPUTS.json": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3",
+    "EXTENSIONS-REVIEW.json": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3"
+  },
+  "source_files_rechecked": 23,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json
new file mode 100644
index 0000000000..8cfb592501
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json
@@ -0,0 +1,15 @@
+{
+  "base_review_freeze": "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976",
+  "files": {
+    "EXTENSIONS-REPRODUCTION.json": "5991ca1da15d3ffd7778e1de6be870c71f8811c867da6155e963e8bad1570aee",
+    "EXTENSIONS-REVIEW.md": "67efc6a9b0a04be1b9f2454db4ff5746d1bb389c2e80e0cff7f73e2481e4e798",
+    "check_extensions.py": "d6fcc9f2279bdd2e6b466dd42552f8add9a8fb05bef3f7f39030a582d729dd8f",
+    "extensions-normal/EXTENSIONS-INPUTS.json": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3",
+    "extensions-normal/EXTENSIONS-REVIEW.json": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3",
+    "extensions-optimized/EXTENSIONS-INPUTS.json": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3",
+    "extensions-optimized/EXTENSIONS-REVIEW.json": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3"
+  },
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "Exact local native reciprocal-large and rank16 data words. Odd-grid inverse implementation, productive helper progress, recursive host, terminal, and complete supplier remain separate.",
+  "status": "FROZEN_INDEPENDENT_NATIVE_EXTENSIONS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md
new file mode 100644
index 0000000000..8a7aaff05c
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md
@@ -0,0 +1,177 @@
+# Independent native review of the two response extensions
+
+The reciprocal-large and rank-sixteen words pass the independent native
+checks. Each complete word implements its declared response on all 640
+input roles in both directions. The two actual providers have identical
+words and port directions.
+
+The reciprocal-large word uses the exact rank-thirty native sequence.
+The rank-sixteen word uses 685 exact inherited ordered frame pairs and
+876 new edges. All 876 new recipes pass all 512 spatial columns, including
+global phase. The 224 endpoint adapters are unchanged.
+
+## Frozen inputs
+
+The consumed
+[extension freeze](../../new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json)
+has SHA256
+`aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689`.
+Only its final v2 payloads are used:
+
+| Variant | Decompressed SHA256 |
+| --- | --- |
+| reciprocal-large | `e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416` |
+| odd-grid-rank16 | `d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4` |
+
+The accepted base phase dependency is
+[NATIVE-REVIEW-FREEZE.json](NATIVE-REVIEW-FREEZE.json), at SHA256
+`cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976`.
+Its complete input and result receipts are pinned in the extension
+checker. The extension does not repeat an inherited phase calculation.
+
+The separate
+[matrix extension review](../../independent-review-20261017/response-extensions-review-20261020/FREEZE.json)
+has SHA256
+`1c20e6736b1109ce10746472d3e00d464d5ea2629fe30c37a9d51bd5b74feedc`.
+It owns the reciprocal identities, correction rank, principal inverses,
+and clique geometry. This review checks that the literal native streams
+implement those final matrices. The complete inputs are in
+`extensions-normal/EXTENSIONS-INPUTS.json`.
+
+## Inherited and fresh physical operators
+
+A phase recipe is inherited only when both ordered frame bases and the
+complete recipe are exactly equal to an accepted base entry. Equal
+subspaces, equal native ranks, or equal frame names are not sufficient.
+
+For the reciprocal-large variant, the entire native occurrence sequence,
+frame table, and recipe table are equal to the base word. There are 1141
+inherited edges and no fresh edge. Scalar coefficient changes and
+omitted zero-coefficient ADDs do not change this native sequence.
+
+For the rank-sixteen variant, all 685 inherited entries pass that exact
+comparison. Each of the other 876 entries is checked as
+
+\[
+ R T_{\mathrm{old}}=T_{\mathrm{new}}
+\]
+
+on all 512 spatial basis vectors. The independent sparse Gaussian
+interpreter is the same as in the base review. It imports no producer,
+Clifford compiler, or producer phase checker. The fresh checks cover
+448512 complete columns and 41619456 exact nonzero coefficients.
+
+All entry and final frame IDs retain their exact ordered bases from the
+base word. The 224 stored endpoint adapters are equal to the accepted
+records. Their previously checked physical phases therefore apply
+without a new endpoint sweep.
+
+## Complete data maps and legal access
+
+For either variant, let \(A\) be the response in that variant's final
+model. The literal maps are
+
+\[
+ F_A:(x,y,h)\longmapsto(x,y+Ax,h),\qquad
+ B_A:(x,y,h)\longmapsto(x-A^{\mathsf T}y,y,h).
+\]
+
+The physical input is \(X=Qx,\ Y=y\). The physical output is
+\(X=F_9x'\), \(Y=F_9Q^{-1}y'\). No response matrix is moved through \(Q\).
+In particular, the backward map does not use \(A^{-1}\).
+
+The frame ledger verifies each native entry, each strictly nested exit,
+each rank difference, each equal-frame scalar ADD, and every final
+frame. It also checks that transfer metadata selects the actual ADD.
+The complete reverse coefficient propagation checks every one of the
+640 input columns in each direction. An omitted nonzero transfer is
+rejected for both variants and both directions.
+
+Every operation is confined to the 224 data roles. All 416 other live
+roles retain their arbitrary values and frames. There are no owned
+fields, private fields, CLEAR operations, or hidden source accesses.
+As in the base word, this supplies no productive progress on those roles.
+
+For the reciprocal-large variant, the separate matrix review proves
+
+\[
+ A=E_{48}^{-\mathsf T}\oplus C.
+\]
+
+Thus the backward map supplies the old large-sector inverse
+\(-E_{48}^{-1}\). The small sector still supplies \(-C^{\mathsf T}\),
+not \(-C^{-1}\). The native review preserves this exact scope.
+
+## Local invoices
+
+| Variant | Native profile | Children | Mass | Real scalar primitives |
+| --- | --- | ---: | ---: | ---: |
+| reciprocal-large | 1036 H1 + 48 H3 + 55 H4 + 55 H5 + 9 H6 + 9 H7 | 1212 | 1792 | 5288 |
+| odd-grid-rank16 | 1520 H1 + 64 H2 + 48 H3 | 1632 | 1792 | 7384 |
+
+Both directions have the stated profile and scalar bill. Each word has
+224 external endpoint maps. The native side-map upper bounds are 2424
+and 3264, respectively. These maps are not treated as free.
+
+The native mass still telescopes to eight per data role. The number and
+sizes of the children change. Equal mass alone therefore does not prove
+equal recursive cost.
+
+The exact top-level array norm bounds are 30 forward and 46 backward
+for the reciprocal-large variant. The rank-sixteen bound is 22 in either
+direction. These are bounds at the literal event boundaries, not on
+recursive or scalar primitive internals.
+
+The scalar price check admits only nonzero dyadic ADD coefficients and
+dyadic unit scales. Every native phase recipe has Gaussian-dyadic
+entries. No odd division occurs in either emitted native word.
+
+## What the rank-sixteen word does not implement
+
+The separate matrix review proves that the rank-sixteen response is an
+integer matrix whose correction has rank sixteen. Its inverse uses
+denominators five and seven. The selected ordinary normalization also
+uses prime 31.
+
+Those inverse matrices are metadata and later code requirements. They
+are not native instructions in the word checked here. This review does
+not turn division by five, seven, or 31 into a dyadic scalar primitive.
+It does not prove the retained-grid conversion, a denominator-height
+bound, legal access for the inverse queries and scatters, or the final
+conversion.
+
+The rank-sixteen opportunity changes two restrictions. It uses an inverse
+with a nonzero diagonal as a later scalar code, and it permits the odd
+denominators needed by that code. Odd denominators alone do not defeat
+the earlier reciprocal zero-diagonal rank-two obstruction.
+
+Recursive child hosting, productive helper progress, the full precision
+bound, stage access, terminal removal, and the complete supplier remain
+open. The selected frontier and the complete kappa calculation do not
+change as a result of this local review.
+
+## Reproduction
+
+First reproduce the base native review. Then run, from the workspace
+root:
+
+```text
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized
+```
+
+The expected final line is:
+
+```text
+PASS_INDEPENDENT_NATIVE_EXTENSIONS
+```
+
+Both final runs passed, with byte-identical result and input receipts.
+The extension review freeze records that comparison and the final input
+hash check. All producer and base-review bytes are
+preserved. The source packets retain credit for the response, cyclic
+flags, pair factors, and phase construction. AI assistance was used.
+
+No PR, push, commit, or publication is authorized. Before any future PR
+description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json
new file mode 100644
index 0000000000..f19774d033
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "INPUTS.json": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90",
+    "REVIEW.json": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  },
+  "source_files_rechecked": 20,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json
new file mode 100644
index 0000000000..05fc30b335
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "NATIVE-REPRODUCTION.json": "57e3b9367f31183f95a66c9ff8c41350dbbe5d771f97a69b71654e42ce045b0c",
+    "REVIEW.md": "2ef8464d4f8b4867dfacdc7515285d690eb84adc299b7d7ebd1ce46ede1c7b29",
+    "check_native.py": "e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56",
+    "normal/INPUTS.json": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90",
+    "normal/REVIEW.json": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6",
+    "optimized/INPUTS.json": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90",
+    "optimized/REVIEW.json": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  },
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "Exact local native data word and phases. No productive helper progress, recursive host, routed inverse code, terminal, or complete supplier claim.",
+  "status": "FROZEN_INDEPENDENT_NATIVE_RANK30"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..affe6325a2
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md
@@ -0,0 +1,193 @@
+# Independent native review of the rank-thirty data word
+
+The literal native word passes the independent physical checks. It
+implements the declared local response on all 640 input roles. Every one
+of its 1141 distinct native edges and 224 endpoint adapters passes an
+exact check on all 512 spatial input columns, including global phase.
+The local invoice is 1792 native mass, 1212 native children, and 5288 real
+scalar primitives in each direction.
+
+This is a local data operation. It does not provide productive progress
+for the 416 other live roles, a recursive host, a routed inverse code, a
+terminal construction, or a complete supplier bound.
+
+## Sources and separate review
+
+The consumed
+[native freeze](../../new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json)
+has SHA256
+`efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24`.
+The decompressed payload hash is
+`e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558`.
+The reviewer uses only the final `native-normal-v2` payload. It does not
+use an earlier draft.
+
+The
+[matrix and common-frame scalar review](../../independent-review-20261017/rank-thirty-review-20261020/FREEZE.json)
+has SHA256
+`15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189`.
+It owns the matrix factorization, correction rank, inverses, clique
+census, and common-frame scalar codes. This review binds the literal
+native program to that exact response. It does not repeat those matrix
+proofs. In particular, its scalar invoice is the complete native word's
+invoice, not the separate common-frame code invoice.
+
+The physical interpreter is the
+[independent sparse Gaussian interpreter](../isotropic-pair-review-20261018/check.py),
+at SHA256
+`e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18`.
+The reviewer does not import the producer, its Clifford compiler, or its
+Pauli/state checker. All consumed source hashes are in
+`normal/INPUTS.json`.
+
+## Exact edge theorem and phase check
+
+Let \(T_f\) denote the canonical operator built from the literal ordered
+basis of frame \(f\). Let \(R\) denote an emitted recipe for a declared
+edge \(a\longrightarrow b\). The reviewer checks
+
+\[
+ R T_a=T_b
+\]
+
+on all 512 spatial basis vectors. Since \(T_a\) is unitary, this is
+equivalent to \(R=T_bT_a^{-1}\). The check does not replace an ordered
+basis by another basis of the same space. It also does not infer the
+phase from a rank or from a symplectic matrix.
+
+The interpreter uses integer real and imaginary coefficients with
+powers of two as denominators. It applies the literal affine maps,
+quadratic phases, fourth-root phases, and coordinate C gates. It compares
+the complete output coefficient dictionaries. This fixes global phase.
+The output support is also checked against \(2^{\dim b}\) in the displayed
+identity.
+
+For a source endpoint with physical convention \(Q_p=C_{q_p}\), the
+adapter check is
+
+\[
+ A_p Q_p=T_{\mathrm{line}(q_p)}.
+\]
+
+For a target endpoint, it is
+
+\[
+ A_p F_9Q_p^{-1}=T_{\mathrm{hole}(q_p)}.
+\]
+
+Thus the target uses the inverse of its stored adapter at exit. All 224
+adapters are rank zero, each with one explicit monomial map.
+
+The 1365 checks cover 698880 spatial columns and 69706752 exact nonzero
+coefficients. A wrong fourth-root global phase is rejected. The check
+uses no floating-point arithmetic and no sampled input vectors.
+
+Under the inherited columnwise tensor model, the complete one-column
+identity extends to every field width. Constant phases must tensor with
+the operator; a phase \(i^c\) in each of \(f\) columns gives \(i^{cf}\).
+The local test does not replace that factor by a width-independent phase.
+All primitive C kernels and monomial maps have Gaussian-dyadic entries.
+This fact does not supply a recursive implementation or its workspace.
+
+## Complete literal word
+
+The physical input is \(X_p=Q_px_p,\ Y_p=y_p\). The physical output is
+
+\[
+ X_p=F_9x'_p,\qquad Y_p=F_9Q_p^{-1}y'_p.
+\]
+
+The two logical maps are
+
+\[
+ F:(x,y,h)\longmapsto(x,y+Ex,h),\qquad
+ B:(x,y,h)\longmapsto(x-E^{\mathsf T}y,y,h).
+\]
+
+The backward response uses the transpose, not the inverse.
+No scalar response is moved through \(Q\).
+
+The reviewer tracks each role's actual frame at every event. Each
+native edge is strictly nested, and its positive rank equals the
+difference in the two frame dimensions. Each scalar ADD has exactly
+equal source and target frame IDs. All declared frame bases are
+independent. Each source starts at its actual line, and each target ends
+at its actual perpendicular hole.
+
+These checks give a direct induction. If a physical role is \(T_av\),
+the checked edge changes it to \(T_bv\). An equal-frame scalar ADD changes
+the logical contents by the same scalar ADD. The endpoint checks give
+the displayed physical conventions.
+
+A separate reverse propagation computes the complete scalar map.
+For \(t\leftarrow t+cs\), an output coefficient at \(t\) contributes \(c\)
+times that coefficient at \(s\). This proves all 640 columns at once.
+The two providers' complete serialized words are equal, and their
+actual port directions agree. Both directions are checked. These
+checks therefore cover all four provider/direction uses.
+
+Every operation reads or writes only the 224 data roles. The 416
+remaining roles are arbitrary and unchanged, with their input frames
+retained. There is no owned field, private field, CLEAR, or hidden source.
+The actual transfer metadata selects the claimed ADD event. Removing a
+nonzero transfer changes the complete response and is rejected.
+
+## Invoice and scope
+
+| Rank | Child count |
+| --- | ---: |
+| 1 | 1036 |
+| 3 | 48 |
+| 4 | 55 |
+| 5 | 55 |
+| 6 | 9 |
+| 7 | 9 |
+
+There are 1212 children and native mass 1792. Each X role advances from
+dimension one to dimension nine, and each Y role advances from dimension
+zero to dimension eight. Since all edges are nested, the rank sums
+telescope to eight per role. This explains the total mass but does not
+make different child profiles have the same recursive price.
+
+There are 224 external endpoint maps and at most 2424 native side maps.
+The complete scalar bill is 5288 real primitives. The reviewer sums the
+accepted cost of every literal dyadic ADD and unit scale.
+
+At top-level operation boundaries, each forward array has norm at most
+46 times the maximum input-array norm. The backward bound is 30.
+The reviewer computes the exact prefix row absolute sums. These bounds
+do not cover scalar primitive internals or recursive child internals.
+
+At the level of the literal word, there is no borrowed-state restoration
+debt because those roles are never accessed. The word also makes no
+productive progress on them.
+That distinction is required before this word can replace an actual
+supplier component. Recursive child hosting, complete precision,
+routed controller access, and terminal work remain separate obligations.
+The selected frontier and the complete kappa calculation do not change
+as a result of this review.
+
+## Reproduction
+
+From the workspace root:
+
+```text
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/optimized
+```
+
+The expected final line is:
+
+```text
+PASS_INDEPENDENT_FULL_NATIVE_RANK30
+```
+
+Both final runs passed. Their review and input receipts are byte-identical.
+The native review freeze records the two-mode comparison and the final
+input hash check. All source files remain unchanged. AI assistance was used.
+The response, cyclic flag, pair-code, and native phase predecessors keep
+the credit given in their pinned source packets.
+
+No PR, push, commit, or publication is authorized. Before any future PR
+description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py
new file mode 100644
index 0000000000..33c667c847
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py
@@ -0,0 +1,158 @@
+#!/usr/bin/env python3
+"""Check exact path reuse and the fresh native edges in the frozen extensions."""
+from hashlib import sha256
+from pathlib import Path
+from fractions import Fraction as F
+import argparse
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+SOURCE = LANES/'new-core-transfer-20261017/low-displacement-20261020'
+
+
+def load(name, path, pin):
+    if sha256(path.read_bytes()).hexdigest() != pin:
+        raise ValueError('Independent interpreter pin: '+str(path))
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=True)
+    review = load('rank30_native_review', HERE/'check_native.py',
+                  'e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56')
+    need = review.need
+    review.read(HERE/'check_native.py',
+                'e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56')
+    review.frozen(HERE, 'NATIVE-REVIEW-FREEZE.json',
+                  'cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976')
+    review.frozen(LANES/'independent-review-20261017/response-extensions-review-20261020',
+                  'FREEZE.json', '1c20e6736b1109ce10746472d3e00d464d5ea2629fe30c37a9d51bd5b74feedc')
+    base_receipts = {
+        'REVIEW.json': 'ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6',
+        'INPUTS.json': '8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90',
+    }
+    for name, digest in base_receipts.items():
+        a = (HERE/'normal'/name).read_bytes()
+        b = (HERE/'optimized'/name).read_bytes()
+        need(a == b, 'Completed independent base runs agree')
+        review.read(HERE/'normal'/name, digest)
+        review.read(HERE/'optimized'/name, digest)
+    checked = json.loads((HERE/'normal/REVIEW.json').read_text())
+    need(checked['status'] == 'PASS_INDEPENDENT_FULL_NATIVE_RANK30'
+         and len(checked['native_phase_checks']) == 1141
+         and len(checked['endpoint_phase_checks']) == 224, 'Complete base phase dependency')
+    review.frozen(SOURCE, 'EXTENSIONS-FREEZE.json',
+                  'aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689')
+    raw = json.loads(review.read(SOURCE/'native-normal-v2/NATIVE-PROGRAM.json.gz',
+                                 'e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558', True))
+    base = raw['providers']['base']['forward']
+    known = {}
+    for key, record in base['native_recipes'].items():
+        before, after = map(int, key.split(':'))
+        pair = tuple(base['frames'][before]), tuple(base['frames'][after])
+        need(pair not in known or known[pair] == record, 'Unambiguous base physical edge')
+        known[pair] = record
+    phase_path = HERE.parent/'isotropic-pair-review-20261018/check.py'
+    phase_pin = 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18'
+    review.read(phase_path, phase_pin)
+    phase = load('full_spatial_extension_review', phase_path, phase_pin)
+    pins = {
+        'reciprocal-large': ('reciprocal-normal-v2', 'e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416'),
+        'odd-grid-rank16': ('odd16-normal-v2', 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4'),
+    }
+    reports = {}
+    for kind, (directory, digest) in pins.items():
+        data = json.loads(review.read(SOURCE/directory/'EXTENSION-PROGRAM.json.gz', digest, True))
+        need(data['kind'] == kind and set(data['providers']) == {'base', 'extra'}, 'Exact extension family')
+        need(data['providers']['base'] == data['providers']['extra'], 'Both provider words are byte-equal')
+        words = data['providers']['base']
+        need(set(words) == {'forward', 'backward'}, 'Both extension directions')
+        word = words['forward']
+        ports = data['model']['ports']
+        frames = word['frames']
+        response = [{int(k): F(v) for k, v in row.items()} for row in data['model']['response']]
+        need(data['model']['selected_ports'] == raw['selected_ports'], 'Actual selected partition')
+        per_word, used = {}, set()
+        for direction, current in words.items():
+            need(current['frames'] == frames and current['native_recipes'] == word['native_recipes'],
+                 'Directions share exact native phase geometry')
+            need(current['start'] == base['start'] and current['final'] == base['final']
+                 and current['endpoint_adapters'] == base['endpoint_adapters'],
+                 'Exact retained endpoint arrays and adapters')
+            for index in set(current['start']+current['final']):
+                need(frames[index] == base['frames'][index], 'Exact ordered endpoint frame basis')
+            report, edges = review.ledger(current, ports, response, direction)
+            want = ({1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}
+                    if kind == 'reciprocal-large' else {1: 1520, 2: 64, 3: 48})
+            need(report['native_profile'] == want and report['native_mass'] == 1792,
+                 'Complete extension native invoice')
+            need(report['real_scalar_primitives'] == (5288 if kind == 'reciprocal-large' else 7384),
+                 'Complete extension scalar invoice')
+            wanted_bound = ('30' if direction == 'forward' else '46') if kind == 'reciprocal-large' else '22'
+            need(report['top_level_array_norm_bound'] == wanted_bound, 'Complete extension prefix bound')
+            if kind == 'reciprocal-large':
+                old = raw['providers']['base'][direction]
+                need(current['frames'] == old['frames']
+                     and current['native_recipes'] == old['native_recipes'],
+                     'Reciprocal geometry and recipes are byte-equal')
+                need([e for e in current['events'] if e[0] == 'native'] ==
+                     [e for e in old['events'] if e[0] == 'native'],
+                     'Reciprocal native occurrence sequence is byte-equal')
+            per_word[direction] = report
+            used |= edges
+        need(used == set(word['native_recipes']), 'All and only the emitted extension recipes are checked')
+        inherited, fresh = [], []
+        frame_cache = {}
+
+        def frame(index):
+            if index not in frame_cache:
+                frame_cache[index] = phase.canonical(frames[index])
+            return frame_cache[index]
+
+        for key, record in word['native_recipes'].items():
+            before, after = map(int, key.split(':'))
+            pair = tuple(frames[before]), tuple(frames[after])
+            if pair in known:
+                need(record == known[pair], 'Exact inherited recipe at the same ordered frame pair')
+                inherited.append(key)
+                continue
+            result = phase.compare(frame(before)+phase.recipe(record), frame(after),
+                                   kind+' native '+key, 1 << len(frames[after]))
+            fresh.append({'edge': key, 'rank': record['rank'], **result})
+            if len(fresh) % 40 == 0:
+                print('Independent fresh extension edges', kind, len(fresh), flush=True)
+        need((len(inherited), len(fresh)) == ((1141, 0) if kind == 'reciprocal-large' else (685, 876)),
+             'Exact inherited and fresh phase counts')
+        for direction, current in words.items():
+            missing = list(current['events'])
+            del missing[current['transfer_records'][0]['event']]
+            need(review.reverse(missing) != review.response_columns(response, direction),
+                 'An omitted transfer changes the full extension response')
+        reports[kind] = {
+            'literal_words': per_word, 'both_providers': ['base', 'extra'],
+            'exact_inherited_frame_pairs': inherited, 'fresh_native_phase_checks': fresh,
+            'inherited_endpoints': 224, 'owned_fields': 0, 'private_fields': 0,
+            'untouched_arbitrary_roles': 416,
+            'inverse_grid_implementation': 'Not supplied or priced by this native review.',
+        }
+        print('Literal extension', kind, 'PASS', flush=True)
+    output = {
+        'status': 'PASS_INDEPENDENT_NATIVE_EXTENSIONS',
+        'extensions': reports, 'spatial_columns_per_fresh_edge': 512,
+        'scope': 'Complete local native data responses and physical phases. Matrix and inverse-code claims require their separate reviews. No odd-grid implementation, productive helper progress, recursive host, stage or terminal construction, or full supplier claim.',
+    }
+    for name, value in (('EXTENSIONS-REVIEW.json', output), ('EXTENSIONS-INPUTS.json', review.INPUTS)):
+        (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print(output['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py
new file mode 100644
index 0000000000..d8a4b0dd76
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py
@@ -0,0 +1,268 @@
+#!/usr/bin/env python3
+"""Check all native edges, endpoint phases, and complete literal data words."""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+SOURCE = LANES/'new-core-transfer-20261017/low-displacement-20261020'
+PEER = LANES/'independent-review-20261017/rank-thirty-review-20261020'
+INPUTS = {}
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(path, pin=None, compressed=False):
+    data = path.read_bytes()
+    digest = sha256(data).hexdigest()
+    content = gzip.decompress(data) if compressed else data
+    need(pin is None or sha256(content).hexdigest() == pin, 'Input pin: '+str(path))
+    INPUTS[str(path.relative_to(LANES))] = {'sha256': digest}
+    if compressed:
+        INPUTS[str(path.relative_to(LANES))]['decompressed_sha256'] = sha256(content).hexdigest()
+    return content
+
+
+def frozen(path, name, pin):
+    record = json.loads(read(path/name, pin))
+    for file, digest in record['files'].items():
+        read(path/file, digest)
+    return record
+
+
+def add(target, source, coefficient):
+    for key, value in source.items():
+        result = target.get(key, F(0))+coefficient*value
+        if result:
+            target[key] = result
+        else:
+            target.pop(key, None)
+
+
+def span(vectors):
+    result = {0}
+    for vector in vectors:
+        result |= {x ^ vector for x in result}
+    return result
+
+
+def reverse(events):
+    """Return the full map by reverse propagation of output coefficients."""
+    columns = [{i: F(1)} for i in range(640)]
+    for event in reversed(events):
+        if event[0] != 'scalar':
+            continue
+        op, target, origin, coefficient = event[1]
+        c = F(coefficient)
+        if op == 'scale':
+            columns[target] = {j: c*v for j, v in columns[target].items()}
+        else:
+            need(op == 'add' and target != origin, 'Scalar grammar')
+            add(columns[origin], columns[target], c)
+    return columns
+
+
+def response_columns(response, direction):
+    columns = [{i: F(1)} for i in range(640)]
+    for target, row in enumerate(response):
+        for origin, coefficient in row.items():
+            if direction == 'forward':
+                add(columns[origin], {112+target: coefficient}, F(1))
+            else:
+                add(columns[112+target], {origin: -coefficient}, F(1))
+    return columns
+
+
+def scalar_price(events):
+    count = 0
+    for event in events:
+        if event[0] != 'scalar':
+            continue
+        op, _, _, value = event[1]
+        c = F(value)
+        n, d = abs(c.numerator), c.denominator
+        need(n > 0 and d & (d-1) == 0, 'Nonzero dyadic scalar coefficient')
+        if op == 'scale':
+            need(n & (n-1) == 0, 'Dyadic unit scale')
+            count += 2*(abs(n.bit_length()-d.bit_length())+(c < 0))
+        else:
+            count += 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1)
+    return count
+
+
+def ledger(word, ports, response, direction):
+    current = list(word['start'])
+    frames = word['frames']
+    spaces = [span(basis) for basis in frames]
+    need(len(current) == len(word['final']) == 640, 'Exactly 640 live roles')
+    need(all(len(s) == 1 << len(b) and all(0 <= x < 512 for x in s)
+             for s, b in zip(spaces, frames)), 'Independent literal frame bases')
+    for p, q in enumerate(ports):
+        need(spaces[current[p]] == {0, q} and spaces[current[112+p]] == {0},
+             'Actual physical source line and target I')
+        need(len(spaces[word['final'][p]]) == 512, 'Final X is FULL')
+        need(spaces[word['final'][112+p]] ==
+             {x for x in range(512) if (x & q).bit_count() % 2 == 0},
+             'Final Y is the actual q hole')
+    used = set()
+    prefix_rows = [{i: F(1)} for i in range(224)]
+    maximum = F(1)
+    for event in word['events']:
+        if event[0] == 'native':
+            _, target, before, after, rank, key = event
+            need(0 <= target < 224 and current[target] == before, 'Actual native source role and frame')
+            need(spaces[before] < spaces[after], 'Strictly nested native frame')
+            need(rank == len(frames[after])-len(frames[before])
+                 == word['native_recipes'][key]['rank'], 'Native rank and dimension difference')
+            need(key == str(before)+':'+str(after), 'Native occurrence has the exact edge key')
+            current[target] = after
+            used.add(key)
+        else:
+            need(event[0] == 'scalar', 'No hidden operation')
+            gate, frame = event[1:]
+            op, target, origin, coefficient = gate
+            need(0 <= target < 224 and current[target] == frame, 'Scalar target has the declared frame')
+            c = F(coefficient)
+            if op == 'scale':
+                need(origin is None, 'Scale has no hidden source')
+                prefix_rows[target] = {j: c*v for j, v in prefix_rows[target].items()}
+            else:
+                need(op == 'add' and 0 <= origin < 224 and origin != target
+                     and current[origin] == frame, 'Scalar source has the same actual frame')
+                add(prefix_rows[target], prefix_rows[origin], c)
+            maximum = max(maximum, sum(abs(v) for v in prefix_rows[target].values()))
+    need(current == word['final'], 'Every final frame')
+    need(current[224:] == word['start'][224:], 'All 416 other roles remain in their input frame')
+    need(reverse(word['events']) == response_columns(response, direction), 'All 640 reverse columns')
+    profile = Counter(e[4] for e in word['events'] if e[0] == 'native')
+    for transfer in word['transfer_records']:
+        event = word['events'][transfer['event']]
+        need(event[0] == 'scalar' and event[1][0] == 'add'
+             and event[1][-1] == transfer['coefficient'], 'Transfer metadata selects the actual ADD')
+    return {
+        'all_input_columns': 640, 'untouched_arbitrary_roles': 416,
+        'owned_fields': 0, 'private_fields': 0, 'used_native_edges': len(used),
+        'native_profile': dict(sorted(profile.items())),
+        'native_mass': sum(rank*count for rank, count in profile.items()),
+        'native_children': sum(profile.values()), 'real_scalar_primitives': scalar_price(word['events']),
+        'top_level_array_norm_bound': str(maximum),
+    }, used
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=True)
+    frozen(SOURCE, 'NATIVE-FREEZE.json',
+           'efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24')
+    frozen(SOURCE, 'RESPONSE-FREEZE.json',
+           '59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9')
+    frozen(PEER, 'FREEZE.json',
+           '15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189')
+    payload = json.loads(read(SOURCE/'native-normal-v2/NATIVE-PROGRAM.json.gz',
+                             'e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558', True))
+    for relative, (mode, pin) in payload['source_pins'].items():
+        read(LANES/relative, pin, mode == 'decompressed')
+    cyclic = json.loads(read(LANES/'independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json',
+                             '3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585'))
+    core = json.loads(read(LANES/'new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz',
+                           'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa', True))
+    model = json.loads(read(SOURCE/'run-normal/RESPONSE-PROGRAM.json',
+                            '5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c'))
+    need(payload['response'] == model['response'], 'Exact matrix-layer response')
+    ports = cyclic['ports']
+    need(all(p['canonical']['ports'] == ports for p in core['providers'].values()),
+         'Both actual providers have the same port labels')
+    interpreter = HERE.parent/'isotropic-pair-review-20261018/check.py'
+    read(interpreter, 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18')
+    spec = importlib.util.spec_from_file_location('spatial_native_review', interpreter)
+    phase = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(phase)
+    need(set(payload['providers']) == {'base', 'extra'}, 'Both providers')
+    need(payload['providers']['base'] == payload['providers']['extra'], 'Byte-equal provider words')
+    words = payload['providers']['base']
+    need(set(words) == {'forward', 'backward'}, 'Both directions')
+    first = words['forward']
+    for word in words.values():
+        need(word['frames'] == first['frames'] and word['native_recipes'] == first['native_recipes']
+             and word['endpoint_adapters'] == first['endpoint_adapters'], 'One exact native geometry')
+        need(word['start'] == cyclic['start'] and word['final'] == cyclic['final'],
+             'Exact inherited input and output frame declarations')
+    frame_cache = {}
+
+    def frame(index):
+        if index not in frame_cache:
+            frame_cache[index] = phase.canonical(first['frames'][index])
+        return frame_cache[index]
+
+    response = [{int(k): F(v) for k, v in row.items()} for row in payload['response']]
+    reports, union = {}, set()
+    for direction, word in words.items():
+        report, used = ledger(word, ports, response, direction)
+        need(report['native_profile'] == {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9},
+             'Complete declared native profile')
+        need(report['native_mass'] == 1792 and report['native_children'] == 1212
+             and report['real_scalar_primitives'] == 5288, 'Complete local invoice')
+        need(report['top_level_array_norm_bound'] == ('46' if direction == 'forward' else '30'),
+             'Exact top-level prefix bound')
+        reports[direction] = report
+        union |= used
+    need(union == set(first['native_recipes']) and len(union) == 1141,
+         'Every fresh recipe is used and every used edge is checked')
+    phases = []
+    for i, (key, record) in enumerate(first['native_recipes'].items(), 1):
+        before, after = map(int, key.split(':'))
+        result = phase.compare(frame(before)+phase.recipe(record), frame(after),
+                               'Native '+key, 1 << len(first['frames'][after]))
+        phases.append({'edge': key, 'rank': record['rank'], **result})
+        if i % 40 == 0:
+            print('Independent full native columns', i, '/ 1141', flush=True)
+    endpoints = first['endpoint_adapters']
+    need(len(endpoints) == 224 and {(r['port'], r['role']) for r in endpoints} ==
+         {(p, role) for p in range(112) for role in ('source', 'target')}, 'All 224 endpoints')
+    endpoint_checks = []
+    full = [('C', 1 << j, 1) for j in range(9)]
+    for i, record in enumerate(endpoints, 1):
+        p, role = record['port'], record['role']
+        target_frame = first['start'][p] if role == 'source' else first['final'][112+p]
+        need(record['rank'] == 0 and record['right'] is None and record['frame'] == target_frame,
+             'One explicit endpoint monomial with the actual endpoint frame')
+        conventional = [('C', ports[p], 1)] if role == 'source' else [('C', ports[p], -1)]+full
+        result = phase.compare(conventional+phase.recipe(record), frame(target_frame),
+                               'Endpoint '+role+' '+str(p), 1 << len(first['frames'][target_frame]))
+        endpoint_checks.append({'port': p, 'role': role, **result})
+        if i % 32 == 0:
+            print('Independent full endpoint columns', i, '/ 224', flush=True)
+    key = next(iter(first['native_recipes']))
+    before, after = map(int, key.split(':'))
+    bad = frame(before)+phase.recipe(first['native_recipes'][key])+phase.compile_circuit([['phase', 1]])
+    need(phase.run(bad, 0) != phase.run(frame(after), 0), 'Wrong global phase control')
+    missing = list(first['events'])
+    del missing[first['transfer_records'][0]['event']]
+    need(reverse(missing) != response_columns(response, 'forward'), 'Missing transfer control')
+    result = {
+        'status': 'PASS_INDEPENDENT_FULL_NATIVE_RANK30',
+        'literal_words': reports, 'providers_share_exact_words': ['base', 'extra'],
+        'native_phase_checks': phases, 'endpoint_phase_checks': endpoint_checks,
+        'native_edges': 1141, 'endpoint_maps': 224, 'spatial_columns_per_check': 512,
+        'negative_controls': ['wrong global phase', 'one omitted nonzero transfer'],
+        'matrix_layer_review': 'independent-review-20261017/rank-thirty-review-20261020/FREEZE.json',
+        'scope': 'Complete local data maps and physical phases. No productive helper progress, recursive host, routed inverse code, terminal decoder, or complete supplier claim.',
+    }
+    for name, value in (('REVIEW.json', result), ('INPUTS.json', INPUTS)):
+        (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print(result['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json
new file mode 100644
index 0000000000..8e38cab0a9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json
@@ -0,0 +1,74 @@
+{
+  "independent-review-20261017/response-extensions-review-20261020/CHECKS.json": {
+    "sha256": "e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a"
+  },
+  "independent-review-20261017/response-extensions-review-20261020/FREEZE.json": {
+    "sha256": "1c20e6736b1109ce10746472d3e00d464d5ea2629fe30c37a9d51bd5b74feedc"
+  },
+  "independent-review-20261017/response-extensions-review-20261020/REPRODUCTION.json": {
+    "sha256": "39c6300f307be4edf100a0ad53ca163f6d28ca0f01f51fce65ab5b200c09b731"
+  },
+  "independent-review-20261017/response-extensions-review-20261020/REVIEW.md": {
+    "sha256": "ab9192c4e9a6cec5a864189bd24a4f208a9242c55c5a6a329b4f4e3e25edb8b7"
+  },
+  "independent-review-20261017/response-extensions-review-20261020/check_extensions.py": {
+    "sha256": "97e6c35e916b3cc6b4512e82b554ca33189fe91c89d00a269cf83719f61a073c"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json": {
+    "sha256": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md": {
+    "sha256": "2328ec60c1cf89efe7661b3696839f8eb32a95e11c67a62dd653781a8b0ed5fb"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json": {
+    "sha256": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/emit_followthrough.py": {
+    "sha256": "b03568530696ab810070ba3243b59dd74740fb634fe7f26b2cbdb1d3283d045f"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz": {
+    "decompressed_sha256": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    "sha256": "aca3b3364b73e3c2115ede3082088e7566d789273711031381e44406c0ae793c"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json": {
+    "sha256": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": {
+    "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/reciprocal-normal-v2/EXTENSION-CHECKS.json": {
+    "sha256": "cfea59ca775a7350c2e9bcded1c52f2f19df12465f6d8736fd2a907599839adc"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz": {
+    "decompressed_sha256": "e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416",
+    "sha256": "825f27e5b3705dace14c75ae53aa21ea94b9dc69284bbdbd3377591fbcce7439"
+  },
+  "new-native-recipes-20261017/isotropic-pair-review-20261018/check.py": {
+    "sha256": "e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json": {
+    "sha256": "57e3b9367f31183f95a66c9ff8c41350dbbe5d771f97a69b71654e42ce045b0c"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json": {
+    "sha256": "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md": {
+    "sha256": "2ef8464d4f8b4867dfacdc7515285d690eb84adc299b7d7ebd1ce46ede1c7b29"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/check_native.py": {
+    "sha256": "e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json": {
+    "sha256": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/normal/REVIEW.json": {
+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/INPUTS.json": {
+    "sha256": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/REVIEW.json": {
+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-REVIEW.json
new file mode 100644
index 0000000000..d25caa171b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-REVIEW.json
@@ -0,0 +1,8068 @@
+{
+  "extensions": {
+    "odd-grid-rank16": {
+      "both_providers": [
+        "base",
+        "extra"
+      ],
+      "exact_inherited_frame_pairs": [
+        "0:10",
+        "0:100",
+        "0:102",
+        "0:103",
+        "0:104",
+        "0:105",
+        "0:109",
+        "0:110",
+        "0:111",
+        "0:14",
+        "0:19",
+        "0:20",
+        "0:21",
+        "0:226",
+        "0:24",
+        "0:25",
+        "0:26",
+        "0:28",
+        "0:3",
+        "0:30",
+        "0:31",
+        "0:32",
+        "0:33",
+        "0:34",
+        "0:35",
+        "0:36",
+        "0:37",
+        "0:40",
+        "0:41",
+        "0:42",
+        "0:47",
+        "0:5",
+        "0:50",
+        "0:51",
+        "0:52",
+        "0:56",
+        "0:57",
+        "0:58",
+        "0:6",
+        "0:60",
+        "0:61",
+        "0:62",
+        "0:66",
+        "0:67",
+        "0:68",
+        "0:69",
+        "0:7",
+        "0:70",
+        "0:71",
+        "0:75",
+        "0:76",
+        "0:77",
+        "0:79",
+        "0:8",
+        "0:82",
+        "0:84",
+        "0:85",
+        "0:86",
+        "0:87",
+        "0:88",
+        "0:90",
+        "0:95",
+        "0:97",
+        "0:98",
+        "0:99",
+        "101:293",
+        "106:356",
+        "107:437",
+        "108:326",
+        "10:611",
+        "10:614",
+        "111:614",
+        "112:351",
+        "113:321",
+        "11:329",
+        "12:406",
+        "13:297",
+        "14:611",
+        "14:613",
+        "15:272",
+        "16:281",
+        "17:288",
+        "18:368",
+        "226:227",
+        "226:232",
+        "226:238",
+        "226:247",
+        "226:254",
+        "226:259",
+        "226:267",
+        "226:272",
+        "226:281",
+        "226:288",
+        "226:293",
+        "226:297",
+        "226:314",
+        "226:321",
+        "226:326",
+        "226:329",
+        "226:351",
+        "226:356",
+        "226:363",
+        "226:368",
