From 81f3b5d12977eba09e06fbff729167d59faabe90 Mon Sep 17 00:00:00 2001
From: Marius-Paul Dumitrean <mdumitrean@gmail.com>
Date: Fri, 16 Oct 2026 08:17:55 -0400
Subject: [PATCH] Add a cap-attaining allocation of PR2917's words: conditional
 kappa 0.001722499906443274564357 - 1e-46 - 1e-70

PR2917's literal T74 fill is 9.11e-7 below the exact fixed-capacity packing
optimum of its own inventory {4:26,5:2,7:62,8:96,9:222} with local profile
{1:2416,2:640,3:280,4:110,5:26,8:8}. The optimum's basis is integral per
replica, so a literal allocation can reach it with no residue: built with
PR2857's chronological flow model on PR2833's T37 chronology and doubled to
PR2917's own T74 order, its complete paid profile equals the fractional
optimum {1:1626372,2:426240,3:192474,4:73260,5:24198,8:5328,48:27158}.

Words, order, dispatch, widths, 82 private buffers and the owner engine are
PR2917's, byte for byte; only FILL/PROFILE/SEARCH change. The registered check
reruns the owner engine with five rejection controls, PR2917's exact moment
auditor re-pinned to the PR2917 headline, a Fractions-only certificate of the
relaxation optimum with literal-profile equality, and binds the stored
receipts. reproduce.py replays the complete chain from exact Git exports with
a fresh retained bootstrap, fresh native chains and complete admission:
PASS_RELEASE at kappa 0.001722499906443274564357 - 1e-46 - 1e-70, exactly
113907405684085469/125000000000000000000000 above PR2917.

Credits: Mason Hale (PR2917), Jeremy Diviney (PR2908), Jeremy Kothe
(PR2894/2833), Yiyang Lu (PR2857/2848), Dugongue (PR2863/2839), Tekalign.
Prepared with substantial AI assistance (Claude Code).
---
 .../paired-extension-cap-fill/.gitattributes  |   2 +
 .../ALLOCATION-PINS.json                      |  14 +
 research/paired-extension-cap-fill/CLAIM.json |  38 +
 research/paired-extension-cap-fill/CREDITS.md |   9 +
 .../paired-extension-cap-fill/MANIFEST.json   |  72 ++
 research/paired-extension-cap-fill/NOTICE     |  14 +
 research/paired-extension-cap-fill/PINS.json  |  10 +
 research/paired-extension-cap-fill/README.md  | 128 +++
 .../paired-extension-cap-fill/SOURCES.json    | 214 +++++
 research/paired-extension-cap-fill/TASK.json  |  68 ++
 .../paired-extension-cap-fill/VERIFY.json     |  14 +
 .../allocation/DISPATCH.json                  |   1 +
 .../allocation/FILL.json.gz                   | Bin 0 -> 1323836 bytes
 .../allocation/ORDER.json                     |   1 +
 .../allocation/PROFILE.json                   |   9 +
 .../allocation/PROVIDERS.json                 | 842 ++++++++++++++++++
 .../allocation/SEARCH.json                    |  51 ++
 .../allocation/baseline/CLAIM.json            |  35 +
 .../allocation/baseline/ORDER.json            |   1 +
 .../allocation/baseline/PROFILE.json          |  13 +
 .../allocation/vendor/PLAN.json.gz            | Bin 0 -> 29933 bytes
 .../allocation/vendor/TEMPLATE.json.gz        | Bin 0 -> 1124331 bytes
 .../allocation/vendor/independent_owners.py   | 111 +++
 .../certificates/RELAX-CAP.json               | 113 +++
 .../check_allocation.py                       | 111 +++
 .../paired-extension-cap-fill/check_cap.py    |  77 ++
 .../construction/T37-FLOW.json.gz             | Bin 0 -> 12176 bytes
 .../construction/T37-MODEL.json               |   1 +
 .../construction/T37-PATTERNS.json            |   1 +
 .../construction/T37-SOLVER.json              |   1 +
 .../construction/controls.py                  |  75 ++
 .../construction/double.py                    |  48 +
 .../construction/fill17.py                    | 552 ++++++++++++
 .../data/WORD-base.json.gz                    | Bin 0 -> 69818 bytes
 .../data/WORD-extra.json.gz                   | Bin 0 -> 69814 bytes
 .../evidence/ADAPTER-DERIVATION.json          | 124 +++
 .../evidence/ADMISSION-RESULT.json            | 382 ++++++++
 .../evidence/ADMISSION-STAGES.json            | 113 +++
 .../evidence/ENVIRONMENT.json                 |  13 +
 .../evidence/FULL-NATIVE-RECEIPT.json         | 113 +++
 .../evidence/FULL-NATIVE-RESULT.json          |  41 +
 .../evidence/FULL-REPLAY-RESULT.json          |  73 ++
 .../evidence/FULL-REPLAY-STAGES.json          |  62 ++
 .../evidence/RELEASE-RECEIPT.json             |   7 +
 .../evidence/RETAINED-BOOTSTRAP-RECEIPT.json  | 113 +++
 .../evidence/RUNTIME-PATCHES.json             | 225 +++++
 .../evidence/logs/admission-discovery.log.txt |   8 +
 .../admission-outer-check_ledger.py.log.txt   |   2 +
 ...mission-outer-independent_check.py.log.txt |  43 +
 .../evidence/logs/admission-owners.log.txt    |   1 +
 .../logs/admission-parent-lift.log.txt        |   1 +
 .../evidence/logs/admission-rebind.log.txt    |   1 +
 .../evidence/logs/admission-release.log.txt   |   2 +
 .../evidence/logs/complete-admission.log.txt  |   8 +
 .../logs/derive-closed-adapters.log.txt       |   1 +
 .../evidence/logs/export-pr2833.log.txt       |   1 +
 .../evidence/logs/export-pr2894.log.txt       |   1 +
 .../evidence/logs/four-kernel-stage.log.txt   |   1 +
 .../logs/fresh-current-native.log.txt         |   3 +
 .../logs/fresh-retained-bootstrap.log.txt     |   6 +
 .../logs/paired-extension-stage.log.txt       |   1 +
 .../evidence/logs/parent-paired-stage.log.txt |   1 +
 .../evidence/logs/preload-stage.log.txt       |   1 +
 .../paired-extension-cap-fill/reproduce.py    | 147 +++
 .../run_registered.py                         |  83 ++
 .../tools/audit_allocation_moment.py          |  82 ++
 .../tools/derive_adapters.py                  | 100 +++
 .../paired-extension-cap-fill/tools/relax.py  | 329 +++++++
 .../tools/relax_exact.py                      | 108 +++
 .../paired-extension-cap-fill/tools/root.py   | 254 ++++++
 .../vendor/preload_move.py                    | 133 +++
 71 files changed, 5210 insertions(+)
 create mode 100644 research/paired-extension-cap-fill/.gitattributes
 create mode 100644 research/paired-extension-cap-fill/ALLOCATION-PINS.json
 create mode 100644 research/paired-extension-cap-fill/CLAIM.json
 create mode 100644 research/paired-extension-cap-fill/CREDITS.md
 create mode 100644 research/paired-extension-cap-fill/MANIFEST.json
 create mode 100644 research/paired-extension-cap-fill/NOTICE
 create mode 100644 research/paired-extension-cap-fill/PINS.json
 create mode 100644 research/paired-extension-cap-fill/README.md
 create mode 100644 research/paired-extension-cap-fill/SOURCES.json
 create mode 100644 research/paired-extension-cap-fill/TASK.json
 create mode 100644 research/paired-extension-cap-fill/VERIFY.json
 create mode 100644 research/paired-extension-cap-fill/allocation/DISPATCH.json
 create mode 100644 research/paired-extension-cap-fill/allocation/FILL.json.gz
 create mode 100644 research/paired-extension-cap-fill/allocation/ORDER.json
 create mode 100644 research/paired-extension-cap-fill/allocation/PROFILE.json
 create mode 100644 research/paired-extension-cap-fill/allocation/PROVIDERS.json
 create mode 100644 research/paired-extension-cap-fill/allocation/SEARCH.json
 create mode 100644 research/paired-extension-cap-fill/allocation/baseline/CLAIM.json
 create mode 100644 research/paired-extension-cap-fill/allocation/baseline/ORDER.json
 create mode 100644 research/paired-extension-cap-fill/allocation/baseline/PROFILE.json
 create mode 100644 research/paired-extension-cap-fill/allocation/vendor/PLAN.json.gz
 create mode 100644 research/paired-extension-cap-fill/allocation/vendor/TEMPLATE.json.gz
 create mode 100644 research/paired-extension-cap-fill/allocation/vendor/independent_owners.py
 create mode 100644 research/paired-extension-cap-fill/certificates/RELAX-CAP.json
 create mode 100644 research/paired-extension-cap-fill/check_allocation.py
 create mode 100644 research/paired-extension-cap-fill/check_cap.py
 create mode 100644 research/paired-extension-cap-fill/construction/T37-FLOW.json.gz
 create mode 100644 research/paired-extension-cap-fill/construction/T37-MODEL.json
 create mode 100644 research/paired-extension-cap-fill/construction/T37-PATTERNS.json
 create mode 100644 research/paired-extension-cap-fill/construction/T37-SOLVER.json
 create mode 100644 research/paired-extension-cap-fill/construction/controls.py
 create mode 100644 research/paired-extension-cap-fill/construction/double.py
 create mode 100644 research/paired-extension-cap-fill/construction/fill17.py
 create mode 100644 research/paired-extension-cap-fill/data/WORD-base.json.gz
 create mode 100644 research/paired-extension-cap-fill/data/WORD-extra.json.gz
 create mode 100644 research/paired-extension-cap-fill/evidence/ADAPTER-DERIVATION.json
 create mode 100644 research/paired-extension-cap-fill/evidence/ADMISSION-RESULT.json
 create mode 100644 research/paired-extension-cap-fill/evidence/ADMISSION-STAGES.json
 create mode 100644 research/paired-extension-cap-fill/evidence/ENVIRONMENT.json
 create mode 100644 research/paired-extension-cap-fill/evidence/FULL-NATIVE-RECEIPT.json
 create mode 100644 research/paired-extension-cap-fill/evidence/FULL-NATIVE-RESULT.json
 create mode 100644 research/paired-extension-cap-fill/evidence/FULL-REPLAY-RESULT.json
 create mode 100644 research/paired-extension-cap-fill/evidence/FULL-REPLAY-STAGES.json
 create mode 100644 research/paired-extension-cap-fill/evidence/RELEASE-RECEIPT.json
 create mode 100644 research/paired-extension-cap-fill/evidence/RETAINED-BOOTSTRAP-RECEIPT.json
 create mode 100644 research/paired-extension-cap-fill/evidence/RUNTIME-PATCHES.json
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/admission-discovery.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/admission-outer-check_ledger.py.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/admission-outer-independent_check.py.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/admission-owners.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/admission-parent-lift.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/admission-rebind.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/admission-release.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/complete-admission.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/derive-closed-adapters.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/export-pr2833.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/export-pr2894.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/four-kernel-stage.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/fresh-current-native.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/fresh-retained-bootstrap.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/paired-extension-stage.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/parent-paired-stage.log.txt
 create mode 100644 research/paired-extension-cap-fill/evidence/logs/preload-stage.log.txt
 create mode 100644 research/paired-extension-cap-fill/reproduce.py
 create mode 100644 research/paired-extension-cap-fill/run_registered.py
 create mode 100644 research/paired-extension-cap-fill/tools/audit_allocation_moment.py
 create mode 100644 research/paired-extension-cap-fill/tools/derive_adapters.py
 create mode 100644 research/paired-extension-cap-fill/tools/relax.py
 create mode 100644 research/paired-extension-cap-fill/tools/relax_exact.py
 create mode 100644 research/paired-extension-cap-fill/tools/root.py
 create mode 100644 research/paired-extension-cap-fill/vendor/preload_move.py

diff --git a/research/paired-extension-cap-fill/.gitattributes b/research/paired-extension-cap-fill/.gitattributes
new file mode 100644
index 0000000000..e1d75a2b2d
--- /dev/null
+++ b/research/paired-extension-cap-fill/.gitattributes
@@ -0,0 +1,2 @@
+# Keep vendored, data, allocation and evidence bytes exact (the repository default normalizes text).