+        "226:377",
+        "226:389",
+        "226:406",
+        "226:437",
+        "227:228",
+        "227:242",
+        "227:263",
+        "227:276",
+        "228:229",
+        "228:250",
+        "229:230",
+        "229:256",
+        "22:377",
+        "230:231",
+        "230:260",
+        "231:1",
+        "231:262",
+        "232:233",
+        "232:242",
+        "232:421",
+        "232:428",
+        "233:234",
+        "233:243",
+        "234:235",
+        "234:244",
+        "235:236",
+        "235:245",
+        "236:1",
+        "236:237",
+        "237:114",
+        "237:141",
+        "238:228",
+        "238:239",
+        "238:359",
+        "238:372",
+        "239:229",
+        "239:240",
+        "23:314",
+        "240:230",
+        "240:241",
+        "241:231",
+        "241:236",
+        "242:243",
+        "242:250",
+        "243:244",
+        "243:251",
+        "244:245",
+        "244:252",
+        "245:1",
+        "245:246",
+        "246:116",
+        "246:139",
+        "247:239",
+        "247:248",
+        "247:302",
+        "247:310",
+        "248:240",
+        "248:249",
+        "249:235",
+        "249:241",
+        "250:251",
+        "250:256",
+        "251:252",
+        "251:257",
+        "252:1",
+        "252:253",
+        "253:184",
+        "253:205",
+        "254:248",
+        "254:255",
+        "254:447",
+        "254:454",
+        "255:234",
+        "255:249",
+        "256:257",
+        "256:260",
+        "257:1",
+        "257:258",
+        "258:185",
+        "258:204",
+        "259:233",
+        "259:255",
+        "259:334",
+        "259:342",
+        "260:1",
+        "260:261",
+        "261:186",
+        "261:203",
+        "262:190",
+        "262:201",
+        "263:264",
+        "263:284",
+        "264:265",
+        "264:290",
+        "265:266",
+        "265:294",
+        "266:1",
+        "266:296",
+        "267:268",
+        "267:276",
+        "267:394",
+        "267:402",
+        "268:269",
+        "268:277",
+        "269:270",
+        "269:278",
+        "270:271",
+        "270:279",
+        "271:1",
+        "271:237",
+        "272:263",
+        "272:273",
+        "272:330",
+        "272:339",
+        "273:264",
+        "273:274",
+        "274:265",
+        "274:275",
+        "275:266",
+        "275:271",
+        "276:277",
+        "276:284",
+        "277:278",
+        "277:285",
+        "278:279",
+        "278:286",
+        "279:1",
+        "279:280",
+        "27:238",
+        "280:127",
+        "280:165",
+        "281:273",
+        "281:282",
+        "281:443",
+        "281:451",
+        "282:274",
+        "282:283",
+        "283:270",
+        "283:275",
+        "284:285",
+        "284:290",
+        "285:286",
+        "285:291",
+        "286:1",
+        "286:287",
+        "287:128",
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+      "inherited_endpoints": 224,
+      "inverse_grid_implementation": "Not supplied or priced by this native review.",
+      "literal_words": {
+        "backward": {
+          "all_input_columns": 640,
+          "native_children": 1212,
+          "native_mass": 1792,
+          "native_profile": {
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+          "used_native_edges": 1141
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+        "forward": {
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+          "native_profile": {
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+            "3": 48,
+            "4": 55,
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+            "6": 9,
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+          "owned_fields": 0,
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+      "owned_fields": 0,
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+  },
+  "scope": "Complete local native data responses and physical phases. Matrix and inverse-code claims require their separate reviews. No odd-grid implementation, productive helper progress, recursive host, stage or terminal construction, or full supplier claim.",
+  "spatial_columns_per_fresh_edge": 512,
+  "status": "PASS_INDEPENDENT_NATIVE_EXTENSIONS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-INPUTS.json
new file mode 100644
index 0000000000..8e38cab0a9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-INPUTS.json
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diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-REVIEW.json
new file mode 100644
index 0000000000..d25caa171b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-REVIEW.json
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diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json
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+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json
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diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/REVIEW.json
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+      "edge": "68:531",
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+      "edge": "76:588",
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+      "edge": "76:591",
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+      "edge": "78:232",
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+      "edge": "79:606",
+      "nonzero_coefficients": 2048,
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+      "nonzero_coefficients": 2048,
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+      "edge": "7:467",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
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+    {
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+      "edge": "7:470",
+      "nonzero_coefficients": 2048,
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+    {
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+      "edge": "80:293",
+      "nonzero_coefficients": 2048,
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+      "edge": "81:363",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
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+    {
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+      "edge": "82:498",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
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+    {
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+      "edge": "82:501",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
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+    },
+    {
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+      "edge": "83:267",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
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+    },
+    {
+      "digest": "9cc0cff5d79991e40df8b79f3208729bb5b6263f404280ef96c656d7642a829d",
+      "edge": "84:498",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "1c831c2bc2a50eaea7f11a7ae16c8c3e58e34c7776834f86a6daf6b3855c3181",
+      "edge": "84:500",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "51f5532846edaa4227d803bf49d3bdba0c8e723220c09ee0ddfb38be5f843a7e",
+      "edge": "85:528",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "0767b4ca5851c9a0b9bfc2a9d90109863d490ce8e961a13309fb989632d7bc83",
+      "edge": "85:530",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "34827bf34755ec2bc515259a1d952823effb0a607ca2c44cb1355328fc63cf2b",
+      "edge": "86:603",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "b4d9126b925d763bc9ddb8cd53c4e9092ec34deea9dd58b077c55efb2b3010aa",
+      "edge": "86:604",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "b7c344e7815b76f0fc2f820f6cac230365ec7ee8101caa24f45bd7f376fffb36",
+      "edge": "87:468",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "e0b4ab8c86d6b794931713d2f9f989e03fc6536e134c69b973a678ba2c252bac",
+      "edge": "87:471",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
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+    },
+    {
+      "digest": "2fd4b1bea5607bdb9bb3577457a2050904aedcafba3b9c8ea0459ac32ee0a861",
+      "edge": "88:609",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "780fab807d8881d80ea04ee8bf559dd67ce1c292d585c007d3643efd16def40a",
+      "edge": "88:610",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "ea3ae395bbf534a0a8e1e3e8773052ae9468719fbdb7b061274ce768f783c34b",
+      "edge": "89:232",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "c7241c31cb6dad5dc87923cabe52dde518998ecc3071269cc89814067bb6f4a9",
+      "edge": "8:611",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "07435aae79b6ba800c9cad06245b8a04325789d519af7fd3434d65852bdf689d",
+      "edge": "8:614",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "82a45994369012b2b40a6152d3af5b322da87f01396e880561f96818ce3337ff",
+      "edge": "90:588",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "ee7e13f32dc2740ef760927f75b2f45a4ab5279db97a0edde026b3e5379839df",
+      "edge": "90:590",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "3c67738b78c53906c8228ac3e1a2b1216c9bfaefb3ec7afabb25018181175fe1",
+      "edge": "91:259",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "3856c5accbb2cc53426205e12d45f75c1058eed973d2a23fa88b007139cb9620",
+      "edge": "92:254",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "0a8db60b2db249d0030a6ecba9a6531c105cc92d06a63396931786b4497856af",
+      "edge": "93:247",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "52f2653884dc2db1eebbc83971dc637cfe27c93eb6a0e875cb488eaebad3fd82",
+      "edge": "94:267",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "28e41bfa97a585b28fa60436bf5806e08c9476756d5b753711d516baa97088b5",
+      "edge": "95:627",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "345f60a9cc2db2348f2767aa884e29d1459253806646a49bdbdc2a1a07ae55d8",
+      "edge": "95:630",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "74f7803df918623636d062bcf675325ea868dd8ce568f98db7710d99ae9e0228",
+      "edge": "96:363",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "271c5c179239e9bac94240e4f4b46db247a36ec22d3f5b6f51c659f1add6e703",
+      "edge": "97:483",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "b4cd07479133fddc7bba1384d06ef6a3aa4e779de79dd965f48eb7f5efaffa96",
+      "edge": "97:485",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "6dd46f62d519acfd94194906321c2a54d5916e703f73853eb8535d7bd157471a",
+      "edge": "98:573",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "66e913aeb023c549555f673b1ee1c76e0a7eaa9a30990cc3ce3defa9d7d6c034",
+      "edge": "98:575",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "b7c344e7815b76f0fc2f820f6cac230365ec7ee8101caa24f45bd7f376fffb36",
+      "edge": "99:468",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "ab568d3336db1a50cc7aa98c6a67f2c7a4c7dff0af12fe5eb5d9b15a674b4184",
+      "edge": "99:470",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "3ab1e84df00151c98d40f9355db57e42a4b4114a891c4a93a17ffe96a97ded16",
+      "edge": "9:389",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    }
+  ],
+  "negative_controls": [
+    "wrong global phase",
+    "one omitted nonzero transfer"
+  ],
+  "providers_share_exact_words": [
+    "base",
+    "extra"
+  ],
+  "scope": "Complete local data maps and physical phases. No productive helper progress, recursive host, routed inverse code, terminal decoder, or complete supplier claim.",
+  "spatial_columns_per_check": 512,
+  "status": "PASS_INDEPENDENT_FULL_NATIVE_RANK30"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..77345b3119
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/FREEZE.json
@@ -0,0 +1,17 @@
+{
+  "base_review_freeze": "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976",
+  "extension_review_freeze": "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c",
+  "files": {
+    "REPRODUCTION.json": "8885671a677176cc50f77a7932c5b741dab215819583b7465ab76553ba625f65",
+    "REVIEW.md": "d272e97e8b2d68fae87163c83308da4c6f81f5310cf568f04323f77ffd01bb8c",
+    "check.py": "a0f6fed3b062f53d3d7237b7bc1ac95518a27eb94abaf1c9b731473547beb3c6",
+    "normal/INPUTS.json": "9994025ddba20b0ffea519cc86168514e09968b4fdafbddca74a8a9e16083708",
+    "normal/REVIEW.json": "9161f559d162d008e3927aa4cffcff9205f141f2d140596056681f031e3eae1f",
+    "optimized/INPUTS.json": "9994025ddba20b0ffea519cc86168514e09968b4fdafbddca74a8a9e16083708",
+    "optimized/REVIEW.json": "9161f559d162d008e3927aa4cffcff9205f141f2d140596056681f031e3eae1f"
+  },
+  "producer_freeze": "28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af",
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "All four complete raw local words, 640 arbitrary inputs, 297 fresh full spatial phase checks, 752 exact inherited phase entries, 224 unchanged endpoint adapters, complete native and scalar invoice. Model and capture-code algebra require separate review. No root gauge, code transition, productive helper progress, recursive host, terminal or complete supplier claim.",
+  "status": "FROZEN_INDEPENDENT_ROUTE32_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..773c1b2138
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "INPUTS.json": "9994025ddba20b0ffea519cc86168514e09968b4fdafbddca74a8a9e16083708",
+    "REVIEW.json": "9161f559d162d008e3927aa4cffcff9205f141f2d140596056681f031e3eae1f"
+  },
+  "source_files_rechecked": 28,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..0635279f60
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/REVIEW.md
@@ -0,0 +1,182 @@
+# Independent native review of route32
+
+All stated local native checks pass. There is no material finding.
+
+This review checks the complete raw native word for the frozen route32
+response. It checks the declared response on all 640 input columns, the
+actual frames and endpoint adapters, every new physical phase recipe,
+and the complete local native and scalar invoice.
+
+The response model and its centre capture codes have separate proof
+obligations. This native review does not prove those algebraic claims.
+It does not include the proposed common-root output gauge.
+
+## Frozen sources
+
+The producer
+[freeze](../../new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json)
+has SHA256
+`28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af`.
+The decompressed native payload SHA256 is
+`2f037b4757c46efb849bcfd8ad6cc2919d8486c5a9001d6325152446caf0f3e5`.
+Its embedded model must equal the model file at SHA256
+`85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52`.
+
+The prior accepted native tables are fixed by
+[NATIVE-REVIEW-FREEZE.json](../low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json)
+and
+[EXTENSIONS-REVIEW-FREEZE.json](../low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json),
+at SHA256
+`cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976`
+and
+`c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c`.
+Their raw payloads are pinned separately in the checker.
+
+The new word retains the actual 112 supplier port directions from the
+accepted cyclic geometry. It declares no selected ports and uses all
+112 ports in its ordinary bank. The review does not transfer a principal
+inverse from the old selected-eight partition.
+
+## Exact phases and legal access
+
+The checker imports no producer, Clifford compiler, or producer phase
+checker. It uses the previously frozen independent reverse coefficient
+interpreter and the independent sparse Gaussian spatial interpreter.
+
+The complete native table has 1049 entries. Of these, 752 have exactly
+the same ordered input basis, ordered output basis, and full phase
+recipe as an accepted rank-thirty or rank-sixteen entry. Each reused
+entry records its accepted source key. Equal spaces or equal ranks
+are not sufficient for reuse.
+
+For each of the 297 new entries, the spatial interpreter checks
+
+\[
+ R T_{\rm old}=T_{\rm new}
+\]
+
+on all 512 input basis vectors. This proves the complete physical
+operator \(R=T_{\rm new}T_{\rm old}^{-1}\), including its global phase.
+Each exact comparison uses Gaussian integer numerators and powers of
+two as denominators.
+
+The fresh checks cover 152064 complete spatial columns and 25726976
+exact nonzero coefficients.
+
+All 224 external endpoint adapters are exactly equal to accepted
+records. Their frame IDs also retain exactly the same ordered bases.
+Their previous phase checks therefore apply. This review does not
+repeat those accepted calculations.
+
+Under the inherited tensor model, the full one-column operator
+identity holds for every field width. Constant phases remain part of
+the tensor operator: \(i^c\) on each of f columns gives \(i^{cf}\).
+The review does not replace this phase by one width-independent factor.
+
+At each native occurrence the frame ledger checks the actual field
+and input frame, strict subspace inclusion, the ordered frame key,
+and the exact child rank. Each scalar ADD must have the same actual
+source and target frame.
+
+These checks justify the coordinate interpretation of the scalar
+word. If two fields have frame T, the physical ADD is
+\(Tz_t+cTz_s=T(z_t+cz_s)\). A native step changes T but retains the
+logical field. No spatial operator is commuted through a scalar
+coefficient matrix.
+
+## Complete maps and arbitrary state
+
+Let E be the pinned response matrix. The exact logical maps are
+
+\[
+ F(x,y,h)=(x,y+Ex,h),\qquad
+ B(x,y,h)=(x-E^{\mathsf T}y,y,h).
+\]
+
+The physical input is \(X=Qx,\ Y=y\). The physical output is
+\(X=F_9x'\), \(Y=F_9Q^{-1}y'\). In particular, the backward response
+is \(-E^{\mathsf T}\), not \(-E^{-1}\).
+
+The checker replays both directions for each of the two providers.
+It checks all 640 independent input columns by reverse propagation
+of the output coefficients. It also confirms that the two providers
+have exactly equal words. All final frames are checked.
+
+Every operation acts on the 224 data roles. The other 416 roles keep
+their arbitrary input values and frames. There are no owned fields,
+private fields, CLEAR operations, or hidden helper accesses. These
+unchanged roles receive no productive advance.
+
+For each provider and direction, a negative control removes an actual
+nonzero transfer. The resulting complete map must differ from the
+declared response.
+
+## Local invoice
+
+Both directions and both providers have the same invoice:
+
+| Item | Count |
+| --- | ---: |
+| H1 children | 944 |
+| H3 children | 48 |
+| H5 children | 64 |
+| H6 children | 64 |
+| Native children | 1120 |
+| Native mass | 1792 |
+| Real scalar primitives | 4312 |
+| External endpoint maps | 224 |
+| Native side-map upper bound | 2240 |
+| Owned or private fields | 0 |
+
+The scalar price check admits only the accepted dyadic ADD and unit
+scale words. No odd division occurs in this native word. The endpoint
+maps and child side maps are counted separately; they are not free.
+
+The complete scalar prefix array norm bound is 14 in each direction.
+This bound applies at the top-level event boundaries. It does not
+bound the internals of a scalar primitive or a recursive child, or
+give the full roundoff estimate.
+
+The native mass still telescopes to eight for each data role. The
+child profile and scalar cost differ from the earlier responses.
+Equal mass alone is not an equality of recursive cost.
+
+## Scope and reproduction
+
+The checker establishes a native implementation of the exact response
+stored in the pinned model. The determinant, correction rank,
+route-class preservation, principal inverses, and two centre capture
+codes require the separate model review. The cost of a capture code
+is not included in the native invoice above.
+
+The common-root gauge, moving-code transitions, legal access for a
+subsequent inverse code, odd-denominator implementation, productive
+helper progress, recursive hosting, terminal decoding, and the complete
+supplier remain separate. This review does not change the selected
+frontier or prove an improvement in the complete kappa calculation.
+
+Run from the workspace root, with one CPU:
+
+```text
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/route32-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/route32-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/route32-native-review-20261020/optimized
+```
+
+The required final line is:
+
+```text
+PASS_INDEPENDENT_ROUTE32_NATIVE
+```
+
+The final result and input receipts must be byte-identical.
+`REPRODUCTION.json` records that comparison and a new hash check of
+all consumed sources.
+
+Both final runs passed. The result and input receipts are byte-identical.
+All 28 consumed source files retain their pinned hashes.
+
+The source packets retain credit for the route split, shared-root
+geometry, cyclic flags, response, capture codes, and native lowering.
+AI assistance was used. No PR, push, commit, or publication is
+authorized. Before any future PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/check.py
new file mode 100644
index 0000000000..734fcbe8c2
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/check.py
@@ -0,0 +1,148 @@
+#!/usr/bin/env python3
+"""Check the complete route32 native words and their fresh physical phases."""
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+PREVIOUS = HERE.parent/'low-displacement-review-20261020'
+SOURCE = LANES/'new-core-transfer-20261017/low-displacement-20261020'
+
+
+def load(name, path, pin):
+    if sha256(path.read_bytes()).hexdigest() != pin:
+        raise ValueError('Independent interpreter pin: '+str(path))
+    spec = importlib.util.spec_from_file_location(name, path)
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    args.out.mkdir(parents=True, exist_ok=True)
+    review = load('accepted_native_review', PREVIOUS/'check_native.py',
+                  'e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56')
+    need = review.need
+    review.frozen(PREVIOUS, 'NATIVE-REVIEW-FREEZE.json',
+                  'cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976')
+    review.frozen(PREVIOUS, 'EXTENSIONS-REVIEW-FREEZE.json',
+                  'c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c')
+    review.frozen(SOURCE/'route32', 'FREEZE.json',
+                  '28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af')
+    payload = json.loads(review.read(SOURCE/'route32/native-normal/ROUTE32-NATIVE.json.gz',
+                                    '2f037b4757c46efb849bcfd8ad6cc2919d8486c5a9001d6325152446caf0f3e5', True))
+    model = json.loads(review.read(SOURCE/'route32/model-normal/ROUTE32-MODEL.json',
+                                  '85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52'))
+    need(payload['schema'] == 'route32-native-v1' and payload['model'] == model,
+         'Exact frozen route32 model')
+    sources = [
+        ('rank30', 'native-normal-v2/NATIVE-PROGRAM.json.gz',
+         'e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558'),
+        ('rank16', 'odd16-normal-v2/EXTENSION-PROGRAM.json.gz',
+         'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4'),
+    ]
+    accepted, known = {}, {}
+    for name, relative, pin in sources:
+        data = json.loads(review.read(SOURCE/relative, pin, True))
+        old = data['providers']['base']['forward']
+        accepted[name] = old
+        for key, record in old['native_recipes'].items():
+            before, after = map(int, key.split(':'))
+            pair = tuple(old['frames'][before]), tuple(old['frames'][after])
+            need(pair not in known or known[pair]['record'] == record,
+                 'Accepted ordered phase pairs agree')
+            known.setdefault(pair, {'record': record, 'sources': []})['sources'].append([name, key])
+    cyclic = json.loads(review.read(LANES/'independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json',
+                                   '3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585'))
+    need(model['ports'] == cyclic['ports'], 'Actual supplier port directions')
+    need(model['selected_ports'] == [] and model['ordinary_ports'] == list(range(112)),
+         'Explicit empty selection and complete ordinary bank')
+    phase_path = HERE.parent/'isotropic-pair-review-20261018/check.py'
+    phase_pin = 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18'
+    review.read(phase_path, phase_pin)
+    phase = load('route32_spatial_review', phase_path, phase_pin)
+    need(set(payload['providers']) == {'base', 'extra'}, 'Both providers')
+    need(payload['providers']['base'] == payload['providers']['extra'], 'Exact equal provider words')
+    first = payload['providers']['base']['forward']
+    frames = first['frames']
+    base = accepted['rank16']
+    response = [{int(k): F(v) for k, v in row.items()} for row in model['response']]
+    need(len(response) == 112 and all(0 <= j < 112 for row in response for j in row),
+         'Complete 112 by 112 response')
+    reports, used, controls = {}, set(), {}
+    for provider, words in payload['providers'].items():
+        need(set(words) == {'forward', 'backward'}, 'Both native directions')
+        reports[provider] = {}
+        controls[provider] = {}
+        for direction, word in words.items():
+            need(word['frames'] == frames and word['native_recipes'] == first['native_recipes'],
+                 'Exact common ordered phase geometry')
+            need(word['start'] == base['start'] and word['final'] == base['final']
+                 and word['endpoint_adapters'] == base['endpoint_adapters'],
+                 'Exact accepted endpoint arrays and all 224 adapters')
+            for index in set(word['start']+word['final']):
+                need(frames[index] == base['frames'][index], 'Exact ordered endpoint frame')
+            report, edges = review.ledger(word, model['ports'], response, direction)
+            need(report['native_profile'] == {1: 944, 3: 48, 5: 64, 6: 64},
+                 'Complete route32 native profile')
+            need(report['native_children'] == 1120 and report['native_mass'] == 1792
+                 and report['real_scalar_primitives'] == 4312,
+                 'Complete route32 native and scalar invoice')
+            need(report['top_level_array_norm_bound'] == '14', 'Complete route32 prefix bound')
+            report['external_endpoint_maps'] = len(word['endpoint_adapters'])
+            report['native_side_map_bound'] = 2*report['native_children']
+            reports[provider][direction] = report
+            used |= edges
+            bad = list(word['events'])
+            index = word['transfer_records'][0]['event']
+            removed = bad.pop(index)
+            need(review.reverse(bad) != review.response_columns(response, direction),
+                 'Removal of a nonzero transfer changes the complete map')
+            controls[provider][direction] = {'removed_event_index': index, 'removed_event': removed}
+    need(used == set(first['native_recipes']) and len(used) == 1049,
+         'All and only the complete native phase table is used')
+    cache = {}
+
+    def frame(index):
+        if index not in cache:
+            cache[index] = phase.canonical(frames[index])
+        return cache[index]
+
+    inherited, fresh = [], []
+    for key, record in first['native_recipes'].items():
+        before, after = map(int, key.split(':'))
+        pair = tuple(frames[before]), tuple(frames[after])
+        if pair in known:
+            need(record == known[pair]['record'], 'Exact inherited ordered frame-pair recipe')
+            inherited.append({'edge': key, 'accepted_sources': known[pair]['sources']})
+            continue
+        result = phase.compare(frame(before)+phase.recipe(record), frame(after),
+                               'Route32 edge '+key, 1 << len(frames[after]))
+        fresh.append({'edge': key, 'rank': record['rank'], **result})
+        if len(fresh) % 24 == 0:
+            print('Independent fresh route32 phases', len(fresh), '/ 297', flush=True)
+    need(len(inherited) == 752 and len(fresh) == 297, 'Exact inherited and fresh phase counts')
+    result = {
+        'status': 'PASS_INDEPENDENT_ROUTE32_NATIVE',
+        'literal_words': reports,
+        'inherited_native_phases': inherited,
+        'fresh_native_phases': fresh,
+        'inherited_endpoint_phases': 224,
+        'spatial_columns_per_fresh_edge': 512,
+        'missing_transfer_controls': controls,
+        'scope': 'Complete raw local native words for the pinned route32 response. Model, principal inverse and capture-code theorems require separate review. No root-gauge code, transition, odd-division implementation, productive helper progress, recursive hosting or complete supplier claim.',
+    }
+    for name, value in (('REVIEW.json', result), ('INPUTS.json', review.INPUTS)):
+        (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print(result['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..a7cdeb48dc
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal/INPUTS.json
@@ -0,0 +1,89 @@
+{
+  "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": {
+    "sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz": {
+    "decompressed_sha256": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    "sha256": "aca3b3364b73e3c2115ede3082088e7566d789273711031381e44406c0ae793c"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": {
+    "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json": {
+    "sha256": "28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md": {
+    "sha256": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/emit_model.py": {
+    "sha256": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/emit_native.py": {
+    "sha256": "f961d989a708b40b26780860caa88bf73b86d451b603add3f254d0d0a7a709ff"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/CHECKS.json": {
+    "sha256": "69ee6905c99ab4d93f48d828c378f6c902d5e8a9844df68acbc8971158d76502"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/ROUTE32-MODEL.json": {
+    "sha256": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/native-normal/CHECKS.json": {
+    "sha256": "304b30eb8f9810ff36fcf0a4181bd630a0eb041a6fba89a53fbeea227860cae3"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/route32/native-normal/ROUTE32-NATIVE.json.gz": {
+    "decompressed_sha256": "2f037b4757c46efb849bcfd8ad6cc2919d8486c5a9001d6325152446caf0f3e5",
+    "sha256": "69342058ffb9128ecc743cf478772896fd037c7aeeac845326d65626d7f3b425"
+  },
+  "new-native-recipes-20261017/isotropic-pair-review-20261018/check.py": {
+    "sha256": "e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json": {
+    "sha256": "5991ca1da15d3ffd7778e1de6be870c71f8811c867da6155e963e8bad1570aee"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json": {
+    "sha256": "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md": {
+    "sha256": "67efc6a9b0a04be1b9f2454db4ff5746d1bb389c2e80e0cff7f73e2481e4e798"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json": {
+    "sha256": "57e3b9367f31183f95a66c9ff8c41350dbbe5d771f97a69b71654e42ce045b0c"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json": {
+    "sha256": "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md": {
+    "sha256": "2ef8464d4f8b4867dfacdc7515285d690eb84adc299b7d7ebd1ce46ede1c7b29"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py": {
+    "sha256": "d6fcc9f2279bdd2e6b466dd42552f8add9a8fb05bef3f7f39030a582d729dd8f"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/check_native.py": {
+    "sha256": "e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json": {
+    "sha256": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-REVIEW.json": {
+    "sha256": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-INPUTS.json": {
+    "sha256": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-REVIEW.json": {
+    "sha256": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json": {
+    "sha256": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/normal/REVIEW.json": {
+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/INPUTS.json": {
+    "sha256": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/REVIEW.json": {
+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal/REVIEW.json
new file mode 100644
index 0000000000..bb15996ce5
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/route32-native-review-20261020/normal/REVIEW.json
@@ -0,0 +1,11681 @@
+{
+  "fresh_native_phases": [
+    {
+      "digest": "58c37c5d303422cfdc4161d98c4fed026a1ca4ae461756944903efe8e4bb84a5",
+      "edge": "100:556",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "9642e83903361d65c7e029bba455bafd06e4948a036a37b702f16e07f1d8a833",
+      "edge": "100:558",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "f3ff05ed22474d72da827a25a046751c00902e9ebea3ac1953846ed87a8a1d17",
+      "edge": "102:581",
+      "nonzero_coefficients": 2048,
+      "rank": 1,
+      "spatial_columns": 512
+    },
+    {
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+  "spatial_columns_per_fresh_edge": 512,
+  "status": "PASS_INDEPENDENT_ROUTE32_NATIVE"
+}
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index 0000000000..a7cdeb48dc
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+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "59:389"
+        ],
+        [
+          "rank16",
+          "59:389"
+        ]
+      ],
+      "edge": "59:389"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "5:515"
+        ]
+      ],
+      "edge": "5:483"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "61:809"
+        ]
+      ],
+      "edge": "61:588"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "62:520"
+        ]
+      ],
+      "edge": "62:493"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "63:329"
+        ],
+        [
+          "rank16",
+          "63:329"
+        ]
+      ],
+      "edge": "63:329"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "64:406"
+        ],
+        [
+          "rank16",
+          "64:406"
+        ]
+      ],
+      "edge": "64:406"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "65:297"
+        ],
+        [
+          "rank16",
+          "65:297"
+        ]
+      ],
+      "edge": "65:297"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "66:472"
+        ]
+      ],
+      "edge": "66:468"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "67:513"
+        ],
+        [
+          "rank16",
+          "67:713"
+        ]
+      ],
+      "edge": "67:549"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "6:515"
+        ]
+      ],
+      "edge": "6:483"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "70:513"
+        ],
+        [
+          "rank16",
+          "70:713"
+        ]
+      ],
+      "edge": "70:549"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "71:522"
+        ]
+      ],
+      "edge": "71:484"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "72:247"
+        ],
+        [
+          "rank16",
+          "72:247"
+        ]
+      ],
+      "edge": "72:247"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "73:254"
+        ],
+        [
+          "rank16",
+          "73:254"
+        ]
+      ],
+      "edge": "73:254"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "74:259"
+        ],
+        [
+          "rank16",
+          "74:259"
+        ]
+      ],
+      "edge": "74:259"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "75:474"
+        ]
+      ],
+      "edge": "75:477"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "76:809"
+        ]
+      ],
+      "edge": "76:588"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "78:232"
+        ],
+        [
+          "rank16",
+          "78:232"
+        ]
+      ],
+      "edge": "78:232"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "79:569"
+        ]
+      ],
+      "edge": "79:500"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "7:469"
+        ]
+      ],
+      "edge": "7:467"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "80:293"
+        ],
+        [
+          "rank16",
+          "80:293"
+        ]
+      ],
+      "edge": "80:293"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "81:363"
+        ],
+        [
+          "rank16",
+          "81:363"
+        ]
+      ],
+      "edge": "81:363"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "82:522"
+        ]
+      ],
+      "edge": "82:484"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "83:267"
+        ],
+        [
+          "rank16",
+          "83:267"
+        ]
+      ],
+      "edge": "83:267"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "84:468"
+        ]
+      ],
+      "edge": "84:476"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "84:474"
+        ]
+      ],
+      "edge": "84:477"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "85:468"
+        ]
+      ],
+      "edge": "85:476"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "85:530"
+        ],
+        [
+          "rank16",
+          "85:470"
+        ]
+      ],
+      "edge": "85:478"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "86:603"
+        ]
+      ],
+      "edge": "86:494"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "87:564"
+        ]
+      ],
+      "edge": "87:508"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "88:564"
+        ]
+      ],
+      "edge": "88:508"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "88:566"
+        ]
+      ],
+      "edge": "88:510"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "89:232"
+        ],
+        [
+          "rank16",
+          "89:232"
+        ]
+      ],
+      "edge": "89:232"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "8:563"
+        ]
+      ],
+      "edge": "8:507"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "8:566"
+        ]
+      ],
+      "edge": "8:510"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "90:616"
+        ]
+      ],
+      "edge": "90:516"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "91:259"
+        ],
+        [
+          "rank16",
+          "91:259"
+        ]
+      ],
+      "edge": "91:259"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "92:254"
+        ],
+        [
+          "rank16",
+          "92:254"
+        ]
+      ],
+      "edge": "92:254"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "93:247"
+        ],
+        [
+          "rank16",
+          "93:247"
+        ]
+      ],
+      "edge": "93:247"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "94:267"
+        ],
+        [
+          "rank16",
+          "94:267"
+        ]
+      ],
+      "edge": "94:267"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "96:363"
+        ],
+        [
+          "rank16",
+          "96:363"
+        ]
+      ],
+      "edge": "96:363"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "97:662"
+        ]
+      ],
+      "edge": "97:534"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "98:756"
+        ]
+      ],
+      "edge": "98:564"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank16",
+          "99:756"
+        ]
+      ],
+      "edge": "99:564"
+    },
+    {
+      "accepted_sources": [
+        [
+          "rank30",
+          "9:389"
+        ],
+        [
+          "rank16",
+          "9:389"
+        ]
+      ],
+      "edge": "9:389"
+    }
+  ],
+  "literal_words": {
+    "base": {
+      "backward": {
+        "all_input_columns": 640,
+        "external_endpoint_maps": 224,
+        "native_children": 1120,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 944,
+          "3": 48,
+          "5": 64,
+          "6": 64
+        },
+        "native_side_map_bound": 2240,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 4312,
+        "top_level_array_norm_bound": "14",
+        "untouched_arbitrary_roles": 416,
+        "used_native_edges": 1049
+      },
+      "forward": {
+        "all_input_columns": 640,
+        "external_endpoint_maps": 224,
+        "native_children": 1120,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 944,
+          "3": 48,
+          "5": 64,
+          "6": 64
+        },
+        "native_side_map_bound": 2240,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 4312,
+        "top_level_array_norm_bound": "14",
+        "untouched_arbitrary_roles": 416,
+        "used_native_edges": 1049
+      }
+    },
+    "extra": {
+      "backward": {
+        "all_input_columns": 640,
+        "external_endpoint_maps": 224,
+        "native_children": 1120,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 944,
+          "3": 48,
+          "5": 64,
+          "6": 64
+        },
+        "native_side_map_bound": 2240,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 4312,
+        "top_level_array_norm_bound": "14",
+        "untouched_arbitrary_roles": 416,
+        "used_native_edges": 1049
+      },
+      "forward": {
+        "all_input_columns": 640,
+        "external_endpoint_maps": 224,
+        "native_children": 1120,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 944,
+          "3": 48,
+          "5": 64,
+          "6": 64
+        },
+        "native_side_map_bound": 2240,
+        "owned_fields": 0,
+        "private_fields": 0,
+        "real_scalar_primitives": 4312,
+        "top_level_array_norm_bound": "14",
+        "untouched_arbitrary_roles": 416,
+        "used_native_edges": 1049
+      }
+    }
+  },
+  "missing_transfer_controls": {
+    "base": {
+      "backward": {
+        "removed_event": [
+          "scalar",
+          [
+            "add",
+            2,
+            182,
+            "1"
+          ],
+          238
+        ],
+        "removed_event_index": 304
+      },
+      "forward": {
+        "removed_event": [
+          "scalar",
+          [
+            "add",
+            182,
+            2,
+            "-1"
+          ],
+          238
+        ],
+        "removed_event_index": 304
+      }
+    },
+    "extra": {
+      "backward": {
+        "removed_event": [
+          "scalar",
+          [
+            "add",
+            2,
+            182,
+            "1"
+          ],
+          238
+        ],
+        "removed_event_index": 304
+      },
+      "forward": {
+        "removed_event": [
+          "scalar",
+          [
+            "add",
+            182,
+            2,
+            "-1"
+          ],
+          238
+        ],
+        "removed_event_index": 304
+      }
+    }
+  },
+  "scope": "Complete raw local native words for the pinned route32 response. Model, principal inverse and capture-code theorems require separate review. No root-gauge code, transition, odd-division implementation, productive helper progress, recursive hosting or complete supplier claim.",
+  "spatial_columns_per_fresh_edge": 512,
+  "status": "PASS_INDEPENDENT_ROUTE32_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md
new file mode 100644
index 0000000000..64df4c61d3
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md
@@ -0,0 +1,98 @@
+# Independent derivation of the selected-row service
+
+This derivation precedes the review of the emitted word. It gives the
+map that the word must implement. It does not certify that word.
+
+Let V have r independent rows. Let P be an ordered set of r ports,
+and let V_P be the square submatrix on those columns. Assume V_P is
+invertible. Put W=V_P^{-1}V. Then W_P=I.
+
+Define C to have rows W on P and identity rows on the other ports.
+If B=W-pi_P, where pi_P selects P, then
+
+\[
+C=I+\iota_P B,\qquad B\iota_P=0,\qquad
+C^{-1}=I-\iota_P B.
+\]
+
+Here iota_P inserts r coordinates at P. Thus C is a shear. Its
+determinant is one. If W is dyadic, both C and its inverse are dyadic.
+Every addition uses an unchanged coordinate outside P. No extra field
+or zero-input assumption is needed. Reversing the literal additions
+gives the inverse.
+
+The row code is independent of the basis used for the row space of V.
+Replacing V by A V, for any invertible A, leaves W unchanged.
+
+For the present response E, direct normalization of the pinned V gives
+eight rows of support 21 and eight rows of support 8. The first rows
+have pivot coefficient 1 and twenty coefficients of magnitude 1/2.
+The other rows have pivot coefficient 1 and seven coefficients 1.
+The precode therefore has 216 complex additions, at 2048 old real
+scalar units under the retained scalar invoice.
+
+These rows are left eigenvectors:
+
+\[
+WE=\Lambda W,\qquad
+\Lambda=\operatorname{diag}(-5I_8,-7I_8).
+\]
+
+Therefore the selected rows of CE are exactly Lambda W. Their direct
+late additions cost 3696 old real scalar units. These are separate
+costs; they do not include the retained core or the new native children.
+
+## Physical operation
+
+Use Q for the diagonal family of positive input line operators,
+q=Q^{-1}, and F for the common full operator. The raw forward word has
+physical contract
+
+\[
+(Qx,y)\longmapsto(Fx,Fq(y+Ex)).
+\]
+
+Suppose the exact event list permits all operations on the selected
+target fields to be removed. Every retained operation must have no
+read from those fields. The source subsystem and the other targets
+must retain their original event lists.
+
+Apply C to current input Y while all target fields have the I frame.
+Apply F to each selected target. Run the retained source and ordinary
+target operations. After all source fields have reached F, add
+the selected rows of CE from those source fields to the selected
+targets. The physical result is
+
+\[
+X'=Fx,\qquad
+Y'_P=F[C(y+Ex)]_P,\qquad
+Y'_R=F[q(y+Ex)]_R.
+\]
+
+Scalar coefficients commute with the common F in the final query.
+No step commutes C or E through Q. In particular, the precode acts
+on the physical current-I target values. It does not act on a
+changed logical frame.
+
+Write T for the output operator that is F on P and Fq on R.
+Then the full target contract is T C(y+Ex), since C is identity
+on the rows in R. This is an invertible output representation.
+Its entry into a later word, inverse, final decode, and recursive
+hosting require their own implementation and cost.
+
+## Required literal checks
+
+The review must check the selected set and every removed event.
+It must reject a retained read of a removed target. It must check
+the exact full-frame recipe, including its global phase, and all
+inherited native records. It must check that every source has
+reached the same F frame before the final query.
+
+The complete word must pass every arbitrary input column. The
+unchanged helper fields must retain their arbitrary values.
+The native and scalar invoice must include the precode, all retained
+events, the sixteen full children, and the late query.
+
+No PR, push, commit, or publication is authorized. Before any future
+PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..60530966a8
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json
@@ -0,0 +1,15 @@
+{
+  "files": {
+    "DERIVATION.md": "74bfa14362b8a704d409cb3995fe645173e99205653528bcf6b47f62de7455a1",
+    "REPRODUCTION.json": "9525e5e1871d60a01c8acd222944abe6edab71f9d5448410265859dcece6901f",
+    "REVIEW.md": "39cb0df65e81f92854d0238d9023eaa092205bdce8e3b81724c2e4d19a3ef4f1",
+    "check.py": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84",
+    "normal/INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1",
+    "normal/REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56",
+    "optimized/INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1",
+    "optimized/REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56"
+  },
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "Both complete local providers, direct-FULL refinement, exact physical phases, arbitrary inputs, and local invoice. No recursive hosting, later-stage conversion, full decoder, supplier, or kappa claim.",
+  "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..b8d020d7f9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1",
+    "REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56"
+  },
+  "source_files_rechecked": 44,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..8bdaaa327e
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md
@@ -0,0 +1,255 @@
+# Independent review of the selected-row native service
+
+The frozen word forms the sixteen centre rows of the actual rank16
+response in sixteen existing target fields. It preserves arbitrary
+target baselines and all 416 fields outside the two data banks.
+It uses no new field, private field, or odd-arithmetic scan.
+
+The local service and its direct-FULL refinement pass the independent
+checks below. No material defect was found. The output representation
+has changed. Its use by a complete recursive caller remains open.
+
+## Inputs and independent method
+
+The main producer
+[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/FREEZE.json)
+has SHA256
+`5321a8ff856042c5ca30ce6b29b90a51ccd4dcf02317820243bfffbb433c84d8`.
+Its decompressed payload SHA256 is
+`7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2`.
+
+The separate direct-FULL
+[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL-FREEZE.json)
+has SHA256
+`f0d3b0d7c8d93e391089a2d28066dd02b4a9b28e306dea5f4e7cb5fc895b054e`.
+Its decompressed payload SHA256 is
+`fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c`.
+
+The actual source word is the rank16 extension at decompressed SHA256
+`d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4`.
+The controller's scalar
+[freeze](../../controller-followthrough-20261017/row-capture-20261020/FREEZE.json)
+has SHA256
+`0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf`.
+
+The checker imports no producer code. It constructs the pivot inverse
+from the exact signed Hadamard Gram matrix. It then constructs C,
+its inverse, CE, and the encoded response independently. It checks
+the scalar words by reverse output-column propagation. A separate
+forward row pass checks the complete map and every scalar prefix.
+
+The physical phase interpreter is the pinned independent integer
+Gaussian interpreter from the isotropic-pair review. It uses literal
+address maps and exact Gaussian coefficients. It does not import
+the producer's Clifford compiler or phase checker.
+
+## Exact code and physical contract
+
+The independent derivation is in [DERIVATION.md](DERIVATION.md).
+Let \(E=I+UV\), and let P be the ordered set
+
+```text
+0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23.
+```
+
+Put \(W=V_P^{-1}V\). The actual pivot Gram matrix is
+\(\operatorname{diag}(2I_8,I_8)\). This gives a direct exact inverse
+for \(V_P\), with both inverse orders checked.
+
+Define C to have rows W on P and identity rows elsewhere. The
+correction \(C-I\) has square zero and rank sixteen. Thus
+
+\[
+C=I+\iota_P(W-\pi_P),\qquad
+C^{-1}=I-\iota_P(W-\pi_P).
+\]
+
+The checker verifies both matrix inverse orders and both literal
+scalar inverse orders. The code and inverse are dyadic and each
+cost 1760 old real scalar units. They need no extra field.
+
+The actual rows satisfy
+
+\[
+WE=\operatorname{diag}(-5I_8,-7I_8)W.
+\]
+
+The selected rows of CE are therefore those same sixteen queries
+with multipliers -5 or -7. The scalar late-query word adds these
+rows to an arbitrary existing target value. It costs 3424 units.
+It does not divide by five or seven.
+
+Write \(q=Q^{-1}\). For physical input \((Qx,y)\), the exact output is
+
+\[
+X'=F_9x,\qquad
+Y'_P=F_9[C(y+Ex)]_P,\qquad
+Y'_R=F_9[q(y+Ex)]_R.
+\]
+
+The selected values include the arbitrary baseline \(Wy\). No
+baseline is set to zero or removed from the output contract.
+Equivalently, \(Y'=TC(y+Ex)\), where T is \(F_9\) on P and
+\(F_9q\) on R. This is an invertible output representation.
+No step commutes C or E through Q.
+
+## Complete operation order
+
+The checker derives the deletion from the original literal word.
+It removes all events whose target is selected Y. For each provider,
+this is exactly 128 H1 calls and 122 scalar events. Those scalar
+events cost 928 units.
+
+Every retained event is inspected. No retained scalar event reads a
+selected target. All retained events appear in their original order
+and with their exact original bytes. Removing only one member of a
+selected large pair fails the retained-read check.
+
+The new complete word has four stages:
+
+| Stage | Event interval, end excluded | Real scalar units |
+| --- | --- | ---: |
+| Current-I precode C | 0 to 232 | 1760 |
+| Retained original word | 232 to 2622 | 6456 |
+| Sixteen I-to-FULL children | 2622 to 2638 | 0 |
+| Late common-FULL query | 2638 to 2886 | 3424 |
+
+Every source and selected target has frame FULL before the late
+query. Every scalar addition has the same actual source and target
+frame. All final frame declarations are checked. The 96 ordinary
+target declarations are unchanged. The selected targets end in FULL.
+
+Both providers pass all 640 independent input columns. A separate
+forward pass gives the same complete map. Every field numbered
+224 through 639 retains its arbitrary input. No operation addresses
+these fields. There is no CLEAR, hidden zero field, or new owned state.
+Deleting the precode or late query is rejected by the full-column test.
+
+## Physical phases
+
+There are 1447 distinct retained native recipes. Each is byte equal
+to the exact ordered frame pair in the already accepted rank16 word.
+The inherited phase proof is pinned by
+[the independent extension freeze](../low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json),
+at SHA256
+`c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c`,
+and its base native review. This review does not repeat that full
+phase sweep.
+
+The new rank-nine recipe occurs sixteen times. The independent
+interpreter checks all 512 spatial input columns against the exact
+nine positive coordinate kernels. Every column has 512 exact
+nonzero coefficients. The comparison includes the global phase.
+A wrong global phase is rejected.
+
+All 112 source entry adapters are exact inherited records. The
+96 ordinary outgoing adapters are new explicit inverse monomials.
+For each, the checker composes it with the accepted incoming
+target adapter in both orders. Every one of the 512 input columns
+is exactly the identity in both orders. This proves the outgoing
+map to \(F_9q_p\), including phase.
+
+No outgoing hole adapter is present on a selected target. Its
+canonical FULL frame is exactly \(F_9\). These exact spatial
+identities tensor to every width admitted by the retained primitive
+contract. They are exact equalities, not equalities up to phase.
+
+The checker verifies the executed recipes. The producer's
+descriptive compiler circuits are not executed by this review.
+Their intended endpoint functions are checked through the exact
+inverse-adapter identities above.
+
+## Direct-FULL refinement
+
+The accepted native recipe convention uses
+\(C_{e_0}\cdots C_{e_{r-1}}\) between its two monomial maps.
+At rank nine, this is already the required \(F_9\). Identity
+left and right maps therefore suffice.
+
+The checker verifies that direct recipe on every spatial column.
+It then compares both complete refined provider words with the
+main packet. All events, frames, endpoint views, and matrices are
+byte equal. Only the shared rank-nine recipe changes. Thus the
+complete-word correctness proof transfers by exact substitution.
+There is no need for a new logical-column replay of an unchanged
+event list.
+
+The refinement removes the two nontrivial side maps from each of
+the sixteen new calls. It does not change their sizes or number.
+The native side-map upper bound drops from 3040 to 3008.
+
+## Complete local invoice and precision scope
+
+Each provider has the profile
+
+```text
+1392 H1 + 64 H2 + 48 H3 + 16 H9.
+```
+
+This is 1520 recursive calls and native mass 1808. The complete
+old scalar invoice is 11640. The direct refinement has 112 input
+monomial views, 96 output monomial views, and at most 3008 native
+side maps. It uses no odd-arithmetic scan or new field.
+
+The high-rank calls remain sixteen rank-nine calls. A complete
+recurrence must use their exact sizes. Replacing their costs by
+native mass alone is not a complete cost calculation.
+
+The exact content row one-norm over the entire emitted word is at
+most 132. The additional content binary denominator height is one.
+Both bounds include the precode and the late scaled queries.
+Under the unitary native charts, the first bound also applies to
+the per-field Hilbert norm at operation boundaries.
+
+These are local content bounds. They do not price primitive
+internals, recursive-child guards, rounding error, outer owner
+views, or the full numerical precision requirement.
+
+## Reuse and remaining scope
+
+The row-replacement argument is structural. If a forward word has
+independent source progress, an isolated selected target set, and
+an invertible row code that can be formed at the common input
+frame, replace those target paths by frame advances and a late
+coded response query. The output retains every arbitrary target
+baseline. The present word verifies all these premises.
+
+The separate
+[access packet](../../bridge-access-20261017/row-capture-access-20261020/FREEZE.json),
+at SHA256
+`9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11`,
+binds the construction to its literal D25 owner views. This review
+pins that packet but does not rerun its phase census.
+
+That packet gives the next current-entry type as Q on selected
+carriers and I elsewhere. This is not the old all-I target type.
+A later caller must consume that type or implement its conversion.
+No such conversion, final decoder, full controller, or recursive
+host is included in the local invoice.
+
+This review establishes local centre formation in existing output
+fields. It does not establish a complete supplier or a kappa
+improvement.
+
+## Reproduction and credit
+
+Run from the workspace root:
+
+```text
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized
+```
+
+The required final line is `PASS_INDEPENDENT_ROW_CAPTURE_NATIVE`.
+`REPRODUCTION.json` records the byte comparison and final source
+hash checks.
+Both runs completed with that result. Their result and input
+receipts are byte identical. All 44 consumed source files were
+rechecked and are unchanged.
+
+The producer proof records the source, cyclic, controller, and
+bridge-access contributions. The independent review supplied the
+direct-FULL identity-map deduction. AI assistance was used.
+No PR, push, commit, or publication is authorized. Before any future
+PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py
new file mode 100644
index 0000000000..6fa689d442
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py
@@ -0,0 +1,450 @@
+#!/usr/bin/env python3
+"""Check the selected-row code and its complete native service."""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+INPUTS = {}
+P = [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23]
+RAW = LANES/'new-core-transfer-20261017/low-displacement-20261020'
+ALG = LANES/'controller-followthrough-20261017/row-capture-20261020'
+NATIVE = RAW/'row-only-capture-20261020'
+ACCEPTED = LANES/'new-native-recipes-20261017/low-displacement-review-20261020'
+
+
+def need(test, message):
+    if not test:
+        raise ValueError(message)
+
+
+def read(path, pin=None, compressed=False):
+    data = path.read_bytes()
+    content = gzip.decompress(data) if compressed else data
+    need(pin is None or sha256(content).hexdigest() == pin,
+         'Input pin: '+str(path))
+    INPUTS[str(path.relative_to(LANES))] = {'sha256': sha256(data).hexdigest()}
+    if compressed:
+        INPUTS[str(path.relative_to(LANES))]['decompressed_sha256'] = sha256(content).hexdigest()
+    return content
+
+
+def frozen(path, name, pin):
+    obj = json.loads(read(path/name, pin))
+    for name, digest in obj['files'].items():
+        read(path/name, digest)
+    return obj
+
+
+def rows(value):
+    return [{int(k): F(v) for k, v in row.items() if F(v)} for row in value]
+
+
+def unit(n):
+    return [{i: F(1)} for i in range(n)]
+
+
+def add(target, source, coefficient=F(1)):
+    for key, value in source.items():
+        x = target.get(key, F(0))+coefficient*value
+        if x:
+            target[key] = x
+        else:
+            target.pop(key, None)
+
+
+def mul(a, b):
+    out = []
+    for row in a:
+        result = {}
+        for k, v in row.items():
+            add(result, b[k], v)
+        out.append(result)
+    return out
+
+
+def rank(a):
+    pivots = {}
+    for original in a:
+        row = dict(original)
+        while row:
+            j = min(row)
+            if j not in pivots:
+                value = row[j]
+                pivots[j] = {k: v/value for k, v in row.items()}
+                break
+            add(row, pivots[j], -row[j])
+    return len(pivots)
+
+
+def transpose(a, n):
+    out = [{} for _ in range(n)]
+    for i, row in enumerate(a):
+        for j, v in row.items():
+            out[j][i] = v
+    return out
+
+
+def price(events):
+    total = 0
+    for op, _, _, value in events:
+        c = F(value)
+        n, d = abs(c.numerator), c.denominator
+        need(n > 0 and d & (d-1) == 0, 'Nonzero dyadic coefficient')
+        if op == 'scale':
+            need(n & (n-1) == 0, 'Dyadic unit scale')
+            total += 2*(abs(n.bit_length()-d.bit_length())+(c < 0))
+        else:
+            need(op == 'add', 'Scalar opcode')
+            total += 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1)
+    return total
+
+
+def reverse(events, n):
+    """Propagate output columns through the scalar word in reverse order."""
+    columns = unit(n)
+    for op, target, origin, value in reversed(events):
+        c = F(value)
+        if op == 'scale':
+            columns[target] = {k: c*v for k, v in columns[target].items()}
+        else:
+            need(op == 'add' and target != origin, 'Distinct ADD fields')
+            add(columns[origin], columns[target], c)
+    return columns
+
+
+def prefix(events, n):
+    """Compute exact prefix rows, separately from the reverse pass."""
+    state = unit(n)
+    norm, height = F(1), 0
+    for op, target, origin, value in events:
+        c = F(value)
+        if op == 'scale':
+            state[target] = {k: c*v for k, v in state[target].items()}
+        else:
+            add(state[target], state[origin], c)
+        norm = max(norm, sum(map(abs, state[target].values()), F(0)))
+        for x in state[target].values():
+            d = x.denominator
+            need(d & (d-1) == 0, 'Dyadic prefix coefficient')
+            height = max(height, d.bit_length()-1)
+    return state, {'row_one_norm': str(norm), 'binary_height': height}
+
+
+def algebra(raw, code):
+    model = raw['model']
+    e, u, v = (rows(model[name]) for name in ('response', 'correction_U', 'correction_V'))
+    uv = mul(u, v)
+    expected_e = unit(112)
+    for row, correction in zip(expected_e, uv):
+        add(row, correction)
+    need(e == expected_e, 'Actual response factorization')
+    vp = [{j: row[p] for j, p in enumerate(P) if p in row} for row in v]
+    # The actual pivot blocks are signed two-coordinate Hadamards and units.
+    vp_t = transpose(vp, 16)
+    gram = [{i: F(2 if i < 8 else 1)} for i in range(16)]
+    need(mul(vp, vp_t) == gram, 'Actual pivot Gram matrix')
+    vi = [{j: x/(2 if j < 8 else 1) for j, x in row.items()} for row in vp_t]
+    need(mul(vi, vp) == unit(16) and mul(vp, vi) == unit(16), 'Pivot inverse orders')
+    w = mul(vi, v)
+    c, ci, b = unit(112), unit(112), []
+    for i, p in enumerate(P):
+        need({j: w[i].get(q, F(0)) for j, q in enumerate(P)} ==
+             {j: F(i == j) for j in range(16)}, 'Normalized pivot columns')
+        c[p] = dict(w[i])
+        correction = dict(w[i])
+        add(correction, {p: F(1)}, F(-1))
+        b.append(correction)
+        add(ci[p], correction, F(-1))
+    need(mul(c, ci) == unit(112) and mul(ci, c) == unit(112), 'Shear inverse orders')
+    need(rank(b) == 16, 'Exact shear displacement rank')
+    lamb = [{i: F(-5 if i < 8 else -7)} for i in range(16)]
+    need(mul(w, e) == mul(lamb, w), 'Selected left eigenvectors')
+    ce = mul(c, e)
+    encoded = mul(ce, ci)
+    need(all(set(row)-{i} <= set(P) for i, row in enumerate(encoded)),
+         'Encoded response changes only pivot columns')
+    for name, value in [('pivot_minor', vp), ('pivot_minor_inverse', vi),
+                        ('centre_reader', w), ('code', c), ('code_inverse', ci),
+                        ('response', e), ('selected_capture_response', ce),
+                        ('encoded_response', encoded)]:
+        need(rows(code[name]) == value, 'Independent algebra: '+name)
+    need(code['pivots'] == P, 'Exact selected ports')
+    for name, matrix in [('scalar_word', c), ('inverse_scalar_word', ci)]:
+        events = code[name]
+        need(reverse(events, 112) == transpose(matrix, 112), 'Reverse code: '+name)
+        need(price(events) == 1760, 'Code scalar price')
+        for op, target, origin, _ in events:
+            need(target in P and (op == 'scale' or origin not in P), 'Unchanged shear source')
+    word = code['scalar_word']+code['inverse_scalar_word']
+    need(reverse(word, 112) == unit(112), 'Literal inverse order')
+    need(reverse(code['inverse_scalar_word']+code['scalar_word'], 112) == unit(112),
+         'Other literal inverse order')
+    query = unit(224)
+    for p in P:
+        add(query[p], {112+j: x for j, x in ce[p].items()})
+    need(reverse(code['final_query_word'], 224) == transpose(query, 224),
+         'Arbitrary-baseline late query')
+    need(price(code['final_query_word']) == 3424, 'Late query scalar price')
+    a, pre_bound = prefix(code['scalar_word'], 112)
+    need(a == c, 'Separate forward code')
+    a, query_bound = prefix(code['final_query_word'], 224)
+    need(a == query, 'Separate forward late query')
+    return e, c, ce, {
+        'code_price': 1760, 'query_price': 3424,
+        'code_prefix': pre_bound, 'query_prefix_on_independent_inputs': query_bound,
+        'displacement_rank': 16, 'extra_fields': 0, 'odd_scans': 0,
+    }
+
+
+def inherit():
+    frozen(ACCEPTED, 'NATIVE-REVIEW-FREEZE.json',
+           'cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976')
+    frozen(ACCEPTED, 'EXTENSIONS-REVIEW-FREEZE.json',
+           'c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c')
+    phase_path = LANES/'new-native-recipes-20261017/isotropic-pair-review-20261018/check.py'
+    read(phase_path, 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18')
+    spec = importlib.util.spec_from_file_location('independent_spatial_phase', phase_path)
+    phase = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(phase)
+    return phase
+
+
+def select_raw(raw_word, selected):
+    indices, removed = [], []
+    for i, event in enumerate(raw_word['events']):
+        need(event[0] in ('native', 'scalar'), 'Raw event grammar')
+        target = event[1] if event[0] == 'native' else event[1][1]
+        (removed if target in selected else indices).append(i)
+    for i in indices:
+        event = raw_word['events'][i]
+        if event[0] == 'scalar' and event[1][0] == 'add':
+            need(event[1][2] not in selected, 'Retained read of removed target')
+    return indices, removed
+
+
+def check_word(word, old, code, e, c, ce):
+    need(word['frames'] == old['frames'] and word['start'] == old['start'],
+         'Unchanged exact input geometry')
+    selected = {112+p for p in P}
+    indices, removed = select_raw(old, selected)
+    need(word['retained_original_event_indices'] == indices, 'Exact removal indices')
+    kept = [old['events'][i] for i in indices]
+    cut = [old['events'][i] for i in removed]
+    need(Counter(x[0] for x in cut) == {'native': 128, 'scalar': 122},
+         'Complete removed inventory')
+    need(Counter(x[4] for x in cut if x[0] == 'native') == {1: 128},
+         'Only the selected rank-one children are removed')
+    need(price([x[1] for x in cut if x[0] == 'scalar']) == 928, 'Removed scalar price')
+    pre = [['scalar', [op, 112+t, None if s is None else 112+s, v], 0]
+           for op, t, s, v in code['scalar_word']]
+    progress = [['native', 112+p, 0, 1, 9, 'capture-full'] for p in P]
+    late = [['scalar', [op, 112+t, None if s is None else s-112, v], 1]
+            for op, t, s, v in code['final_query_word']]
+    need(word['events'] == pre+kept+progress+late, 'Exact complete operation order')
+    stages = [('precode', pre), ('retained_core', kept),
+              ('selected_full_progress', progress), ('late_query', late)]
+    cursor, expected_ranges = 0, {}
+    for name, events in stages:
+        expected_ranges[name] = [cursor, cursor+len(events)]
+        cursor += len(events)
+    need(word['stage_ranges'] == expected_ranges, 'Exact stage boundaries')
+    need(cursor == 2886, 'Complete event count')
+    final = list(old['final'])
+    for field in selected:
+        final[field] = 1
+    need(word['final'] == final, 'Exact changed output frames')
+    need(old['frames'][0] == [] and len(old['frames'][1]) == 9, 'I and FULL declarations')
+    current = list(word['start'])
+    count, used = Counter(), set()
+    for i, event in enumerate(word['events']):
+        if i == expected_ranges['late_query'][0]:
+            need(all(current[p] == 1 for p in range(112)) and
+                 all(current[p] == 1 for p in selected), 'Late common-FULL cut')
+        if event[0] == 'native':
+            _, field, before, after, r, key = event
+            need(0 <= field < 224 and current[field] == before, 'Native field and old frame')
+            need(word['native_recipes'][key]['rank'] == r, 'Native rank binding')
+            if key == 'capture-full':
+                need(field in selected and (before, after, r) == (0, 1, 9),
+                     'Only selected complete FULL replacements')
+            else:
+                need(word['native_recipes'][key] == old['native_recipes'][key],
+                     'Exact inherited phase record')
+                need(key == str(before)+':'+str(after), 'Ordered inherited frame pair')
+            current[field] = after
+            count[r] += 1
+            used.add(key)
+        else:
+            _, scalar, frame = event
+            op, target, origin, _ = scalar
+            need(0 <= target < 224 and current[target] == frame, 'Scalar target frame')
+            if op == 'add':
+                need(0 <= origin < 224 and current[origin] == frame, 'Scalar source frame')
+            else:
+                need(op == 'scale' and origin is None, 'Scale grammar')
+    need(current == final, 'Complete final frame ledger')
+    need(used == set(word['native_recipes']), 'Every stored recipe is used')
+    need(count == {1: 1392, 2: 64, 3: 48, 9: 16}, 'Complete native profile')
+    scalars = [event[1] for event in word['events'] if event[0] == 'scalar']
+    expected = unit(640)
+    for p in range(112):
+        target = 112+p
+        expected[target] = {112+j: v for j, v in c[p].items()}
+        add(expected[target], ce[p] if p in P else e[p])
+    need(reverse(scalars, 640) == transpose(expected, 640), 'All640 reverse input columns')
+    actual, growth = prefix(scalars, 640)
+    need(actual == expected and actual[224:] == unit(640)[224:], 'Separate forward row check')
+    need(growth == {'row_one_norm': '132', 'binary_height': 1},
+         'Complete operation-boundary content bounds')
+    need(price(scalars) == 11640, 'Complete scalar invoice')
+    stage_prices = {name: price([e[1] for e in events if e[0] == 'scalar'])
+                    for name, events in stages}
+    need(stage_prices == {'precode': 1760, 'retained_core': 6456,
+                          'selected_full_progress': 0, 'late_query': 3424},
+         'All four scalar stage bills')
+    input_views = [r for r in old['endpoint_adapters'] if r['role'] == 'source']
+    need(word['input_views'] == input_views, 'All112 exact input phase adapters')
+    outputs = word['output_views']
+    need(len(outputs) == 96 and {r['port'] for r in outputs} == set(range(112))-set(P),
+         'Exactly the96 ordinary output adapters')
+    for r in outputs:
+        need(r['frame'] == final[112+r['port']] and r['recipe']['rank'] == 0 and
+             r['recipe']['right'] is None, 'One output monomial in the actual ordinary frame')
+    full = [['C', 1 << j, 1] for j in range(9)]
+    need(word['new_full_recipe_circuit'] == full, 'Declared complete positive FULL kernel')
+    need(reverse([x[1] for x in kept+progress+late if x[0] == 'scalar'], 640) !=
+         transpose(expected, 640), 'Missing precode control')
+    need(reverse([x[1] for x in pre+kept+progress if x[0] == 'scalar'], 640) !=
+         transpose(expected, 640), 'Missing late query control')
+    try:
+        select_raw(old, selected-{112+27})
+    except ValueError:
+        pass
+    else:
+        raise ValueError('Incomplete selected-pair control')
+    return {
+        'input_columns': 640, 'unchanged_arbitrary_roles': 416, 'events': cursor,
+        'removed_events': len(removed), 'removed_scalar_price': 928,
+        'native_profile': dict(sorted(count.items())),
+        'native_children': sum(count.values()), 'native_mass': sum(r*n for r, n in count.items()),
+        'real_scalar_primitives': price(scalars), 'scalar_stage_prices': stage_prices,
+        'input_views': 112, 'output_views': 96,
+        'native_side_maps_upper_bound': 2*sum(count.values()),
+        'inherited_distinct_native_recipes': len(used)-1,
+        'new_distinct_native_recipes': 1, 'growth': growth,
+        'private_fields': 0, 'new_fields': 0, 'odd_scans': 0,
+    }
+
+
+def phases(word, old, phase):
+    full = [('C', 1 << j, 1) for j in range(9)]
+    record = word['native_recipes']['capture-full']
+    result = {'full': phase.compare(phase.recipe(record), full, 'New complete F9', 512)}
+    old_target = {r['port']: r for r in old['endpoint_adapters'] if r['role'] == 'target'}
+    inverse_checks = []
+    for view in word['output_views']:
+        p = view['port']
+        inherited = phase.recipe(old_target[p])
+        new = phase.recipe(view['recipe'])
+        left = phase.compare(inherited+new, [], 'Output inverse '+str(p), 1)
+        right = phase.compare(new+inherited, [], 'Output inverse other order '+str(p), 1)
+        inverse_checks.append({'port': p, 'orders': [left, right]})
+    result['output_inverse_monomials'] = inverse_checks
+    identity = {'matrix_rows': [1 << j for j in range(9)],
+                'quadratic_rows': [0]*9, 'linear_Z4': [0]*9, 'offset': 0, 'phase': 0}
+    direct = {'rank': 9, 'left': identity, 'right': identity}
+    result['identity_wrapper_corollary'] = phase.compare(
+        phase.recipe(direct), full, 'Direct identity-wrapper F9', 512)
+    bad = phase.recipe(record)+phase.compile_circuit([['phase', 1]])
+    need(phase.run(bad, 0) != phase.run(full, 0), 'Wrong global phase control')
+    result['scope'] = 'Exact executed recipes; descriptive compiler circuits are not executed.'
+    return result
+
+
+def direct_refinement(payload):
+    frozen(NATIVE, 'DIRECT-FULL-FREEZE.json',
+           'f0d3b0d7c8d93e391089a2d28066dd02b4a9b28e306dea5f4e7cb5fc895b054e')
+    direct = json.loads(read(NATIVE/'direct-normal/DIRECT-FULL-CAPTURE.json.gz',
+                             'fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c', True))
+    need(direct['refinement_source_decompressed_sha256'] ==
+         '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2',
+         'Exact refinement source')
+    need(set(direct) == set(payload)|{'refinement_source_decompressed_sha256'},
+         'No additional refinement state')
+    for key in set(payload)-{'providers', 'schema'}:
+        need(direct[key] == payload[key], 'Unchanged refinement metadata: '+key)
+    identity = {'matrix_rows': [1 << j for j in range(9)],
+                'quadratic_rows': [0]*9, 'linear_Z4': [0]*9, 'offset': 0, 'phase': 0}
+    expected = {'rank': 9, 'left': identity, 'right': identity}
+    for name, word in payload['providers'].items():
+        changed = direct['providers'][name]
+        need(set(changed) == set(word), 'Unchanged word schema')
+        for key in set(word)-{'native_recipes'}:
+            need(changed[key] == word[key], 'Exact unchanged complete word: '+key)
+        need(set(changed['native_recipes']) == set(word['native_recipes']),
+             'No additional native recipe')
+        for key, record in word['native_recipes'].items():
+            need(changed['native_recipes'][key] == (expected if key == 'capture-full' else record),
+                 'Only the direct FULL recipe changes')
+    return {'providers': ['base', 'extra'], 'changed_occurrences_per_word': 16,
+            'all_events_and_boundary_views_byte_equal': True,
+            'real_scalar_primitives': 11640, 'native_children': 1520, 'native_mass': 1808,
+            'native_side_maps_upper_bound': 3008,
+            'proof': 'Exact complete-word substitution using the independently checked identity-wrapper kernel.'}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    frozen(ALG, 'FREEZE.json', '0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf')
+    raw = json.loads(read(RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz',
+                          'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True))
+    code = json.loads(read(ALG/'run-normal/ROW-CAPTURE.json',
+                           '4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7'))
+    e, c, ce, algebra_report = algebra(raw, code)
+    frozen(NATIVE, 'FREEZE.json',
+           '5321a8ff856042c5ca30ce6b29b90a51ccd4dcf02317820243bfffbb433c84d8')
+    frozen(LANES/'bridge-access-20261017/row-capture-access-20261020', 'FREEZE.json',
+           '9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11')
+    payload = json.loads(read(NATIVE/'run-normal/PRODUCTIVE-CAPTURE.json.gz',
+                              '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', True))
+    need(payload['schema'] == 'productive-sixteen-full-capture-v1', 'Native schema')
+    need(payload['selected_ports'] == P and payload['ports'] == raw['model']['ports'],
+         'Exact physical selected ports and line directions')
+    need(payload['ordinary_ports'] == sorted(set(range(112))-set(P)) and
+         payload['inverse_code'] == code['code_inverse'], 'Complete inverse and ordinary metadata')
+    for key, expected in [('response', e), ('code', c), ('captured_response', ce)]:
+        need(rows(payload[key]) == expected, 'Native matrix contract: '+key)
+    need(set(payload['providers']) == {'base', 'extra'}, 'Both providers')
+    need(payload['providers']['base'] == payload['providers']['extra'],
+         'Byte-equal provider payloads')
+    word_reports = {}
+    for provider, word in payload['providers'].items():
+        word_reports[provider] = check_word(word, raw['providers'][provider]['forward'], code, e, c, ce)
+    phase = inherit()
+    phase_report = phases(payload['providers']['base'], raw['providers']['base']['forward'], phase)
+    refinement_report = direct_refinement(payload)
+    report = {
+        'status': 'PASS_INDEPENDENT_ROW_CAPTURE_NATIVE',
+        'algebra': algebra_report, 'literal_words': word_reports,
+        'phases': phase_report, 'direct_full_refinement': refinement_report,
+        'negative_controls': ['missing precode', 'missing late query',
+                              'incomplete selected pair', 'wrong global phase'],
+        'scope': 'Complete local forward native service with changed output representation. No free later-stage conversion, global decoder, recursive host, or complete supplier claim.',
+    }
+    args.out.mkdir(parents=True, exist_ok=True)
+    (args.out/'REVIEW.json').write_text(json.dumps(report, indent=2, sort_keys=True)+'\n')
+    (args.out/'INPUTS.json').write_text(json.dumps(INPUTS, indent=2, sort_keys=True)+'\n')
+    print(report['status'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..7ef7d475fc
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json
@@ -0,0 +1,137 @@
+{
+  "bridge-access-20261017/row-capture-access-20261020/ACCESS.md": {
+    "sha256": "b28785e70fd700a4ed564f4cfc9d154c1b154939541053dc8fb802911c1448b1"
+  },
+  "bridge-access-20261017/row-capture-access-20261020/FREEZE.json": {
+    "sha256": "9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11"
+  },
+  "bridge-access-20261017/row-capture-access-20261020/check_access.py": {
+    "sha256": "48baba6e09b787924c496c8d4ce89c9dd3f77585946516f90ff8803d45adb5cd"
+  },
+  "bridge-access-20261017/row-capture-access-20261020/run-normal/ACCESS-PROGRAM.json": {
+    "sha256": "c2d6a3300f759c4052236fec5ca8ef446f35b444f78369eaa9aed9ab9625f139"
+  },
+  "bridge-access-20261017/row-capture-access-20261020/run-normal/CHECKS.json": {
+    "sha256": "fc30fa5c4923633ff2aac86881656a086416193a90511bf06754fc9f7c17174b"
+  },
+  "bridge-access-20261017/row-capture-access-20261020/run-optimized/ACCESS-PROGRAM.json": {
+    "sha256": "c2d6a3300f759c4052236fec5ca8ef446f35b444f78369eaa9aed9ab9625f139"
+  },
+  "bridge-access-20261017/row-capture-access-20261020/run-optimized/CHECKS.json": {
+    "sha256": "fc30fa5c4923633ff2aac86881656a086416193a90511bf06754fc9f7c17174b"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/FREEZE.json": {
+    "sha256": "0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/ROW-CAPTURE.md": {
+    "sha256": "0caea104839f0e9726c892ab2b21c2c3501deb818ab0c844e4fa5234cb870eee"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/check_row_capture.py": {
+    "sha256": "ccf661107a790c3d858a3f2bd4d8adc5269f588bfd989bd2e2029e26cbb14081"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/run-normal/CHECKS.json": {
+    "sha256": "7054fe6350d900561111b81f2ce46057edb62aef1f5581c4adac66f1c1742081"
+  },
+  "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json": {
+    "sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": {
+    "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL-FREEZE.json": {
+    "sha256": "f0d3b0d7c8d93e391089a2d28066dd02b4a9b28e306dea5f4e7cb5fc895b054e"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL.md": {
+    "sha256": "905d4ae107dcc014e28bb01a0e6090d02ad075ed219e4e1b921fe50a86ba032c"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/FREEZE.json": {
+    "sha256": "5321a8ff856042c5ca30ce6b29b90a51ccd4dcf02317820243bfffbb433c84d8"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/PRODUCTIVE-CAPTURE.md": {
+    "sha256": "de842ef7745cc86ab21a7e05472bc99ef47e7d0c75185b70cfe40219715aee66"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/CHECKS.json": {
+    "sha256": "267b3b0cfff10073d0edc497d5f1ee3290e789124eca7e9e3c63a7e2fc3605f3"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz": {
+    "decompressed_sha256": "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c",
+    "sha256": "b1bade79c227366b9c283acfbbb4cbdc5dbf3f6a1764bac0e69abd2493e38487"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-optimized/CHECKS.json": {
+    "sha256": "267b3b0cfff10073d0edc497d5f1ee3290e789124eca7e9e3c63a7e2fc3605f3"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-optimized/DIRECT-FULL-CAPTURE.json.gz": {
+    "sha256": "b1bade79c227366b9c283acfbbb4cbdc5dbf3f6a1764bac0e69abd2493e38487"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_capture.py": {
+    "sha256": "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_direct_full.py": {
+    "sha256": "fbe845f577874795b83de0f7733e90c904aabebb7d33bf1a8874d10c6e0fa574"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/CHECKS.json": {
+    "sha256": "8f769610ac2a5bd905a89566dde512bfa7ab47a46770b76897deb0536f004c2d"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz": {
+    "decompressed_sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2",
+    "sha256": "943b23d9d41801ffced2e19e765f097eecf2e5ecc5e83079fd63af4b907fa788"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-optimized/CHECKS.json": {
+    "sha256": "8f769610ac2a5bd905a89566dde512bfa7ab47a46770b76897deb0536f004c2d"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-optimized/PRODUCTIVE-CAPTURE.json.gz": {
+    "sha256": "943b23d9d41801ffced2e19e765f097eecf2e5ecc5e83079fd63af4b907fa788"
+  },
+  "new-native-recipes-20261017/isotropic-pair-review-20261018/check.py": {
+    "sha256": "e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json": {
+    "sha256": "5991ca1da15d3ffd7778e1de6be870c71f8811c867da6155e963e8bad1570aee"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json": {
+    "sha256": "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md": {
+    "sha256": "67efc6a9b0a04be1b9f2454db4ff5746d1bb389c2e80e0cff7f73e2481e4e798"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json": {
+    "sha256": "57e3b9367f31183f95a66c9ff8c41350dbbe5d771f97a69b71654e42ce045b0c"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json": {
+    "sha256": "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md": {
+    "sha256": "2ef8464d4f8b4867dfacdc7515285d690eb84adc299b7d7ebd1ce46ede1c7b29"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py": {
+    "sha256": "d6fcc9f2279bdd2e6b466dd42552f8add9a8fb05bef3f7f39030a582d729dd8f"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/check_native.py": {
+    "sha256": "e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json": {
+    "sha256": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-REVIEW.json": {
+    "sha256": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-INPUTS.json": {
+    "sha256": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized/EXTENSIONS-REVIEW.json": {
+    "sha256": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json": {
+    "sha256": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/normal/REVIEW.json": {
+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/INPUTS.json": {
+    "sha256": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90"
+  },
+  "new-native-recipes-20261017/low-displacement-review-20261020/optimized/REVIEW.json": {
+    "sha256": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/REVIEW.json
new file mode 100644
index 0000000000..5a086387f6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/REVIEW.json
@@ -0,0 +1,1563 @@
+{
+  "algebra": {
+    "code_prefix": {
+      "binary_height": 1,
+      "row_one_norm": "22"
+    },
+    "code_price": 1760,
+    "displacement_rank": 16,
+    "extra_fields": 0,
+    "odd_scans": 0,
+    "query_prefix_on_independent_inputs": {
+      "binary_height": 1,
+      "row_one_norm": "112"
+    },
+    "query_price": 3424
+  },
+  "direct_full_refinement": {
+    "all_events_and_boundary_views_byte_equal": true,
+    "changed_occurrences_per_word": 16,
+    "native_children": 1520,
+    "native_mass": 1808,
+    "native_side_maps_upper_bound": 3008,
+    "proof": "Exact complete-word substitution using the independently checked identity-wrapper kernel.",
+    "providers": [
+      "base",
+      "extra"
+    ],
+    "real_scalar_primitives": 11640
+  },
+  "literal_words": {
+    "base": {
+      "events": 2886,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "132"
+      },
+      "inherited_distinct_native_recipes": 1447,
+      "input_columns": 640,
+      "input_views": 112,
+      "native_children": 1520,
+      "native_mass": 1808,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "9": 16
+      },
+      "native_side_maps_upper_bound": 3040,
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+        "port": 107
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+        "port": 108
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+      {
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+          {
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+        "port": 109
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+      {
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+        ],
+        "port": 110
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+    ],
+    "scope": "Exact executed recipes; descriptive compiler circuits are not executed."