+* -text
diff --git a/research/paired-extension-cap-fill/ALLOCATION-PINS.json b/research/paired-extension-cap-fill/ALLOCATION-PINS.json
new file mode 100644
index 0000000000..aca7827264
--- /dev/null
+++ b/research/paired-extension-cap-fill/ALLOCATION-PINS.json
@@ -0,0 +1,14 @@
+{
+ "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+ "allocation/FILL.json.gz": "e045aa613f8fba06d81313f5e1c2cbec9ee94552163b8d1eb9205bf2fa7f2285",
+ "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+ "allocation/PROFILE.json": "8b6f825a93cb1fa94047b062f1b1b8d489b2c397ec0c8114d0e53737f56c065e",
+ "allocation/PROVIDERS.json": "1fbbe45a0b70b909bf764fab7d89ec05b10c6c3dec5340a59a69b871d309c6ab",
+ "allocation/SEARCH.json": "9ac59657d263ab7181503020aaae2dad4d73412eb62846b4c6992aebd8891987",
+ "allocation/baseline/CLAIM.json": "e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac",
+ "allocation/baseline/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+ "allocation/baseline/PROFILE.json": "07ee0cfe8d88073de9b75cd3262a98f4ac428b1bdd3922b5a077dbf3436be00c",
+ "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+ "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+ "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461"
+}
diff --git a/research/paired-extension-cap-fill/CLAIM.json b/research/paired-extension-cap-fill/CLAIM.json
new file mode 100644
index 0000000000..4f8ea2dbe4
--- /dev/null
+++ b/research/paired-extension-cap-fill/CLAIM.json
@@ -0,0 +1,38 @@
+{
+ "admitted_package_manifest_sha256": "b690eab49b010091973a4e7d1b8d58306200fd09f4c2281bbeeec57aa1b077d5",
+ "baseline_head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+ "baseline_kappa": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+ "baseline_pr": 2917,
+ "calls": 666,
+ "complex_lower": "1722499906443274564357/1000000000000000000000000",
+ "coverage_law_ceiling_approx": "0.0017580218062580484",
+ "fill_sha256": "e045aa613f8fba06d81313f5e1c2cbec9ee94552163b8d1eb9205bf2fa7f2285",
+ "fixed_inventory_cap": {
+  "cap_lower": "1722499906443274564357/1000000000000000000000000",
+  "cap_upper": "17224999064432745643571/10000000000000000000000000",
+  "realized": "attained (profile equals the fractional optimum)"
+ },
+ "gain": "113907405684085469/125000000000000000000000",
+ "helpers": 408,
+ "independent_inputs": 632,
+ "kappa": "17224999064432745643569999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+ "kappa_decimal": "0.0017224999064432745643569999999999999999999998999999999999999999999999",
+ "live_families": 66304,
+ "native_receipt_sha256": "9a2e23c80436cf257c6f21fa4bd3f796fdb569bf30005ca2c2bb16d8f2094969",
+ "physical_families": 66804,
+ "profile": {
+  "1": 1626372,
+  "2": 426240,
+  "3": 192474,
+  "4": 73260,
+  "48": 27158,
+  "5": 24198,
+  "8": 5328
+ },
+ "release_receipt_sha256": "efc5eebdc42e976b0500cd032e1b6f4b8755fa33d9a23ac27415e27922e85b75",
+ "replicas": 74,
+ "scope": "Conditional finite supplier/outer certificate for PR2917's unchanged words with a new literal T74 allocation. Inherited all-size/compiler/theorem hypotheses remain. No selected-frontier change or independent-human-review claim.",
+ "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+ "status": "CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE",
+ "zero_buffers": 82
+}
diff --git a/research/paired-extension-cap-fill/CREDITS.md b/research/paired-extension-cap-fill/CREDITS.md
new file mode 100644
index 0000000000..d694ca64b4
--- /dev/null
+++ b/research/paired-extension-cap-fill/CREDITS.md
@@ -0,0 +1,9 @@
+# Credits
+
+- **PR #2917, Mason Hale**: the nine additional paired extractions, the final 82-endpoint words used here unchanged, the T74 chronology (ORDER/DISPATCH), the allocation checker, moment auditor, extension stage and adapter derivation that this package reuses.
+- **PR #2908, Jeremy Diviney**: the paired input/output extraction, its structural certificate and the closed-adapter admission chain.
+- **PR #2894 / #2833, Jeremy Kothe**: the preload re-synthesis supplier, the frame accounting and cleanup (vendor/preload_move.py), the source materializer and the inherited supplier lineage.
+- **PR #2857 / #2848, Yiyang Lu (Lyy-iiis)**: the shared-kernel words and the chronological flow model and realization (edge colouring) used to construct this allocation; PR2843 (Marius-Paul Dumitrean) is that flow model's starting point.
+- **PR #2863 / #2839, Dugongue**: the precedent of attaining a fixed-inventory packing optimum, and the PR2839 owner engine lineage.
+- **Tekalign**: the independent owner/chronology checker (allocation/vendor/independent_owners.py) and admission tooling.
+- **New here (Marius-Paul Dumitrean, with substantial AI assistance from Anthropic Claude via Claude Code)**: the exact fixed-capacity relaxation of PR2917's inventory and its Fractions-only certificate, the integral pattern mix, the cap-attaining literal T74 allocation of PR2917's unchanged words, the generalized adapter derivation with the PR2917 comparator, and the complete fresh replay.