+  },
+  "scope": "Complete local forward native service with changed output representation. No free later-stage conversion, global decoder, recursive host, or complete supplier claim.",
+  "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized/INPUTS.json
new file mode 100644
index 0000000000..7ef7d475fc
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+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized/REVIEW.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized/REVIEW.json
new file mode 100644
index 0000000000..5a086387f6
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized/REVIEW.json
@@ -0,0 +1,1563 @@
+{
+  "algebra": {
+    "code_prefix": {
+      "binary_height": 1,
+      "row_one_norm": "22"
+    },
+    "code_price": 1760,
+    "displacement_rank": 16,
+    "extra_fields": 0,
+    "odd_scans": 0,
+    "query_prefix_on_independent_inputs": {
+      "binary_height": 1,
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+    "query_price": 3424
+  },
+  "direct_full_refinement": {
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+    "changed_occurrences_per_word": 16,
+    "native_children": 1520,
+    "native_mass": 1808,
+    "native_side_maps_upper_bound": 3008,
+    "proof": "Exact complete-word substitution using the independently checked identity-wrapper kernel.",
+    "providers": [
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+    ],
+    "real_scalar_primitives": 11640
+  },
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+      "input_views": 112,
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+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 96
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 97
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 98
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 99
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 100
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 101
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 102
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 103
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 104
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 105
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 106
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 107
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 108
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 109
+      },
+      {
+        "orders": [
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          },
+          {
+            "digest": "2dcf477f39973bad989fd7a77c1c76a29d007948a4e30f7b880961593920434c",
+            "nonzero_coefficients": 512,
+            "spatial_columns": 512
+          }
+        ],
+        "port": 110
+      }
+    ],
+    "scope": "Exact executed recipes; descriptive compiler circuits are not executed."
+  },
+  "scope": "Complete local forward native service with changed output representation. No free later-stage conversion, global decoder, recursive host, or complete supplier claim.",
+  "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..6dfd6604fa
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "REPRODUCTION.json": "94062c4856248dda973b6095fefcc8502e4752c04bd797f8c0de7cdb16309cd0",
+    "REVIEW.md": "3d7c72015cde33add3f2287aa4ed58e6b90c2e51c73bbe851eafb7c3ca4d274c",
+    "check.py": "b411d3eb6352b71a0e8200cac88c8a01569e254cbbeaba9acb04edf6441134bf",
+    "normal/INPUTS.json": "7193dec4a19d2750b6f053e09d3062a1cf11cc12c7334e32e5add9f95f48949d",
+    "normal/REVIEW.json": "5c2bbc8076679da2e14db052c9445a42c60f71fefadf05bb7f09c007187a9b10",
+    "optimized/INPUTS.json": "7193dec4a19d2750b6f053e09d3062a1cf11cc12c7334e32e5add9f95f48949d",
+    "optimized/REVIEW.json": "5c2bbc8076679da2e14db052c9445a42c60f71fefadf05bb7f09c007187a9b10"
+  },
+  "publication": "No PR, push, commit, or publication.",
+  "scope": "All eight complete A/AT local words, exact physical frames, unchanged phase records, arbitrary data and helper identity, and complete local invoice. No routed caller, common-frame gauge words, recursive host, or full supplier claim.",
+  "status": "PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..17e6c810e9
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/REPRODUCTION.json
@@ -0,0 +1,8 @@
+{
+  "normal_optimized_byte_identical": {
+    "INPUTS.json": "7193dec4a19d2750b6f053e09d3062a1cf11cc12c7334e32e5add9f95f48949d",
+    "REVIEW.json": "5c2bbc8076679da2e14db052c9445a42c60f71fefadf05bb7f09c007187a9b10"
+  },
+  "source_files_rechecked": 28,
+  "status": "PASS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..be62fbe031
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/REVIEW.md
@@ -0,0 +1,202 @@
+# Independent review of the native involution services
+
+All eight frozen local words pass. The words cover two providers, the
+responses \(A\) and \(A^T\), and both shear directions. There is no material
+native defect. This review does not establish a complete supplier.
+
+## Frozen inputs and method
+
+The native producer is
+`new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/`.
+Its `FREEZE.json` has SHA256
+`ad8a365247b60ff3621e701bb88d8692cc4f545ae09b3ec8fbe8d69b7f348ea1`.
+The decompressed final native payload has SHA256
+`aa5356c5cb618984ba3c76c40a255ebd26a66f0a88ac9f57792ab8f6677f9a30`.
+This review uses `run-normal-final/`, not the earlier development words.
+
+The matrix source is
+`controller-followthrough-20261017/row-involution-20261020/`.
+Its main freeze has SHA256
+`538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2`.
+Its final matrix payload has SHA256
+`a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b`.
+
+The independent checker does not import a producer module. It uses exact
+rational arithmetic. It derives the matrices in two ways, reconstructs
+each event list from the old native word, and runs a reverse column pass
+and a separate forward row pass. Each pass covers all 640 input fields.
+The checker binds each native occurrence to the accepted ordered frame
+pair and phase recipe. `normal/INPUTS.json` lists every consumed file and
+its hash.
+
+## Matrix proof
+
+Write the old response as \(E=I+UV\). Let \(P\) be the ordered set of
+sixteen physical pivots and let \(R\) be its complement. The actual
+\(V_P\) is invertible. Preserve \(U_R\), and set
+
+\[
+ U'_P=V_P^{-1}(-2I-V_RU_R),\qquad A=I+U'V.
+\]
+
+Then \(VU'=-2I\), so
+\[
+ A^2=I+U'(2I+VU')V=I.
+\]
+The matrix \(A^T\) is also an involution. Over a field with
+characteristic different from two, \(U'\) is injective and \(V\) is
+surjective. Thus \(\operatorname{rank}(A-I)=16\).
+The image of \(U'\) is the minus-one eigenspace; the kernel of \(V\)
+is the plus-one eigenspace. Therefore \(\det A=(-1)^{16}=1\).
+
+The checker derives the physical pivot inverse from the actual signed
+Gram matrices. It then derives the same \(A\) from the sixteen disjoint
+mode blocks. There are eight blocks of size six and eight of size eight.
+For a signed block vector \(d\), with pivot \(p\) and \(d_p=1\), the
+block is
+\[
+ A_k=I+\big((k-2)e_p-d\big)d^T.
+\]
+The inner product of the two update vectors is \(-2\). Hence each
+block is an involution with determinant \(-1\). The actual signed
+two-port transforms and their inverses convert these blocks to the
+physical matrix. The conversion agrees exactly with the first
+derivation, including the physical transpose.
+
+The exact checks give
+\[
+ \operatorname{rank}(A-I)=16,\quad
+ \operatorname{rank}(A-E)=16,\quad
+ \operatorname{tr}A=80,\quad \det A=1.
+\]
+Only the selected physical rows change from \(E\).
+The general construction proves the first rank statement. It does not
+prove the second rank statement for every source. The source's separate
+`COMPLETION-LIMITS.md` states this distinction. Its SHA256 is
+`91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607`;
+its freeze is
+`775c1b565ec0aa969f2dbecebb04f4b9a82a561e7e7d842c2b1abae7a75509a6`.
+This resolves the ambiguous phrase “The change has rank r” in the
+original proof. This review does not accept the other results in that
+addendum by this reference alone.
+
+## Complete event and phase check
+
+For each family and direction, the checker identifies the old transfer
+slots from the actual source metadata. It derives the new coefficients
+from the two mode matrices. Exactly 96 source slots change. Their
+support and order stay fixed.
+
+The checker then reconstructs the selected-path deletion. Exactly 250
+events are removed: 128 rank-one child calls and 122 scalar events.
+There is no retained read from a removed selected target. The exact
+retained index list agrees with the payload. At the end of this core,
+all 112 source fields are in FULL, and the sixteen selected target
+fields are still in I. The word then applies sixteen positive FULL
+children and the late scalar query.
+
+The late forward query adds the raw selected rows \(M_P X\), where
+\(M=A\) or \(A^T\). There is no row precode in these words.
+The late backward query is the gatewise inverse transpose of that
+forward query in the same chronological order:
+
+- \(t\leftarrow t+c\,s\) becomes \(s\leftarrow s-c\,t\).
+- \(t\leftarrow a\,t\) becomes \(t\leftarrow a^{-1}t\).
+
+For a forward product \(F=M_n\cdots M_1\),
+\(F^{-T}=M_n^{-T}\cdots M_1^{-T}\). This explains the chronological
+order. Both matrix product orders of the isolated query and its inverse
+transpose equal identity. The complete backward replay also restores
+all 112 target baselines and their temporary scales.
+
+Each frame array, input view, output view, and native phase record is
+byte equal to the accepted direct-FULL formation packet. Its independent
+review freeze is
+`488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532`.
+The sixteen FULL calls use that packet's exact identity side maps.
+Every scalar event is between fields in its declared common frame.
+Every native occurrence has the correct input and output frame. All
+recipes are used, and the final frame ledger agrees with the payload.
+
+There are no new phase operators in this change. This review inherits
+the pinned complete phase checks; it does not claim a second phase
+interpreter run. The coefficient substitutions do not change a native
+operator or a boundary map.
+
+## Exact physical contract
+
+Let \(Q\) be the block diagonal input line operator and write \(q_U\)
+for its ordinary-port restriction. With physical input
+\(X=Qx,\ Y=y\), the forward output is
+\[
+ X'=F_9x,\qquad
+ Y'_P=F_9(y+Mx)_P,\qquad
+ Y'_U=F_9q_U(y+Mx)_U.
+\]
+The backward output is
+\[
+ X'=F_9(x-M^Ty),\qquad
+ Y'_P=F_9y_P,\qquad
+ Y'_U=F_9q_Uy_U.
+\]
+
+These formulas retain the order of the frame operators. The proof
+does not commute \(Q\) through \(M\), and does not identify the two
+complete physical words as literal inverse adjoints without their
+boundary conversions.
+
+All 640 arbitrary input columns pass in each word. All 416 other
+fields remain unchanged for arbitrary values. No field is assumed
+zero, and no extra or private field is introduced. Two negative
+controls fail as required: omission of the late query and reversal of
+the backward query chronology.
+
+## Local invoice and numerical scope
+
+Both providers have the following exact scalar invoices.
+
+| Response | Direction | Retained core | Late query | Total |
+|---|---|---:|---:|---:|
+| \(A\) | Forward | 6456 | 2960 | 9416 |
+| \(A\) | Backward | 6456 | 2960 | 9416 |
+| \(A^T\) | Forward | 6952 | 1984 | 8936 |
+| \(A^T\) | Backward | 6952 | 1984 | 8936 |
+
+Every word has 1392 H1, 64 H2, 48 H3, and 16 H9 children:
+1520 children and native mass 1808. It has 112 input views, 96 output
+views, and a native side-map upper bound of 3008. It has no odd scan.
+The child profile and map counts remain separate from the old real
+scalar tariff.
+
+The maximum exact scalar-content row one-norms are 70 and 22 for the
+forward and backward \(A\) words, and 30 and 62 for the corresponding
+\(A^T\) words. Each word adds at most one binary denominator level
+relative to its input coordinates at scalar operation boundaries.
+These checks do not bound primitive internals, recursive child
+internals, or roundoff propagation.
+
+The 2960 and 1984 queries are raw selected response rows. They are not
+the separate captured-reader query \(WA=-W\). This review does not
+certify the source's additional common-frame gauge words, a routed
+reader, an endpoint decoder, child hosting, or a complete recursive
+precision and supplier cost.
+
+## Reproduction and credit
+
+Run from the workspace root:
+
+```sh
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/normal
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/optimized
+```
+
+Both runs print `PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS`.
+`REPRODUCTION.json` records the byte comparison and the final source
+hash check.
+
+The controller-followthrough lane supplied the row completion.
+The new-core-transfer lane supplied the native words and invoices.
+This lane supplied the separate matrix derivations, event reconstruction,
+reverse replay, and review. The accepted formation and raw phase
+reviews supply the unchanged native phase evidence. This work used AI
+assistance. No PR, push, commit, or publication was made.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/check.py
new file mode 100644
index 0000000000..41ff6f6ffc
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/check.py
@@ -0,0 +1,314 @@
+#!/usr/bin/env python3
+"""Check all eight native services for the dyadic involution pair."""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import importlib.util
+import json
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+ACCEPTED = HERE.parent/'row-capture-native-review-20261020'
+HELPER = ACCEPTED/'check.py'
+PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84'
+if sha256(HELPER.read_bytes()).hexdigest() != PIN:
+    raise ValueError('Independent helper pin')
+spec = importlib.util.spec_from_file_location('independent_row_review', HELPER)
+q = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(q)
+q.read(HELPER, PIN)
+need, read, frozen = q.need, q.read, q.frozen
+P = q.P
+SOURCE = q.RAW/'row-involution-native-20261020'
+ALG = LANES/'controller-followthrough-20261017/row-involution-20261020'
+
+
+def pair_matrices(cyclic):
+    h, hi, covered = q.unit(112), q.unit(112), set()
+    for item in cyclic['pair_codes']:
+        ports = item['ports']
+        need(len(ports) == 2 and not covered.intersection(ports), 'Disjoint actual pair')
+        covered.update(ports)
+        need(not set(ports).intersection(P) or set(ports) <= set(P), 'Complete selected pair')
+        a, b = map(F, item['matrix'][0])
+        c, d = map(F, item['matrix'][1])
+        det = a*d-b*c
+        need(abs(det) == 2, 'Actual signed pair determinant')
+        inverse = [[d/det, -b/det], [-c/det, a/det]]
+        for i, p in enumerate(ports):
+            h[p] = {r: F(v) for r, v in zip(ports, item['matrix'][i]) if F(v)}
+            hi[p] = {r: v for r, v in zip(ports, inverse[i]) if v}
+    need(len(covered) == 48 and q.mul(h, hi) == q.unit(112) and q.mul(hi, h) == q.unit(112),
+         'Actual physical pair transform inverse orders')
+    return h, hi
+
+
+def matrices(raw, algebra, cyclic):
+    e = q.rows(raw['model']['response'])
+    u, v = q.rows(raw['model']['correction_U']), q.rows(raw['model']['correction_V'])
+    vp = [{j: row[p] for j, p in enumerate(P) if p in row} for row in v]
+    vpt = q.transpose(vp, 16)
+    vi = [{j: x/(2 if j < 8 else 1) for j, x in row.items()} for row in vpt]
+    need(q.mul(vi, vp) == q.unit(16) and q.mul(vp, vi) == q.unit(16), 'Actual pivot inverse')
+    vrur = []
+    for row in v:
+        acc = {}
+        for p, x in row.items():
+            if p not in P:
+                q.add(acc, u[p], x)
+        vrur.append(acc)
+    rhs = [{i: F(-2)} for i in range(16)]
+    for row, old in zip(rhs, vrur):
+        q.add(row, old, F(-1))
+    up = q.mul(vi, rhs)
+    new_u = [dict(row) for row in u]
+    for p, row in zip(P, up):
+        new_u[p] = row
+    need(q.mul(v, new_u) == [{i: F(-2)} for i in range(16)], 'Completion centre action')
+    a = q.unit(112)
+    for row, correction in zip(a, q.mul(new_u, v)):
+        q.add(row, correction)
+    at = q.transpose(a, 112)
+    need(q.mul(a, a) == q.unit(112) and q.mul(at, at) == q.unit(112), 'Both involutions')
+    displacement = [dict(row) for row in a]
+    for i, row in enumerate(displacement):
+        q.add(row, {i: F(1)}, F(-1))
+    need(q.rank(displacement) == 16, 'Actual displacement rank16')
+    source_change = [dict(row) for row in a]
+    for row, old in zip(source_change, e):
+        q.add(row, old, F(-1))
+    need(q.rank(source_change) == 16, 'Actual source change rank16')
+    need(sum(row.get(i, F(0)) for i, row in enumerate(a)) == 80, 'Actual trace80')
+    need(all(a[p] == e[p] for p in range(112) if p not in P), 'Only selected physical rows change')
+    h, hi = pair_matrices(cyclic)
+    drows = q.mul(v, hi)
+    mode = q.unit(112)
+    seen = set()
+    for j, d in enumerate(drows):
+        size, p = len(d), P[j]
+        need(size == (6 if j < 8 else 8) and d.get(p) == 1 and set(d.values()) <= {F(-1), F(1)},
+             'Actual signed block and positive pivot')
+        need(not seen.intersection(d), 'Disjoint mode blocks')
+        seen.update(d)
+        for i, value in d.items():
+            q.add(mode[i], d, -value+(size-2 if i == p else 0))
+    need(seen == set(range(112)), 'Sixteen blocks cover all actual ports')
+    need(q.mul(q.mul(hi, mode), h) == a, 'Separate signed-mode construction')
+    mode_at = q.mul(q.mul(h, at), hi)
+    need(mode_at == q.transpose(mode, 112), 'Physical transpose in actual mode coordinates')
+    for name, value in [('response', a), ('response_transpose', at),
+                        ('response_inverse', a), ('response_inverse_transpose', at),
+                        ('correction_U', new_u), ('correction_V', v),
+                        ('mode_response', mode), ('mode_response_transpose', mode_at),
+                        ('original_response', e)]:
+        need(q.rows(algebra[name]) == value, 'Independent matrix binding: '+name)
+    need(algebra['pivots'] == P, 'Actual ordered pivots')
+    return {'A': a, 'AT': at}, {'A': mode, 'AT': mode_at}, q.mul(q.mul(h, e), hi), {
+        'block_sizes': [len(r) for r in drows], 'rank_A_minus_I': 16,
+        'rank_A_minus_E': 16, 'trace_A': 80,
+        'centre_action': '-2I16', 'both_involution_orders': True,
+        'determinant': '1', 'determinant_proof': 'Sixteen rank-one mode blocks each have determinant1+d^T u=-1.',
+    }
+
+
+def retuned_events(old, oldmode, newmode, cyclic):
+    parameters = {r['id']: r for r in cyclic['parameters']}
+    events, updates, claimed = deepcopy(old['events']), [], set()
+    for item in old['transfer_records']:
+        index = item['event']
+        need(index not in claimed, 'Distinct actual transfer slot')
+        claimed.add(index)
+        if item['part'] == 'large48':
+            par = parameters[item['parameter']]
+            carriers = cyclic['cyclic_carriers'][par['vertex']]
+            r, c = carriers[par['row']], carriers[par['column']]
+        else:
+            need(item['part'] == 'small64', 'Actual transfer family')
+            r, c = item['target_port'], item['source_port']
+        before, after = oldmode[r][c], newmode[r][c]
+        event = events[index]
+        need(event[0] == 'scalar' and event[1][0] == 'add', 'Actual scalar transfer event')
+        sign = F(event[1][3])/before
+        need(sign in (F(-1), F(1)) and after and after.denominator == 1,
+             'Original support and exact orientation')
+        if before != after:
+            updates.append({'original_event': index, 'mode_row': r, 'mode_column': c,
+                            'old_coefficient': str(sign*before), 'new_coefficient': str(sign*after)})
+        event[1][3] = str(sign*after)
+    need(len(updates) == 96, 'Exactly96 changed source transfer slots')
+    return events, updates
+
+
+def expected_columns(response, direction):
+    out = q.unit(640)
+    for r, row in enumerate(response):
+        if direction == 'forward':
+            q.add(out[112+r], row)
+        else:
+            for c, value in row.items():
+                q.add(out[c], {112+r: -value})
+    return q.transpose(out, 640)
+
+
+def check_word(word, old, reference, algebra, response, oldmode, mode, cyclic, name, direction, ledger):
+    selected = {112+p for p in P}
+    retuned, updates = retuned_events(old, oldmode, mode, cyclic)
+    kept, removed, indices = [], [], []
+    for i, event in enumerate(retuned):
+        target = event[1] if event[0] == 'native' else event[1][1]
+        read_selected = event[0] == 'scalar' and event[1][0] == 'add' and event[1][2] in selected
+        if target in selected or (direction == 'backward' and read_selected):
+            removed.append(event)
+        else:
+            need(not read_selected, 'No retained selected-target read')
+            kept.append(event)
+            indices.append(i)
+    need(word['retained_original_event_indices'] == indices, 'Exact retained index ledger')
+    need(len(removed) == 250 and Counter(e[4] for e in removed if e[0] == 'native') == {1: 128},
+         'Exactly250 selected-path events removed')
+    need(ledger['changed_original_transfer_weights'] == updates, 'Exact retuning receipt')
+    need(ledger['removed_events'] == len(removed) and
+         ledger['removed_scalar_primitives_after_retuning'] ==
+         q.price([e[1] for e in removed if e[0] == 'scalar']), 'Exact removal invoice')
+    query = []
+    for op, target, origin, value in algebra['final_query_words'][name]:
+        if direction == 'forward':
+            query.append(['scalar', [op, 112+target, None if origin is None else origin-112, value], 1])
+        elif op == 'scale':
+            query.append(['scalar', [op, 112+target, None, str(1/F(value))], 1])
+        else:
+            need(op == 'add', 'Late query grammar')
+            query.append(['scalar', ['add', origin-112, 112+target, str(-F(value))], 1])
+    progress = [['native', 112+p, 0, 1, 9, 'capture-full'] for p in P]
+    need(word['events'] == kept+progress+query, 'Exact native and scalar chronology')
+    need(word['stage_ranges'] == {
+        'retained_core': [0, len(kept)], 'selected_full_progress': [len(kept), len(kept)+16],
+        'late_query': [len(kept)+16, len(word['events'])]}, 'Exact stage boundaries')
+    for key in ('frames', 'start', 'final', 'input_views', 'output_views'):
+        need(word[key] == reference[key], 'Exact accepted physical geometry: '+key)
+    need(word['native_recipes'] == reference['native_recipes'], 'Every accepted native phase record')
+    current = list(word['start'])
+    count, used = Counter(), set()
+    for i, event in enumerate(word['events']):
+        if i == len(kept):
+            need(all(current[p] == 1 for p in range(112)) and
+                 all(current[p] == 0 for p in selected), 'Late source cut and unadvanced selected Y')
+        if event[0] == 'native':
+            _, field, before, after, rank, key = event
+            need(0 <= field < 224 and current[field] == before, 'Exact native input frame')
+            need(rank == word['native_recipes'][key]['rank'], 'Exact native rank')
+            if key == 'capture-full':
+                need(field in selected and (before, after, rank) == (0, 1, 9), 'Accepted FULL child binding')
+            else:
+                need(key == str(before)+':'+str(after), 'Accepted ordered native frame pair')
+            current[field] = after
+            count[rank] += 1
+            used.add(key)
+        else:
+            _, scalar, frame = event
+            op, target, origin, _ = scalar
+            need(0 <= target < 224 and current[target] == frame, 'Exact scalar target frame')
+            if op == 'add':
+                need(0 <= origin < 224 and current[origin] == frame and origin != target,
+                     'Exact scalar source frame')
+            else:
+                need(op == 'scale' and origin is None, 'Exact scale grammar')
+    need(current == word['final'] and used == set(word['native_recipes']), 'Complete frame and recipe ledger')
+    need(count == {1: 1392, 2: 64, 3: 48, 9: 16}, 'Complete profile')
+    scalars = [e[1] for e in word['events'] if e[0] == 'scalar']
+    columns = q.reverse(scalars, 640)
+    need(columns == expected_columns(response, direction), 'All640 independent input columns')
+    rows, growth = q.prefix(scalars, 640)
+    need(q.transpose(rows, 640) == columns and rows[224:] == q.unit(640)[224:],
+         'Separate forward row pass and416 arbitrary outside roles')
+    if direction == 'backward':
+        need(rows[112:224] == q.unit(640)[112:224], 'All target baselines restored')
+    norm = {('A', 'forward'): '70', ('A', 'backward'): '22',
+            ('AT', 'forward'): '30', ('AT', 'backward'): '62'}[name, direction]
+    need(growth == {'row_one_norm': norm, 'binary_height': 1}, 'Exact complete content prefix bound')
+    core_price, query_price = (6456, 2960) if name == 'A' else (6952, 1984)
+    need(q.price(scalars) == core_price+query_price and
+         q.price([e[1] for e in kept if e[0] == 'scalar']) == core_price and
+         q.price([e[1] for e in query]) == query_price, 'Complete local scalar invoice')
+    need(q.reverse([e[1] for e in kept if e[0] == 'scalar'], 640) != columns,
+         'Omitted late query control')
+    if direction == 'backward':
+        reversed_query = [e[1] for e in kept if e[0] == 'scalar']+[e[1] for e in reversed(query)]
+        need(q.reverse(reversed_query, 640) != columns, 'Wrong reversed inverse-transpose chronology')
+    return {
+        'input_columns': 640, 'unchanged_arbitrary_roles': 416,
+        'native_profile': dict(sorted(count.items())), 'native_children': sum(count.values()),
+        'native_mass': sum(k*v for k, v in count.items()), 'real_scalar_primitives': core_price+query_price,
+        'retained_scalar_primitives': core_price, 'late_query_scalar_primitives': query_price,
+        'input_views': 112, 'output_views': 96, 'native_side_maps_upper_bound': 3008,
+        'new_fields': 0, 'private_fields': 0, 'odd_scans': 0, 'growth': growth,
+        'retuned_source_slots': len(updates), 'removed_events': len(removed),
+        'phase_scope': 'All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.',
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    frozen(ACCEPTED, 'FREEZE.json', '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532')
+    frozen(ALG, 'FREEZE.json', '538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2')
+    read(ALG/'LIMITS-FREEZE.json', '775c1b565ec0aa969f2dbecebb04f4b9a82a561e7e7d842c2b1abae7a75509a6')
+    read(ALG/'COMPLETION-LIMITS.md', '91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607')
+    frozen(SOURCE, 'FREEZE.json', 'ad8a365247b60ff3621e701bb88d8692cc4f545ae09b3ec8fbe8d69b7f348ea1')
+    raw = json.loads(read(q.RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz',
+                          'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True))
+    algebra = json.loads(read(ALG/'run-normal/ROW-INVOLUTION.json',
+                              'a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b'))
+    reference = json.loads(read(q.NATIVE/'direct-normal/DIRECT-FULL-CAPTURE.json.gz',
+                                'fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c', True))
+    cyclic = json.loads(read(LANES/'independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json',
+                             '3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585'))
+    payload = json.loads(read(SOURCE/'run-normal-final/ROW-INVOLUTION-NATIVE.json.gz',
+                              'aa5356c5cb618984ba3c76c40a255ebd26a66f0a88ac9f57792ab8f6677f9a30', True))
+    responses, modes, oldmode, algebra_report = matrices(raw, algebra, cyclic)
+    need(payload['selected_ports'] == P and payload['ports'] == raw['model']['ports'], 'Actual port arrays')
+    need(set(payload['providers']) == {'base', 'extra'} and
+         payload['providers']['base'] == payload['providers']['extra'], 'Both providers')
+    for name in responses:
+        need(q.rows(payload['responses'][name]) == responses[name], 'Actual response contract')
+    reports = {}
+    for provider, families in payload['providers'].items():
+        need(set(families) == {'A', 'AT'}, 'Both response matrices')
+        reports[provider] = {}
+        for name, directions in families.items():
+            need(set(directions) == {'forward', 'backward'}, 'Both shear directions')
+            reports[provider][name] = {}
+            for direction, word in directions.items():
+                reports[provider][name][direction] = check_word(
+                    word, raw['providers'][provider][direction], reference['providers'][provider],
+                    algebra, responses[name], oldmode, modes[name], cyclic, name, direction,
+                    payload['transfer_ledgers'][provider][name][direction])
+            fword = directions['forward']
+            bword = directions['backward']
+            fs = [e[1] for e in fword['events'][slice(*fword['stage_ranges']['late_query'])]]
+            bs = [e[1] for e in bword['events'][slice(*bword['stage_ranges']['late_query'])]]
+            fm = q.transpose(q.reverse(fs, 224), 224)
+            bm = q.transpose(q.reverse(bs, 224), 224)
+            ft = q.transpose(fm, 224)
+            need(q.mul(ft, bm) == q.unit(224) and q.mul(bm, ft) == q.unit(224),
+                 'Both exact isolated-query inverse-transpose orders')
+    report = {
+        'status': 'PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS',
+        'algebra': algebra_report, 'literal_words': reports,
+        'new_phase_operators': 0, 'phase_source_review':
+        '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532',
+        'negative_controls': ['omitted late query', 'reversed backward-query chronology'],
+        'scope': 'All eight complete local mixed-output words. Common-frame gauge words and routed caller, decoder, recursive host, or supplier cost are not established here.',
+    }
+    args.out.mkdir(parents=True, exist_ok=True)
+    for name, value in [('REVIEW.json', report), ('INPUTS.json', q.INPUTS)]:
+        (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n')
+    print(report['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..7eea604b7f
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/row-involution-native-review-20261020/normal/INPUTS.json
@@ -0,0 +1,89 @@
+{
+  "controller-followthrough-20261017/row-involution-20261020/COMPLETION-LIMITS.md": {
+    "sha256": "91bd564b31766300cc89b87cf808439135d89c27bde655a2fc1842646c304607"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/FREEZE.json": {
+    "sha256": "538ec208e510af7ee29aff4783d304e393c967697a6612e5c42e38fbc0ab9be2"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/LIMITS-FREEZE.json": {
+    "sha256": "775c1b565ec0aa969f2dbecebb04f4b9a82a561e7e7d842c2b1abae7a75509a6"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/ROW-INVOLUTION.md": {
+    "sha256": "c8470cc2280a057cbebf4a31ee679495990b200a6d6c033cc39e459eb2cf139f"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/check_row_involution.py": {
+    "sha256": "a675e5578de4bc264524f7c1a75c5685a1967a65f7d3cd020fb0dc19352d31e9"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/run-normal/CHECKS.json": {
+    "sha256": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json": {
+    "sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/run-optimized/CHECKS.json": {
+    "sha256": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6"
+  },
+  "controller-followthrough-20261017/row-involution-20261020/run-optimized/ROW-INVOLUTION.json": {
+    "sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": {
+    "sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": {
+    "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4",
+    "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/FREEZE.json": {
+    "sha256": "ad8a365247b60ff3621e701bb88d8692cc4f545ae09b3ec8fbe8d69b7f348ea1"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/ROW-INVOLUTION-NATIVE.md": {
+    "sha256": "3cb445c5216f9a3371ad938da1f663408c6db6b8d3f66875d86d83e830bd7e86"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/emit_involution.py": {
+    "sha256": "418137de0328111682a5232877196d59ed7f9246345f05ea7058749c75c909b5"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-normal-final/CHECKS.json": {
+    "sha256": "fe908f18cdcb242551715a88365aaa110bc37814824dd63fafcf86d3ed0c8812"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-normal-final/ROW-INVOLUTION-NATIVE.json.gz": {
+    "decompressed_sha256": "aa5356c5cb618984ba3c76c40a255ebd26a66f0a88ac9f57792ab8f6677f9a30",
+    "sha256": "b045fcc338dbb53bd686d5d332d7b51147c43fcc645279db0e8159d3ca8c80ee"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-optimized-final/CHECKS.json": {
+    "sha256": "fe908f18cdcb242551715a88365aaa110bc37814824dd63fafcf86d3ed0c8812"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-involution-native-20261020/run-optimized-final/ROW-INVOLUTION-NATIVE.json.gz": {
+    "sha256": "b045fcc338dbb53bd686d5d332d7b51147c43fcc645279db0e8159d3ca8c80ee"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz": {
+    "decompressed_sha256": "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c",
+    "sha256": "b1bade79c227366b9c283acfbbb4cbdc5dbf3f6a1764bac0e69abd2493e38487"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md": {
+    "sha256": "74bfa14362b8a704d409cb3995fe645173e99205653528bcf6b47f62de7455a1"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json": {
+    "sha256": "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json": {
+    "sha256": "9525e5e1871d60a01c8acd222944abe6edab71f9d5448410265859dcece6901f"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md": {
+    "sha256": "39cb0df65e81f92854d0238d9023eaa092205bdce8e3b81724c2e4d19a3ef4f1"
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new file mode 100644
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+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        },
+        "forward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "30"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 1984,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        }
+      }
+    },
+    "extra": {
+      "A": {
+        "backward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "22"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 2960,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6456,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        },
+        "forward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "70"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 2960,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6456,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        }
+      },
+      "AT": {
+        "backward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "62"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 1984,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        },
+        "forward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "30"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 1984,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        }
+      }
+    }
+  },
+  "negative_controls": [
+    "omitted late query",
+    "reversed backward-query chronology"
+  ],
+  "new_phase_operators": 0,
+  "phase_source_review": "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532",
+  "scope": "All eight complete local mixed-output words. Common-frame gauge words and routed caller, decoder, recursive host, or supplier cost are not established here.",
+  "status": "PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS"
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/FREEZE.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/FREEZE.json
new file mode 100644
index 0000000000..1bfa8db27b
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/FREEZE.json
@@ -0,0 +1,14 @@
+{
+  "files": {
+    "REPRODUCTION.json": "39239b24099ac101d0d543fe0fd95aaa89885ca5d7bc8b0562318e8a15e152b8",
+    "REVIEW.md": "06b782821db7d45cc05aecb8eff34ca2732202c9e32948be6b5c8f7952b0716f",
+    "check.py": "637db7eba7629a522e41e96333cda9a1af713c0d1403b1caada2827c2e3447f9",
+    "normal/INPUTS.json": "3afffef723776daea5f8de1f9e4a0c45de8d8294517f17173efc63350caa46fd",
+    "normal/REVIEW-CHECKS.json": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784",
+    "optimized/INPUTS.json": "3afffef723776daea5f8de1f9e4a0c45de8d8294517f17173efc63350caa46fd",
+    "optimized/REVIEW-CHECKS.json": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784"
+  },
+  "producer_freeze_sha256": "1e08caf1376ffb3a74eac87200e6165c969a08d71d5c028a7c8940093f830089",
+  "schema": "independent-direct-simple-clean-native-review-v1",
+  "scope": "Two complete local native words, all209 full spatial kernels and all640 content columns. No routed caller, recursive helper host, or complete supplier claim."
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/REPRODUCTION.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/REPRODUCTION.json
new file mode 100644
index 0000000000..dc20e8a838
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/REPRODUCTION.json
@@ -0,0 +1,11 @@
+{
+  "exact_nonzero_coefficients": 15040512,
+  "local_links_checked": true,
+  "normal_optimized_files": [
+    "REVIEW-CHECKS.json",
+    "INPUTS.json"
+  ],
+  "spatial_columns": 107008,
+  "status": "PASS_NORMAL_OPTIMIZED_AND_PINS",
+  "unchanged_input_files": 19
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/REVIEW.md b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/REVIEW.md
new file mode 100644
index 0000000000..6a56219019
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/REVIEW.md
@@ -0,0 +1,275 @@
+# Independent review of the direct clean pair
+
+Both direct native words pass. All 209 distinct physical kernels pass
+all 512 exact spatial columns, including global phase. The complete
+words pass all 640 arbitrary input columns and preserve all 416
+outside fields. No material defect was found.
+
+Each word costs 2912 real scalar primitives. Its native profile is
+\(96H_1+128H_8+96H_9\), with 320 children and mass 1984. The native
+side-map upper bound is 448. There is no boundary adapter or new
+field. This is a local result. It does not close a routed caller or
+construct a recursive helper host.
+
+## Inputs and independent method
+
+The producer is
+[SIMPLE-CLEAN-NATIVE.md](../../new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/SIMPLE-CLEAN-NATIVE.md).
+Its freeze SHA-256 is
+`1e08caf1376ffb3a74eac87200e6165c969a08d71d5c028a7c8940093f830089`.
+The decompressed payload has SHA-256
+`1bdddb7955d0ada6dabcf150fce0a568cd336a846f51be3324c081f10dd374c7`.
+
+The source ports and row code are bound to the frozen clean exchange,
+with decompressed SHA-256
+`b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083`,
+and to the controller's row-capture payload, with SHA-256
+`4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7`.
+The earlier independent
+[clean-exchange review](../clean-centre-exchange-review-20261020/REVIEW.md)
+has freeze
+`6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d`.
+
+The new checker imports only the pinned independent arithmetic
+helper. It imports no producer module, Clifford compiler, or Pauli
+interpreter. The physical check uses explicit Gaussian-integer
+matrix coefficients. The content check uses reverse coefficient
+columns and a separate forward-prefix pass.
+
+The two prior providers have the same consumed ports and row code.
+The new packet has one direct pair that applies to those common
+inputs. It does not retain either provider's old native path.
+
+## Exact physical kernel check
+
+On one nine-bit alphabet define
+
+\[
+C_v=\frac{(1+i)I+(1-i)X_v}{2},\qquad
+F_9=\prod_{j=0}^{8}C_{2^j}.
+\]
+
+Write
+\[
+b_r(t)=(1+i)^{r-|t|}(1-i)^{|t|}.
+\]
+Then the exact kernel of \(F_9\) at displacement \(t\) is
+\(b_9(t)/2^9\). If \(q_p=C_{v_p}^{-1}\), the exact kernel of
+\(F_9q_p\) is
+
+\[
+\frac{(1-i)b_9(t)+(1+i)b_9(t\mathbin{\mathrm{xor}}v_p)}{2^{10}}.
+\]
+
+The exact kernel of \(q_p\) is \((1-i)/2\) at displacement zero
+and \((1+i)/2\) at displacement \(v_p\). These formulas include
+the scalar phase.
+
+For each serialized native recipe, the checker evaluates the right
+and left monomial maps as full address and Z4 phase tables. It then
+uses \(b_r(t)/2^r\) for the native rank-r child. For every input
+column, it compares every nonzero coefficient with the independent
+kernel above. It also checks the complete support, the address
+permutations, and every monomial record field. Cross multiplication
+uses integers only.
+
+The checks cover:
+
+| Kernel class | Distinct kernels | Columns per kernel |
+| --- | ---: | ---: |
+| \(F_9\) | 1 | 512 |
+| \(F_9q_p\) | 112 | 512 |
+| \(q_p\) on ordinary targets | 96 | 512 |
+
+In total this is 107008 spatial columns and 15040512 nonzero exact
+coefficients. The rank-eight kernels have support 256 in every
+column; the rank-nine kernel has support 512; the negative-line
+kernels have support two. The direct FULL recipe has identity
+left and right maps.
+
+The checker also verifies every literal physical frame. Each
+line-to-FULL kernel maps the actual positive \(C_{v_p}\) input
+to \(F_9\). Each ordinary exit kernel maps \(F_9\) to
+\(F_9q_p\). This is an operator check, not an inference from a
+frame name. Since all \(X_v\) commute, \(F_9q_p=q_pF_9\).