diff --git a/research/paired-extension-cap-fill/MANIFEST.json b/research/paired-extension-cap-fill/MANIFEST.json
new file mode 100644
index 0000000000..e3f3cbb839
--- /dev/null
+++ b/research/paired-extension-cap-fill/MANIFEST.json
@@ -0,0 +1,72 @@
+{
+ ".gitattributes": "056f4f66161e333f3a8d4c20de323ca05599a7deac1aa02d47ba6f6b96335573",
+ "ALLOCATION-PINS.json": "f07d3079149f056d3948054ed0d3c9af1c7f09582680a05e07a29cfd7c1a5c82",
+ "CLAIM.json": "9c2c14158780a677b3661623d7476acc4f535ac9e0481addfa1d6c4c7633b74b",
+ "CREDITS.md": "8d6cdb5abe3b5df137b502e71b49d96c8305ecbf35fd105c10a8324d7aa8745c",
+ "NOTICE": "efe81e972dedee779c7241d7ae2cead22725658aa3464b454ac2081c5c7293e3",
+ "PINS.json": "e8572a413719715c6537e20238955d2926d5a5659435baadd5d5eee13526f0c5",
+ "README.md": "b0c6a1719fa039551dfdd9a1c20213b4bcae3d5181ad6ae882cd4d375bcc0810",
+ "SOURCES.json": "40decf367d6ff91bdfbac32545f0ff5536f1aa25c1ff5dea90cf0d9f65b2e5c7",
+ "TASK.json": "1b0c80c3f3255c2ed2336f3cfe5e8061bc08975bb195c100157a0e84a54da12b",
+ "VERIFY.json": "4fafdf99d05974d08bc20d9e5500f4742d8253ca2da6758d0563e55aa117b22b",
+ "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+ "allocation/FILL.json.gz": "e045aa613f8fba06d81313f5e1c2cbec9ee94552163b8d1eb9205bf2fa7f2285",
+ "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+ "allocation/PROFILE.json": "8b6f825a93cb1fa94047b062f1b1b8d489b2c397ec0c8114d0e53737f56c065e",
+ "allocation/PROVIDERS.json": "1fbbe45a0b70b909bf764fab7d89ec05b10c6c3dec5340a59a69b871d309c6ab",
+ "allocation/SEARCH.json": "9ac59657d263ab7181503020aaae2dad4d73412eb62846b4c6992aebd8891987",
+ "allocation/baseline/CLAIM.json": "e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac",
+ "allocation/baseline/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+ "allocation/baseline/PROFILE.json": "07ee0cfe8d88073de9b75cd3262a98f4ac428b1bdd3922b5a077dbf3436be00c",
+ "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+ "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+ "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461",
+ "certificates/RELAX-CAP.json": "518ba849ece61bf191d161aa3e61c0f1229c4fda6f8171f8eca5761bc0fc1644",
+ "check_allocation.py": "0672d17458d837a2064b4fc7d26cfdc4931a93a7a3a39a71f6a2ed7b8b7e90a3",
+ "check_cap.py": "19e0502c8f7618f0dc88566f4eac425fa9772c9e75d6109375064685ab4f1ae0",
+ "construction/T37-FLOW.json.gz": "3ff02610ba7bc1e9fc4e141bc9c9233bfa11c0887908529b6fd46d3cf8be956f",
+ "construction/T37-MODEL.json": "db012cdd24470ce5ce7f9ecde44cb849f55e017b58d93914ab2af2a55c0d7308",
+ "construction/T37-PATTERNS.json": "d420d228a051974ee79b3e09e9a2294e085fd1b8c6683977f4675c163569d938",
+ "construction/T37-SOLVER.json": "e02af4643322b4b4e1dde4a0049fd8899a40e77d6c5bb17ea90d74c7086be119",
+ "construction/controls.py": "4f07c315bc66821695fdb3ea92a245a663f3026a9e2c596b7eccffbaed14ab2a",
+ "construction/double.py": "426462c181333b3b56ddeab4b21d0523a2d52874033dbb2a3546ba9990fe15cd",
+ "construction/fill17.py": "ecd49f72a6f42969c4157c5c51370f66cf09db3f82d74b2e852383eeff77b58c",
+ "data/WORD-base.json.gz": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+ "data/WORD-extra.json.gz": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+ "evidence/ADAPTER-DERIVATION.json": "554d6d5f0959f11b122b3700d997d667bd51a467d7c860627e39209d84db75d6",
+ "evidence/ADMISSION-RESULT.json": "75e941faed996af9656b3bdd69e227964033bf080e8dfe2bee2e9faec4a198d9",
+ "evidence/ADMISSION-STAGES.json": "7a075cde897e06ebf080c066d771ffb28635fa1cb1148c1e22e81b974424f4e0",
+ "evidence/ENVIRONMENT.json": "c6faaaa9b538ddbf0ea3c624bbe2f1c7e4074f8cb504d4bee0f3353f1e7f32a1",
+ "evidence/FULL-NATIVE-RECEIPT.json": "9a2e23c80436cf257c6f21fa4bd3f796fdb569bf30005ca2c2bb16d8f2094969",
+ "evidence/FULL-NATIVE-RESULT.json": "32ff4570a520e9f395142c3daf33398d2257027dd51b06c11de283b86effd8a7",
+ "evidence/FULL-REPLAY-RESULT.json": "8712530cf2240ab697af45eb28f91c1775894a6cf5ad16f53162091aba431b84",
+ "evidence/FULL-REPLAY-STAGES.json": "c5cf6c867a4d3cc90bff634caf1ac4e0175558c0476da05a7061008a1d6a1bac",
+ "evidence/RELEASE-RECEIPT.json": "efc5eebdc42e976b0500cd032e1b6f4b8755fa33d9a23ac27415e27922e85b75",
+ "evidence/RETAINED-BOOTSTRAP-RECEIPT.json": "eec93526dafc5d6fb8f6b4318efb57b15209b7a31bbd670d470b1a65de244720",
+ "evidence/RUNTIME-PATCHES.json": "c342c27f065c4710792d181e17c2bade42373b069113e2484ffc711742fa651a",
+ "evidence/logs/admission-discovery.log.txt": "19dec04aaef58a5b7e349eef83a702575d0d747c8a4ab665456dabd9455d7e87",
+ "evidence/logs/admission-outer-check_ledger.py.log.txt": "4d04f73fa3b7dac96c30f5401ab6afe9e0fe83dc5dde59a9007bac53e67e8af5",
+ "evidence/logs/admission-outer-independent_check.py.log.txt": "91a7ed8a166901a19690f2172ddb1066bd6cf4c692b217bcb620bd4a5a13d990",
+ "evidence/logs/admission-owners.log.txt": "3cd9ba8872ab07f8f92a91ffbd26832abb91c5e51f14715a95adf318ae5665da",
+ "evidence/logs/admission-parent-lift.log.txt": "7b6249a123ca39fae7b7a6339dd9e8ae8777b081f4336418f2cc101704b70644",
+ "evidence/logs/admission-rebind.log.txt": "4503a92b598c31af5d39cfafdc0e4bc97bc8a1194576d632a0690ff17d2479ad",
+ "evidence/logs/admission-release.log.txt": "e01086be77ae2169e978708e1f7417f1ea2195ed3fc21579102986f1b2115778",
+ "evidence/logs/complete-admission.log.txt": "9a738eed12d381021f68a5a4221485bbf00e4982d508e5d616631367d9d02672",
+ "evidence/logs/derive-closed-adapters.log.txt": "d39b2faff6f37fffdd06722fea4b58e065b19b886c0b148d5639ec64dbf18938",
+ "evidence/logs/export-pr2833.log.txt": "6727020814b72c6d919999190845a46ffb33f2589ed65c501fcf66142d6f30de",
+ "evidence/logs/export-pr2894.log.txt": "6bd8df30779863897e48441608240db6a7e3fcbd0754511e44f854f3a5c462a6",
+ "evidence/logs/four-kernel-stage.log.txt": "f2bbb6462b3f5bb8a6415bb33c0c35355353b13343ddb90961660f7473caa5a2",
+ "evidence/logs/fresh-current-native.log.txt": "d7581123b0f3330f2598e7758ccbca466018d2599124fc6ceb1b678a9ee27dec",
+ "evidence/logs/fresh-retained-bootstrap.log.txt": "4a1625fdd9a947187583e67492c492f309e28669082f2e6f2aa97b5da345ea29",
+ "evidence/logs/paired-extension-stage.log.txt": "61cc77beeae833d7473b5c5338b176b150f95f6652a888c0307f080674cfde35",
+ "evidence/logs/parent-paired-stage.log.txt": "d80d8494c48816e3acf662db00cc0077a888b82392d736826f73beb1c4248299",
+ "evidence/logs/preload-stage.log.txt": "2eb7601c48840a39c58eb838886aed00a531349b259f0bbc3ea6421376b8ea3c",
+ "reproduce.py": "290a088c82c4f001151dd8e97853c17ff6da51da5ea3f56d5244af559b365fa7",
+ "run_registered.py": "ba2cc644fd3cea513b04e72cc30557456a8559898e072f27049a46979e560922",
+ "tools/audit_allocation_moment.py": "1dd0072f377ed2cea986b0aafcdb4175a4ae397d456b2f0d07d704bff7ace7d4",
+ "tools/derive_adapters.py": "631895d159ca25fd11d3665b2ebecb43d46381355d596d87111b021c9a606800",
+ "tools/relax.py": "0fed1c56b50a2e6d44deeeb6db0f1c7e1f71b86d1747130e1a9202216249a728",
+ "tools/relax_exact.py": "baf1855d6095c951a90d19a0d8094bd33290519940b732e2b758c5647830f044",
+ "tools/root.py": "55f5aca39b5ee2fe4687ac8863e6c24569010f27a332883c069b8e14b8fe09e3",
+ "vendor/preload_move.py": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044"
+}
diff --git a/research/paired-extension-cap-fill/NOTICE b/research/paired-extension-cap-fill/NOTICE
new file mode 100644
index 0000000000..af55b97e91
--- /dev/null
+++ b/research/paired-extension-cap-fill/NOTICE
@@ -0,0 +1,14 @@
+research/paired-extension-cap-fill
+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 #2917 (Mason Hale, head
+224bd5e56041c40078ff6b5fa7393733a215de5c, research/paired-helper-extension): data/WORD-base.json.gz,
+data/WORD-extra.json.gz, vendor/preload_move.py (Jeremy Kothe's PR2894 frame accounting and cleanup),
+allocation/ORDER.json, allocation/DISPATCH.json, allocation/PROVIDERS.json, allocation/vendor/
+(independent_owners.py: Tekalign's independent owner checker as vendored by PR2839/PR2917; PLAN.json.gz,
+TEMPLATE.json.gz) and allocation/baseline/ (PR2917's CLAIM.json, ORDER.json, PROFILE.json).
+tools/audit_allocation_moment.py is PR2917's exact moment auditor with only its authenticated baseline
+changed; tools/derive_adapters.py generalizes PR2917's adapter derivation (PR2908, Jeremy Diviney) by an
+extra comparator. construction/ 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.
diff --git a/research/paired-extension-cap-fill/PINS.json b/research/paired-extension-cap-fill/PINS.json
new file mode 100644
index 0000000000..40287b8224
--- /dev/null
+++ b/research/paired-extension-cap-fill/PINS.json
@@ -0,0 +1,10 @@
+{
+ "data/WORD-base.json.gz": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+ "data/WORD-extra.json.gz": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+ "tools/audit_allocation_moment.py": "1dd0072f377ed2cea986b0aafcdb4175a4ae397d456b2f0d07d704bff7ace7d4",
+ "tools/derive_adapters.py": "631895d159ca25fd11d3665b2ebecb43d46381355d596d87111b021c9a606800",
+ "tools/relax.py": "0fed1c56b50a2e6d44deeeb6db0f1c7e1f71b86d1747130e1a9202216249a728",
+ "tools/relax_exact.py": "baf1855d6095c951a90d19a0d8094bd33290519940b732e2b758c5647830f044",
+ "tools/root.py": "55f5aca39b5ee2fe4687ac8863e6c24569010f27a332883c069b8e14b8fe09e3",
+ "vendor/preload_move.py": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044"
+}
diff --git a/research/paired-extension-cap-fill/README.md b/research/paired-extension-cap-fill/README.md
new file mode 100644
index 0000000000..75fece42d9
--- /dev/null
+++ b/research/paired-extension-cap-fill/README.md
@@ -0,0 +1,128 @@
+# A cap-attaining allocation of PR #2917's words: conditional κ = 0.001722499906443274564357 − 10⁻⁴⁶ − 10⁻⁷⁰
+
+```text
+Status / UTC update / priority revision: DONE (conditional candidate) · 2026-10-16 · priority revision 5 · base main 8c8bcecb
+Concrete question and changed premise: PR #2917 ships a literal T74 fill 9.11e-7 below the exact fixed-capacity packing
+    optimum of its own inventory. Can PR2917's UNCHANGED words be packed at that optimum and admitted?