+
+## Complete forward word
+
+Let P be the actual sixteen selected ports and U the other 96
+ports. Write
+
+\[
+C(a,u)=(a+Bu,u),\qquad L=[I,B].
+\]
+
+The checker verifies that the source code has identity ordinary
+rows and identity selected columns. Thus \(C=I+e_PB\), with
+\(B_P=0\). It independently replays the complete scalar C word
+and verifies its price 1760.
+
+The input types are
+\[
+X=Q(a,u),\qquad Y_P=Q_Pz,\qquad Y_U=v.
+\]
+
+The exact chronology is:
+
+1. Apply \(F_9q_p\) on all 112 X fields.
+2. Apply \(F_9q_p\) on all sixteen selected Y fields.
+3. Apply \(F_9\) on all 96 ordinary Y fields.
+4. Add each ordinary X field to its Y partner, at common FULL.
+5. Apply \(q_p\) on each ordinary Y field.
+6. Apply C on common-FULL X.
+7. Apply the signed rotation on each selected X/Y pair.
+
+The last rotation consists of
+
+```text
+Y += X;
+X -= Y;
+Y += X.
+```
+
+It maps \((a+Bu,z)\) to \((-z,a+Bu)\). Each operand is FULL
+at its actual event. The ordinary target has already become
+\(F_9q_U(v+u)\) and is not used by the later code or rotations.
+The full content map is therefore
+
+\[
+F_{\rm simple}(a,u,z,v)=(-z,\ u,\ a+Bu,\ v+u).
+\]
+
+The checker constructs this event list independently from the
+pinned row code and the displayed chronology. It requires exact
+equality with the serialized list and stage ranges.
+
+## Complete selected-conjugate inverse-adjoint
+
+Let M be the forward content matrix. Let
+
+\[
+A_{\rm in}=\operatorname{diag}(Q,Q_P,I_U),\qquad
+A_{\rm out}=\operatorname{diag}(F_9,F_9,F_9q_U),
+\]
+
+where the first entry acts on all X and the last two act on selected
+and ordinary Y. Both are unitary. The exact physical forward map is
+\(W=A_{\rm out}MA_{\rm in}^{-1}\). Hence
+
+\[
+W^{-*}=A_{\rm out}M^{-T}A_{\rm in}^{-1}.
+\]
+
+Every native kernel is unitary, so its inverse-adjoint is the same
+exact kernel, with the same scalar phase. For a scalar ADD, the
+inverse-adjoint exchanges source and target and negates the real
+coefficient. For a scale, it takes the reciprocal coefficient.
+The operation \(W\mapsto W^{-*}\) preserves the chronological
+instruction order.
+
+Let S exchange the two physical fields at each selected port.
+The selected input operators are the same Q on both banks. The
+selected output operators are the same FULL on both banks.
+Thus S commutes with both complete boundary operators.
+Conjugating every instruction by S only renames its field labels.
+The intervening S factors cancel. No runtime swaps are required.
+
+The checker constructs every inverse-adjoint instruction in the
+original order and applies S to each target and source. It checks
+the full serialized list, wire permutation, and endpoint arrays.
+It also checks every intermediate scalar frame after this change.
+
+Direct inversion gives
+
+\[
+M^{-1}(a,u,z,v)=(z-Bu,\ u,\ -a,\ v-u).
+\]
+
+Transposing and applying the selected permutation on both sides
+gives
+
+\[
+B_{\rm custom}(a,u,z,v)
+=(z,\ u-B^Tz-v,\ -a,\ v).
+\]
+
+The checker constructs this formula independently. It compares it
+with the complete literal replay and with \(SM^{-T}S\). Both
+content inverse orders pass for both words.
+
+All 640 inputs are independent. The 416 outside fields remain
+identity output rows and have zero influence on the 224 data
+outputs. No helper is assumed zero. No helper progress is claimed.
+
+## Tensor scope
+
+The phase checks above prove exact one-alphabet operator identities.
+For width f, take the tensor power of each complete monomial map
+and child operator. Equality is preserved by tensor power. This
+gives the same field transition for every f.
+
+Each scalar ADD uses two fields with the same current physical
+type. Thus it acts on their contents with the stated coefficient
+at every width. The two native words and their scalar instructions
+therefore have the proved content maps at every width.
+
+This argument does not substitute \(X_v^{\otimes f}\) into a
+one-bit polynomial for \(C_v\). Such a substitution would in
+general give the wrong operator. The construction uses the full
+tensor power of the exact kernel and its complete wrappers.
+
+## Full local invoice and bounds
+
+| Part | Scalar primitives | Native calls |
+| --- | ---: | --- |
+| X and selected-Y progress | 0 | 128 H8 |
+| Ordinary-Y FULL progress | 0 | 96 H9 |
+| Ordinary self ADDs | 768 | 0 |
+| Ordinary negative-line exits | 0 | 96 H1 |
+| Complete C code | 1760 | 0 |
+| Sixteen signed rotations | 384 | 0 |
+| Total | 2912 | 320 |
+
+The inverse-adjoint word has the same price. All 96 H9 calls have
+identity wrappers. The other 224 calls retain two wrappers each,
+so the side-map upper bound is 448. There are no boundary adapters,
+new fields, private zero fields, or odd divisions.
+
+The scalar-prefix content row-sum peak is 22 for Fsimple and four
+for Bcustom. Both have additional binary denominator height one.
+These are exact ideal content bounds at scalar-event boundaries.
+They exclude child internals, rounding, and recursive precision.
+
+Deleting an ordinary self ADD or a reader ADD fails the independent
+endpoint check in both words. Normal and optimized checks give
+identical receipts. The reproduction record checks every consumed
+file hash again.
+
+The higher native mass 1984 must be compared using the complete
+profile above, not only the scalar count. The different 320-child
+profile must not be replaced by the older 1520-child profile.
+No complete kappa claim follows from this local invoice.
+
+## Reproduction and credit
+
+From this review directory run:
+
+```text
+python3 -B check.py --out normal
+python3 -O -B check.py --out optimized
+```
+
+Both runs must print
+`PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE`.
+The receipts and input manifests must be byte equal.
+
+The new-core-transfer lane supplied the direct construction and
+its native recipes. The controller lane supplied the row code.
+The earlier clean-exchange work supplied the selected rotation
+and its physical input and output types. This lane supplied the
+independent full spatial-column checks and complete word review.
+AI agents prepared these local research records.
+
+No PR, push, commit, or publication is authorized. Before any future
+PR description, read
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`.
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/check.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/check.py
new file mode 100644
index 0000000000..3e46c5a95a
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/check.py
@@ -0,0 +1,305 @@
+#!/usr/bin/env python3
+"""Check the direct native pair with exact columns."""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import importlib.util
+import json
+import struct
+
+
+HERE = Path(__file__).resolve().parent
+LANES = HERE.parents[1]
+HELPER = HERE.parent/'row-capture-native-review-20261020/check.py'
+HELPER_PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84'
+if sha256(HELPER.read_bytes()).hexdigest() != HELPER_PIN:
+    raise ValueError('Independent arithmetic helper pin')
+spec = importlib.util.spec_from_file_location('independent_row_tools', HELPER)
+q = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(q)
+q.read(HELPER, HELPER_PIN)
+need = q.need
+SOURCE = q.RAW/'simple-clean-native-20261020'
+
+
+def multiply(a, b):
+    return a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0]
+
+
+def rotate(a, power):
+    r, i = a
+    return ((r, i), (-i, r), (-r, -i), (i, -r))[power % 4]
+
+
+def full_kernel(rank):
+    result = {}
+    for mask in range(1 << rank):
+        value = (1, 0)
+        for j in range(rank):
+            value = multiply(value, (1, -1 if mask >> j & 1 else 1))
+        result[mask] = value
+    return result
+
+
+def monomial_table(record):
+    if record is None:
+        return list(range(512)), [0]*512
+    need(set(record) == {'matrix_rows', 'quadratic_rows', 'linear_Z4', 'offset', 'phase'},
+         'Complete monomial record')
+    rows, quadratic, linear = (record[k] for k in ('matrix_rows', 'quadratic_rows', 'linear_Z4'))
+    need(len(rows) == len(quadratic) == len(linear) == 9, 'Nine-axis monomial')
+    need(all(0 <= row < 512 for row in rows+quadratic) and
+         all(0 <= value < 4 for value in linear) and
+         0 <= record['offset'] < 512 and 0 <= record['phase'] < 4, 'Literal monomial domain')
+    image, phases = [], []
+    for x in range(512):
+        image.append(record['offset'] ^ sum(((row & x).bit_count() & 1) << j
+                                            for j, row in enumerate(rows)))
+        phase = record['phase']
+        for j in range(9):
+            if x >> j & 1:
+                phase += linear[j]+2*((quadratic[j] & x) >> (j+1)).bit_count()
+        phases.append(phase % 4)
+    need(sorted(image) == list(range(512)), 'Monomial address permutation')
+    return image, phases
+
+
+def phase_check(record, expected, denominator):
+    rank = record['rank']
+    left, lp = monomial_table(record['left'])
+    right, rp = monomial_table(record['right'])
+    child = full_kernel(rank)
+    need(len(expected) == 1 << rank, 'Exact support rank')
+    digest = sha256()
+    for x in range(512):
+        result = []
+        for mask, value in child.items():
+            address = right[x] ^ mask
+            y = left[address]
+            actual = rotate(value, rp[x]+lp[address])
+            target = expected.get(x ^ y, (0, 0))
+            need((actual[0] << denominator, actual[1] << denominator) ==
+                 (target[0] << rank, target[1] << rank), 'Exact spatial coefficient and phase')
+            result.append((y, actual))
+        need(len({y for y, _ in result}) == len(expected), 'Complete spatial support')
+        digest.update(b''.join(struct.pack('<HHii', x, y, value[0], value[1])
+                               for y, value in sorted(result)))
+    return {'columns': 512, 'nonzero_coefficients': 512*(1 << rank),
+            'exact_column_digest': digest.hexdigest()}
+
+
+def kernels(payload, ports, selected):
+    full = [['C', 1 << j, 1] for j in range(9)]
+    frames = [[], full]+[[['C', v, 1]] for v in ports]+[
+        [['C', v, -1]]+full for v in ports]
+    need(payload['physical_frame_circuits'] == frames, 'Every literal physical type')
+    wanted = {'full'} | {'advance:'+str(p) for p in range(112)} | {
+        'exit:'+str(p) for p in range(112) if p not in selected}
+    need(set(payload['native_kernels']) == wanted, 'All209 distinct kernels')
+    f9 = full_kernel(9)
+    report = {}
+    identity = list(range(512)), [0]*512
+    for index, (key, item) in enumerate(sorted(payload['native_kernels'].items())):
+        if key == 'full':
+            edge, rank, kernel, denominator = [0, 1], 9, f9, 9
+            need(monomial_table(item['recipe']['left']) == identity and
+                 monomial_table(item['recipe']['right']) == identity, 'Direct FULL identity wrappers')
+        else:
+            kind, port = key.split(':')
+            p, vector = int(port), ports[int(port)]
+            if kind == 'exit':
+                edge, rank, denominator = [1, 114+p], 1, 1
+                kernel = {0: (1, -1), vector: (1, 1)}
+            else:
+                need(kind == 'advance', 'Kernel class')
+                edge, rank, denominator = [2+p, 1], 8, 10
+                kernel = {}
+                for mask in range(512):
+                    a, b = multiply((1, -1), f9[mask]), multiply((1, 1), f9[mask ^ vector])
+                    value = a[0]+b[0], a[1]+b[1]
+                    if value != (0, 0):
+                        kernel[mask] = value
+        need(item['edge'] == edge and item['rank'] == item['recipe']['rank'] == rank,
+             'Declared physical edge and rank')
+        report[key] = phase_check(item['recipe'], kernel, denominator)
+        if (index+1) % 32 == 0:
+            print('Exact independent kernels', index+1, '/209', flush=True)
+    return report
+
+
+def direct_events(capture, ports, pivots):
+    selected = set(pivots)
+    ordinary = [p for p in range(112) if p not in selected]
+    stages = [
+        ('source_progress', [['native', p, 2+p, 1, 8, 'advance:'+str(p)] for p in range(112)]),
+        ('selected_progress', [['native', 112+p, 2+p, 1, 8, 'advance:'+str(p)] for p in pivots]),
+        ('ordinary_full_progress', [['native', 112+p, 0, 1, 9, 'full'] for p in ordinary]),
+        ('ordinary_self_adds', [['scalar', ['add', 112+p, p, '1'], 1] for p in ordinary]),
+        ('ordinary_negative_lines', [['native', 112+p, 1, 114+p, 1, 'exit:'+str(p)] for p in ordinary]),
+        ('source_row_code', [['scalar', gate, 1] for gate in capture]),
+        ('signed_selected_exchanges', [
+            event for p in pivots for event in (
+                ['scalar', ['add', 112+p, p, '1'], 1],
+                ['scalar', ['add', p, 112+p, '-1'], 1],
+                ['scalar', ['add', 112+p, p, '1'], 1])]),
+    ]
+    events, ranges = [], {}
+    for name, records in stages:
+        ranges[name] = [len(events), len(events)+len(records)]
+        events.extend(records)
+    return events, ranges
+
+
+def adjoint_events(events, permutation):
+    result = []
+    for event in events:
+        if event[0] == 'native':
+            result.append([event[0], permutation[event[1]]]+event[2:])
+        else:
+            op, target, source, coefficient = event[1]
+            coefficient = F(coefficient)
+            gate = (['add', permutation[source], permutation[target], str(-coefficient)]
+                    if op == 'add' else ['scale', permutation[target], None, str(1/coefficient)])
+            result.append(['scalar', gate, event[2]])
+    return result
+
+
+def endpoints(code, selected):
+    forward, inverse, custom, custom_inverse = (q.unit(640) for _ in range(4))
+    for p in range(112):
+        if p in selected:
+            forward[p], forward[112+p] = {112+p: F(-1)}, dict(code[p])
+            inverse[p] = {112+p: F(1)}
+            q.add(inverse[p], {j: -v for j, v in code[p].items() if j != p})
+            inverse[112+p] = {p: F(-1)}
+            custom[p], custom[112+p] = {112+p: F(1)}, {p: F(-1)}
+            custom_inverse[p], custom_inverse[112+p] = {112+p: F(-1)}, {p: F(1)}
+        else:
+            q.add(forward[112+p], {p: F(1)})
+            q.add(inverse[112+p], {p: F(-1)})
+            q.add(custom[p], {112+p: F(-1)})
+            q.add(custom_inverse[p], {112+p: F(1)})
+            for j in selected:
+                q.add(custom[p], {112+j: -code[j].get(p, F(0))})
+                q.add(custom_inverse[p], {j: code[j].get(p, F(0))})
+    for word, back in ((forward, inverse), (custom, custom_inverse)):
+        need(q.mul(word, back) == q.mul(back, word) == q.unit(640), 'Both complete inverse orders')
+    return {'Fsimple': forward, 'Bcustom': custom}, inverse
+
+
+def replay(word, expected, start, final, kernels, ranges):
+    need(word['start'] == start and word['final'] == final and word['stage_ranges'] == ranges,
+         'Exact full boundary and stage ledger')
+    current, used, profile = list(start), set(), Counter()
+    for event in word['events']:
+        if event[0] == 'native':
+            _, field, before, after, rank, key = event
+            need(0 <= field < 224 and current[field] == before, 'Native field and input type')
+            need(kernels[key]['edge'] == [before, after] and kernels[key]['rank'] == rank,
+                 'Exact checked kernel occurrence')
+            current[field] = after
+            used.add(key)
+            profile[rank] += 1
+        else:
+            need(event[0] == 'scalar', 'Complete event grammar')
+            (op, target, source, _), frame = event[1:]
+            need(0 <= target < 224 and current[target] == frame, 'Scalar target physical type')
+            if op == 'add':
+                need(0 <= source < 224 and source != target and current[source] == frame,
+                     'Equal source and target physical types')
+            else:
+                need(op == 'scale' and source is None, 'Scalar scale grammar')
+    need(current == final and used == set(kernels), 'Complete final and used-kernel ledger')
+    need(profile == {1: 96, 8: 128, 9: 96}, 'Exact full native profile')
+    scalars = [e[1] for e in word['events'] if e[0] == 'scalar']
+    need(q.reverse(scalars, 640) == q.transpose(expected, 640), 'All640 reverse columns')
+    rows, growth = q.prefix(scalars, 640)
+    need(rows == expected and rows[224:] == q.unit(640)[224:] and
+         all(j < 224 for row in rows[:224] for j in row), 'Forward rows and416 arbitrary outside roles')
+    prices = {name: q.price([e[1] for e in word['events'][a:b] if e[0] == 'scalar'])
+              for name, (a, b) in ranges.items()}
+    need(sum(prices.values()) == q.price(scalars) == 2912, 'Complete scalar price')
+    need(prices['ordinary_self_adds'] == 768 and prices['source_row_code'] == 1760 and
+         prices['signed_selected_exchanges'] == 384, 'Exact scalar stage prices')
+    for stage in ('ordinary_self_adds', 'source_row_code'):
+        a, b = ranges[stage]
+        missing = next(i for i in range(a, b) if word['events'][i][0] == 'scalar'
+                       and word['events'][i][1][0] == 'add')
+        bad = [e[1] for i, e in enumerate(word['events']) if e[0] == 'scalar' and i != missing]
+        need(q.reverse(bad, 640) != q.transpose(expected, 640), 'Missing ADD negative control')
+    return {'input_columns': 640, 'unchanged_arbitrary_roles': 416, 'native_profile': dict(profile),
+            'native_mass': sum(r*n for r, n in profile.items()), 'native_children': sum(profile.values()),
+            'scalar_price': 2912, 'scalar_stage_prices': prices, 'growth': growth,
+            'native_side_maps_upper_bound': 448, 'boundary_adapters': 0,
+            'extra_fields': 0, 'private_fields': 0, 'odd_divisions': 0}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    q.frozen(SOURCE, 'FREEZE.json', '1e08caf1376ffb3a74eac87200e6165c969a08d71d5c028a7c8940093f830089')
+    q.frozen(HERE.parent/'clean-centre-exchange-review-20261020', 'FREEZE.json',
+             '6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d')
+    payload = json.loads(q.read(SOURCE/'run-normal/SIMPLE-CLEAN-NATIVE.json.gz',
+                                '1bdddb7955d0ada6dabcf150fce0a568cd336a846f51be3324c081f10dd374c7', True))
+    clean = json.loads(q.read(q.RAW/'clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz',
+                              'b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083', True))
+    capture = json.loads(q.read(q.ALG/'run-normal/ROW-CAPTURE.json',
+                                '4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7'))
+    need(payload['ports'] == clean['ports'] and payload['selected_ports'] == clean['selected_ports'] == q.P,
+         'Actual common ports and selected set')
+    need(payload['code'] == clean['code'] == capture['code'], 'Exact reviewed row code')
+    code, selected = q.rows(payload['code']), set(q.P)
+    for p, row in enumerate(code):
+        need(row == {p: F(1)} if p not in selected else
+             {j: v for j, v in row.items() if j in selected} == {p: F(1)},
+             'Row code I+e_P B with B_P zero')
+    need(q.reverse(capture['scalar_word'], 112) == q.transpose(code, 112) and
+         q.price(capture['scalar_word']) == 1760, 'Actual complete row code')
+    phase_report = kernels(payload, payload['ports'], selected)
+    events, ranges = direct_events(capture['scalar_word'], payload['ports'], q.P)
+    start, final = [0]*640, [0]*640
+    for p in range(112):
+        start[p], final[p] = 2+p, 1
+        start[112+p], final[112+p] = (2+p, 1) if p in selected else (0, 114+p)
+    permutation = list(range(640))
+    for p in q.P:
+        permutation[p], permutation[112+p] = 112+p, p
+    need([start[p] for p in permutation] == start and [final[p] for p in permutation] == final,
+         'Selected permutation preserves literal endpoint operators')
+    need(set(payload['words']) == {'Fsimple', 'Bcustom'}, 'Both complete words')
+    need(payload['words']['Fsimple']['events'] == events, 'Exact direct chronology')
+    need(payload['words']['Bcustom']['events'] == adjoint_events(events, permutation),
+         'Same-order physical inverse-adjoint and every field relabeling')
+    need(payload['words']['Bcustom']['wire_permutation'] ==
+         {str(i): j for i, j in enumerate(permutation) if i != j}, 'Exact wire permutation')
+    expected, back = endpoints(code, selected)
+    inverse_transpose = q.transpose(back, 640)
+    conjugate = [{permutation[j]: value for j, value in inverse_transpose[permutation[i]].items()}
+                 for i in range(640)]
+    need(conjugate == expected['Bcustom'], 'Complete selected-conjugate inverse-adjoint identity')
+    reports = {}
+    for name, word in payload['words'].items():
+        need(q.rows(payload['content_maps'][name]) == expected[name][:224], 'Declared content map')
+        reports[name] = replay(word, expected[name], start, final, payload['native_kernels'], ranges)
+    need(reports['Fsimple']['growth'] == {'row_one_norm': '22', 'binary_height': 1} and
+         reports['Bcustom']['growth'] == {'row_one_norm': '4', 'binary_height': 1}, 'Exact prefix bounds')
+    report = {
+        'status': 'PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE',
+        'words': reports, 'phase_kernels': phase_report,
+        'phase_method': 'Every exact spatial column from Gaussian integer convolution coefficients; no compiler or Pauli interpreter.',
+        'total_spatial_columns': sum(r['columns'] for r in phase_report.values()),
+        'total_nonzero_spatial_coefficients': sum(r['nonzero_coefficients'] for r in phase_report.values()),
+        'scope': 'Two complete local tensor-liftable words. No routed caller, recursive hosting, or complete supplier bound.',
+    }
+    args.out.mkdir(parents=True, exist_ok=True)
+    for name, value in [('REVIEW-CHECKS.json', report), ('INPUTS.json', q.INPUTS)]:
+        (args.out/name).write_text(json.dumps(value, sort_keys=True, indent=2)+'\n')
+    print(report['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/INPUTS.json
new file mode 100644
index 0000000000..1352fde88d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/INPUTS.json
@@ -0,0 +1,61 @@
+{
+  "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json": {
+    "sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz": {
+    "decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083",
+    "sha256": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/FREEZE.json": {
+    "sha256": "1e08caf1376ffb3a74eac87200e6165c969a08d71d5c028a7c8940093f830089"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/SIMPLE-CLEAN-NATIVE.md": {
+    "sha256": "8c64af43d7f43c5fc28056715c5cc277d8580ca4cf05dcabb7ff4bd0911738e7"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/emit_simple.py": {
+    "sha256": "6a4bacced0962b4f29d5b29743c6f07382ba98f850c57bb4dd828f9e98b1ea0b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-normal/CHECKS.json": {
+    "sha256": "12a231a54878a31a71b83e800772c200c80b637073b8f6bac97bfb1cfdf9121a"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-normal/SIMPLE-CLEAN-NATIVE.json.gz": {
+    "decompressed_sha256": "1bdddb7955d0ada6dabcf150fce0a568cd336a846f51be3324c081f10dd374c7",
+    "sha256": "35f18c7fd11d975bb12d03e82ec387700738c41a1cf93cb5ed1668370e7c77ee"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-optimized/CHECKS.json": {
+    "sha256": "12a231a54878a31a71b83e800772c200c80b637073b8f6bac97bfb1cfdf9121a"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/simple-clean-native-20261020/run-optimized/SIMPLE-CLEAN-NATIVE.json.gz": {
+    "sha256": "35f18c7fd11d975bb12d03e82ec387700738c41a1cf93cb5ed1668370e7c77ee"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/DERIVATION.md": {
+    "sha256": "d8e77e0c3537a007a3674d03611dd8d6458589b8256cc2bc9bdb5c86d52124a9"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/FREEZE.json": {
+    "sha256": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/REPRODUCTION.json": {
+    "sha256": "65193ab9f017a3d9b49c46cf64bc93fc7dbc1b38789f692f8bbea11148186bce"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/REVIEW.md": {
+    "sha256": "2a290ee65bb86a0a9c9acfb36b44735d98134350360b60a831c968a8c9c3ccd0"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/check.py": {
+    "sha256": "e6564514a878cfa2411a41990a3d9c012f97a464c1b8361fb358fa741968f35c"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/INPUTS.json": {
+    "sha256": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/normal/REVIEW.json": {
+    "sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/INPUTS.json": {
+    "sha256": "928a4b4354b09f062bedfa4a0cc21411fc9674d63c6a666b6ea1816e9f5bc763"
+  },
+  "new-native-recipes-20261017/clean-centre-exchange-review-20261020/optimized/REVIEW.json": {
+    "sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5"
+  },
+  "new-native-recipes-20261017/row-capture-native-review-20261020/check.py": {
+    "sha256": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84"
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/REVIEW-CHECKS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..7bab98d1be
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/normal/REVIEW-CHECKS.json
@@ -0,0 +1,1116 @@
+{
+  "phase_kernels": {
+    "advance:0": {
+      "columns": 512,
+      "exact_column_digest": "a2a3d843bac4c44369db67ae38a819372bfb8b3e4b43eeb401e852ff9d59bf72",
+      "nonzero_coefficients": 131072
+    },
+    "advance:1": {
+      "columns": 512,
+      "exact_column_digest": "072709d051c72d9f5d22596c28308100f4da8d494cc92da859c145fbec3470d0",
+      "nonzero_coefficients": 131072
+    },
+    "advance:10": {
+      "columns": 512,
+      "exact_column_digest": "10cbc38e40171d45ddc4f241e64ad59bf6448d4a4210a34e7b6bb055ce5241d8",
+      "nonzero_coefficients": 131072
+    },
+    "advance:100": {
+      "columns": 512,
+      "exact_column_digest": "82b3540023a9bf07d3f8846ca60a6f9794ea478cb95e10840904afe4d35d30ca",
+      "nonzero_coefficients": 131072
+    },
+    "advance:101": {
+      "columns": 512,
+      "exact_column_digest": "8b8091b5e48227aa2029778d5d7386af249591f81ff10f6eceb5129193c4b3a8",
+      "nonzero_coefficients": 131072
+    },
+    "advance:102": {
+      "columns": 512,
+      "exact_column_digest": "b76f18d5aec52a561ec9683fa60e6156b00c7ac66da78566f6084f46ed782d78",
+      "nonzero_coefficients": 131072
+    },
+    "advance:103": {
+      "columns": 512,
+      "exact_column_digest": "523f280bb8eceb5b822e2e99500d38894b2aa869f50873f49521bd65e81f9685",
+      "nonzero_coefficients": 131072
+    },
+    "advance:104": {
+      "columns": 512,
+      "exact_column_digest": "27209dc83e40e9580990ab49c385eaba753e3d7d7911b1edc954d796f407ff2b",
+      "nonzero_coefficients": 131072
+    },
+    "advance:105": {
+      "columns": 512,
+      "exact_column_digest": "33fdc77126b9d04b69fbc2c1c32460c467bb0916515fdad14ef3a916d78e90e5",
+      "nonzero_coefficients": 131072
+    },
+    "advance:106": {
+      "columns": 512,
+      "exact_column_digest": "fa4659d193d847874b5ad797098f859ab18dbae8e3b12651a68c8c6f54f69278",
+      "nonzero_coefficients": 131072
+    },
+    "advance:107": {
+      "columns": 512,
+      "exact_column_digest": "13575d381d568b469bef5cd27a28cc1e1302b8a7ee7c6f409fd8acd9c70236d9",
+      "nonzero_coefficients": 131072
+    },
+    "advance:108": {
+      "columns": 512,
+      "exact_column_digest": "55b6e587bab8129eb9656afdc37cd4b033de07f0f01da6440d54a4f63676292c",
+      "nonzero_coefficients": 131072
+    },
+    "advance:109": {
+      "columns": 512,
+      "exact_column_digest": "e3cf6a7dd112e4691cc2f0619a5703d614171e13afca1d39a2562a253c7a5d44",
+      "nonzero_coefficients": 131072
+    },
+    "advance:11": {
+      "columns": 512,
+      "exact_column_digest": "fa9c771574822dcfc35cece54aaf107fdf088f4bf08023846c7f29f22cf85769",
+      "nonzero_coefficients": 131072
+    },
+    "advance:110": {
+      "columns": 512,
+      "exact_column_digest": "e1a05cdcc8b3bf81500077a8122fdc2aa8fd181b73dfe045b60683f9d78024c7",
+      "nonzero_coefficients": 131072
+    },
+    "advance:111": {
+      "columns": 512,
+      "exact_column_digest": "3dd4a1c8797e3757c8389f31950c72d2b3453cf9de566c735308c7e2c115f6e5",
+      "nonzero_coefficients": 131072
+    },
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diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/optimized/INPUTS.json b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/optimized/INPUTS.json
new file mode 100644
index 0000000000..1352fde88d
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/simple-clean-native-review-20261020/optimized/INPUTS.json
@@ -0,0 +1,61 @@
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+      "exact_column_digest": "7895153cec17de27b87784ee14d7ffdaac86b88344b022d32ea9b28b48ed3d1a",
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+      "exact_column_digest": "364175277bf5a1b060a69ae6e1ed7e9537233873b51ecc377f63712838799db8",
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+      "exact_column_digest": "4e31d03d7adde73d4526983b8b1375eb683967472e80957bca4cda3441614848",
+      "nonzero_coefficients": 1024
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+      "exact_column_digest": "0b3479656a12439a28fb5cba52f7ceda565918d8122e5d5360bea6537710e3c6",
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+      "exact_column_digest": "c53ba710a73e683a50d3431879272dab189758297da2f1df84bf61064770fadc",
+      "nonzero_coefficients": 1024
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+      "exact_column_digest": "88f813f8ce467bb9fef62154d9850cecac1d0ec2fe5c4b5428e4e21bac78c13c",
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+    "exit:80": {
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+      "exact_column_digest": "56b54798b304ef430539681a8ce547cc8b491daa2b20b6075584d900683a1675",
+      "nonzero_coefficients": 1024
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+      "exact_column_digest": "97569af9ad1fd878c662a2b7e22aa21312972355fa49fb816812a496ca8734cb",
+      "nonzero_coefficients": 1024
+    },
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+      "exact_column_digest": "9ac491f611fa9b894f0e7bca8fafe5ae308e7bda0811eab8b2aeee28fd6ba424",
+      "nonzero_coefficients": 1024
+    },
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+      "exact_column_digest": "0abb528627d861edf74f2fdd9432cccbd2c72b52534cbf45d02017bf2b444324",
+      "nonzero_coefficients": 1024
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+    "exit:84": {
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+      "exact_column_digest": "9458890c35d68b2d6898f2b8c2e63667691f649aea2d5efa9573c847dc8806ce",
+      "nonzero_coefficients": 1024
+    },
+    "exit:85": {
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+      "exact_column_digest": "524a58db3d94d64f970cee1b93d25c9aacdaf6d167db953f4ca4e47896c191dd",
+      "nonzero_coefficients": 1024
+    },
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+      "exact_column_digest": "2d3dc0f212ce0e6dfc087f5e2271610d4f98c3abdfc6ea1c82ca897bece49ee9",
+      "nonzero_coefficients": 1024
+    },
+    "exit:87": {
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+      "exact_column_digest": "b2f64507d3a7b78d79a1af2da32a8e9740b90f41e5a0f2fb6acfe96d54a52d97",
+      "nonzero_coefficients": 1024
+    },
+    "exit:88": {
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+      "exact_column_digest": "42faac5487179cd01e61ca579d07eac73255e4c6308a57fe35061858700def84",
+      "nonzero_coefficients": 1024
+    },
+    "exit:89": {
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+      "exact_column_digest": "3a851d93dbddeacf405cfe2c93fd9b1606438782969bb9ab4f9ed602aca7500a",
+      "nonzero_coefficients": 1024
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+    "exit:9": {
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+      "exact_column_digest": "646f7b28c8102c427fda72190035a9dcf1e06e95a966ae70133e40537f80854c",
+      "nonzero_coefficients": 1024
+    },
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+      "exact_column_digest": "691b6d74e5ef13eac9c5c635df69003d721ecf108abd6cb1d2c9acd90a3580ec",
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+    },
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+      "exact_column_digest": "74de777679da43e9d259d77d0f5b46fd06ed3bb1ece0877d8958ca3b650b675e",
+      "nonzero_coefficients": 1024
+    },
+    "exit:92": {
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+      "exact_column_digest": "eb55a9ecdb4f37eff4b4288235f313dd259a5b3ebe995c6372078a7356ec0013",
+      "nonzero_coefficients": 1024
+    },
+    "exit:93": {
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+      "exact_column_digest": "b34ebf2afa34582dc41664c06ed3f232c4c326c06287ebb77c563b8c95f3fff5",
+      "nonzero_coefficients": 1024
+    },
+    "exit:94": {
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+      "exact_column_digest": "510e8757ff178a3e61e934dea352f304e986e5f07e44a3103d3c0db93b2a7927",
+      "nonzero_coefficients": 1024
+    },
+    "exit:95": {
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+      "exact_column_digest": "3bc25c4a6808b3d8f2ee9624453f47306bec628cc574b5d27c3e08408641869f",
+      "nonzero_coefficients": 1024
+    },
+    "exit:96": {
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+      "exact_column_digest": "0a847a593197c09348ed7e01719ce2687dba62541309693016d9e3cc07b49256",
+      "nonzero_coefficients": 1024
+    },
+    "exit:97": {
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+      "exact_column_digest": "7d280219cfb2de2da4ddcd835d95ce84e42948b1643a692ab45b6646ecb77227",
+      "nonzero_coefficients": 1024
+    },
+    "exit:98": {
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+      "exact_column_digest": "bf815c34f7b2ec5562d5f05c1f5467ab7d9a6351086a2921bb5111835faf423c",
+      "nonzero_coefficients": 1024
+    },
+    "exit:99": {
+      "columns": 512,
+      "exact_column_digest": "9fd28eceee8f74eb6a834cfb480c2242b00d9210663bb00422caf597dddfa49e",
+      "nonzero_coefficients": 1024
+    },
+    "full": {
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+      "exact_column_digest": "a15c9986977c74a606e78e00b50d392cd70d458ba1eb9f950573f8616897f98e",
+      "nonzero_coefficients": 262144
+    }
+  },
+  "phase_method": "Every exact spatial column from Gaussian integer convolution coefficients; no compiler or Pauli interpreter.",
+  "scope": "Two complete local tensor-liftable words. No routed caller, recursive hosting, or complete supplier bound.",
+  "status": "PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE",
+  "total_nonzero_spatial_coefficients": 15040512,
+  "total_spatial_columns": 107008,
+  "words": {
+    "Bcustom": {
+      "boundary_adapters": 0,
+      "extra_fields": 0,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "4"
+      },
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+      "native_children": 320,
+      "native_mass": 1984,
+      "native_profile": {
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+        "8": 128,
+        "9": 96
+      },
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+      "odd_divisions": 0,
+      "private_fields": 0,
+      "scalar_price": 2912,
+      "scalar_stage_prices": {
+        "ordinary_full_progress": 0,
+        "ordinary_negative_lines": 0,
+        "ordinary_self_adds": 768,
+        "selected_progress": 0,
+        "signed_selected_exchanges": 384,
+        "source_progress": 0,
+        "source_row_code": 1760
+      },
+      "unchanged_arbitrary_roles": 416
+    },
+    "Fsimple": {
+      "boundary_adapters": 0,
+      "extra_fields": 0,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "22"
+      },
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+      "native_children": 320,
+      "native_mass": 1984,
+      "native_profile": {
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+        "8": 128,
+        "9": 96
+      },
+      "native_side_maps_upper_bound": 448,
+      "odd_divisions": 0,
+      "private_fields": 0,
+      "scalar_price": 2912,
+      "scalar_stage_prices": {
+        "ordinary_full_progress": 0,
+        "ordinary_negative_lines": 0,
+        "ordinary_self_adds": 768,
+        "selected_progress": 0,
+        "signed_selected_exchanges": 384,
+        "source_progress": 0,
+        "source_row_code": 1760
+      },
+      "unchanged_arbitrary_roles": 416
+    }
+  }
+}
diff --git a/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/native-centre-capture/frozen/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/native-centre-capture/frozen/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz b/research/native-centre-capture/frozen/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz
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diff --git a/research/native-centre-capture/historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/certificates/selected-result.json b/research/native-centre-capture/historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/certificates/selected-result.json
new file mode 100644
index 0000000000..ae6a99f28a
--- /dev/null
+++ b/research/native-centre-capture/historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/certificates/selected-result.json
@@ -0,0 +1,222 @@
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diff --git a/research/native-centre-capture/historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1094-audit/ASSEMBLY.json b/research/native-centre-capture/historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1094-audit/ASSEMBLY.json
new file mode 100644
index 0000000000..5fd676df06
--- /dev/null
+++ b/research/native-centre-capture/historical/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1094-audit/ASSEMBLY.json
@@ -0,0 +1,345 @@
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+    "unit_beta"
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/native-centre-capture/notices/PR2226-NOTICE.md b/research/native-centre-capture/notices/PR2226-NOTICE.md
new file mode 100644
index 0000000000..5ea70357a0
--- /dev/null
+++ b/research/native-centre-capture/notices/PR2226-NOTICE.md
@@ -0,0 +1,22 @@
+# Attribution and license
+
+New construction, proof text and checkers: Cinna Davis (@1337isnot1337), with
+substantial OpenAI Codex assistance, Apache-2.0.
+
+The selected complex canonical word is the PR1042 ancestry retained in PR1094.
+Jeremy Kothe, Rohan Arun, Hao Yan, Chafik Boukhalfa, icekylinx, Jonathan Capalbo
+and the source package's full provider/frame/controller lineage retain credit.
+Ali Romman supplied the source-bound fixed-block theorem and certificate;
+Thomas DiFiore supplied the earlier block discovery. The borrowing construction
+does not attribute its changed interface to those predecessor results.
+
+`price_engine.py` is an unchanged copy of the incorporated
+`research/complex-local-word-ceiling/ceiling.py`: Douglas Colkitt, with Claude
+(Anthropic) assistance; original SPDX/license context and docstring retained.
+General Clifford frame and exact Gaussian normal forms are inherited from
+`notes/general-clifford-frames.tex` and the repository's credited phase/compiler
+lineage. The package independently checks its actual local Gaussian products.
+
+Source hashes, base commits and the copied engine's Git blob are in SOURCES.json.
+No full native supplier, all-size compiler, precision theorem or new kappa is
+claimed. No independent human review is claimed.
diff --git a/research/native-centre-capture/notices/PR2588-NOTICE b/research/native-centre-capture/notices/PR2588-NOTICE
new file mode 100644
index 0000000000..46411b80b2
--- /dev/null
+++ b/research/native-centre-capture/notices/PR2588-NOTICE
@@ -0,0 +1,10 @@
+Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls.
+
+New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained.
+Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance.
+
+T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance.
+
+PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged.