+Established result and evidence status: yes. A literal allocation whose complete paid profile EQUALS the fractional optimum
+    passes the owner engine, PR2917's moment auditor, and the complete fresh-native admission and modern outer release:
+    κ = 0.001722499906443274564357 − 10⁻⁴⁶ − 10⁻⁷⁰, exactly 113907405684085469/125000000000000000000000 ≈ 9.1126e-7 above
+    PR2917 (head 224bd5e5). Author-checked (AI-assisted); not maintainer-reviewed.
+Public artifact URL + exact commit: this package (see the PR).
+Next useful task: change the words (further paired extractions on the final 82-endpoint word); the fill layer of these
+    words is exhausted by this allocation.
+Active claim / expiry: released.
+```
+
+## Result
+
+| | κ (headline) | complete paid profile |
+|---|---|---|
+| PR #2917 (Mason Hale) | 0.001721588647197801880605 − 10⁻⁴⁶ − 10⁻⁷⁰ | {1:1625724, 2:426240, 3:191980, 4:73260, 5:24951, 6:167, 7:45, 8:5328, 24:1, 32:207, 48:26958} |
+| **this package** | **0.001722499906443274564357 − 10⁻⁴⁶ − 10⁻⁷⁰** | **{1:1626372, 2:426240, 3:192474, 4:73260, 5:24198, 8:5328, 48:27158}** |
+
+The gain is exactly `113907405684085469/125000000000000000000000` ≈ **9.1126e-7** (about 0.053%). The two provider words, the call
+order, the dispatch, the per-helper widths, the owner engine and its plan/template are PR2917's, byte for byte. Only the literal
+allocation changes: `allocation/FILL.json.gz`, `allocation/PROFILE.json` and `allocation/SEARCH.json`. Same words, same
+82 private buffers, same physical stock 66,304 + 408 + 8 + 82 + 2 = 66,804, same 271,728 helper roles.
+
+## Why PR2917's fill was below its cap, and why this one is optimal
+
+The fixed-capacity fractional relaxation (bins 672/448/448/448 per replica of capacity 8/16/32/48, all 1,163 count-vector
+patterns, one idle child per bin, the complete local profile paid) of PR2917's inventory {4:26, 5:2, 7:62, 8:96, 9:222} with
+local profile {1:2416, 2:640, 3:280, 4:110, 5:26, 8:8} has optimum
+
+`cap ∈ [0.001722499906443274564357, 0.0017224999064432745643571]`, 11 tight patterns, and an **integral** optimal basis per replica:
+[8]×672, [7,9]×352, [8,8]×96, [7,7,9,9]×103, [5,9,9,9]×18, [9,9,9]×93, [4,9,9,9]×234, [9⁵]×81, []×367, i.e. idle children
+{1:234, 3:81, 5:93, 48:367} per replica.
+
+PR2917's literal fill pays 207 empty cap-32 bins, one rank-24 and 212 rank-6/7 idle children, and parks 5,378 width-8 roles in
+cap-32/48 bins instead of [8,8] cap-16 bins. Every single whole-role relocation from it is uphill (a single-move fixed point:
+the first move of a width-9 role out of a [9⁵] bin costs +0.021 H-units before the drain completes), which is why bounded
+exchange/relocation repair stops there.
+
+Because the optimal basis is integral, an allocation with exactly the optimal pattern mix has **no rounding residue**: its
+complete profile is 666 × local + 74 × idle_per_replica, which is the profile above. `check_cap.py` verifies, with exact
+rationals only, the basis' primal feasibility, the sign of every one of the 1,163 reduced costs at the upper end of the root
+bracket (weak duality), that the literal profile equals the optimum's, and that its exact root bracket is the cap bracket.
+So no allocation of these words, under these bin capacities and this relaxation, has a larger complex endpoint. This is a
+statement about the packing of fixed words only; changed words, templates or coverage laws are outside it. For reference, the
+coverage-law local-word ceiling of `research/complex-local-word-ceiling` for this local profile is about 0.00175802181; the
+headline realizes about 97.98% of it.
+
+## Construction
+
+1. `tools/relax.py` (exact relaxation, scipy/HiGHS only to locate the basis) gives the integral pattern mix above.
+2. `construction/fill17.py`: PR2857's chronological flow model (PR2843 lineage) on PR2833's T37 owner chronology with the
+   integral mix as global pattern targets and PR2917's exact per-helper widths; CP-SAT (OR-Tools 9.15, one worker; several
+   workers deadlock on our machine) finds a feasible flow, realized as literal bins by regular-bipartite edge colouring.
+   The recorded run used seed 7 with PR2857's flow as a hint (`construction/T37-SOLVER.json`); an unhinted run is faster.
+3. `construction/double.py`: PR2917's T74 order is exactly two interleaved copies of the PR2833 T37 chronology
+   (order74[2k] = order37[k], order74[2k+1] = (stage, replica+37), dispatch copied), so each T37 row (t,h,o,c,p,z) maps to
+   (2t,h,o,c,p,z) and (2t+1,h,o+37,c,p,z): a T74 allocation on PR2917's own chronology.
+4. `construction/controls.py`: fresh engine load, claimed-profile check, five rejection controls, 82-buffer stock and
+   PR2917's exact moment auditor. The flow, model and pattern targets of the recorded run are in `construction/` (scratch
+   paths replaced by placeholders; provenance, not a portable entry point).
+
+## Verification
+
+**Registered, bounded** (`run_registered.py`, standard library, about a minute):
+- complete package pins; the vendored owner engine on the new allocation (271,728 roles, compact prefixes, windows,
+  same-call family distinctness, capacities, complete profile, rank mass, physical 66,804) and five rejection controls
+  (missing role, duplicate helper, same-call family collision, capacity overflow, changed profile);
+- PR2917's exact dyadic moment auditor with its authenticated baseline re-pinned to the PR2917 headline (strict gain);
+- the Fractions-only cap certificate and literal-profile equality (`check_cap.py`), with two rejection controls;
+- binding of the stored complete native/admission/release receipts in `evidence/` to the exact words, allocation and claim.
+
+**Complete replay** (`reproduce.py`): exact Git exports of PR2908 (51309592) and PR2917 (224bd5e5), through them PR2894
+(18d03c44) and PR2833 (e9307b48); fresh retained bootstrap by PR2894's `prepare_retained.py`; PR2857's four-kernel stage,
+PR2894's preload stage, PR2908's paired stage and PR2917's extension stage, giving PR2917's derived source (manifest
+98d57c82, 632 files); closed adapters with the PR2917 headline as comparator; fresh five-stage native chains for both
+providers; complete admission (owners, parent lift, rebind, discovery, block-norm, physical/prefix invoice, independent
+outer checks, release).
+
+The recorded run (`evidence/`) is a single invocation of this package's `reproduce.py --jobs 2` on macOS arm64,
+CPython 3.12.13 (numpy 2.4.5, scipy 1.16.1, sympy 1.14.0, mpmath 1.3.0, gmpy2 2.3.2, psutil 7.2.1): fresh retained bootstrap
+279 s, source stages 2 s, fresh native chains for both providers 25 s, complete admission 256 s (release 201 s), 563 s wall,
+ending `PASS_CAP_FILL_COMPLETE_REPLAY`. The native receipt's "reused retained" fields refer to the retained cache that the
+same run had just bootstrapped (`evidence/FULL-REPLAY-RESULT.json`: `fresh_retained_bootstrap: true`). Hash-bound receipts
+are stored verbatim (they contain the run's absolute paths); logs under `evidence/logs/` have paths replaced by placeholders.
+
+```sh
+# exact predecessor commits must be present locally (no network access during the replay)
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git \
+  224bd5e56041c40078ff6b5fa7393733a215de5c 51309592971e3b5be935599eed2a95404dc7781e \
+  18d03c447886895ef9abf888398178e0428533ca e9307b48d7d1b690939935ecef0f8e524e6d92f4
+python3.12 scripts/research_package.py --package research/paired-extension-cap-fill
+OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
+  python3.12 -B research/paired-extension-cap-fill/reproduce.py --repo . --work /tmp/cap-fill-complete
+```
+
+The complete replay needs Python 3.12 with numpy, scipy, sympy, mpmath, gmpy2 and psutil (versions of the recorded run in
+`evidence/ENVIRONMENT.json`). `--retained DIR` reuses an authenticated retained cache instead of the fresh bootstrap.
+
+## Scope
+
+Conditional finite supplier and modern outer certificate, exactly as inherited by PR2917; all inherited all-size, compiler,
+hosting, precision and analytic hypotheses remain. No selected-frontier change, no unconditional multiplication theorem and
+no independent human review is claimed. The optimality statement is for the fixed words and the stated packing relaxation.
+
+## Open next questions
+
+1. **Change the words.** This allocation exhausts the fill layer of PR2917's words, so further gains must lower the paid
+   local profile or the width inventory, e.g. further paired extractions on the final 82-endpoint word (PR2917 stopped
+   searching once its nine-step word was frozen). One more 9→8 extraction at PR2917-step-1 cost ({1:+3, 2:−2}) is worth
+   about +3.6e-7 after a cap-attaining re-pack. First step: recompute the paired nullspaces on the final word and price
+   each nominee with a relaxation certificate for the changed inventory before synthesis.
+2. **A general constructor.** The cap basis was integral per replica here; inventories with fractional optimal
+   multiplicities additionally need PR2863-style lockstep copies and vacancy relays.
+
+Details are in `TASK.json`.