+
+Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance.
diff --git a/research/native-centre-capture/notices/PR2588-NOTICE-PR2226.md b/research/native-centre-capture/notices/PR2588-NOTICE-PR2226.md
new file mode 100644
index 0000000000..a14b299ef5
--- /dev/null
+++ b/research/native-centre-capture/notices/PR2588-NOTICE-PR2226.md
@@ -0,0 +1,21 @@
+# Credit: anticipatory dirty borrowing (PR2226)
+
+The construction realised by this native chain is **PR2226, "anticipatory dirty borrowing"**, by Cinna Davis
+(@1337isnot1337), prepared with substantial OpenAI Codex assistance (Apache-2.0): the logical reference change
+K_G of a lender register (a monomial Clifford: a permutation of the 512 columns with phase mod 4), the initial
+compensation terms c K_G z, the early cold tail, the exact cold restoration and the private zero buffers of the
+FULL-frame cleanup.  `vendor/pr2226_operators.py`, `vendor/pr2226_replay.py` and `vendor/PR2226-NOTICE.md` are byte copies
+of PR2226's `operators.py`, `replay.py` and `NOTICE.md`.  `bw_gauss.py` is a port of `operators.py` (change, monomial,
+apply_mono, coord, frame, check) and adds a decoder from a serialized `clifford_exact` monomial to its exact 512 x 512
+Gaussian matrix.
+
+What this chain adds (the P3 native realisation, with the borrowing work's explicit chronological BORROW-WORD as input):
+warp events and zero buffers in `LOCAL-PROGRAMS`, warp recipes in `CLIFFORD-RECIPES.json` (lowered with the unchanged
+`lower_child`, rank zero, then compared with the exact numpy column product), logical K_G recipes in
+`RESIDUAL-ADAPTERS.json`, an independent local replay in both orientations that checks every warp product on all 512
+columns, and the negative controls listed in `INDEPENDENT-LOCAL-REPLAY.json`, `WRAPPER-CHECKS.json`, `WARP-RECIPE-CHECKS.json`
+and `bw_tamper.py`.
+
+Lineage retained: icekylinx (PR425/433/514, scalar and wrapper machinery), DreamingOfClouds (PR458/484/593 hyperplane/cold-HPE
+extensions), the clifford_exact compiler (vendor531), and the owners named in the package README.  `vendor/clifford/clifford_exact.py`
+is a byte copy.
diff --git a/research/native-centre-capture/notices/PR3133-CREDITS.md b/research/native-centre-capture/notices/PR3133-CREDITS.md
new file mode 100644
index 0000000000..24f00912d4
--- /dev/null
+++ b/research/native-centre-capture/notices/PR3133-CREDITS.md
@@ -0,0 +1,19 @@
+# Credits
+
+- **PR #2908, Jeremy Diviney**: the paired input/output extraction, its compensation rule `C*S`, the exact two-sided certificate (`structure.py`, vendored unchanged) and the closed-adapter admission chain.
+- **PR #2917, Mason Hale**: the nine paired extractions and 82-endpoint words under PR2942, the refit/compose producer model that stage 2 follows, the T74 chronology (ORDER/DISPATCH), the allocation checker, moment auditor, extension stage and adapter derivation reused here.
+- **PR #2957 / #2948 / #2966, Jeremy Kothe (jeremykothe2)**: the fourteen declared exactness-preserving gate rewrites in five classes (R-retime, A3779-cut-start-read, PM-carrier-lender-entry, B-carrier-retime, A-commuting-swap) and their pure applier (`vendor/declared_rewrites.py`, vendored unchanged); stage 3 composes exactly these rewrites onto this package's stage-2 word (`data/REWRITES-2957.json`, re-addressed with exact preimages). PR2966 composed the same rewrites onto our PR2942 words.
+- **PR #2969, Dugongue**: the PR2942 + PR2957 composition at T370 and its cap-level headline nomination, this package's comparator and moment baseline (`allocation/baseline/`). Our stage 3 composes the same fourteen rewrites, here onto the stage-2 word.
+- **PR #2918 (research/helper408-rank7-pairing), RossRichardson**: the fixed-cut rank-seven obstruction for helper408; this package's census of fresh rank-7 extractions reproduces it exactly and is consistent with it.
+- **PR #2894 / #2833, Jeremy Kothe**: the preload re-synthesis supplier, the frame accounting and inverse-reverse cleanup (`vendor/preload_move.py`), the source materializer and the inherited supplier lineage.
+- **PR #2857 / #2848, Yiyang Lu (Lyy-iiis)**: the shared-kernel words, the staged native/overlay tooling and the chronological flow model and realization (edge colouring) used to construct the allocation; PR2843 (Marius-Paul Dumitrean) is that flow model's starting point.
+- **PR #2863 / #2839, Dugongue**: the packing lineage and the PR2839 owner engine.
+- **Tekalign**: the independent owner/chronology checker (`allocation/vendor/independent_owners.py`) and admission tooling.
+- **icekylinx**: the exact free-operator auditor retained as `vendor/audit_local.py` (PR2833).
+- **themilkman216**: the observation that a cap-level allocation of these inventories needs a T whose basic counts are integral, which the allocation's degenerate-face step builds on.
+- **Gareth Davidson (bitplane), PR #1995 / #2013**: the fixed-word terminal-subspace bounds that frame stage 1's scope; earlier rank-seven helper ends on other words are in `research/complex-rank7-end-pair`, `research/k8-rank7-composition` and the PR1090/PR1104 lineage (credited there).
+- **PR #2930 / #2942, Marius-Paul Dumitrean**: the cap allocation of PR2917's words, the four normal-45 extractions under these words, the relaxation tools and the overlay/producer conventions reused here.
+- **PR #2979, Marius-Paul Dumitrean (with substantial AI assistance from Anthropic Claude via Claude Code)**: the codimension-2 census on paired-extraction words, the joint end-frame lowering of 22 restored helpers in five groups (stage 1), the five further extractions it makes profitable (stage 2), the exact composition with PR2957's rewrites (stage 3), the producer and local verification for all three stages, the overlay stage `rank7-joint-endframes` with its rebuild guards, the adapter generalization to six width classes, the literal T74 allocation of the changed inventory, its relaxation certificates and recorded gap, and the complete fresh replay.
+- **PR #3015, Jeremy Kothe (jeremykothe2)**: the declared literal edit stage (`edits/`, `tools/build_edits.py`) with its independent review (`edits/edits_review.py`), and edit R1 on PR #2979's restore section (carrier 61 for register 63).
+- **PR #3042, dcharb78 (with AI assistance)**: the six restore carrier/pivot skips (`R1_E42` at `restore[162:188]`, `26 -> 33` gates skipping `{22, 40, 54, 63}`, and `R2_E7` at `restore[190:203]`, `13 -> 15` gates skipping `{5, 73}`) on PR #2979's words that serve as the direct starting words for `B_586_438` and `B_588_440`.
+- **New here (dcharb78, with AI assistance)**: the two coupled `B` + `restore` dying-helper carrier folds (`B_586_438` and `B_588_440`, `6` hunks / `6 -> 5` gates each) and `helper_final` lowerings on entering helpers `586` ($E_{30} \to V_{30,76,82}$) and `588` ($E_{30} \to V_{30,97,127}$) shifting the helper width inventory from `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` to `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}` (`+665` net profit per helper, `+1,330` joint), the literal `T74_optimal_idle39` allocation (`allocation/FILL.json.gz`), the 21-control per-word edit review (`edits/edits_review.py`) and 100-control four-stage replay (`verify.py`), and the re-derived paid profile, cap certificate (`certificates/RELAX-CAP.json`), and complete fresh-native admission and release receipts. PR #2979 (mdumitrean), PR #3015 (jeremykothe2), and PR #3042 (dcharb78) are credited first.
diff --git a/research/native-centre-capture/notices/PR3133-NOTICE b/research/native-centre-capture/notices/PR3133-NOTICE
new file mode 100644
index 0000000000..89c20926ea
--- /dev/null
+++ b/research/native-centre-capture/notices/PR3133-NOTICE
@@ -0,0 +1,28 @@
+research/rank7-joint-endframes
+Copyright 2026 Marius-Paul Dumitrean. Licensed under the Apache License, Version 2.0.
+Prepared with substantial AI assistance (Anthropic Claude, via Claude Code).
+
+This package retains, byte-identical, Apache-2.0 files from: PR #2942 (Marius-Paul Dumitrean, head
+a027b0f6fdb0ab2b42ba10fc31b53960166bf2bf, research/paired-extension-normal45): data/PARENT-base.json.gz and
+data/PARENT-extra.json.gz (its data/WORD-*.json.gz), comparators/PR2942-CLAIM.json and tools/wordedit.py; PR #2917
+(Mason Hale, head 224bd5e56041c40078ff6b5fa7393733a215de5c, research/paired-helper-extension): structure.py (Jeremy
+Diviney's PR2908 two-sided certificate checker), vendor/audit_local.py (PR2833's independent exact auditor, icekylinx
+attribution), vendor/preload_move.py (Jeremy Kothe's PR2894 frame accounting and cleanup), allocation/ORDER.json,
+allocation/DISPATCH.json and allocation/vendor/ (independent_owners.py: Tekalign's independent owner checker as vendored
+by PR2839/PR2917; PLAN.json.gz, TEMPLATE.json.gz); PR #2957 (Jeremy Kothe, head b74b25f3ccc84c16e1a801d73b2f47e5ea764c78,
+research/paired-extension-cap-fill-swaps): vendor/declared_rewrites.py (the pure applier of the fourteen declared
+rewrites) and comparators/PR2957-CLAIM.json; PR #2966 (Jeremy Kothe, head e62d3eb9005117d82a9babcfa937ecc53237c490,
+research/paired-extension-normal45-rewrites): comparators/PR2966-CLAIM.json; PR #2969 (Dugongue, head
+e2ca469b08385d3d5e29a918d66dbefaf889e9f3, research/paired-swap-normal45): allocation/baseline/ (its CLAIM.json and its
+allocation ORDER.json and PROFILE.json); and PR #2930 (head 81f3b5d12977eba09e06fbff729167d59faabe90): tools/relax.py,
+tools/root.py, tools/relax_exact.py.
+data/REWRITES-2957.json is Jeremy Kothe's PR2957 rewrite list, re-addressed to this package's stage-2 word with exact
+preimages (every entry keeps a credit field). producer.py follows PR2917's producer.py (Mason Hale) for its paired steps;
+verify.py, check_allocation.py, check_cap.py, run_registered.py and reproduce.py adapt our PR2942 versions of PR2917's and
+PR2930's; tools/audit_allocation_moment.py is PR2917's exact moment auditor with only its authenticated baseline changed (to
+the PR2969 headline); tools/derive_adapters.py generalizes PR2917's adapter derivation (PR2908, Jeremy Diviney);
+tools/build_overlay.py follows the overlay conventions of PR2908's and PR2917's builders. construction/allocation/ retains
+the flow model of PR2857/PR2843 (Yiyang Lu, Marius-Paul Dumitrean) as adapted for this allocation. All original notices of
+the exported predecessor packages remain in force.
+
+Derived work (Apache-2.0): this package (`research/rank7-restore-carrier-skips`) builds on PR #2979 (Marius-Paul Dumitrean, head be191346, research/rank7-joint-endframes) and PR #3015 (Jeremy Kothe, jeremykothe2, research/rank7-joint-endframes-restore-edit), retained byte-identical except for the files named in README.md, plus two declared restore edit blocks (`R1_E42` and `R2_E7` in `edits/EDITS.json` and `edits/FINAL-WORD-*.json.gz`) and their re-derived certificates and complete fresh-native admission and release receipts by dcharb78, with AI assistance. PR #2979's own evidence is kept under evidence/pr2979/.
diff --git a/research/native-centre-capture/replay.py b/research/native-centre-capture/replay.py
new file mode 100644
index 0000000000..76181d8882
--- /dev/null
+++ b/research/native-centre-capture/replay.py
@@ -0,0 +1,75 @@
+#!/usr/bin/env python3
+"""Replay the frozen reviews from a copied source tree."""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+ROOT = Path(__file__).resolve().parent
+STAGES = [
+    ('formation', 'new-native-recipes-20261017/row-capture-native-review-20261020', 'check.py', '--out', 'normal/REVIEW.json', 'PASS_INDEPENDENT_ROW_CAPTURE_NATIVE'),
+    ('line-entry', 'new-native-recipes-20261017/line-entry-reuse-review-20261020', 'check.py', '--out', 'normal/REVIEW.json', 'PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE'),
+    ('clean-exchange', 'new-native-recipes-20261017/clean-centre-exchange-review-20261020', 'check.py', '--out', 'normal/REVIEW.json', 'PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE'),
+    ('clean-dual', 'new-native-recipes-20261017/clean-dual-review-20261020', 'check.py', '--out', 'normal/REVIEW.json', 'PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE'),
+    ('involution-model', 'independent-review-20261017/row-involution-review-20261020', 'check_review.py', '--out', 'verified-normal/CHECKS.json', 'PASS'),
+    ('involution-native', 'new-native-recipes-20261017/row-involution-native-review-20261020', 'check.py', '--out', 'normal/REVIEW.json', 'PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS'),
+    ('reader-forward', 'bridge-review-20261017/involution-reader-review-20261020', 'check_review.py', '--output', 'normal/REVIEW-CHECKS.json', 'PASS_INDEPENDENT_ROUTED_INVOLUTION_READER'),
+    ('reader-dual', 'new-native-recipes-20261017/complete-reader-dual-review-20261020', 'check.py', '--out', 'normal/REVIEW-CHECKS.json', 'PASS_INDEPENDENT_COMPLETE_READER_DUAL'),
+    ('route32-model', 'independent-review-20261017/route32-capture-review-20261020', 'check_review.py', '--out', 'run-normal/CHECKS.json', 'PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE'),
+    ('simple-clean', 'new-native-recipes-20261017/simple-clean-native-review-20261020', 'check.py', '--out', 'normal/REVIEW-CHECKS.json', 'PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE'),
+    ('route32-native', 'new-native-recipes-20261017/route32-native-review-20261020', 'check.py', '--out', 'normal/REVIEW.json', 'PASS_INDEPENDENT_ROUTE32_NATIVE'),
+]
+
+def digest(raw):
+    return hashlib.sha256(raw).hexdigest()
+
+def need(value, reason):
+    if not value:
+        raise ValueError(reason)
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--out', type=Path, required=True)
+    parser.add_argument('--optimized', action='store_true')
+    parser.add_argument('--stage', choices=[x[0] for x in STAGES])
+    args = parser.parse_args()
+    output = args.out.resolve()
+    need(not output.exists(), 'The output directory must be absent.')
+    manifest = json.loads((ROOT/'SOURCE-MANIFEST.json').read_text())
+    for row in manifest['files']:
+        need(digest((ROOT/row['path']).read_bytes()) == row['sha256'], 'Source pin: '+row['path'])
+    need(shutil.disk_usage(ROOT).free >= 3*1024**3, 'Keep at least 3 GiB free.')
+    output.mkdir(parents=True)
+    campaign = output/'campaign'
+    shutil.copytree(ROOT/'frozen', campaign)
+    env = dict(os.environ, OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1', MKL_NUM_THREADS='1', VECLIB_MAXIMUM_THREADS='1', NUMEXPR_NUM_THREADS='1')
+    results = []
+    for name, directory, script, option, expected, status in STAGES:
+        if args.stage and args.stage != name:
+            continue
+        target = output/name
+        command = [sys.executable, '-I', '-B'] + (['-O'] if args.optimized else []) + [str(campaign/'lanes'/directory/script), option, str(target)]
+        start = time.monotonic()
+        run = subprocess.run(command, cwd=output, env=env, text=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT)
+        (output/(name+'.log')).write_text(run.stdout)
+        need(run.returncode == 0, name+' failed; see '+str(output/(name+'.log')))
+        need(status in run.stdout, name+' did not report its expected status')
+        expected_path = ROOT/'frozen/lanes'/directory/expected
+        result_path = target/Path(expected).name
+        need(result_path.read_bytes() == expected_path.read_bytes(), name+' receipt differs from the frozen receipt')
+        inputs = ROOT/'frozen/lanes'/directory/'normal/INPUTS.json'
+        if inputs.exists():
+            need((target/'INPUTS.json').read_bytes() == inputs.read_bytes(), name+' input receipt differs')
+        results.append(dict(stage=name, status=status, receipt_sha256=digest(result_path.read_bytes()), seconds=round(time.monotonic()-start,3)))
+        print(name+': PASS; exact frozen receipt', flush=True)
+    receipt = dict(status='PASS_NATIVE_CENTRE_CAPTURE_REPLAY', optimized=args.optimized, source_manifest_sha256=digest((ROOT/'SOURCE-MANIFEST.json').read_bytes()), source_files=len(manifest['files']), stages=results)
+    (output/'REPLAY.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n')
+    print(receipt['status'], flush=True)
+
+if __name__ == '__main__':
+    main()
diff --git a/research/native-centre-capture/replay_budgets.py b/research/native-centre-capture/replay_budgets.py
new file mode 100644
index 0000000000..e1d4e65bad
--- /dev/null
+++ b/research/native-centre-capture/replay_budgets.py
@@ -0,0 +1,69 @@
+#!/usr/bin/env python3
+"""Replay the three historical conditional budget reviews."""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import time
+
+ROOT=Path(__file__).resolve().parent
+
+def need(test, reason):
+    if not test:
+        raise ValueError(reason)
+
+def digest(raw):
+    return hashlib.sha256(raw).hexdigest()
+
+def main():
+    parser=argparse.ArgumentParser()
+    parser.add_argument('--out',type=Path,required=True)
+    parser.add_argument('--optimized',action='store_true')
+    args=parser.parse_args()
+    out=args.out.resolve()
+    need(not out.exists(),'The output directory must be absent.')
+    manifest=json.loads((ROOT/'SOURCE-MANIFEST.json').read_text())
+    for row in manifest['files']:
+        need(digest((ROOT/row['path']).read_bytes())==row['sha256'],'Source pin: '+row['path'])
+    need(shutil.disk_usage(ROOT).free>=3*1024**3,'Keep at least 3 GiB free.')
+    out.mkdir(parents=True)
+    shutil.copytree(ROOT/'frozen',out/'campaign')
+    shutil.copytree(ROOT/'historical',out/'historical')
+    lane=out/'campaign/lanes/bridge-review-20261017'
+    adaptations=json.loads((ROOT/'adapters/ADAPTATIONS.json').read_text())
+    for row in adaptations['files']:
+        need(digest((ROOT/row['original']).read_bytes())==row['original_sha256'],'Original checker pin')
+        need(digest((ROOT/row['adapter']).read_bytes())==row['adapter_sha256'],'Adapter pin')
+        name=Path(row['original']).parent.name
+        shutil.copyfile(ROOT/row['adapter'],lane/name/'portable_check_review.py')
+    jobs=[
+        ('low-displacement','low-displacement-budget-review-20261020','portable_check_review.py',[str(out/'low-displacement.json')],'REVIEW.json',out/'low-displacement.json','PASS 176 exact profile intervals; 24 literal words; 16 unchanged scalar sequences'),
+        ('clean-exchange','clean-exchange-budget-review-20261020','portable_check_review.py',['--output',str(out/'clean-exchange')],'normal/REVIEW-CHECKS.json',out/'clean-exchange/REVIEW-CHECKS.json','PASS_INDEPENDENT_CLEAN_EXCHANGE_BUDGET'),
+        ('coalesced','coalesced-budget-review-20261020','check_budget.py',[str(out/'coalesced.json')],'normal.json',out/'coalesced.json','PASS_THIRD_ENGINE_COALESCED_BUDGET')]
+    results=[]
+    env=dict(os.environ,OPENBLAS_NUM_THREADS='1',OMP_NUM_THREADS='1',MKL_NUM_THREADS='1',VECLIB_MAXIMUM_THREADS='1')
+    for name,directory,script,arguments,expected,receipt,status in jobs:
+        command=[sys.executable,'-I','-B']+(['-O'] if args.optimized else [])+[str(lane/directory/script)]+arguments
+        start=time.monotonic()
+        run=subprocess.run(command,cwd=out,env=env,text=True,stdout=subprocess.PIPE,stderr=subprocess.STDOUT)
+        (out/(name+'.log')).write_text(run.stdout)
+        need(run.returncode==0,name+' failed; see '+str(out/(name+'.log')))
+        need(status in run.stdout,name+' status differs')
+        actual=json.loads(receipt.read_text())
+        original=json.loads((ROOT/'frozen/lanes/bridge-review-20261017'/directory/expected).read_text())
+        if script=='portable_check_review.py':
+            need(actual['checker_sha256']==digest((lane/directory/script).read_bytes()),'Actual adapter checksum')
+            actual['checker_sha256']=original['checker_sha256']
+        need(actual==original,name+' mathematical receipt differs')
+        results.append(dict(stage=name,status=status,receipt_sha256=digest(receipt.read_bytes()),seconds=round(time.monotonic()-start,3),comparison='All fields match; only the two adapter self-hashes differ.'))
+        print(name+': PASS; historical mathematical receipt matches',flush=True)
+    report=dict(status='PASS_NATIVE_CAPTURE_HISTORICAL_BUDGETS',optimized=args.optimized,source_manifest_sha256=digest((ROOT/'SOURCE-MANIFEST.json').read_bytes()),stages=results)
+    (out/'REPLAY.json').write_text(json.dumps(report,indent=2,sort_keys=True)+'\n')
+    print(report['status'])
+
+if __name__=='__main__':
+    main()
diff --git a/research/native-centre-capture/validation/normal/BUDGET-REPLAY.json b/research/native-centre-capture/validation/normal/BUDGET-REPLAY.json
new file mode 100644
index 0000000000..9b9799460d
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/BUDGET-REPLAY.json
@@ -0,0 +1,28 @@
+{
+  "optimized": false,
+  "source_manifest_sha256": "f5ce04e8e029fcbe8eadfaa1b20ef823586732777815544fe25aaaaee32827f8",
+  "stages": [
+    {
+      "comparison": "All fields match; only the two adapter self-hashes differ.",
+      "receipt_sha256": "dc0e8a7a61003ea6801b4bef21885716b67420ccb42c8c44f89b38ac6b8bc9d2",
+      "seconds": 0.375,
+      "stage": "low-displacement",
+      "status": "PASS 176 exact profile intervals; 24 literal words; 16 unchanged scalar sequences"
+    },
+    {
+      "comparison": "All fields match; only the two adapter self-hashes differ.",
+      "receipt_sha256": "0f7769f5d399153569c49caea5e10eec64679923ccb057091763114047e3be9a",
+      "seconds": 0.159,
+      "stage": "clean-exchange",
+      "status": "PASS_INDEPENDENT_CLEAN_EXCHANGE_BUDGET"
+    },
+    {
+      "comparison": "All fields match; only the two adapter self-hashes differ.",
+      "receipt_sha256": "13335f11799d34af003fbb7dc76eddc27423ee1d1ff54d473b49dd0030da4db6",
+      "seconds": 0.046,
+      "stage": "coalesced",
+      "status": "PASS_THIRD_ENGINE_COALESCED_BUDGET"
+    }
+  ],
+  "status": "PASS_NATIVE_CAPTURE_HISTORICAL_BUDGETS"
+}
diff --git a/research/native-centre-capture/validation/normal/NATIVE-REPLAY.json b/research/native-centre-capture/validation/normal/NATIVE-REPLAY.json
new file mode 100644
index 0000000000..430056ed30
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/NATIVE-REPLAY.json
@@ -0,0 +1,74 @@
+{
+  "optimized": false,
+  "source_files": 345,
+  "source_manifest_sha256": "f5ce04e8e029fcbe8eadfaa1b20ef823586732777815544fe25aaaaee32827f8",
+  "stages": [
+    {
+      "receipt_sha256": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56",
+      "seconds": 1.325,
+      "stage": "formation",
+      "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE"
+    },
+    {
+      "receipt_sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f",
+      "seconds": 6.278,
+      "stage": "line-entry",
+      "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE"
+    },
+    {
+      "receipt_sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5",
+      "seconds": 0.323,
+      "stage": "clean-exchange",
+      "status": "PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE"
+    },
+    {
+      "receipt_sha256": "c9abd280df35e3fa2270c8853a5e5f32d380e3d87a5ca0337e99e7bc400fcda2",
+      "seconds": 0.303,
+      "stage": "clean-dual",
+      "status": "PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE"
+    },
+    {
+      "receipt_sha256": "57039f8f9603f4b101a3960bfca4472f9617855213c8247c2470d84f31171f92",
+      "seconds": 5.448,
+      "stage": "involution-model",
+      "status": "PASS"
+    },
+    {
+      "receipt_sha256": "5c2bbc8076679da2e14db052c9445a42c60f71fefadf05bb7f09c007187a9b10",
+      "seconds": 0.486,
+      "stage": "involution-native",
+      "status": "PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS"
+    },
+    {
+      "receipt_sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830",
+      "seconds": 1.745,
+      "stage": "reader-forward",
+      "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER"
+    },
+    {
+      "receipt_sha256": "6107e7fe7f9e7821774a80cab51961147cbfaa81d325f95d4644fc57d4c4d80d",
+      "seconds": 7.27,
+      "stage": "reader-dual",
+      "status": "PASS_INDEPENDENT_COMPLETE_READER_DUAL"
+    },
+    {
+      "receipt_sha256": "42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596",
+      "seconds": 4.438,
+      "stage": "route32-model",
+      "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE"
+    },
+    {
+      "receipt_sha256": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784",
+      "seconds": 6.823,
+      "stage": "simple-clean",
+      "status": "PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE"
+    },
+    {
+      "receipt_sha256": "9161f559d162d008e3927aa4cffcff9205f141f2d140596056681f031e3eae1f",
+      "seconds": 39.991,
+      "stage": "route32-native",
+      "status": "PASS_INDEPENDENT_ROUTE32_NATIVE"
+    }
+  ],
+  "status": "PASS_NATIVE_CENTRE_CAPTURE_REPLAY"
+}
diff --git a/research/native-centre-capture/validation/normal/budget-clean-exchange.json b/research/native-centre-capture/validation/normal/budget-clean-exchange.json
new file mode 100644
index 0000000000..9dd5c4fa8d
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/budget-clean-exchange.json
@@ -0,0 +1,580 @@
+{
+  "checker_sha256": "1d55f32fa742bc79a395ae7b7b0d3d727ec4f1ca751189cc6b80130677c49c82",
+  "historical_b": "67018507072324140917/40000000000000000000000",
+  "historical_certificate_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "invoices": {
+    "clean/base/I": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 208,
+        "9": 16
+      },
+      "input_maps": 112,
+      "native_mass": 1808,
+      "native_side_map_bound": 3008,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "9": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3216
+    },
+    "clean/base/Q": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "clean/extra/I": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 208,
+        "9": 16
+      },
+      "input_maps": 112,
+      "native_mass": 1808,
+      "native_side_map_bound": 3008,
+      "output_maps": 96,
+      "profile": {
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+        "3": 48,
+        "9": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3216
+    },
+    "clean/extra/Q": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
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+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "dual/base/inverse_adjoint": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "dual/base/selected_swap_conjugate": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
+        "8": 1032
+      },
+      "total_map_bound": 3264
+    },
+    "dual/extra/inverse_adjoint": {
+      "children": 1520,
+      "field_rank_census": {
+        "8": 224
+      },
+      "input_maps": 128,
+      "native_mass": 1792,
+      "native_side_map_bound": 3040,
+      "output_maps": 96,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
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+      "scalar_primitives": 8600,
+      "scalar_tariff_census": {
+        "2": 96,
+        "4": 38,
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+      },
+      "total_map_bound": 3264
+    },
+    "dual/extra/selected_swap_conjugate": {
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+      },
+      "input_maps": 128,
+      "native_mass": 1792,
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+        "2": 96,
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+      },
+      "total_map_bound": 3264
+    }
+  },
+  "producer_freeze_sha256": "c2ee7b116d5b177c06b94fffb167354c3e6b49d759f2df16a4599eefded121d5",
+  "results": {
+    "one_I_two_Q": {
+      "all_H1_H2_mixtures": {
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+        "cheapest_next_profile": {
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+        },
+        "total_rank_limit": 180
+      },
+      "all_legal_ranks": {
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+        ],
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+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      },
+      "extra/backward": {
+        "children": 1164,
+        "endpoint_maps": 176,
+        "field_rank_census": {
+          "7": 96,
+          "8": 128
+        },
+        "inline_maps": 48,
+        "map_bound": 2552,
+        "native_mass": 1696,
+        "profile": {
+          "1": 988,
+          "2": 48,
+          "4": 55,
+          "5": 55,
+          "6": 9,
+          "7": 9
+        },
+        "scalar_census": {
+          "add:-1": 156,
+          "add:-2": 4,
+          "add:-3": 8,
+          "add:1": 410,
+          "add:2": 28,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      },
+      "extra/forward": {
+        "children": 1164,
+        "endpoint_maps": 176,
+        "field_rank_census": {
+          "7": 96,
+          "8": 128
+        },
+        "inline_maps": 48,
+        "map_bound": 2552,
+        "native_mass": 1696,
+        "profile": {
+          "1": 988,
+          "2": 48,
+          "4": 55,
+          "5": 55,
+          "6": 9,
+          "7": 9
+        },
+        "scalar_census": {
+          "add:-1": 410,
+          "add:-2": 28,
+          "add:1": 156,
+          "add:2": 4,
+          "add:3": 8,
+          "scale:-1": 32,
+          "scale:-1/2": 22,
+          "scale:-2": 22,
+          "scale:1/2": 26,
+          "scale:2": 26
+        },
+        "scalar_primitives": 5288
+      }
+    }
+  },
+  "literal_words_checked": 24,
+  "mixed_limits": {
+    "odd_rank16": {
+      "1": {
+        "1": 66,
+        "2": 33
+      },
+      "2": {
+        "1": 162,
+        "2": 81
+      },
+      "3": {
+        "1": 258,
+        "2": 129
+      }
+    },
+    "rank30": {
+      "1": {
+        "1": 71,
+        "2": 35
+      },
+      "2": {
+        "1": 167,
+        "2": 83
+      },
+      "3": {
+        "1": 263,
+        "2": 131
+      }
+    }
+  },
+  "profile_intervals_checked": 176,
+  "scope": "Literal event invoices and conditional D25 histograms. No native phase replay, routed caller, recursive admission, finite map cost, precision, or kappa claim.",
+  "selected_assembly": "research/community-frontier1094-audit/ASSEMBLY.json",
+  "selected_b_snapshot": "67018507072324140917/40000000000000000000000",
+  "selected_certificate": "certificates/selected-result.json",
+  "selected_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "source_pins": {
+    "assembly": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+    "low_freeze": "c730e61f7446b072c60411f9cb6af903e5b252b12ce9a4d9bce906990303fbef",
+    "low_receipt": "12836f56beffb0c136b075b44ec25377bba88d122924c67bd0a159a5037b84d2",
+    "mixed_freeze": "99f084410fcba6228d396d8c547dd4ed74835dc97de7fce004387b6de6ab92a5",
+    "mixed_receipt": "7359fbab24858a21ea9879fff0b61883134ee3bb754916085689136f6d833224",
+    "rank9_review": "50f2e168cdbf08e2bdad445bf2aa28f96d699cbc669a39892927bf94593e3b51",
+    "selected": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+  },
+  "status": "PASS_INDEPENDENT_LITERAL_AND_RATIONAL_BUDGET_REVIEW",
+  "unchanged_changed_scalar_sequences": 16,
+  "upstream_source_pins": {
+    "lanes/bridge-access-20261017/rank9-completion-20261020/CHECKS.json": "c4b92b37441c095ff3c4d51ea920dd918edd54113764d76ce721a30ec435a2b0",
+    "lanes/bridge-access-20261017/rank9-completion-20261020/FREEZE.json": "6177f89c88b503765a724e8c1baa934da582c490089dbe29e0f6ce2371f9904b",
+    "lanes/budget-geometry-20261017/matched-native-budget-20261018/MATCHED-NATIVE-BUDGET.json": "a1832aeb1d82498f423637ba8cab0ff11262383665ed440159759bc54fe5775e",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS-FREEZE.json": "f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json": "b36bee542add54bac48e409c6a4a054b3bca5fba9c98d5513a90a6a92628d576",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-PROGRAM.json.gz": "7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-CHECKS.json": "8acc084b5cd1d9513fdd3373eede998bd08e7f3fe1624f9fd41f758d4de7cb82",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+  }
+}
diff --git a/research/native-centre-capture/validation/normal/budget-low-displacement.log b/research/native-centre-capture/validation/normal/budget-low-displacement.log
new file mode 100644
index 0000000000..ebf75dd768
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/budget-low-displacement.log
@@ -0,0 +1 @@
+PASS 176 exact profile intervals; 24 literal words; 16 unchanged scalar sequences
diff --git a/research/native-centre-capture/validation/normal/clean-dual.json b/research/native-centre-capture/validation/normal/clean-dual.json
new file mode 100644
index 0000000000..e12fcb18af
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/clean-dual.json
@@ -0,0 +1,137 @@
+{
+  "actual_D_equals_negative_B_transpose": true,
+  "actual_E_PP_zero": true,
+  "actual_E_self_adjoint": true,
+  "all_content_inverse_orders": true,
+  "literal_words": {
+    "base": {
+      "inverse_adjoint": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      },
+      "selected_swap_conjugate": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    },
+    "extra": {
+      "inverse_adjoint": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      },
+      "selected_swap_conjugate": {
+        "growth": {
+          "binary_height": 2,
+          "row_one_norm": "12"
+        },
+        "input_columns": 640,
+        "input_views": 128,
+        "native_children": 1520,
+        "native_mass": 1792,
+        "native_profile": {
+          "1": 1392,
+          "2": 64,
+          "3": 48,
+          "8": 16
+        },
+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "runtime_boundary_swaps": 0,
+        "scalar_stage_prices": {
+          "retained_core": 6456,
+          "selected_progress": 0,
+          "signed_selected_exchanges": 384,
+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    }
+  },
+  "negative_control": "Reversing scalar chronology changes the complete map.",
+  "new_phase_operators": 0,
+  "phase_source_review": "6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d",
+  "scope": "Four complete local physical inverse-adjoint words, exact target-field phase symmetry, and unchanged local invoice. No routed two-call computation, helper host, or full supplier claim.",
+  "status": "PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE"
+}
diff --git a/research/native-centre-capture/validation/normal/clean-dual.log b/research/native-centre-capture/validation/normal/clean-dual.log
new file mode 100644
index 0000000000..d52e1bdf6b
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/clean-dual.log
@@ -0,0 +1 @@
+PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE
diff --git a/research/native-centre-capture/validation/normal/clean-exchange.json b/research/native-centre-capture/validation/normal/clean-exchange.json
new file mode 100644
index 0000000000..c77114708c
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/clean-exchange.json
@@ -0,0 +1,1064 @@
+{
+  "algebra": {
+    "code_prefix": {
+      "binary_height": 1,
+      "row_one_norm": "22"
+    },
+    "code_price": 1760,
+    "displacement_rank": 16,
+    "extra_fields": 0,
+    "odd_scans": 0,
+    "query_prefix_on_independent_inputs": {
+      "binary_height": 1,
+      "row_one_norm": "112"
+    },
+    "query_price": 3424
+  },
+  "content_inverse_both_orders": true,
+  "literal_words": {
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+        "growth": {
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+        "input_columns": 640,
+        "input_views": 112,
+        "native_children": 1520,
+        "native_mass": 1808,
+        "native_profile": {
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+          "2": 64,
+          "3": 48,
+          "9": 16
+        },
+        "native_side_maps_upper_bound": 3008,
+        "new_fields": 0,
+        "odd_scans": 0,
+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "source_fields": [
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+          "selected_progress": 0,
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+      "Q": {
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+        "native_mass": 1792,
+        "native_profile": {
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+        "native_side_maps_upper_bound": 3040,
+        "new_fields": 0,
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+        "output_views": 96,
+        "private_fields": 0,
+        "real_scalar_primitives": 8600,
+        "source_fields": [
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+        "stage_prices": {
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+          "source_row_code": 1760
+        },
+        "unchanged_arbitrary_roles": 416
+      }
+    },
+    "extra": {
+      "I": {
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diff --git a/research/native-centre-capture/validation/normal/clean-exchange.log b/research/native-centre-capture/validation/normal/clean-exchange.log
new file mode 100644
index 0000000000..7b4d97e427
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/clean-exchange.log
@@ -0,0 +1 @@
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diff --git a/research/native-centre-capture/validation/normal/formation.json b/research/native-centre-capture/validation/normal/formation.json
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index 0000000000..5a086387f6
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+    ],
+    "scope": "Exact executed recipes; descriptive compiler circuits are not executed."
+  },
+  "scope": "Complete local forward native service with changed output representation. No free later-stage conversion, global decoder, recursive host, or complete supplier claim.",
+  "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE"
+}
diff --git a/research/native-centre-capture/validation/normal/formation.log b/research/native-centre-capture/validation/normal/formation.log
new file mode 100644
index 0000000000..6bbe871b96
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/formation.log
@@ -0,0 +1 @@
+PASS_INDEPENDENT_ROW_CAPTURE_NATIVE
diff --git a/research/native-centre-capture/validation/normal/involution-model.json b/research/native-centre-capture/validation/normal/involution-model.json
new file mode 100644
index 0000000000..e90c9de0ce
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/involution-model.json
@@ -0,0 +1,79 @@
+{
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+    "check_row_involution.py": "a675e5578de4bc264524f7c1a75c5685a1967a65f7d3cd020fb0dc19352d31e9",
+    "limits-normal/CHECKS.json": "eb60b314a3cb6896c6afd33b8dc88d422f5ce12ac5ab73ce9a704950c6975276",
+    "limits-normal/COMPLETION-LIMITS.json": "25b15d03837fa2b3544bb2189208bacb06fcfc7dc6d4c8aee6d98174c8a512aa",
+    "run-normal/CHECKS.json": "130cb9ca1eedb58554b259b4a71dac5c4efd75de6790db54aafaec75593110e6",
+    "run-normal/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b"
+  },
+  "rank_A_minus_E": 16,
+  "rank_A_minus_I": 16,
+  "reports": {
+    "common_frame_words/A": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 3276,
+      "prefix_row_one_norm": "68"
+    },
+    "common_frame_words/AT": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 3276,
+      "prefix_row_one_norm": "18"
+    },
+    "common_frame_words/S": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2508,
+      "prefix_row_one_norm": "22"
+    },
+    "common_frame_words/S_inverse": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2508,
+      "prefix_row_one_norm": "28"
+    },
+    "direct_physical_words/A": {
+      "binary_denominator_height": 2,
+      "old_real_scalar_units": 5600,
+      "prefix_row_one_norm": "69"
+    },
+    "direct_physical_words/AT": {
+      "binary_denominator_height": 2,
+      "old_real_scalar_units": 5600,
+      "prefix_row_one_norm": "14"
+    },
+    "late_query/A": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 2960,
+      "prefix_row_one_norm": "70"
+    },
+    "late_query/AT": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 1984,
+      "prefix_row_one_norm": "30"
+    },
+    "late_query/S": {
+      "binary_denominator_height": 1,
+      "old_real_scalar_units": 1904,
+      "prefix_row_one_norm": "24"
+    }
+  },
+  "scope": "Exact completion algebra, actual transpose metric, scalar words and baseline queries. No native service or caller.",
+  "status": "PASS_INDEPENDENT_ROW_INVOLUTION",
+  "symmetric_determinant": "1",
+  "symmetric_displacement_rank": 32,
+  "trace": 80,
+  "unchanged_ordinary_rows": 96
+}
diff --git a/research/native-centre-capture/validation/normal/involution-model.log b/research/native-centre-capture/validation/normal/involution-model.log
new file mode 100644
index 0000000000..93cc817efd
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/involution-model.log
@@ -0,0 +1,2 @@
+PASS_INDEPENDENT_ROW_INVOLUTION
+receipt_sha256=57039f8f9603f4b101a3960bfca4472f9617855213c8247c2470d84f31171f92
diff --git a/research/native-centre-capture/validation/normal/involution-native.json b/research/native-centre-capture/validation/normal/involution-native.json
new file mode 100644
index 0000000000..338db6cc8f
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/involution-native.json
@@ -0,0 +1,275 @@
+{
+  "algebra": {
+    "block_sizes": [
+      6,
+      6,
+      6,
+      6,
+      6,
+      6,
+      6,
+      6,
+      8,
+      8,
+      8,
+      8,
+      8,
+      8,
+      8,
+      8
+    ],
+    "both_involution_orders": true,
+    "centre_action": "-2I16",
+    "determinant": "1",
+    "determinant_proof": "Sixteen rank-one mode blocks each have determinant1+d^T u=-1.",
+    "rank_A_minus_E": 16,
+    "rank_A_minus_I": 16,
+    "trace_A": 80
+  },
+  "literal_words": {
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+          "input_views": 112,
+          "late_query_scalar_primitives": 2960,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
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+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6456,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        },
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+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 2960,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
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+          "odd_scans": 0,
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+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6456,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        }
+      },
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+          "input_views": 112,
+          "late_query_scalar_primitives": 1984,
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+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        },
+        "forward": {
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+            "row_one_norm": "30"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 1984,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        }
+      }
+    },
+    "extra": {
+      "A": {
+        "backward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "22"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 2960,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
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+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6456,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        },
+        "forward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "70"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 2960,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 9416,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6456,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        }
+      },
+      "AT": {
+        "backward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "62"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 1984,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        },
+        "forward": {
+          "growth": {
+            "binary_height": 1,
+            "row_one_norm": "30"
+          },
+          "input_columns": 640,
+          "input_views": 112,
+          "late_query_scalar_primitives": 1984,
+          "native_children": 1520,
+          "native_mass": 1808,
+          "native_profile": {
+            "1": 1392,
+            "2": 64,
+            "3": 48,
+            "9": 16
+          },
+          "native_side_maps_upper_bound": 3008,
+          "new_fields": 0,
+          "odd_scans": 0,
+          "output_views": 96,
+          "phase_scope": "All native recipes, exact frame arrays, and boundary maps are inherited byte-for-byte.",
+          "private_fields": 0,
+          "real_scalar_primitives": 8936,
+          "removed_events": 250,
+          "retained_scalar_primitives": 6952,
+          "retuned_source_slots": 96,
+          "unchanged_arbitrary_roles": 416
+        }
+      }
+    }
+  },
+  "negative_controls": [
+    "omitted late query",
+    "reversed backward-query chronology"
+  ],
+  "new_phase_operators": 0,
+  "phase_source_review": "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532",
+  "scope": "All eight complete local mixed-output words. Common-frame gauge words and routed caller, decoder, recursive host, or supplier cost are not established here.",
+  "status": "PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS"
+}
diff --git a/research/native-centre-capture/validation/normal/involution-native.log b/research/native-centre-capture/validation/normal/involution-native.log
new file mode 100644
index 0000000000..6e11803111
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/involution-native.log
@@ -0,0 +1 @@
+PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS
diff --git a/research/native-centre-capture/validation/normal/line-entry.json b/research/native-centre-capture/validation/normal/line-entry.json
new file mode 100644
index 0000000000..9d50305f8d
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/line-entry.json
@@ -0,0 +1,185 @@
+{
+  "exact_response_inverse_orders": true,
+  "fresh_phase_checks": [
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 2,
+      "nonzero_coefficients": 262144,
+      "port": 0,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 29,
+      "nonzero_coefficients": 262144,
+      "port": 27,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 38,
+      "nonzero_coefficients": 262144,
+      "port": 36,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 113,
+      "nonzero_coefficients": 262144,
+      "port": 111,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 22,
+      "nonzero_coefficients": 262144,
+      "port": 20,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 9,
+      "nonzero_coefficients": 262144,
+      "port": 7,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 59,
+      "nonzero_coefficients": 262144,
+      "port": 57,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 48,
+      "nonzero_coefficients": 262144,
+      "port": 46,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 3,
+      "nonzero_coefficients": 262144,
+      "port": 1,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 5,
+      "nonzero_coefficients": 262144,
+      "port": 3,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 8,
+      "nonzero_coefficients": 262144,
+      "port": 6,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 10,
+      "nonzero_coefficients": 262144,
+      "port": 8,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 19,
+      "nonzero_coefficients": 262144,
+      "port": 17,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 20,
+      "nonzero_coefficients": 262144,
+      "port": 18,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 26,
+      "nonzero_coefficients": 262144,
+      "port": 24,
+      "spatial_columns": 512
+    },
+    {
+      "digest": "493167f1aeab09c7a681f15ca4c66f335f009d60765656775737736a473b0b37",
+      "frame": 25,
+      "nonzero_coefficients": 262144,
+      "port": 23,
+      "spatial_columns": 512
+    }
+  ],
+  "literal_words": {
+    "base": {
+      "arbitrary_selected_records": 16,
+      "events": 2654,
+      "fresh_distinct_recipes": 16,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "112"
+      },
+      "inherited_distinct_recipes": 1447,
+      "input_columns": 640,
+      "input_views": 128,
+      "late_query_scalar_primitives": 3424,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
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+        "3": 48,
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+      },
+      "native_side_maps_upper_bound": 3040,
+      "new_fields": 0,
+      "odd_scans": 0,
+      "output_views": 96,
+      "private_fields": 0,
+      "real_scalar_primitives": 9880,
+      "retained_scalar_primitives": 6456,
+      "unchanged_arbitrary_roles": 416
+    },
+    "extra": {
+      "arbitrary_selected_records": 16,
+      "events": 2654,
+      "fresh_distinct_recipes": 16,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "112"
+      },
+      "inherited_distinct_recipes": 1447,
+      "input_columns": 640,
+      "input_views": 128,
+      "late_query_scalar_primitives": 3424,
+      "native_children": 1520,
+      "native_mass": 1792,
+      "native_profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "native_side_maps_upper_bound": 3040,
+      "new_fields": 0,
+      "odd_scans": 0,
+      "output_views": 96,
+      "private_fields": 0,
+      "real_scalar_primitives": 9880,
+      "retained_scalar_primitives": 6456,
+      "unchanged_arbitrary_roles": 416
+    }
+  },
+  "negative_controls": [
+    "wrong selected I input frame",
+    "omitted late query",
+    "wrong global phase"
+  ],
+  "reader_scope": "The required update for a stored reader L is L E. Since E is invertible, equality with W E on all inputs requires L=W. No routed reader change is priced here.",
+  "scope": "Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.",
+  "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE"
+}
diff --git a/research/native-centre-capture/validation/normal/line-entry.log b/research/native-centre-capture/validation/normal/line-entry.log
new file mode 100644
index 0000000000..1584761701
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/line-entry.log
@@ -0,0 +1 @@
+PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE
diff --git a/research/native-centre-capture/validation/normal/reader-dual.json b/research/native-centre-capture/validation/normal/reader-dual.json
new file mode 100644
index 0000000000..f9e73b56fd
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/reader-dual.json
@@ -0,0 +1,160 @@
+{
+  "DATA_phase_equations": {
+    "DATA_entry": 448,
+    "DATA_exit": 448
+  },
+  "late_queries": {
+    "0:1": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 113,
+      "scalar": 8440
+    },
+    "0:2": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 113,
+      "scalar": 8440
+    },
+    "1:2": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "30"
+      },
+      "maps": 672,
+      "phase_records": 224,
+      "scalar": 8440
+    }
+  },
+  "method": "Independent full reverse coefficient columns, forward prefixes, and Boolean Z4 phase coefficients.",
+  "native_prefixes": {
+    "base": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "12"
+      },
+      "native_children": 1520,
+      "native_mass": 1792,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar": 6456,
+      "unchanged_arbitrary_fields": 416,
+      "unitary_monomial_records": 3150
+    },
+    "extra": {
+      "columns": 640,
+      "growth": {
+        "binary_height": 1,
+        "row_one_norm": "12"
+      },
+      "native_children": 1520,
+      "native_mass": 1792,
+      "profile": {
+        "1": 1392,
+        "2": 64,
+        "3": 48,
+        "8": 16
+      },
+      "scalar": 6456,
+      "unchanged_arbitrary_fields": 416,
+      "unitary_monomial_records": 3150
+    }
+  },
+  "new_native_phase_operators": 0,
+  "scope": "Six complete typed data services. No new recursive helper host, finite map cost, closed caller, or supplier claim.",
+  "services": {
+    "0:1:base": {
+      "both_inverse_products": true,
+      "growth": {
+        "binary_height": 2,
+        "row_one_norm": "40"
+      },
+      "input_columns": 640,
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+    "1:2:extra": {
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+      "native_mass": 1792,
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+      "unchanged_arbitrary_fields": 416
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+  },
+  "status": "PASS_INDEPENDENT_COMPLETE_READER_DUAL"
+}
diff --git a/research/native-centre-capture/validation/normal/reader-dual.log b/research/native-centre-capture/validation/normal/reader-dual.log
new file mode 100644
index 0000000000..a427b37055
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/reader-dual.log
@@ -0,0 +1,4 @@
+Independent complete pair 0:1
+Independent complete pair 0:2
+Independent complete pair 1:2
+PASS_INDEPENDENT_COMPLETE_READER_DUAL
diff --git a/research/native-centre-capture/validation/normal/reader-forward.json b/research/native-centre-capture/validation/normal/reader-forward.json
new file mode 100644
index 0000000000..7aa6839fde
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/reader-forward.json
@@ -0,0 +1,523 @@
+{
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+  "rank_certificate": "V U_tilde = -2 I16",
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+  "unchanged_ordinary_rows": 96
+}
diff --git a/research/native-centre-capture/validation/normal/reader-forward.log b/research/native-centre-capture/validation/normal/reader-forward.log
new file mode 100644
index 0000000000..3bb6100a6f
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/reader-forward.log
@@ -0,0 +1,2 @@
+PASS_INDEPENDENT_ROUTED_INVOLUTION_READER
+280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830
diff --git a/research/native-centre-capture/validation/normal/route32-model.json b/research/native-centre-capture/validation/normal/route32-model.json
new file mode 100644
index 0000000000..5455bfc745
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/route32-model.json
@@ -0,0 +1,183 @@
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+  "reflection_blocks": 24,
+  "relative_q_rank_counts": {
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+    "3": 24
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+  "response_columns_per_direction": 112,
+  "response_symmetric": true,
+  "restricted_monochromatic_maximum_clique": 4,
+  "route_classes": {
+    "30": 64,
+    "45": 32,
+    "75": 16
+  },
+  "scope": "Exact response, scalar capture words, and route binding. Native phases and a complete caller have separate reviews.",
+  "selection": [],
+  "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE"
+}
diff --git a/research/native-centre-capture/validation/normal/route32-model.log b/research/native-centre-capture/validation/normal/route32-model.log
new file mode 100644
index 0000000000..72da092aa6
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/route32-model.log
@@ -0,0 +1,2 @@
+PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE
+receipt_sha256=42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596
diff --git a/research/native-centre-capture/validation/normal/route32-native.json b/research/native-centre-capture/validation/normal/route32-native.json
new file mode 100644
index 0000000000..bb15996ce5
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/route32-native.json
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+  },
+  "scope": "Complete raw local native words for the pinned route32 response. Model, principal inverse and capture-code theorems require separate review. No root-gauge code, transition, odd-division implementation, productive helper progress, recursive hosting or complete supplier claim.",
+  "spatial_columns_per_fresh_edge": 512,
+  "status": "PASS_INDEPENDENT_ROUTE32_NATIVE"
+}
diff --git a/research/native-centre-capture/validation/normal/route32-native.log b/research/native-centre-capture/validation/normal/route32-native.log
new file mode 100644
index 0000000000..b78de27817
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/route32-native.log
@@ -0,0 +1,13 @@
+Independent fresh route32 phases 24 / 297
+Independent fresh route32 phases 48 / 297
+Independent fresh route32 phases 72 / 297
+Independent fresh route32 phases 96 / 297
+Independent fresh route32 phases 120 / 297
+Independent fresh route32 phases 144 / 297
+Independent fresh route32 phases 168 / 297
+Independent fresh route32 phases 192 / 297
+Independent fresh route32 phases 216 / 297
+Independent fresh route32 phases 240 / 297
+Independent fresh route32 phases 264 / 297
+Independent fresh route32 phases 288 / 297
+PASS_INDEPENDENT_ROUTE32_NATIVE
diff --git a/research/native-centre-capture/validation/normal/simple-clean.json b/research/native-centre-capture/validation/normal/simple-clean.json
new file mode 100644
index 0000000000..7bab98d1be
--- /dev/null
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diff --git a/research/native-centre-capture/validation/normal/simple-clean.log b/research/native-centre-capture/validation/normal/simple-clean.log
new file mode 100644
index 0000000000..eafcb2195d
--- /dev/null
+++ b/research/native-centre-capture/validation/normal/simple-clean.log
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+Exact independent kernels 64 /209
+Exact independent kernels 96 /209
+Exact independent kernels 128 /209
+Exact independent kernels 160 /209
+Exact independent kernels 192 /209
+PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE
diff --git a/research/publication-reviews/native-centre-capture/COLD-INVOCATION.json b/research/publication-reviews/native-centre-capture/COLD-INVOCATION.json
new file mode 100644
index 0000000000..48c709791f
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index 0000000000..7749464ce8
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index 0000000000..0550c960dd
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+      "sha256": "7193dec4a19d2750b6f053e09d3062a1cf11cc12c7334e32e5add9f95f48949d"
+    },
+    {
+      "bytes": 8364,
+      "path": "cold/main-optimized/involution-native/REVIEW.json",
+      "sha256": "5c2bbc8076679da2e14db052c9445a42c60f71fefadf05bb7f09c007187a9b10"
+    },
+    {
+      "bytes": 40,
+      "path": "cold/main-optimized/involution-native.log",
+      "sha256": "090ccc6eb2866863a17a8d665b865efb9f4066884c4cd5d61a9fe67cb14a0984"
+    },
+    {
+      "bytes": 6699,
+      "path": "cold/main-optimized/line-entry/INPUTS.json",
+      "sha256": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5"
+    },
+    {
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+    },
+    {
+      "bytes": 40,
+      "path": "cold/main-optimized/line-entry.log",
+      "sha256": "627aae7b7ed8b9fcc796eed82f70ff5a3805a2c303adbdd48999844ed8d36354"
+    },
+    {
+      "bytes": 5977,
+      "path": "cold/main-optimized/reader-dual/INPUTS.json",
+      "sha256": "56112f8b986929079ad0e89ddec068e482230d6e967bde1db40c4b1bb55ca880"
+    },
+    {
+      "bytes": 3852,
+      "path": "cold/main-optimized/reader-dual/REVIEW-CHECKS.json",
+      "sha256": "6107e7fe7f9e7821774a80cab51961147cbfaa81d325f95d4644fc57d4c4d80d"
+    },
+    {
+      "bytes": 128,
+      "path": "cold/main-optimized/reader-dual.log",
+      "sha256": "d906b391eeac93ffb0764afb8061a01fb44fc87c989f001a42a5b092f2e19cb9"
+    },
+    {
+      "bytes": 12130,
+      "path": "cold/main-optimized/reader-forward/REVIEW-CHECKS.json",
+      "sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830"
+    },
+    {
+      "bytes": 107,
+      "path": "cold/main-optimized/reader-forward.log",
+      "sha256": "03724a686b1377e9190f9be83b15dd2e1bbafafbdd6dbedd427da1d836acdfdc"
+    },
+    {
+      "bytes": 4182,
+      "path": "cold/main-optimized/route32-model/CHECKS.json",
+      "sha256": "42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596"
+    },
+    {
+      "bytes": 126,
+      "path": "cold/main-optimized/route32-model.log",
+      "sha256": "be14914042c0ceb480e04a7fe6ef9ba7e05d6930a4abd7478c997e981d8eab45"
+    },
+    {
+      "bytes": 5286,
+      "path": "cold/main-optimized/route32-native/INPUTS.json",
+      "sha256": "9994025ddba20b0ffea519cc86168514e09968b4fdafbddca74a8a9e16083708"
+    },
+    {
+      "bytes": 204902,
+      "path": "cold/main-optimized/route32-native/REVIEW.json",
+      "sha256": "9161f559d162d008e3927aa4cffcff9205f141f2d140596056681f031e3eae1f"
+    },
+    {
+      "bytes": 544,
+      "path": "cold/main-optimized/route32-native.log",
+      "sha256": "407889165ee50d908dbc9264b8a55be089aa0429b5e16361d2416cffe34a2e49"
+    },
+    {
+      "bytes": 3729,
+      "path": "cold/main-optimized/simple-clean/INPUTS.json",
+      "sha256": "3afffef723776daea5f8de1f9e4a0c45de8d8294517f17173efc63350caa46fd"
+    },
+    {
+      "bytes": 39775,
+      "path": "cold/main-optimized/simple-clean/REVIEW-CHECKS.json",
+      "sha256": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784"
+    },
+    {
+      "bytes": 251,
+      "path": "cold/main-optimized/simple-clean.log",
+      "sha256": "b03f4f52cecf3b1a36976120acb299edbe802dcaf4a31d2f19ef58f2d2503fab"
+    },
+    {
+      "bytes": 17168,
+      "path": "evidence/CONTRIBUTOR-EVIDENCE.json",
+      "sha256": "d1189913c401178dcc879fa798291d919a7182d1d715c1f8c0360bcc33eff533"
+    },
+    {
+      "bytes": 15291,
+      "path": "evidence/PR3148-README-SOURCE.json",
+      "sha256": "88d5f4295da68222374e77b3185195c0436a1851f646e16dcf47826a1dc6a668"
+    },
+    {
+      "bytes": 10217,
+      "path": "evidence/PR3148-README.md",
+      "sha256": "1442d0a676e2f7528c5eea000d9abdbddf4649ee8e7a85f03f903f96eaad18a5"
+    }
+  ],
+  "package_manifest_sha256": "f08a62ad92f7387dfb13ee725c2bf5db8f0978bc909e974f3360ab5561bd9c1d",
+  "schema": "independent-review-files-v1"
+}
diff --git a/research/publication-reviews/native-centre-capture/REVIEW.json b/research/publication-reviews/native-centre-capture/REVIEW.json
new file mode 100644
index 0000000000..a3dc701a84
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/REVIEW.json
@@ -0,0 +1,105 @@
+{
+  "accepted_claim_ids": [
+    "formation",
+    "line-entry",
+    "clean-exchange",
+    "clean-dual",
+    "involution-model",
+    "involution-native",
+    "reader-forward",
+    "reader-dual",
+    "route32-model",
+    "simple-clean",
+    "route32-native",
+    "budget-low-displacement",
+    "budget-clean-exchange",
+    "budget-coalesced"
+  ],
+  "claim_index_references_checked": 67,
+  "clarifications": [
+    "Frozen preliminary formation costs 2048 and 3696 are superseded by final checked costs 1760 and 3424.",
+    "The general completion rank is rank(A-I)=16; rank(A-E)=16 is checked separately for the actual source.",
+    "The original N35 producer method differs from the independent checker. The executed independent code enumerates every spatial input column.",
+    "The complete D25 dual includes the native prefix, DATA views, owner routes, barrier, and query.",
+    "The direct 2912-scalar comparator has native mass 1984 and cannot inherit the mass-1792 budget allowances."
+  ],
+  "date": "2026-10-22",
+  "evidence_sha256": {
+    "COLD-INVOCATION.json": "3ab5866b9a91154d84f4b4bc9022b775387d1e01c1e720fc63296bd54b9ea62a",
+    "FINAL-PACKAGE-AUDIT.json": "e240f8fba4c431049a70abc8681bd6f32c6861ab533e97df2f2e093687d9e783",
+    "PR-DRAFT-REVIEW.json": "e2ae180c892603c8458defe97fc4c0e8677545a735c2d50791d75878d6b4a096",
+    "PRIOR-REVIEW-SOURCE-AUDIT.json": "b6baa80803c493851739b3750376f09fffe7362326932e65dc5e72f47974d893",
+    "REVIEW.md": "72577d620918818e63daffaf5603b4098e38d1904a58b545c4277a19144d6823",
+    "SOURCE-AND-ADAPTER-AUDIT.json": "048e2a190abf796d0df041fcde0f3fe430c527f2c9e58023ea8e21facef61949",
+    "SPATIAL-COLUMN-AUDIT.json": "1bc80441b4effd6cff833cb4b15c647022467a2432a43c58caa2637c35e69803",
+    "cold/budgets-optimized/REPLAY.json": "4d4d7b541f3f4ee642d51a10561c864d2877f0e86c5e6de1cd146ea1a47f2eac",
+    "cold/main-optimized/REPLAY.json": "879f2c656f0e5b4ebb2d198452c93745c2bab69861336615a6ef79208fade5ac"
+  },
+  "excluded_claims": [
+    "route32 common-W lift",
+    "route32 whole-W reflection decoder",
+    "global response or native optimum",
+    "complete recursive helper host",
+    "closed recursive caller",
+    "finite physical-map price",
+    "terminal decoder admission",
+    "complete precision argument",
+    "current selected-supplier transfer or replay",
+    "complete kappa improvement"
+  ],
+  "fresh_replay": {
+    "budgets": {
+      "comparison": "All fields equal the originals after replacement of only the two declared adapter self-hashes; coalesced is unchanged.",
+      "seconds": 0.563,
+      "stages": 3,
+      "status": "PASS_NATIVE_CAPTURE_HISTORICAL_BUDGETS"
+    },
+    "main": {
+      "comparison": "All result and emitted input-manifest bytes equal the frozen originals.",
+      "seconds": 77.53,
+      "stages": 11,
+      "status": "PASS_NATIVE_CENTRE_CAPTURE_REPLAY"
+    },
+    "maximum_child_processes": 1,
+    "mode": "optimized",
+    "path": "/nonexistent",
+    "python": "3.14.7",
+    "relocated": true
+  },
+  "mathematical_review": "Producer proofs, later independent reviews, main checkers, relevant exact interpreters, budget checkers, and wrapper scope and cost documents were read.",
+  "not_run": [
+    "complete historical compiler regeneration",
+    "full repeat of inherited spatial phase censuses",
+    "current selected-supplier replay",
+    "complete helper host or caller admission",
+    "complete precision or kappa calculation",
+    "new GitHub object verification",
+    "GitHub Markdown rendering",
+    "published body or HTML readback"
+  ],
+  "package_bytes_excluding_manifest": 21155491,
+  "package_files_excluding_manifest": 392,
+  "package_manifest_sha256": "f08a62ad92f7387dfb13ee725c2bf5db8f0978bc909e974f3360ab5561bd9c1d",
+  "prior_independent_review_freezes": 14,
+  "prior_review_files_checked": 103,
+  "publication": {
+    "base": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51",
+    "draft_sha256": "df7e784396feeb68f3804007aa9e3eb0d4e5bd72bb6d87b625ee169a30811bc5",
+    "historical_budget_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+    "package_links_use_final_layout": "research/publication-reviews/native-centre-capture -> research/native-centre-capture",
+    "remote_completion_owner": "Coordinating agent"
+  },
+  "review_payload": "Retain every file listed in REVIEW-FILES.json, including all 38 nested cold logs and receipts and the three retained credit evidence files.",
+  "reviewer": "Separate publication review agent",
+  "schema": "native-centre-capture-independent-publication-review-v1",
+  "source_files": 345,
+  "source_manifest_sha256": "f5ce04e8e029fcbe8eadfaa1b20ef823586732777815544fe25aaaaee32827f8",
+  "source_preservation": {
+    "adapters": "Two explicit I/O adapters only; their full diffs and non-main function ASTs were checked.",
+    "all_retained_source_bytes_equal_originals": true,
+    "package_edited_by_reviewer": false,
+    "runtime_unchanged_after_cold_replay": true
+  },
+  "status": "ACCEPTED_SCOPED_LOCAL_RESULTS_AND_HISTORICAL_CONDITIONAL_BUDGETS",
+  "unresolved_material_findings": []
+}
diff --git a/research/publication-reviews/native-centre-capture/REVIEW.md b/research/publication-reviews/native-centre-capture/REVIEW.md
new file mode 100644
index 0000000000..fce119e035
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/REVIEW.md
@@ -0,0 +1,209 @@
+# Independent review of native centre capture
+
+Accepted for the stated local constructions and historical conditional
+budgets. No material mathematical or dependency gap remains in the adopted
+claims. This is a separate agent proof review and exact replay. It is not
+human peer review, formal-kernel verification, or admission of a complete
+multiplication algorithm. The complete kappa calculation does not improve.
+
+The accepted package manifest has SHA-256
+`f08a62ad92f7387dfb13ee725c2bf5db8f0978bc909e974f3360ab5561bd9c1d`.
+Its source manifest has SHA-256
+`f5ce04e8e029fcbe8eadfaa1b20ef823586732777815544fe25aaaaee32827f8`.
+The [package guide](../../native-centre-capture/README.md) and
+[proof](../../native-centre-capture/PROOF.md) state the adopted interfaces.
+These two links use the final publication layout under research/.
+
+I read the producer proofs, the later independent reviews, the complete
+main checkers, their relevant exact interpreters, and the three budget
+checkers. I checked the new proof, cost table, claim index, notices, and
+validation statement against those sources. The audit covers all fourteen
+claim IDs in the package claim index.
+
+## Source and replay evidence
+
+[FINAL-PACKAGE-AUDIT.json](FINAL-PACKAGE-AUDIT.json) binds all 392 package
+files other than the manifest: 21,155,491 bytes. It checks all 67 claim
+references, the new local Markdown links, the five retained external
+notices, and the validation receipt hashes. There are no unlisted files.
+The final runtime files equal the files used in the cold replay.
+
+[SOURCE-AND-ADAPTER-AUDIT.json](SOURCE-AND-ADAPTER-AUDIT.json) checks all
+345 retained source inputs against both their manifest pins and their
+original local bytes. [PRIOR-REVIEW-SOURCE-AUDIT.json](PRIOR-REVIEW-SOURCE-AUDIT.json)
+checks fourteen earlier independent review freezes and the 103 files
+listed in those freezes. Frozen source text remains unchanged.
+
+I copied the package to a fresh directory outside the workspace and ran
+one process at a time with PATH=/nonexistent. Python 3.14.7 on macOS was
+used. No Git command or network service was available to the replay.
+[COLD-INVOCATION.json](COLD-INVOCATION.json) records the copy, interpreter,
+source manifest, runtime hashes, and initial disk space. More than 3 GiB
+of free disk remained throughout the bounded replay.
+
+From a fresh package copy, the commands are:
+
+```sh
+python3 -I -B replay.py --optimized --out /tmp/native-centre-capture-review-main
+python3 -I -B replay_budgets.py --optimized --out /tmp/native-centre-capture-review-budgets
+```
+
+Use absent output directories. The runner checks the retained source pins
+before it executes the checks. Its child checks use Python -O.
+
+The [main replay receipt](cold/main-optimized/REPLAY.json) records eleven
+passes in 77.530 seconds. Every result receipt and every emitted input
+manifest equals the frozen bytes. The [budget replay receipt](cold/budgets-optimized/REPLAY.json)
+records three passes in 0.563 seconds. All budget receipt fields equal the
+originals after replacement of only the two declared adapter self-hashes.
+The unchanged coalesced checker gives the same original receipt.
+
+The final lines were:
+
+```text
+PASS_NATIVE_CENTRE_CAPTURE_REPLAY
+PASS_NATIVE_CAPTURE_HISTORICAL_BUDGETS
+```
+
+The producer separately ran all fourteen final checks in normal mode.
+This review ran all fourteen in optimized mode from the relocated copy.
+The historical freezes retain their earlier runs. These are distinct
+validation claims.
+
+## Accepted constructions and their limits
+
+All complete local content maps have 112 X fields, 112 Y fields, and
+416 outside fields. Their 640 input values are independent and arbitrary.
+The local maps preserve the outside values and frames. They use no owned
+zero field and no CLEAR operation. Recursive child helper restoration is
+an inherited contract. Preservation of an outside value gives no
+productive transform progress to that value and supplies no recursive
+host.
+
+| Claim group | Accepted result | Required boundary |
+| --- | --- | --- |
+| Formation and direct FULL | The actual dyadic row code costs 1760. Formation costs 11640, with native mass 1808. | The selected output contains the arbitrary Ly baseline. Its physical FULL type is part of the result. |
+| Same-reader line entry | The complete word costs 9880, with native mass 1792. | The prior reader is the same L. This is not a change to a new reader. |
+| Clean selected exchange | The complete I-entry and Q-entry words cost 8600. Their masses are 1808 and 1792. | The selected transition is (Lx,b) to (-b,Lx). The old baseline remains in X. |
+| Clean dual and selected conjugate | The exact inverse-adjoint and its selected-field conjugate retain the stated native profile. | The physical endpoint types match. Each instruction label changes explicitly; no free caller permutation is supplied. |
+| Row-involution model and words | A squared equals I. Native A and A transpose cost 9416 and 8936, in either direction, with mass 1808. | The general rank identity is rank(A-I)=16. The actual rank(A-E)=16 is a separate checked fact. |
+| Complete D25 reader forward and dual | Both providers and all three stage pairs pass. Each full service costs 14896, with 1520 children, mass 1792, and at most 4384 map calls. | This includes the native prefix, DATA views, full-cover barrier, and query. The input level is t-1, also for pair (0,2). |
+| Route32 response and scalar codes | The raw word costs 4312, with 1120 children and mass 1792. The two capture codes cost 1870 and 2486 per direction. | The raw response has an inverse with factors of one third. The capture codes are dyadic. Their route and physical-frame restrictions remain. |
+| Direct simple clean pair | Fsimple and Bcustom each cost 2912, with 320 children, mass 1984, at most 448 native side maps, and no boundary adapters. | This is a separate complete comparator. Its larger native profile does not inherit the mass-1792 budget allowances. |
+
+For row capture, L=V_P^-1 V has L_P=I. The code and its inverse are
+literal dyadic shears. The final pivot code and query costs are 1760 and
+3424. The frozen preliminary derivation still gives 2048 and 3696; the
+new package identifies that difference and uses the final checked counts.
+The direct-FULL refinement includes its changed selected exit kernels.
+
+For clean exchange, the complete map stores the arbitrary old selected
+Y value in X. The inverse-adjoint keeps the chronological order and every
+unitary native operator, including global phase. A scalar ADD changes to
+its negative transpose and a scalar SCALE changes to its reciprocal.
+These rules apply to the complete physical word, not only its abstract
+block matrix.
+
+The row completion preserves the 96 ordinary rows. The transpose proof
+uses the actual pair metric. Its finite dyadic row lower bound concerns
+row replacement in the stated fixed response; it is not a native or
+global optimum.
+
+The D25 service applies A_t, reads with the fixed past reader L_s, and
+applies A_t again to restore X. The complete dual uses the actual inverse
+owner routes and conjugate physical views. The checks include all 640
+formal input columns, 896 DATA phase equations, and the ordered D25 owner
+paths. A late-query-only replacement fails a control. The complete dual
+is not a complete recursive backward caller.
+
+The route32 rank minimum is restricted to the same route-homogeneous
+clique partition family, with no cross-sector blocks. Its raw response
+has rank(E-I)=32 and determinant 3^24. The formal q C q code diagonalizes
+Q E q; it does not diagonalize E alone and is not a raw decoder. The
+reviewed four-mode reflection capture code is included. The producer-only
+common-W lift and whole-W reflection decoder are excluded. The raw
+native denominator height is not reported in the retained receipt; the
+new cost table does not infer one.
+
+For the direct pair, the complete maps are
+Fsimple(a,u,z,v)=(-z,u,a+Bu,v+u) and
+Bcustom(a,u,z,v)=(z,u-B^T z-v,-a,v), with the stated physical input and
+output types. The native profile is 96 H1 + 128 H8 + 96 H9. It is distinct
+from the separate 4632-scalar phase-coded word.
+
+## Phase and tensor-width checks
+
+The new spatial checks retain complete monomial address and Z4 phase
+tables. They compare exact Gaussian-integer kernels, including global
+phase. The fresh route32 replay checks all 297 new kernels on all 512
+spatial columns. The direct pair checks all 209 kernels on all 512
+columns. The formation and line-entry checks also execute their new
+physical kernels. Controls reject missing transfers, wrong signs,
+omitted restoration, a wrong past reader, wrong dual chronology, and
+wrong translation order.
+
+[SPATIAL-COLUMN-AUDIT.json](SPATIAL-COLUMN-AUDIT.json) binds the actual
+column loops and their receipts. The direct check enumerates 107008
+columns and 15040512 nonzero coefficients. Route32 enumerates 152064
+columns and 25726976 nonzero coefficients. The original N35 producer
+proof uses a signed Pauli check and one Gaussian state. That is a
+different method from the independent checker executed here.
+
+The all-width conclusion uses the stated tensor model and the full
+one-alphabet operator identities. Taking tensor powers preserves those
+identities. A constant phase i^c on one column becomes i^(cf) at width f.
+The proof does not use a width-independent replacement phase or replace
+a tensor-power line operator with a one-bit polynomial.
+
+Earlier inherited recipes remain premises. Exact equality of their
+ordered input frames, output frames, and recipe records binds those
+phase checks to this package. This review did not rerun every inherited
+spatial phase census or regenerate the historical producer compilers.
+
+## Historical conditional budgets
+
+The budget base is bce54fb3f895cbe5cd4c0eb477c3afeed100190f and
+b=67018507072324140917/40000000000000000000000. It is not the publication
+base or the selected PR #4470 construction. The checks use exact rational
+outward intervals and verify each strict threshold and its next failing
+integer.
+
+The low-displacement check recounts 24 raw or changed words, verifies
+16 unchanged scalar sequences, and checks 176 profile intervals. The
+mixed-exit comparisons retain their changed entry and exit types. A
+224-H1 terminal cleanup is a budget hypothesis, not an admitted decoder.
+
+The clean check recounts eight words. Three Q calls allow 196 extra H1
+or 98 H2. One I and two Q calls allow 180 H1 or 90 H2. The corresponding
+mixed H1/H2 inequalities and the bounded packed-rank statements retain
+their stated profiles. They are not universal native lower bounds.
+
+The coalesced check applies a third interval engine to the fixed mass-5376
+profile. It allows 198 extra H1 or 99 H2; a stipulated 64-H1 cleanup
+reduces these allowances to 134 H1 or 67 H2. This check is not a new census
+or phase review of twelve coalesced native words.
+
+The two explicit budget adapters change only historical Git reads and
+one output destination. The exact diffs were reviewed. All 18 and 8
+non-main function ASTs, respectively, are unchanged. The arithmetic,
+source checks, invoices, and thresholds remain unchanged. The third
+budget script is byte-exact.
+
+## Publication and remaining obligations
+
+The [draft description check](PR-DRAFT-REVIEW.json) compares the adopted
+claims and fresh receipts after review of PR-DESCRIPTION-STANDARD.md. Its counts and stated
+omissions agree with the review. Retained notices support the predecessor
+credit. This local review does not verify new GitHub objects, the final
+commit links, or rendered Markdown. The publisher must bind the COMMIT
+placeholders, verify the remote targets, render the description, and
+read the published body and HTML back.
+
+No complete recursive helper host, closed caller, physical-map price,
+terminal decoder, complete precision argument, current selected-supplier
+replay, or complete kappa calculation ran. No new construction was made
+to close those obligations. No package source was edited by this reviewer.
+
+[REVIEW.json](REVIEW.json) binds the final verdict and evidence hashes.