+
+## Credit
+
+Mason Hale (PR #2917) for the words, chronology and admission tooling reused unchanged; Jeremy Diviney (PR #2908) for the
+paired extraction and adapter chain; Jeremy Kothe (PR #2894/#2833) for the supplier, frame accounting and source tools;
+Yiyang Lu (PR #2857/#2848) for the flow model and realization; Dugongue (PR #2863/#2839) for the cap-attainment precedent
+and engine lineage; Tekalign for the independent owner checker. See `CREDITS.md` and `NOTICE`. New work by Marius-Paul
+Dumitrean, prepared with substantial AI assistance (Anthropic Claude, via Claude Code). Apache-2.0.
diff --git a/research/paired-extension-cap-fill/SOURCES.json b/research/paired-extension-cap-fill/SOURCES.json
new file mode 100644
index 0000000000..3bdc4f8aa2
--- /dev/null
+++ b/research/paired-extension-cap-fill/SOURCES.json
@@ -0,0 +1,214 @@
+{
+ "schema_version": 1,
+ "base_commit": "8c8bcecb03def61bca701dd3b045932d39c48022",
+ "upstream_repository": "https://github.com/CrocSwap/integer-mult-bounds",
+ "files": [
+  {
+   "path": "certificates/selected-result.json",
+   "usage": "provenance",
+   "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+   "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+  },
+  {
+   "path": "docs/research/agent-task-catalog.json",
+   "usage": "provenance",
+   "git_blob": "889b95d936746df124872133ae1e7cc339adcb92",
+   "sha256": "7d185cd8c2af35988d638d969748ad7b670f902606444dbfc748e4402c340df6"
+  }
+ ],
+ "retained_sources": [
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/data/WORD-base.json.gz",
+   "package_path": "data/WORD-base.json.gz",
+   "git_blob": "9be0aa5349dbc8c928a46089a7695e224d0e4d16",
+   "sha256": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+   "bytes": 69818,
+   "role": "PR2917 final base provider word (82 restored endpoints), unchanged"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/data/WORD-extra.json.gz",
+   "package_path": "data/WORD-extra.json.gz",
+   "git_blob": "40b38365ea4b841101405ebd2c4fdcadcb8b9808",
+   "sha256": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+   "bytes": 69814,
+   "role": "PR2917 final extra provider word, unchanged"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/vendor/preload_move.py",
+   "package_path": "vendor/preload_move.py",
+   "git_blob": "55b435035bbc439a9d55e8abd125993208cef8d9",
+   "sha256": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044",
+   "bytes": 7243,
+   "role": "PR2894 frame accounting (frame_report) as vendored by PR2917"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/ORDER.json",
+   "package_path": "allocation/ORDER.json",
+   "git_blob": "7409c4df1092241729739596c7648bda504e6aad",
+   "sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+   "bytes": 4573,
+   "role": "PR2917 T74 call order (unchanged chronology)"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/DISPATCH.json",
+   "package_path": "allocation/DISPATCH.json",
+   "git_blob": "9544fee4e6ee1f202cee22bfaeaf229ee3b2515e",
+   "sha256": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+   "bytes": 10401,
+   "role": "PR2917 provider dispatch (unchanged)"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/PROVIDERS.json",
+   "package_path": "allocation/PROVIDERS.json",
+   "git_blob": "1bd962152fa7f0766fbaaa93569ac21e08a7cb62",
+   "sha256": "1fbbe45a0b70b909bf764fab7d89ec05b10c6c3dec5340a59a69b871d309c6ab",
+   "bytes": 7684,
+   "role": "PR2917 per-helper widths and local profiles (unchanged)"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/vendor/independent_owners.py",
+   "package_path": "allocation/vendor/independent_owners.py",
+   "git_blob": "16013201b19054f7e45398ecf10af74c9c6a9114",
+   "sha256": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461",
+   "bytes": 10057,
+   "role": "independent owner/chronology engine (Tekalign; PR2839 lineage)"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/vendor/PLAN.json.gz",
+   "package_path": "allocation/vendor/PLAN.json.gz",
+   "git_blob": "7a1db55a4d53ee99280be4f3ab7d29f7b2033adf",
+   "sha256": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+   "bytes": 29933,
+   "role": "parent plan for the owner engine"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/vendor/TEMPLATE.json.gz",
+   "package_path": "allocation/vendor/TEMPLATE.json.gz",
+   "git_blob": "114808c32b1799da53524bdc25cea67efb60009e",
+   "sha256": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+   "bytes": 1124331,
+   "role": "owner template for the owner engine"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/CLAIM.json",
+   "package_path": "allocation/baseline/CLAIM.json",
+   "git_blob": "50cc0eeeba13e48f64127544fcb17fe16bd99c30",
+   "sha256": "e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac",
+   "bytes": 1743,
+   "role": "PR2917 complete headline (comparator)"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/ORDER.json",
+   "package_path": "allocation/baseline/ORDER.json",
+   "git_blob": "7409c4df1092241729739596c7648bda504e6aad",
+   "sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+   "bytes": 4573,
+   "role": "PR2917 order (baseline for the moment auditor)"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "author": "Mason Hale (mason-hale)",
+   "upstream_path": "research/paired-helper-extension/allocation/PROFILE.json",
+   "package_path": "allocation/baseline/PROFILE.json",
+   "git_blob": "a3c711f5c3c8b69b44324c1d3b4ec4454dae3570",
+   "sha256": "07ee0cfe8d88073de9b75cd3262a98f4ac428b1bdd3922b5a077dbf3436be00c",
+   "bytes": 151,
+   "role": "PR2917 complete paid profile (baseline for the moment auditor)"
+  }
+ ],
+ "adapted_sources": [
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "upstream_path": "research/paired-helper-extension/tools/audit_allocation_moment.py",
+   "package_path": "tools/audit_allocation_moment.py",
+   "change": "authenticated baseline re-pinned from the PR2908 headline to the PR2917 headline; nothing else"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "upstream_path": "research/paired-helper-extension/tools/derive_adapters.py",
+   "package_path": "tools/derive_adapters.py",
+   "change": "generalized: buffer count, source profile and an additional comparator (PR2917) as parameters; with PR2917 parameters and the PR2908 comparator only, its adapters equal PR2917s byte for byte"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "upstream_path": "research/paired-helper-extension/check_allocation.py",
+   "package_path": "check_allocation.py",
+   "change": "paths, new allocation, PR2917 comparator, claimed-profile binding"
+  },
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "upstream_path": "research/paired-helper-extension/reproduce.py",
+   "package_path": "reproduce.py",
+   "change": "also exports PR2917 from its commit; PR2917 comparator; this package allocation"
+  }
+ ],
+ "upstream_exports": [
+  {
+   "pr": 2917,
+   "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+   "package": "research/paired-helper-extension",
+   "manifest_sha256": "55c46ddf2e3edc87dfe1ba3320947466d36980d457eb37f6cd6fba341dae0192"
+  },
+  {
+   "pr": 2908,
+   "head": "51309592971e3b5be935599eed2a95404dc7781e",
+   "package": "research/two-sided-helper-extraction",
+   "manifest_sha256": "9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f"
+  },
+  {
+   "pr": 2894,
+   "head": "18d03c447886895ef9abf888398178e0428533ca",
+   "package": "research/shared-kernel-packing",
+   "role": "exported by PR2908 reproduce.py --dry-run"
+  },
+  {
+   "pr": 2833,
+   "head": "e9307b48d7d1b690939935ecef0f8e524e6d92f4",
+   "role": "source materialized and authenticated by PR2894 tools/materialize_source.py"
+  }
+ ],
+ "derived_source": {
+  "manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "files": 632,
+  "builder": "PR2917 tools/build_extension.py"
+ },
+ "source_boundary": "Only this new package is submitted. The words are PR2917s, byte-identical; exact frozen ancestor exports remain unchanged. Full replay performs no network fetch."
+}
diff --git a/research/paired-extension-cap-fill/TASK.json b/research/paired-extension-cap-fill/TASK.json
new file mode 100644
index 0000000000..afc75f7f70
--- /dev/null
+++ b/research/paired-extension-cap-fill/TASK.json
@@ -0,0 +1,68 @@
+{
+ "schema_version": 1,
+ "task_id": "selected-packing",
+ "priority_revision": 5,
+ "base_commit": "8c8bcecb03def61bca701dd3b045932d39c48022",
+ "original_card": {
+  "id": "selected-packing",
+  "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+  "starting_points": [
+   "certificates/selected-result.json",
+   "research/heterogeneous-owner-assembly/README.md",
+   "research/complex-local-word-ceiling/README.md"
+  ],
+  "methods": [
+   "Search a named unclaimed canonical candidate domain with a reproducible partition.",
+   "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
+  ],
+  "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.",
+  "first_step": {
+   "command": [
+    "python3",
+    "-B",
+    "scripts/research_baseline.py"
+   ],
+   "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+   "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.",
+   "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+  },
+  "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.",
+  "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+  "allowed_variations": [
+   "One bounded residual packing instance or exact relaxation.",
+   "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+  ],
+  "scope_change_triggers": [
+   "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+  ],
+  "overlap_terms": [
+   "T16",
+   "owner exchange",
+   "packing"
+  ]
+ },
+ "scope_status": "refined",
+ "actual_scope": "Exact fixed-capacity packing relaxation of the top open claim PR #2917 (inventory {4:26,5:2,7:62,8:96,9:222}, local profile {1:2416,2:640,3:280,4:110,5:26,8:8}) and a literal owner-legal T74 allocation of its unchanged words that attains that relaxation optimum; complete fresh-native admission and modern outer release against the PR2917 headline.",
+ "scope_change_reason": "The card asks for a bounded improvement to the selected packing. The selected record (#1094) is far behind the open frontier; the unsearched, explicitly bounded packing instance with real headroom is the open-PR frontier word itself: PR2917 ships a fill 9.11e-7 below the exact fractional optimum of its own inventory (its own search stopped at a single-move fixed point). This package closes that residual exactly; it does not change the selected frontier.",
+ "bottleneck_link": "A fixed word set has an exact packing cap. PR2917 realized 9.11e-7 less than its cap; this allocation realizes all of it (the complete profile equals the fractional optimum), so further gains on these words must change the words (inventory or local profile), not the fill.",
+ "budget_minutes": 240,
+ "stop_rule": "Stop when a literal allocation of the unchanged words reaches the certified cap with owner-engine PASS and the complete admission passes strictly above the PR2917 headline, or report a scoped finding if any stage rejects it.",
+ "outcome": "completed",
+ "evidence": "run_registered.py (stdlib): package pins; owner engine on the new allocation (271,728 roles, physical 66,804) and five rejection controls; PR2917 moment auditor re-pinned to the PR2917 headline; Fractions-only relaxation certificate and literal-profile equality; stored receipts binding. reproduce.py: exact Git exports of PR2908/PR2917 (and through them PR2894/PR2833), fresh retained bootstrap, PR2917 derived source (manifest 98d57c82), adapters, fresh native chains for both providers and complete admission: PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE and PASS_RELEASE at the claimed kappa.",
+ "author": "Marius-Paul Dumitrean",
+ "ai_assistance": "Substantial AI assistance (Anthropic Claude via Claude Code) for search, implementation, exact computation and checks; no independent human review is claimed.",
+ "open_questions": [
+  {
+   "question": "Can the words of PR2917 be changed so that the fixed-inventory cap itself rises (further paired extractions on the final 82-endpoint word, or narrowings), and can each change be packed at its new cap?",
+   "why_it_matters": "This allocation exhausts the fill layer for these words: every further gain must lower the paid local profile or the width inventory. One more 9->8 extraction at PR2917-step-1 cost ({1:+3,2:-2}) is worth about +3.6e-7 after a cap-attaining re-pack.",
+   "first_step": "Recompute PR2908/PR2917 paired nullspaces on the final 82-endpoint word (existing and lowered terminal frames), price each nominee with the certified frame solver and certificates/RELAX-CAP.json-style relaxation for the changed inventory, then pack it with the same flow route.",
+   "blocked_by": "Search time; PR2917 stopped searching once its nine-step word was frozen."
+  },
+  {
+   "question": "Is the flow-plus-doubling route a general constructor for every PR2917-lineage inventory?",
+   "why_it_matters": "The cap basis was integral per replica here, so no integrality residue remained; other inventories may need lockstep copies (PR2863) to reach their caps.",
+   "first_step": "Run construction/fill17.py with --catalogue tight on a changed inventory; if the integral basis mix has fractional multiplicities, combine with PR2863-style vacancy relays over copies.",
+   "blocked_by": "None for inventories with an integral optimal basis."
+  }
+ ]
+}
diff --git a/research/paired-extension-cap-fill/VERIFY.json b/research/paired-extension-cap-fill/VERIFY.json
new file mode 100644
index 0000000000..6bbc54fff9
--- /dev/null
+++ b/research/paired-extension-cap-fill/VERIFY.json
@@ -0,0 +1,14 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": ["{python}", "-B", "{package}/run_registered.py"],
+      "timeout_seconds": 420,
+      "checks": "Complete package pins; literal T74 owner geometry of the new allocation with PR2917's vendored PR2839 engine (271,728 roles, 82-buffer physical stock 66,804) and five rejection controls; PR2917's exact dyadic moment auditor re-pinned to PR2917's headline (strict gain); Fractions-only verification of the fixed-capacity relaxation basis (1,163 patterns, primal feasibility, dual signs) and equality of the literal complete profile with the fractional optimum; binding of the stored complete native/admission/release receipts to the exact words, allocation and claim. Native and integrated admission are rerun separately by reproduce.py from exact Git sources."
+    }
+  ]
+}
diff --git a/research/paired-extension-cap-fill/allocation/DISPATCH.json b/research/paired-extension-cap-fill/allocation/DISPATCH.json
new file mode 100644
index 0000000000..9544fee4e6
--- /dev/null
+++ b/research/paired-extension-cap-fill/allocation/DISPATCH.json
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diff --git a/research/paired-extension-cap-fill/allocation/SEARCH.json b/research/paired-extension-cap-fill/allocation/SEARCH.json
new file mode 100644
index 0000000000..1e9e932dd1
--- /dev/null
+++ b/research/paired-extension-cap-fill/allocation/SEARCH.json
@@ -0,0 +1,51 @@
+{
+ "calls": 666,
+ "gain_vs_PR2917_claim": "113907405684085469/125000000000000000000000",
+ "gain_vs_PR2917_claim_float": 9.112592454726837e-07,
+ "headline_floor24_minus_1e-46_minus_1e-70": "0.0017224999064432745643569999999999999999999998999999999999999999999999",
+ "idle_histogram": {
+  "1": 17316,
+  "3": 5994,
+  "48": 27158,
+  "5": 6882
+ },
+ "kappa_root_bracket": [
+  "1722499906443274564357/1000000000000000000000000",
+  "17224999064432745643571/10000000000000000000000000"
+ ],
+ "kappa_root_lower_decimal": "0.001722499906443274564357",
+ "lineage": "PR2917 (mason-hale) words/chronology/engine; PR2857 flow model and realization (discover_original.py / PR2843 build_allocation.py); PR2839 owner engine; lane C r12 relax/root/fill tools; r13 lane C1.",
+ "method": [
+  "relax.py (lane C r12): exact 1163-pattern fixed-capacity relaxation of inventory {4:26,5:2,7:62,8:96,9:222} with local {1:2416,2:640,3:280,4:110,5:26,8:8}: cap bracket [1722499906443274564357/1e24, 17224999064432745643571/1e25]; the optimal basic solution is integral per replica ([8] 672, [7,9] 352, [7,7,9,9] 103, [8,8] 96, [9^5] 81, [5,9,9,9] 18, [9,9,9] 93, [4,9,9,9] 234, [] 367).",
+  "fill17.py: PR2857-style chronological flow model (X[window-class,pattern] bins, Z[.,.,call,width] roles, one role per bin per call, exact pattern supply, per-call width demand, global pattern targets = the integral LP mix) under PR2833's T37 owners chronology (333 calls); CP-SAT 9.15.6755, num_search_workers=1, random_seed=7, hint = PR2857 FLOW.json.gz (3065 matching variables) + zeros; first feasible flow at 266.7 s; regular-bipartite edge colouring realizes literal bins.",
+  "double.py: PR2917's T74 ORDER is the exact interleaving of two copies of the T37 chronology (order74[2k]=order37[k], order74[2k+1]=(stage, replica+37)) with the dispatch copied, so row (t,h,o,c,p,z) -> (2t,h,o,c,p,z) and (2t+1,h,o+37,c,p,z) is a T74 fill on PR2917's own chronology.",
+  "Checks: vendored PR2839 owner engine check() (sha 77a84872...) PASS; the five check_allocation.py rejection controls; PR2917's tools/audit_allocation_moment.py exact dyadic moment (source = PR2917 allocation/baseline); root.py exact bracket."
+ ],
+ "order_and_dispatch_unchanged_vs_PR2917": true,
+ "physical": 66804,
+ "pr2917_pins_unchanged": {
+  "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+  "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461"
+ },
+ "profile": {
+  "1": 1626372,
+  "2": 426240,
+  "3": 192474,
+  "4": 73260,
+  "48": 27158,
+  "5": 24198,
+  "8": 5328
+ },
+ "relaxation_cap_bracket": [
+  "1722499906443274564357/1000000000000000000000000",
+  "17224999064432745643571/10000000000000000000000000"
+ ],
+ "replicas": 74,
+ "roles": 271728,
+ "scope": "Literal owner allocation for PR2917's UNCHANGED words (same PROVIDERS widths/local profile, same ORDER/DISPATCH chronology); attains the exact fractional packing cap of the inventory. Local/native/global/outer admission remains separate.",
+ "source_words_unchanged_by_allocation": true,
+ "status": "C1_FLOW_ROUTE_CAP_ATTAINING_LITERAL_FILL"
+}
\ No newline at end of file
diff --git a/research/paired-extension-cap-fill/allocation/baseline/CLAIM.json b/research/paired-extension-cap-fill/allocation/baseline/CLAIM.json
new file mode 100644
index 0000000000..50cc0eeeba
--- /dev/null
+++ b/research/paired-extension-cap-fill/allocation/baseline/CLAIM.json
@@ -0,0 +1,35 @@
+{
+  "baseline_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "baseline_kappa": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "baseline_pr": 2908,
+  "calls": 666,
+  "complete_package_manifest_sha256": "bf852fb4ecfa28dddfb8cc6fe7bf53019b3932114e01cba3e026b63ef2b1babd",
+  "complex_lower": "344317729439560376121/200000000000000000000000",
+  "gain": "595154921781997337/500000000000000000000000",
+  "helpers": 408,
+  "independent_inputs": 632,
+  "kappa": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017215886471978018806049999999999999999999998999999999999999999999999",
+  "live_families": 66304,
+  "native_receipt_sha256": "5c1ea6f03e48673d9b56563494fff2258ee18bc8dacdeb72ba5c07e2044008ca",
+  "physical_families": 66804,
+  "profile": {
+    "1": 1625724,
+    "2": 426240,
+    "24": 1,
+    "3": 191980,
+    "32": 207,
+    "4": 73260,
+    "48": 26958,
+    "5": 24951,
+    "6": 167,
+    "7": 45,
+    "8": 5328
+  },
+  "release_receipt_sha256": "f7639e51fd620070767b8e2a855a0a613ae9bfd19f86a1ba023d88316193ae06",
+  "replicas": 74,
+  "scope": "Conditional finite supplier/outer certificate. Inherited all-size/compiler/theorem hypotheses remain. No selected frontier change, optimality or independent-human-review claim. Both changed native chains are fresh; unchanged retained parent/native evidence is explicitly authenticated and reused.",
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "status": "CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE",
+  "zero_buffers": 82
+}
diff --git a/research/paired-extension-cap-fill/allocation/baseline/ORDER.json b/research/paired-extension-cap-fill/allocation/baseline/ORDER.json
new file mode 100644
index 0000000000..7409c4df10
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diff --git a/research/paired-extension-cap-fill/allocation/baseline/PROFILE.json b/research/paired-extension-cap-fill/allocation/baseline/PROFILE.json
new file mode 100644
index 0000000000..a3c711f5c3
--- /dev/null
+++ b/research/paired-extension-cap-fill/allocation/baseline/PROFILE.json
@@ -0,0 +1,13 @@
+{
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+  "32": 207,
+  "48": 26958
+}
\ No newline at end of file
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new file mode 100644
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diff --git a/research/paired-extension-cap-fill/allocation/vendor/independent_owners.py b/research/paired-extension-cap-fill/allocation/vendor/independent_owners.py
new file mode 100644
index 0000000000..16013201b1
--- /dev/null
+++ b/research/paired-extension-cap-fill/allocation/vendor/independent_owners.py
@@ -0,0 +1,111 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Independent integer-time and mask check of the actual parameterized-replica owner allocation with PR2802 retired7 providers.