+[REVIEW-FILES.json](REVIEW-FILES.json) lists every review file that must
+travel with this review, including all 38 nested cold logs and receipts.
diff --git a/research/publication-reviews/native-centre-capture/SOURCE-AND-ADAPTER-AUDIT.json b/research/publication-reviews/native-centre-capture/SOURCE-AND-ADAPTER-AUDIT.json
new file mode 100644
index 0000000000..62a5f2e4ed
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/SOURCE-AND-ADAPTER-AUDIT.json
@@ -0,0 +1,2093 @@
+{
+  "adapters": [
+    {
+      "adapter": "adapters/low-displacement-budget-review-20261020.py",
+      "diff_sha256": "0f7e9ec755b8887ffd24a7f2c199b4bad0b5a99b79ecec77f96f761f232e4a5e",
+      "manual_main_diff_review": "Only exact historical certificate reads and the first checker output destination change. All source hash checks, arithmetic and thresholds remain.",
+      "sha256": "07a55ce0b090630f4efcd735810cd5de4a7dbdd02a3509ee60165eaeffe3dc37",
+      "unchanged_non_main_functions": 18
+    },
+    {
+      "adapter": "adapters/clean-exchange-budget-review-20261020.py",
+      "diff_sha256": "c375535705c9c4b997f52cf7ad295b9922eaec22eede7acba51fe0748fb63568",
+      "manual_main_diff_review": "Only exact historical certificate reads and the first checker output destination change. All source hash checks, arithmetic and thresholds remain.",
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diff --git a/research/publication-reviews/native-centre-capture/SPATIAL-COLUMN-AUDIT.json b/research/publication-reviews/native-centre-capture/SPATIAL-COLUMN-AUDIT.json
new file mode 100644
index 0000000000..e3e8e26b39
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/SPATIAL-COLUMN-AUDIT.json
@@ -0,0 +1,46 @@
+{
+  "conclusion": "Both independent checkers explicitly enumerate all 512 spatial input columns for each new kernel and retain global phase. The N35 producer proof uses signed Pauli action and one Gaussian state; it is a different method. No further execution was needed for this code and receipt audit.",
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diff --git a/research/publication-reviews/native-centre-capture/cold/budgets-optimized/REPLAY.json b/research/publication-reviews/native-centre-capture/cold/budgets-optimized/REPLAY.json
new file mode 100644
index 0000000000..aa7ffeab40
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/budgets-optimized/REPLAY.json
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diff --git a/research/publication-reviews/native-centre-capture/cold/budgets-optimized/clean-exchange.log b/research/publication-reviews/native-centre-capture/cold/budgets-optimized/clean-exchange.log
new file mode 100644
index 0000000000..4bc6b180e5
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diff --git a/research/publication-reviews/native-centre-capture/cold/budgets-optimized/clean-exchange/REVIEW-CHECKS.json b/research/publication-reviews/native-centre-capture/cold/budgets-optimized/clean-exchange/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..9dd5c4fa8d
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/budgets-optimized/clean-exchange/REVIEW-CHECKS.json
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+  "scope": "Literal event invoices and conditional D25 histograms. No native phase replay, routed caller, recursive admission, finite map cost, precision, or kappa claim.",
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+  "unchanged_changed_scalar_sequences": 16,
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+    "lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-PROGRAM.json.gz": "7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-CHECKS.json": "8acc084b5cd1d9513fdd3373eede998bd08e7f3fe1624f9fd41f758d4de7cb82",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz": "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-CHECKS.json": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197",
+    "lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"
+  }
+}
diff --git a/research/publication-reviews/native-centre-capture/cold/budgets-optimized/low-displacement.log b/research/publication-reviews/native-centre-capture/cold/budgets-optimized/low-displacement.log
new file mode 100644
index 0000000000..ebf75dd768
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/budgets-optimized/low-displacement.log
@@ -0,0 +1 @@
+PASS 176 exact profile intervals; 24 literal words; 16 unchanged scalar sequences
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/REPLAY.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/REPLAY.json
new file mode 100644
index 0000000000..2537f9ef0e
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/REPLAY.json
@@ -0,0 +1,74 @@
+{
+  "optimized": true,
+  "source_files": 345,
+  "source_manifest_sha256": "f5ce04e8e029fcbe8eadfaa1b20ef823586732777815544fe25aaaaee32827f8",
+  "stages": [
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+      "seconds": 1.326,
+      "stage": "formation",
+      "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE"
+    },
+    {
+      "receipt_sha256": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f",
+      "seconds": 6.162,
+      "stage": "line-entry",
+      "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE"
+    },
+    {
+      "receipt_sha256": "0108d659a4cb3b3e569df37de24dd53893db6e8b93d3945f2300c8eb5b2d2ed5",
+      "seconds": 0.378,
+      "stage": "clean-exchange",
+      "status": "PASS_INDEPENDENT_CLEAN_CENTRE_EXCHANGE"
+    },
+    {
+      "receipt_sha256": "c9abd280df35e3fa2270c8853a5e5f32d380e3d87a5ca0337e99e7bc400fcda2",
+      "seconds": 0.345,
+      "stage": "clean-dual",
+      "status": "PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE"
+    },
+    {
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+      "seconds": 7.202,
+      "stage": "involution-model",
+      "status": "PASS"
+    },
+    {
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+      "seconds": 0.559,
+      "stage": "involution-native",
+      "status": "PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS"
+    },
+    {
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+      "seconds": 1.908,
+      "stage": "reader-forward",
+      "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER"
+    },
+    {
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+      "seconds": 9.567,
+      "stage": "reader-dual",
+      "status": "PASS_INDEPENDENT_COMPLETE_READER_DUAL"
+    },
+    {
+      "receipt_sha256": "42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596",
+      "seconds": 5.092,
+      "stage": "route32-model",
+      "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE"
+    },
+    {
+      "receipt_sha256": "10c81c141abd4fe9d0a83dd4d9c4d0e3ffe9874f56062b7382065401bd188784",
+      "seconds": 7.896,
+      "stage": "simple-clean",
+      "status": "PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE"
+    },
+    {
+      "receipt_sha256": "9161f559d162d008e3927aa4cffcff9205f141f2d140596056681f031e3eae1f",
+      "seconds": 37.095,
+      "stage": "route32-native",
+      "status": "PASS_INDEPENDENT_ROUTE32_NATIVE"
+    }
+  ],
+  "status": "PASS_NATIVE_CENTRE_CAPTURE_REPLAY"
+}
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/clean-dual.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/clean-dual.log
new file mode 100644
index 0000000000..d52e1bdf6b
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/clean-dual.log
@@ -0,0 +1 @@
+PASS_INDEPENDENT_CLEAN_DUAL_AND_SELECTED_CONJUGATE
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/clean-dual/INPUTS.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/clean-dual/INPUTS.json
new file mode 100644
index 0000000000..9b2058ac59
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/clean-dual/INPUTS.json
@@ -0,0 +1,58 @@
+{
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md": {
+    "sha256": "1515a8b82ecfcb32d7dc19a4a8bc0fcf0af870ac444bb1628443dfb378360cb9"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json": {
+    "sha256": "fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json": {
+    "sha256": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz": {
+    "decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c",
+    "sha256": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CHECKS.json": {
+    "sha256": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b"
+  },
+  "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-optimized/CLEAN-DUAL.json.gz": {
+    "sha256": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660"
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new file mode 100644
index 0000000000..e12fcb18af
--- /dev/null
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new file mode 100644
index 0000000000..7b4d97e427
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new file mode 100644
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diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/formation.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/formation.log
new file mode 100644
index 0000000000..6bbe871b96
--- /dev/null
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new file mode 100644
index 0000000000..7ef7d475fc
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/formation/INPUTS.json
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index 0000000000..5a086387f6
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+    ],
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+  },
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+  "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE"
+}
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-model.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-model.log
new file mode 100644
index 0000000000..93cc817efd
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-model.log
@@ -0,0 +1,2 @@
+PASS_INDEPENDENT_ROW_INVOLUTION
+receipt_sha256=57039f8f9603f4b101a3960bfca4472f9617855213c8247c2470d84f31171f92
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-model/CHECKS.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-model/CHECKS.json
new file mode 100644
index 0000000000..e90c9de0ce
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-model/CHECKS.json
@@ -0,0 +1,79 @@
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+  "rank_A_minus_I": 16,
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+      "old_real_scalar_units": 5600,
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+    "late_query/A": {
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+    }
+  },
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+  "status": "PASS_INDEPENDENT_ROW_INVOLUTION",
+  "symmetric_determinant": "1",
+  "symmetric_displacement_rank": 32,
+  "trace": 80,
+  "unchanged_ordinary_rows": 96
+}
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native.log
new file mode 100644
index 0000000000..6e11803111
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native.log
@@ -0,0 +1 @@
+PASS_INDEPENDENT_NATIVE_ROW_INVOLUTIONS
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native/INPUTS.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native/INPUTS.json
new file mode 100644
index 0000000000..7eea604b7f
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native/INPUTS.json
@@ -0,0 +1,89 @@
+{
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diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native/REVIEW.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native/REVIEW.json
new file mode 100644
index 0000000000..338db6cc8f
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/involution-native/REVIEW.json
@@ -0,0 +1,275 @@
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new file mode 100644
index 0000000000..1584761701
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new file mode 100644
index 0000000000..668725b9d5
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new file mode 100644
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+  "scope": "Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.",
+  "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE"
+}
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-dual.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-dual.log
new file mode 100644
index 0000000000..a427b37055
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-dual.log
@@ -0,0 +1,4 @@
+Independent complete pair 0:1
+Independent complete pair 0:2
+Independent complete pair 1:2
+PASS_INDEPENDENT_COMPLETE_READER_DUAL
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new file mode 100644
index 0000000000..3a47d697ad
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diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-dual/REVIEW-CHECKS.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-dual/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..f9e73b56fd
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+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-dual/REVIEW-CHECKS.json
@@ -0,0 +1,160 @@
+{
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diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-forward.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-forward.log
new file mode 100644
index 0000000000..3bb6100a6f
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-forward.log
@@ -0,0 +1,2 @@
+PASS_INDEPENDENT_ROUTED_INVOLUTION_READER
+280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-forward/REVIEW-CHECKS.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-forward/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..7aa6839fde
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/reader-forward/REVIEW-CHECKS.json
@@ -0,0 +1,523 @@
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+}
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-model.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-model.log
new file mode 100644
index 0000000000..72da092aa6
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-model.log
@@ -0,0 +1,2 @@
+PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE
+receipt_sha256=42c1e9d1711d92f9e193a6277204e30037691cbb9aa473f5ec728d4c9ae3d596
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-model/CHECKS.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-model/CHECKS.json
new file mode 100644
index 0000000000..5455bfc745
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-model/CHECKS.json
@@ -0,0 +1,183 @@
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+  "restricted_monochromatic_maximum_clique": 4,
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+    "45": 32,
+    "75": 16
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+  "scope": "Exact response, scalar capture words, and route binding. Native phases and a complete caller have separate reviews.",
+  "selection": [],
+  "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE"
+}
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native.log
new file mode 100644
index 0000000000..b78de27817
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native.log
@@ -0,0 +1,13 @@
+Independent fresh route32 phases 24 / 297
+Independent fresh route32 phases 48 / 297
+Independent fresh route32 phases 72 / 297
+Independent fresh route32 phases 96 / 297
+Independent fresh route32 phases 120 / 297
+Independent fresh route32 phases 144 / 297
+Independent fresh route32 phases 168 / 297
+Independent fresh route32 phases 192 / 297
+Independent fresh route32 phases 216 / 297
+Independent fresh route32 phases 240 / 297
+Independent fresh route32 phases 264 / 297
+Independent fresh route32 phases 288 / 297
+PASS_INDEPENDENT_ROUTE32_NATIVE
diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native/INPUTS.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native/INPUTS.json
new file mode 100644
index 0000000000..a7cdeb48dc
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native/INPUTS.json
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diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native/REVIEW.json b/research/publication-reviews/native-centre-capture/cold/main-optimized/route32-native/REVIEW.json
new file mode 100644
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diff --git a/research/publication-reviews/native-centre-capture/cold/main-optimized/simple-clean.log b/research/publication-reviews/native-centre-capture/cold/main-optimized/simple-clean.log
new file mode 100644
index 0000000000..eafcb2195d
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+Exact independent kernels 64 /209
+Exact independent kernels 96 /209
+Exact independent kernels 128 /209
+Exact independent kernels 160 /209
+Exact independent kernels 192 /209
+PASS_INDEPENDENT_DIRECT_SIMPLE_CLEAN_NATIVE
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diff --git a/research/publication-reviews/native-centre-capture/evidence/CONTRIBUTOR-EVIDENCE.json b/research/publication-reviews/native-centre-capture/evidence/CONTRIBUTOR-EVIDENCE.json
new file mode 100644
index 0000000000..5a0b45c20f
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/evidence/CONTRIBUTOR-EVIDENCE.json
@@ -0,0 +1,255 @@
+{
+  "commit": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51",
+  "source": "CONTRIBUTORS.md",
+  "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/b58ad9ef4d4e861b0eaa5dba41742bdc072dca51/CONTRIBUTORS.md",
+  "matches": [
+    {
+      "line": 25,
+      "text": "and framework credit also goes to **Rohan Arun, Cinna Davis, David Ganz,"
+    },
+    {
+      "line": 26,
+      "text": "Jeremy Kothe, Marius-Paul Dumitrean, Erwan Secousses, Vlado-V, Chafik Boukhalfa,"
+    },
+    {
+      "line": 43,
+      "text": "- **Rohan Arun / rohanarun (#8/#9/#12):** geometric-envelope complex alternative,"
+    },
+    {
+      "line": 46,
+      "text": "  Predecessor credit remains with Zhihao Chen / jacklightChen (#7), icekylinx"
+    },
+    {
+      "line": 72,
+      "text": "- **Chafik Boukhalfa / chafreaky:** [#862](https://github.com/CrocSwap/integer-mult-bounds/pull/862), [#905](https://github.com/CrocSwap/integer-mult-bounds/pull/905), [#929](https://github.com/CrocSwap/integer-mult-bounds/pull/929), [#951](https://github.com/CrocSwap/integer-mult-bounds/pull/951)."
+    },
+    {
+      "line": 78,
+      "text": "The historical constructions remain credited to Rohan Arun (#279), eumemic (#210),"
+    },
+    {
+      "line": 126,
+      "text": "Predecessor credit includes Chafik Boukhalfa, Jeremy Kothe, Hao Yan,"
+    },
+    {
+      "line": 127,
+      "text": "DreamingOfClouds, eumemic, icekylinx and Rohan Arun; Jeffrey Cox's small-GL"
+    },
+    {
+      "line": 134,
+      "text": "| [Chafik Boukhalfa](https://github.com/chafreaky) | #795 fixed-profile owner optimum; #741 eight B-frame enlargements; #660/#685 flow, matching and owner certificates; portable complete reconstruction. |"
+    },
+    {
+      "line": 135,
+      "text": "| [Jeremy Kothe](https://github.com/jeremykothe2) | #799 paired read exchanges with enlarged frames; #659 no-triangle, #676 p6n endpoints and #699 read exchanges; cumulative layered constructions. |"
+    },
+    {
+      "line": 136,
+      "text": "| [icekylinx](https://github.com/icekylinx) | #645 source-branch gauge and retained direct-delivery geometry. |"
+    },
+    {
+      "line": 139,
+      "text": "| [Rohan Arun](https://github.com/rohanarun) | #559 native-complex recurrence correction and cumulative construction/accounting work. |"
+    },
+    {
+      "line": 166,
+      "text": "- **Chafik Boukhalfa / chafreaky (#890):** T21 composition, partial-bank checks and fixed-family owner bound."
+    },
+    {
+      "line": 167,
+      "text": "- **Jeremy Kothe / jeremykothe2 (#869/#870):** U8 triangle-hybrid delivery rewrite and T16 integration."
+    },
+    {
+      "line": 168,
+      "text": "- **Hao Yan / FanPUYen (#858, closed dependency):** T16 owner construction, bank lift and independent physical-window/chart audit reused in the new frontier."
+    },
+    {
+      "line": 182,
+      "text": "contributor credit. Predecessors, including Rohan Arun, icekylinx,"
+    },
+    {
+      "line": 192,
+      "text": "| [Jeremy Kothe](https://github.com/jeremykothe2) | #622 K-triangle construction with 492 helpers; #623 dispatch and #625 parallel LNS allocation. |"
+    },
+    {
+      "line": 193,
+      "text": "| [Chafik Boukhalfa](https://github.com/chafreaky) | #626 selected coordinated owner repair, portable sources and independent checks; #619 exact ceiling for the older #615 supplier family. |"
+    },
+    {
+      "line": 199,
+      "text": "Rohan Arun's #559 native recurrence correction and all preceding contributors"
+    },
+    {
+      "line": 210,
+      "text": "| [Jeremy Kothe](https://github.com/jeremykothe2) | #601 commuting cleanup, #615 entering pair and #617 second cold endpoint; #600/#603/#607/#609/#614 dispatch and allocation. |"
+    },
+    {
+      "line": 212,
+      "text": "| [Chafik Boukhalfa](https://github.com/chafreaky) | #616 owner repairs, portable dependencies and independent allocation checks. |"
+    },
+    {
+      "line": 219,
+      "text": "Rohan Arun\u2019s #559 native-complex recurrence correction and all preceding"
+    },
+    {
+      "line": 231,
+      "text": "| [Jeremy Kothe](https://github.com/jeremykothe2) | #591 hyperplane-ended helpers; #592 dispatch and #596 owner-map improvement; #593 Lean helper interface and exact Clifford identities. |"
+    },
+    {
+      "line": 251,
+      "text": "| [Jeremy Kothe](https://github.com/jeremykothe2) | #568 multi-cut cold kernels; #574/#576/#578/#582/#584 provider compositions; #587 declarative verification tools; #588 commuting gate moves and frame coalescences. |"
+    },
+    {
+      "line": 254,
+      "text": "| [Chafik Boukhalfa](https://github.com/chafreaky) | #538/#544/#551 constructions; #549/#557 scoped ceilings; #572/#577/#579 provider packing; #583/#586 frame coalescences and portable proof-content controls. |"
+    },
+    {
+      "line": 257,
+      "text": "| [Rohan Arun](https://github.com/rohanarun) | #539 literal bit charge; #542/#546/#547/#554 frame and composition work; #559 source-scoped removal of the generic complex exceptional-residue surcharge. |"
+    },
+    {
+      "line": 263,
+      "text": "icekylinx's direct-delivery/post-center lineage, the mutable-source and E8"
+    },
+    {
+      "line": 277,
+      "text": "| [icekylinx](https://github.com/icekylinx) | #535 post-center gauge/kernel ordering, rank-four entrances and exact mixed-width allocation; #531 direct delivery and #523 port restriction. |"
+    },
+    {
+      "line": 280,
+      "text": "| [Chafik Boukhalfa](https://github.com/chafreaky) | #533 92-pivot supplier and complete replay; #443/#444/#445/#472 geometry, physical emitters/checkers and invoices; #458 wrappers. |"
+    },
+    {
+      "line": 281,
+      "text": "| [Rohan Arun](https://github.com/rohanarun) | #534 monotone delivery-frame search and #536 certified composition with #533; both alternative witnesses retained. |"
+    },
+    {
+      "line": 302,
+      "text": "| [Rohan Arun](https://github.com/rohanarun) | [#279](https://github.com/CrocSwap/integer-mult-bounds/pull/279): 880-gate common-delivery frame retiming, exact transform, final composition and prime-coverage correction; earlier width-120 bank work in #237. |"
+    },
+    {
+      "line": 306,
+      "text": "| [Chafik Boukhalfa](https://github.com/chafreaky) | #200 physical-word classes, exact checker and predecessor circuit. |"
+    },
+    {
+      "line": 309,
+      "text": "The notices retain icekylinx's paired-cube framework, an664's shared cores,"
+    },
+    {
+      "line": 325,
+      "text": "- **Chafik Boukhalfa (chafreaky), #524:** mixed-radix carry-graded convolution,"
+    },
+    {
+      "line": 327,
+      "text": "- **Rohan Arun, #477:** an attributed experiment archive preserving proposals,"
+    },
+    {
+      "line": 349,
+      "text": "(completed banks), Rohan Arun (width-120 banking and helper refinements),"
+    },
+    {
+      "line": 350,
+      "text": "Chafik Boukhalfa (physical helper/checkers), Avi Eisenberg (complex helper),"
+    },
+    {
+      "line": 367,
+      "text": "| [Chafik Boukhalfa / chafreaky](https://github.com/chafreaky) | [#181](https://github.com/CrocSwap/integer-mult-bounds/pull/181): shared-edge complex supplier used by #186; [#175](https://github.com/CrocSwap/integer-mult-bounds/pull/175): compiler speedup in its frozen prerequisite. [#182](https://github.com/CrocSwap/integer-mult-bounds/pull/182) adds independently reviewed bit-frame and terminal refinements. |"
+    },
+    {
+      "line": 373,
+      "text": "| [Rohan Arun](https://github.com/rohanarun) | [#185](https://github.com/CrocSwap/integer-mult-bounds/pull/185): independently reviewed finite-depth ordinary-leaf bootstrap on #182. A reusable parallel mechanism; it does not improve #186's headline because its complex supplier already binds. |"
+    },
+    {
+      "line": 375,
+      "text": "The construction retains icekylinx's paired-cube/recursive compiler framework,"
+    },
+    {
+      "line": 416,
+      "text": "- **icekylinx:** the principal construction and integration lineage: stopped"
+    },
+    {
+      "line": 446,
+      "text": "**Rohan Arun (@rohanarun), PR #49**, with its full dependency chain retained. It is not a ranking of contributors or a determination of priority."
+    },
+    {
+      "line": 455,
+      "text": "Arun's order search and matching with Chafik Boukhalfa's reordered sums and exact"
+    },
+    {
+      "line": 469,
+      "text": "was submitted at 02:23 UTC, and Rohan Arun's [#8](https://github.com/CrocSwap/integer-mult-bounds/pull/8)"
+    },
+    {
+      "line": 481,
+      "text": "that motif. Rohan Arun's [#9](https://github.com/CrocSwap/integer-mult-bounds/pull/9)"
+    },
+    {
+      "line": 500,
+      "text": "| Rohan Arun (rohanarun) | [#8](https://github.com/CrocSwap/integer-mult-bounds/pull/8), [#9](https://github.com/CrocSwap/integer-mult-bounds/pull/9), [#11](https://github.com/CrocSwap/integer-mult-bounds/pull/11), [#12](https://github.com/CrocSwap/integer-mult-bounds/pull/12), [#14](https://github.com/CrocSwap/integer-mult-bounds/pull/14), [#17](https://github.com/CrocSwap/integer-mult-bounds/pull/17), [#19](https://github.com/CrocSwap/integer-mult-bounds/pull/19), [#25](https://github.com/CrocSwap/integer-mult-bounds/pull/25), [#28](https://github.com/CrocSwap/integer-mult-bounds/pull/28), [#31](https://github.com/CrocSwap/integer-mult-bounds/pull/31), [#37](https://github.com/CrocSwap/integer-mult-bounds/pull/37), [#39](https://github.com/CrocSwap/integer-mult-bounds/pull/39), [#40](https://github.com/CrocSwap/integer-mult-bounds/pull/40), [#42](https://github.com/CrocSwap/integer-mult-bounds/pull/42), [#44](https://github.com/CrocSwap/integer-mult-bounds/pull/44), [#47](https://github.com/CrocSwap/integer-mult-bounds/pull/47), [#49](https://github.com/CrocSwap/integer-mult-bounds/pull/49) | Parallel geometric complex construction; ternary template and matching work; dimension, corner and composition refinements; exact checks and review packages; both-fixed compositions, weighted matching and hill-climbed summand/leave-one-out orders. |"
+    },
+    {
+      "line": 501,
+      "text": "| icekylinx | [#10](https://github.com/CrocSwap/integer-mult-bounds/pull/10), [#18](https://github.com/CrocSwap/integer-mult-bounds/pull/18), [#24](https://github.com/CrocSwap/integer-mult-bounds/pull/24), [#32](https://github.com/CrocSwap/integer-mult-bounds/pull/32), [#36](https://github.com/CrocSwap/integer-mult-bounds/pull/36) | Recursive batching, partial swaps, endpoint gauges, structured projector blocks and copied retained-center schedules. |"
+    },
+    {
+      "line": 506,
+      "text": "| Chafik Boukhalfa (chafreaky) | [#43](https://github.com/CrocSwap/integer-mult-bounds/pull/43), [#46](https://github.com/CrocSwap/integer-mult-bounds/pull/46), [#48](https://github.com/CrocSwap/integer-mult-bounds/pull/48) | Changed-graph/fixed-basis composition, independent finite checkers, exact rational data recovery and reordered exclusion sums. |"
+    },
+    {
+      "line": 621,
+      "text": "Rohan Arun receives explicit mechanism credit for #987\u2019s slot search and first two slots; Hao Yan for #858\u2019s T16 controller. Earlier construction and verification work by Chafik Boukhalfa, Jonathan Capalbo, icekylinx, DreamingOfClouds, eumemic and the full retained lineage remains credited. These are cumulative contributions, not transferred authorship."
+    },
+    {
+      "line": 643,
+      "text": "Selected progression: Jeremy Kothe and Rohan Arun; T16 controller: Hao Yan. Independent current-owner/pricing checks: Josie Elliston and Sagar Thakrar. Earlier frame, geometry, native, bit and formalization contributors retain the full prior attribution."
+    },
+    {
+      "line": 756,
+      "text": "- **James Reed / jwr404** \u2014 [#2888](https://github.com/CrocSwap/integer-mult-bounds/pull/2888), lcm stock, wrapper padding and fourteen fit guards; builds on David Arias, Nick Petalas, Adam Gall, Josie Elliston, Aakash, DreamingOfClouds, eumemic, Rohan Arun and Jeremy Kothe."
+    },
+    {
+      "line": 764,
+      "text": "- These additions retain the package-specific predecessor credit, including Tekalign, Gareth Davidson/bitplane, Dennis/antunishdPursuit, Dugongue, Philippe, Sagar, Cinna, ywz65, Vasek/flyingviper, Adam Gall, commdata, navinor, DreamingOfClouds, icekylinx, Rohan Arun, Jeremy Kothe, Ali Romman, Tuafo, woklerx, waynenilsen and the preceding P104 contributors. Conditional interfaces, finite checks and negative results are credited separately from frontier improvements."
+    },
+    {
+      "line": 769,
+      "text": "- **Ross Richardson / RossRichardson** \u2014 [#2918](https://github.com/CrocSwap/integer-mult-bounds/pull/2918), rank-seven helper408 boundary obstruction, independent exact replay and the fully charged optimistic budget; builds on Jeremy Diviney's paired extraction and Jeremy Kothe's source words."
+    },
+    {
+      "line": 770,
+      "text": "- These numerical and packing contributions retain Nick Petalas, ywz65, Ali Romman, Dugongue, Yiyang/Lyy-iiis, Jeremy Kothe, Jeremy Diviney, Marius-Paul Dumitrean, Philippe Van Velzen, Tekalign and the package-specific native, owner and compiler lineage. Full attribution remains in the source notices."
+    },
+    {
+      "line": 772,
+      "text": "- **Rohan Arun / rohanarun** \u2014 [#928](https://github.com/CrocSwap/integer-mult-bounds/pull/928), early agent-workflow and research-package standardization proposal. The later canonical `AGENTS.md` / `autoresearch.md` workflow supersedes this proposal; its two original instruction documents are retained in the round1900 audit, while the duplicate research tree is not imported."
+    },
+    {
+      "line": 774,
+      "text": "- **Ross Richardson** \u2014 [#1007](https://github.com/CrocSwap/integer-mult-bounds/pull/1007), independent PR116 historical Git-tree and CI-evidence reconciliation, corruption controls and append-only ledger integration. Preserves Rohan Arun and predecessor credit; prepared with substantial OpenAI Codex assistance."
+    },
+    {
+      "line": 1195,
+      "text": "- **FanPUYen** \u2014 [#823](https://github.com/CrocSwap/integer-mult-bounds/pull/823)."
+    },
+    {
+      "line": 1241,
+      "text": "- **FanPUYen** \u2014 [#714](https://github.com/CrocSwap/integer-mult-bounds/pull/714), [#796](https://github.com/CrocSwap/integer-mult-bounds/pull/796)."
+    },
+    {
+      "line": 1297,
+      "text": "- **[icekylinx](https://github.com/icekylinx)**: [#433](https://github.com/CrocSwap/integer-mult-bounds/pull/433), [#645](https://github.com/CrocSwap/integer-mult-bounds/pull/645)."
+    },
+    {
+      "line": 1324,
+      "text": "**Divjot Singh Manchanda (@djsmanchanda)** supplied [#99's nondegenerate readout saturation](https://github.com/CrocSwap/integer-mult-bounds/pull/99), retained in **Rohan Arun's [#103 signed/balanced integration](https://github.com/CrocSwap/integer-mult-bounds/pull/103)**. The [source-retention receipt](research/pr99-retention-seed99/README.md) authenticates all 46 original files and reconciles the saved 177,100-singleton profile reduction. This preserves individual mechanism credit without changing historical review dispositions or claiming a fresh physical replay."
+    },
+    {
+      "line": 1326,
+      "text": "**Rohan Arun (@rohanarun)** supplied [#211's cascade-optimized operation frames on PR #200's banked bit word](https://github.com/CrocSwap/integer-mult-bounds/pull/211), whose 6,191 frame bases are retained in **eumemic's [#210 coordinated crossover](https://github.com/CrocSwap/integer-mult-bounds/pull/210)** and **Henry Grant's (@hcg890) [#217 butterfly-coordinated integration](https://github.com/CrocSwap/integer-mult-bounds/pull/217)**. The [source-retention receipt](research/pr211-retention-receipt/README.md) authenticates all 25 changed paths (12 inherited from [#205](https://github.com/CrocSwap/integer-mult-bounds/pull/205) and 13 direct files) and reconciles the Round-9 replay certificate and 6,191-frame child-histogram delta. This preserves mechanism credit without changing historical review dispositions or claiming a fresh physical replay."
+    },
+    {
+      "line": 1328,
+      "text": "**huxint** supplied [#203's structural ceilings for \u03ba = 0.01, sharp rank-minimal copied-center support lower bound, common-triangular-flag obstruction, and 87-topology balanced-Fano stub-reuse screen](https://github.com/CrocSwap/integer-mult-bounds/pull/203), cited across incorporated `next100` packages ([#204](https://github.com/CrocSwap/integer-mult-bounds/pull/204), [#288](https://github.com/CrocSwap/integer-mult-bounds/pull/288)) and merged three-register bit-obstruction packages on `main`. The [source-retention receipt](research/pr203-retention-receipt/README.md) authenticates all 29 original files, links pinned upstream inputs from **Rohan Arun's (@rohanarun) [#187](https://github.com/CrocSwap/integer-mult-bounds/pull/187)** and **Avi Eisenberg's (@ikeboy) [#193](https://github.com/CrocSwap/integer-mult-bounds/pull/193)**, and reconciles the Round-9 replay log and saved certificates. This preserves mechanism credit without changing historical review dispositions or claiming a fresh C++/solver replay."
+    }
+  ]
+}
diff --git a/research/publication-reviews/native-centre-capture/evidence/PR3148-README-SOURCE.json b/research/publication-reviews/native-centre-capture/evidence/PR3148-README-SOURCE.json
new file mode 100644
index 0000000000..9d69090fb0
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/evidence/PR3148-README-SOURCE.json
@@ -0,0 +1 @@
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aGUgZnVsbCBjb250cm9sbGVyCmNoYW5nZXMgZXhhY3RseSBgLS1m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\nLgo=\n","encoding":"base64","_links":{"self":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research/coupled-carrier-cap740/README.md?ref=f2927a4b8afcf0701a6b945e14f30de1d94f5176","git":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/git/blobs/f540563133ab194eace19d923dc56d637a7c5e51","html":"https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/README.md"}}
\ No newline at end of file
diff --git a/research/publication-reviews/native-centre-capture/evidence/PR3148-README.md b/research/publication-reviews/native-centre-capture/evidence/PR3148-README.md
new file mode 100644
index 0000000000..f540563133
--- /dev/null
+++ b/research/publication-reviews/native-centre-capture/evidence/PR3148-README.md
@@ -0,0 +1,191 @@
+# Attaining the coupled-carrier packing cap at T740
+
+Jeremy Diviney, with substantial OpenAI Codex assistance. Apache-2.0.
+
+**Finite checks and the complete composed release pass.** A new, literal
+145-row exchange attains the fixed-inventory packing cap of dcharb78's
+[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133) words:
+
+```
+kappa = 0.001729777494678597011886 - 10^-46 - 10^-70
+root in [0.0017297774946785970118869,
+         0.0017297774946785970118870]
+```
+
+The gain over Gonzalo Mier's more precise, unchanged-T74
+[PR3143](https://github.com/CrocSwap/integer-mult-bounds/pull/3143) claim is
+approximately **1.4052734766776475e-9**. `BASELINE-PR3143.json` retains its exact
+rational claim at `dcfaf1d1a7cfebaab22b95776a36a543bc684d50`. The PR3133 source
+head is `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. Neither pending claim is
+described as a selected or independently admitted frontier.
+
+This contribution is the changed-inventory packing repair, its deterministic
+generator and full source/word/allocation binding. It uses Nick Petalas's
+existing ten-copy interleaving method, differential checker and cap proof
+(PR3024), and the three-allocation-argument integration pattern (PR3030).
+PR3133's local words, ordered widths and source validators are unchanged.
+The old PR3024 exchange cannot simply be reused on this different inventory.
+
+The pre-submission overlap refresh found Gonzalo Mier's earlier
+[handoff #3145](https://github.com/CrocSwap/integer-mult-bounds/discussions/3145)
+and Hiroki Kumazaki's
+[stopped transport attempt](https://github.com/CrocSwap/integer-mult-bounds/discussions/3145#discussioncomment-18992630).
+That attempt found no matching preimages for the old journals and requested a
+new journal generated from the changed fill. This package provides that new
+journal, constructed before reading that handoff in detail; it does not dispute
+the old-journal failure or claim priority for the T740 objective. No fresh
+flow census is required by this particular deterministic repair. PR3143's fill,
+provider bytes and both words equal the pinned PR3133 inputs. The complete run
+uses PR3133's original endpoint precision and strictly exceeds PR3143's more
+precise T74 result.
+
+## Exact exchange
+
+Start with ten interleaved copies of PR3133's literal T74 fill. Its three
+non-tight bins per copy are two `48:[4,8,9,9,9,9]` bins and one `48:[9]` bin.
+Use 25 compatible `32:[9,9,9]` donor bins:
+
+```
+20 * 48:[4,8,9,9,9,9] + 10 * 48:[9] + 25 * 32:[9,9,9]
+ -> 20 * 32:[4,9,9,9] + 5 * 32:[8,8,8,8]
+    + 21 * 48:[9,9,9,9,9] + 9 * 48:[]
+```
+
+Move the twenty width-4 roles into twenty donor bins. Move the twenty width-8
+roles into five other donor bins, releasing fifteen width-9 roles. Repack those
+fifteen and the ninety width-9 roles in the old 48-bins into twenty-one groups
+of five. Nine 48-bins become empty. `construct.py` chooses concrete legal bins
+deterministically; `EXCHANGE.json` binds every changed row to its exact preimage.
+
+The exchange changes 145 roles in 55 bins and touches 123 calls. The idle-count
+delta is `{1:+20, 3:+21, 5:-25, 39:-10, 48:+9}`. The capacity multiset and each
+helper width are preserved. The unchanged full owner checker checks all
+**2,717,280** rows, including unchanged bins and calls. Chronological source
+availability, compact prefixes, non-overlap and same-call physical-family
+exclusion are required; the aggregate identity alone would not suffice.
+
+## Complete bill and cap
+
+There are 740 replicas, 6,660 invocations and 408 helpers per invocation.
+
+| Component | Exact rank counts |
+|---|---|
+| Local, per invocation | `{1:2433, 2:724, 3:228, 4:102, 5:20, 8:8}` |
+| Idle, all replicas | `{1:173160, 3:48951, 5:13875, 48:282569}` |
+| Total | `{1:16376940, 2:4821840, 3:1567431, 4:679320, 5:147075, 8:53280, 48:282569}` |
+
+The total equals 6,660 local bills plus the idle bill, with rank mass
+`65088 * 740`. Both literal words derive the ordered helper inventory
+`{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}`. The exact forward and dual operator
+audit checks 632 independent inputs for each word, frames, restoration and
+literal inverse cleanup.
+
+`cap_check.py` adapts Petalas's exact rational dual proof to this inventory and
+local bill. It enumerates all 2,551 patterns and proves strictly positive
+reduced cost for 2,539 throughout the root bracket; the same twelve patterns
+are tight. The feasible primal basis is PR3133's retained `RELAX-CAP.json`.
+Our idle bill is exactly 740 times that basis's idle bill, so the attained
+moment and fractional cap are identical, rather than merely close numerically.
+
+The tight-pattern residue identity now reads
+`20 * N_(48:[9,9,9,9,9]) = 1323 * T`. Since `gcd(1323,20)=1`, any cap-attaining
+integral packing requires `20 | T`. The first multiple of the retained T74
+chronology satisfying this is 740. This is not a proof that every possible
+chronology needs 740 replicas.
+
+All **91** private cleanup buffers are charged. Physical stock is
+`896*740 + 408 + 8 + 91 + 2 = 663549`, compared with PR3133's 66,813.
+The larger fixed stock is a material cost of this small exponent improvement.
+The complete strict replay rebuilt the actual prefix and outer invoice: the
+prefix requirement is 1,479 bits, within the paid 2,048-bit payload.
+
+## Reproduction and evidence
+
+The bounded checks use Python 3.12 and its standard library:
+
+```sh
+python3 -B scripts/research_package.py --package research/coupled-carrier-cap740
+```
+
+`verify.py` checks the words, all owners, complete moment, exact cap, and stored
+release bindings. `test_allocation.py` checks regeneration and semantic failures
+(stale or duplicate edits, lost moves, unavailable windows, overlaps, physical
+family collisions, unpaid prefix holes and invalid cap data). `test_bindings.py`
+checks recipe substitution, stale input rejection, compression portability and
+refusal of disabled assertions. Stored receipt validation is not a fresh native
+or outer replay. Regenerated fills are compared by their full decoded payload;
+immutable source containers retain exact byte hashes.
+
+For a complete replay, fetch the pinned Git objects in `FETCH.txt`, install
+`requirements-full.txt` in a Python 3.12 virtual environment, then use a fresh
+output directory:
+
+```sh
+nice -n 15 ionice -c 3 env OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
+  python3 -B research/coupled-carrier-cap740/reproduce.py \
+  --repo . --work /tmp/coupled-cap740-new --jobs 2
+```
+
+The default bootstraps the retained parent fresh. An explicit `--retained PATH`
+reuses the predecessor's authenticated parent/native cache, while rebuilding
+both current providers. `--dry-run` exports exact sources, materializes every
+row and checks the recipe; it does not claim a release. The full controller
+changes exactly `--fill`, `--order`, and `--dispatch` in PR3133's final admission
+command. All scientific source stages remain unchanged.
+
+The recorded full run uses an authenticated retained cache. All eleven source
+stages passed in 30.1 minutes with two low-priority single-thread audit
+workers. Both current native providers were rebuilt; two retained native
+providers and the retained parent were reused explicitly. A full fresh retained
+bootstrap was not rerun in this session. Exact logs, raw receipts and scope are
+in `evidence/`; `RUN.json` records the executed command. The public exporter,
+materializer and recipe dry run also passed independently of this execution.
+
+## Scope and expansion decision
+
+This is a conditional finite supplier and outer certificate. The inherited
+all-size, compiler, physical/native and analytic multiplication-theorem
+obligations remain. No selected record is changed. An archive merge or passing
+CI would not establish independent scientific admission.
+
+The explicit user task was to exceed the strongest reported repository claim.
+Before expanding, we reran Arham Tahir's code-disjoint PR3136 coupled-carrier
+local audit successfully, pinned both providers and their complete bill, and
+bounded the task to the demonstrable packing gap. The changed inventory makes
+the old cap witness inapplicable. The acceptance test requires every role,
+all buffers and the complete native/physical/prefix/outer release; partial
+checks cannot support a released endpoint. See `TASK.json` for the evidence and
+obligation ledger. Failed preliminary operator-valued probes are not claimed
+as a general obstruction or a new contribution here.
+
+## Open next questions
+
+- Independently replay this exact source and allocation and inspect the larger
+  physical bill before any frontier adoption. Maintainer scientific review and
+  inherited theorem obligations remain; the first step is the explicit full
+  reproduction above.
+- Can a different chronology realize the same cap with fewer replicas? The
+  residue certificate permits multiples of 20 but does not construct them.
+  First build a legal owner-window model at T20; reject candidates that fail
+  source availability or pay back the saving in physical/prefix costs.
+- Further exponent improvement needs changed words, widths, capacities or a
+  different moment model: this fixed-word packing relaxation is attained.
+  Start with a concrete paid change and audit both its producer and consumer
+  before another downstream packing search.
+
+## Credit
+
+The coupled folds, literal T74 fill and changed-inventory cap are dcharb78's
+PR3133. The underlying joint rank-7 words and relaxation tools are Marius-Paul
+Dumitrean's PR2979/2942/2930, building on Jeremy Kothe's rewrites/preload chain,
+Mason Hale's paired extension, Jeremy Diviney's paired-extraction certificate,
+Yiyang Lu's shared-kernel/flow work, Dugongue's packing lineage, Tekalign's
+owner/admission checks and icekylinx's exact operator audit. Petalas supplied
+the PR3024 lift/dual argument and PR3030 integration pattern. Gonzalo Mier's
+PR3143 supplies the precise comparison claim; Arham Tahir's PR3136 supplied
+the separately replayed local audit. Retained source notices and full earlier
+credits are in `vendor/PR3133-NOTICE` and `vendor/PR3133-CREDITS.md`.
+
+The new deterministic exchange, integration and verification work are by
+Jeremy Diviney with substantial OpenAI Codex assistance. No independent human
+or formal-kernel review is claimed.