+
+Chronology/mask method derives from Tekalign's PR2751 independent_owners.py;
+Marius-Paul Dumitrean's PR2802 retired7 native construction and the retained
+provider frame checker keep their
+upstream attribution. No solver, producer, emitter or floating arithmetic is
+imported. This checks finite geometry, not global native/outer admission.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+import argparse,hashlib,gzip,json,sys,types
+sys.dont_write_bytecode=True
+def need(v,msg):
+ if not v:raise ValueError(msg)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def read(p):
+ b=Path(p).read_bytes();return json.loads(gzip.decompress(b)if str(p).endswith('.gz')else b)
+def inputs(PROVIDER):
+ provider_pins={'inputs/PLAN.json.gz':'afb3c5c8134fc2cfce0b50a21758490c225574994b2c3c5161e53e2355acc6fa','inputs/GLOBAL-TEMPLATE.json.gz':'21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e','independent_local.py':'ee1faab70095fa312fc61d375ddf015b76104cb1a542ae7876a149e7999faa20','inputs/PROVIDERS.json':'391075b1411a3976850c633f92f58c35ed3f046f09d55bd435d7545124543fd4','inputs/WORD-base.json.gz':'dca8becca633ffc5e998985631bcbcab1123b27ca7f10ac6a96b1ec21ce69a66','inputs/WORD-extra.json.gz':'6bcb3c2c73eaf7558ddc6ef6b484334f8d96b9d2b227e265483b657de00f4bb7'}
+ hashes={}
+ for n,pin in provider_pins.items():
+  p=PROVIDER/n;need(sha(p)==pin,'pinned PR2802 provider source '+n);hashes[str(p)]=pin
+ L=types.ModuleType('retained_independent_frames');exec(compile((PROVIDER/'independent_local.py').read_bytes(),'pinned_PR2802_independent_local.py','exec'),L.__dict__);providers=read(PROVIDER/'inputs/PROVIDERS.json')
+ for tag,pid in [('base','gauge44'),('extra','extra')]:
+  word=read(PROVIDER/f'inputs/WORD-{tag}.json.gz');report,start,ends=L.check_frames(word);L.check_cleanup(word);L.algebra(word)
+  widths=[L.dm(ends[k])-L.dm(start[k])for k in sorted(start)if k>=224]
+  need(widths==providers[pid]['widths']and len(widths)==408,'actual ordered provider frame widths');need(len(word['centers'])==8,'eight centres');providers[pid]['actual_paid_profile']={int(k):v for k,v in report['profile'].items()}
+ return read(PROVIDER/'inputs/PLAN.json.gz'),read(PROVIDER/'inputs/GLOBAL-TEMPLATE.json.gz'),providers,hashes
+
+def windows(template,order,T):
+ ranks={c['child']:c['rank']for c in template['idle_children']};pairs={e['stage']:e['pair']for e in template['recipe']if e['kind']=='local'}
+ blocks={};stage=None
+ for event in template['execution_schedule']:
+  if event['kind']in('bank_padding_cover_sweep','translate_every_live_family'):continue
+  if event['kind']=='local_cover_sweep':stage=event['stage'];blocks[stage]=[]
+  need(stage is not None,'source event before local call');blocks[stage].append(event)
+ need(set(blocks)==set(range(9)),'nine source stages')
+ progress=[0]*T;last={};result={}
+ for t,(stage,replica)in enumerate(order):
+  need(0<=replica<T and stage==progress[replica],'order chronology');progress[replica]+=1
+  for j,event in enumerate(blocks[stage]):
+   kind=event['kind']
+   if kind=='local_cover_sweep':need(j==0,'local first position');last[replica,pairs[stage]]=t
+   elif kind=='bridge':last[replica,event['src']]=last[replica,event['dst']]=t
+   elif kind=='idle_cover_sweep':
+    need(j>0,'idle source position');start=last.get((replica,event['pair']),-1)
+    for child in event['child_indices']:
+     if child in ranks:result[replica,child]=(ranks[child],start,t)
+   elif kind in ('terminal_Y_translations','terminal'):pass  # inherited terminal phase; no pending-window endpoints
+   else:raise ValueError('unknown source event kind')
+ need(progress==[9]*T,'complete replica source progression');return result
+
+def check(T,order,fill,dispatch,claimed,plan,template,providers):
+ need(type(T)is int and T>0,'positive T');N=9*T
+ need(len(order)==N and set(map(tuple,order))=={(s,r)for s in range(9)for r in range(T)},'complete T call coverage')
+ win=windows(template,order,T)
+ need(set(dispatch)==set(map(tuple,order))and all(p in providers for p in dispatch.values()),'provider dispatch coverage')
+ for s,r,pid in fill.get('dispatch_overrides',[]):need(dispatch.get((s,r))==pid,'final dispatch override binding')
+ need(fill['columns']==['time','helper','owner_replica','child','port','offset'],'literal role columns')
+ need(len(fill['rows'])==N*408,'complete role count');helpers=[0]*N;families=[0]*N;occupied={};lastrow={}
+ for idx,row in enumerate(fill['rows']):
+  need(len(row)==6 and all(type(x)is int for x in row),'integer role shape');t,h,o,c,p,z=row
+  need(0<=t<N and 0<=h<408 and 0<=p<112 and(o,c)in win,'role bounds')
+  cap,lo,hi=win[o,c];need(lo<t<=hi,'literal source window');hb=1<<h;need(not helpers[t]&hb,'duplicate helper');helpers[t]|=hb
+  family=o*896+(2*plan['pairs'][str(c)]+plan['sides'][str(c)])*112+p;fb=1<<family
+  need(not families[t]&fb,'same-call family collision');families[t]|=fb
+  w=providers[dispatch[tuple(order[t])]]['widths'][h];need(0<=z and z+w<=cap,'bin capacity')
+  key=(o,c,p);mask=((1<<w)-1)<<z;need(not occupied.get(key,0)&mask,'bin overlap');occupied[key]=occupied.get(key,0)|mask
+  if key not in lastrow or z>lastrow[key][0]:lastrow[key]=(z,idx,w)
+ need(helpers==[(1<<408)-1]*N,'all helper identities');idle=Counter()
+ for(o,c),(cap,_,_)in win.items():
+  for p in range(112):
+   key=(o,c,p);mask=occupied.get(key,0);used=mask.bit_count();need(mask==(1<<used)-1,'compact bin prefix')
+   if used<cap:idle[cap-used]+=1
+ profile=Counter(idle)
+ for call in order:profile.update(providers[dispatch[tuple(call)]]['actual_paid_profile'])
+ if claimed is not None:need(profile==Counter({int(k):v for k,v in claimed.items()}),'complete claimed profile')
+ mass=sum(r*n for r,n in profile.items());need(mass==65088*T,'complete rank-mass identity')
+ return dict(replicas=T,calls=N,roles=N*408,live=896*T,physical=896*T+490,rank_mass=mass,idle=dict(sorted(idle.items())),profile=dict(sorted(profile.items()))),win,lastrow
+
+def write_receipt(out,result):
+ out.parent.mkdir(parents=True,exist_ok=True);lock=out.with_name(out.name+'.lock');handle=lock.open('x')
+ try:
+  with out.open('x',encoding='utf8',newline='\n')as target:target.write(json.dumps(result,sort_keys=True,indent=2)+chr(10))
+ finally:handle.close();lock.unlink()
+
+def main():
+ need(__debug__,'assertions required for retained provider frame checker')
+ ap=argparse.ArgumentParser();ap.add_argument('--provider-root',type=Path,default=Path(__file__).resolve().parent/'vendor/frontier');ap.add_argument('--replicas',type=int,required=True);ap.add_argument('--order',type=Path,required=True);ap.add_argument('--fill',type=Path,required=True);ap.add_argument('--dispatch',type=Path,required=True);ap.add_argument('--profile',type=Path);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();need(not a.out.exists(),'fresh verification output')
+ plan,template,providers,pins=inputs(a.provider_root);files=[a.order,a.fill,a.dispatch]+([a.profile]if a.profile else[]);before={str(p.resolve()):sha(p)for p in files};order=read(a.order);fill=read(a.fill);rawdispatch=read(a.dispatch);need(len(rawdispatch)==9*a.replicas and all(len(row)==3 and type(row[0])is int and type(row[1])is int and type(row[2])is str for row in rawdispatch),'literal dispatch shape and count');dispatch={(s,r):p for s,r,p in rawdispatch};need(len(dispatch)==len(rawdispatch),'unique literal dispatch calls');claimed=read(a.profile)if a.profile else None
+ result,win,lastrow=check(a.replicas,order,fill,dispatch,claimed,plan,template,providers);rejected=[]
+ def reject(name,fn,reason):
+  try:fn()
+  except ValueError as e:need(str(e)==reason,'wrong rejection reason '+name+': '+str(e));rejected.append(dict(name=name,reason=reason))
+  else:raise ValueError('accepted corruption '+name)
+ def rerun(T=a.replicas,f=fill,d=dispatch,p=providers,c=claimed):return check(T,order,f,d,c,plan,template,p)
+ reject('false_replica_count',lambda:rerun(T=a.replicas+1),'complete T call coverage')
+ reject('missing_literal_helper_role',lambda:rerun(f={**fill,'rows':fill['rows'][:-1]}),'complete role count')
+ bad=dict(dispatch);bad[tuple(order[0])]='unknown-provider';reject('unbound_provider_at_actual_call',lambda:rerun(d=bad),'provider dispatch coverage')
+ def mutate(i,new):rows=list(fill['rows']);rows[i]=new;return{**fill,'rows':rows}
+ row=fill['rows'][0];t,h,o,c,p,z=row;owner,child=next(k for k,(cap,lo,hi)in win.items()if not lo<t<=hi)
+ reject('unavailable_source_window',lambda:rerun(f=mutate(0,[t,h,owner,child,p,z])),'literal source window')
+ j=next(i for i,r in enumerate(fill['rows'][1:],1)if r[0]==t);r=fill['rows'][j];reject('same_call_physical_family_collision',lambda:rerun(f=mutate(j,[r[0],r[1],o,c,p,r[5]])),'same-call family collision')
+ key,(z,i,w)=next((k,v)for k,v in lastrow.items()if v[0]+v[2]<win[k[:2]][0]);r=list(fill['rows'][i]);r[5]+=1
+ reject('unpaid_hole_in_compact_pending_prefix',lambda:rerun(f=mutate(i,r)),'compact bin prefix')
+ wrong=dict(result['profile']);wrong[1]=wrong.get(1,0)+1;reject('changed_total_paid_profile',lambda:rerun(c=wrong),'complete claimed profile')
+ need({str(p.resolve()):sha(p)for p in files}==before,'candidate input drift');need(all(sha(Path(p))==h for p,h in pins.items()),'baseline input drift')
+ result.update(status='PASS_INDEPENDENT_T_OWNER_CHRONOLOGY_MASKS',controls=rejected,candidate_sha256={label:sha(path)for label,path in [('ORDER',a.order),('FILL',a.fill),('DISPATCH',a.dispatch)]+([('PROFILE',a.profile)]if a.profile else[])},provider_source_sha256={Path(path).relative_to(a.provider_root).as_posix():digest for path,digest in pins.items()},scope='PR2802 head17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd; finite literal whole-owner geometry, scalar endpoints and paid profile only; full native/global/outer admission remains separate.')
+ write_receipt(a.out,result);print(json.dumps({k:result[k]for k in['status','replicas','roles','live','physical','profile']}),flush=True)
+if __name__=='__main__':main()
diff --git a/research/paired-extension-cap-fill/certificates/RELAX-CAP.json b/research/paired-extension-cap-fill/certificates/RELAX-CAP.json
new file mode 100644
index 0000000000..dbdba6c6d8
--- /dev/null
+++ b/research/paired-extension-cap-fill/certificates/RELAX-CAP.json
@@ -0,0 +1,113 @@
+{
+ "scenario": "pr2917-unchanged-words",
+ "local_per_call": {
+  "1": 2416,
+  "2": 640,
+  "3": 280,
+  "4": 110,
+  "5": 26,
+  "8": 8
+ },
+ "inventory_per_call": {
+  "4": 26,
+  "5": 2,
+  "7": 62,
+  "8": 96,
+  "9": 222
+ },
+ "basis_patterns": [
+  {
+   "capacity": 8,
+   "widths": [
+    8
+   ],
+   "count_per_replica": "672"
+  },
+  {
+   "capacity": 16,
+   "widths": [
+    7,
+    9
+   ],
+   "count_per_replica": "352"
+  },
+  {
+   "capacity": 32,
+   "widths": [
+    7,
+    7,
+    9,
+    9
+   ],
+   "count_per_replica": "103"
+  },
+  {
+   "capacity": 16,
+   "widths": [
+    8,
+    8
+   ],
+   "count_per_replica": "96"
+  },
+  {
+   "capacity": 48,
+   "widths": [
+    9,
+    9,
+    9,
+    9,
+    9
+   ],
+   "count_per_replica": "81"
+  },
+  {
+   "capacity": 32,
+   "widths": [
+    5,
+    9,
+    9,
+    9
+   ],
+   "count_per_replica": "18"
+  },
+  {
+   "capacity": 32,
+   "widths": [
+    9,
+    9,
+    9
+   ],
+   "count_per_replica": "93"
+  },
+  {
+   "capacity": 32,
+   "widths": [
+    4,
+    9,
+    9,
+    9
+   ],
+   "count_per_replica": "234"
+  },
+  {
+   "capacity": 48,
+   "widths": [],
+   "count_per_replica": "367"
+  }
+ ],
+ "cap_lower": "1722499906443274564357/1000000000000000000000000",
+ "cap_upper": "17224999064432745643571/10000000000000000000000000",
+ "cap_lower_decimal": "0.001722499906443274564357",
+ "cap_upper_decimal": "0.0017224999064432745643571",
+ "patterns": 1163,
+ "tight_patterns": 11,
+ "strict_patterns": 1152,
+ "idle_per_replica": {
+  "1": "234",
+  "3": "81",
+  "5": "93",
+  "48": "367"
+ },
+ "rank_mass_identity": true,
+ "status": "PASS_EXACT_RELAXATION_CAP"
+}
\ No newline at end of file
diff --git a/research/paired-extension-cap-fill/check_allocation.py b/research/paired-extension-cap-fill/check_allocation.py
new file mode 100644
index 0000000000..8fbaf19067
--- /dev/null
+++ b/research/paired-extension-cap-fill/check_allocation.py
@@ -0,0 +1,111 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Literal T74 owners, private stock, rejection controls and exact moment of the cap-attaining allocation.
+
+Adapted from Mason Hale's PR2917 check_allocation.py, which retains Tekalign's independent integer
+chronology/mask checker (allocation/vendor/independent_owners.py) and Jeremy Diviney's PR2908 integration.
+The two provider words are PR2917's, byte-identical (data/); only the literal allocation changes.
+Marius-Paul Dumitrean, with substantial AI assistance (Claude Code). Native/global/outer admission is separate.
+"""
+import argparse, gzip, hashlib, json, sys, types
+from pathlib import Path
+P = Path(__file__).resolve().parent
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if raw[:2] == b'\x1f\x8b' else raw)
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+def load(name, path):
+    module = types.ModuleType(name)
+    module.__file__ = str(path)
+    sys.modules[name] = module
+    exec(compile(path.read_bytes(), str(path), 'exec'), module.__dict__)
+    return module
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--work', type=Path, required=True)
+    args = parser.parse_args()
+    if not __debug__:
+        raise SystemExit('refusing python -O: this checker relies on assertions')
+    out = args.work.resolve()
+    assert not out.exists() and not out.is_relative_to(P)
+    allocation_pins = read(P / 'ALLOCATION-PINS.json')
+    actual_pins = {p.relative_to(P).as_posix(): sha(p) for p in (P / 'allocation').rglob('*') if p.is_file()}
+    assert actual_pins == allocation_pins, 'complete allocation inventory binding'
+    word_pins = read(P / 'PINS.json')
+    assert all(sha(P / name) == digest for name, digest in word_pins.items()), 'source word/code pins'
+    out.mkdir(parents=True)
+    owners = load('cap_fill_owners', P / 'allocation/vendor/independent_owners.py')
+    moment = load('cap_fill_moment', P / 'tools/audit_allocation_moment.py')
+    frames = load('cap_fill_frames', P / 'vendor/preload_move.py')
+    providers, word_records, private_counts = {}, {}, set()
+    for tag, provider in [('base', 'gauge44'), ('extra', 'extra')]:
+        path = P / f'data/WORD-{tag}.json.gz'
+        word = read(path)
+        profile, inventory = frames.frame_report(word)
+        assert profile == word['report']['local_profile'] and inventory == word['report']['width_inventory']
+        helpers = sorted(set(range(224, 704)) - set(word['removed']))
+        widths = [len(word['helper_final'].get(str(h), [0] * 9)) - len(word['start_extra'].get(str(h), [])) for h in helpers]
+        assert len(helpers) == 408 and len(word['centers']) == 8
+        buffers = {r for gate in word['cleanup'] for r in (gate[1:3] if gate[0] == 'add' else gate[1:2]) if r >= 704}
+        assert buffers == {704 + int(h) for h in word['helper_final']}, 'actual cleanup buffer/end-point bijection'
+        assert len(buffers) == 82, 'all 82 private buffers charged'
+        private_counts.add(len(buffers))
+        providers[provider] = {'widths': widths, 'actual_paid_profile': {int(k): v for k, v in profile.items()}}
+        word_records[tag] = {'sha256': sha(path), 'local_profile': profile, 'width_inventory': inventory, 'private_buffers': len(buffers)}
+    assert len(private_counts) == 1
+    registry = read(P / 'allocation/PROVIDERS.json')
+    assert {k: {'widths': v['widths'], 'actual_paid_profile': {int(r): n for r, n in v['actual_paid_profile'].items()}} for k, v in registry.items()} == providers
+    base = P / 'allocation'
+    order, fill = read(base / 'ORDER.json'), read(base / 'FILL.json.gz')
+    raw_dispatch = read(base / 'DISPATCH.json')
+    dispatch = {(s, r): provider for s, r, provider in raw_dispatch}
+    assert len(dispatch) == len(raw_dispatch), 'unique actual call/provider binding'
+    profile = read(base / 'PROFILE.json')
+    plan, template = read(base / 'vendor/PLAN.json.gz'), read(base / 'vendor/TEMPLATE.json.gz')
+    T = len(order) // 9
+    def check(candidate=fill, claimed=profile):
+        return owners.check(T, order, candidate, dispatch, claimed, plan, template, providers)
+    result, _, _ = check()
+    assert T == 74 and result['roles'] == 271728
+    result['physical'] = result['live'] + len(helpers) + len(word['centers']) + next(iter(private_counts)) + 2
+    assert result['physical'] == 66804
+    result['physical_source'] = 'Actual 82-register private cleanup namespace, 408 live helpers, eight centres and two guards; global stock checked separately.'
+    controls = {}
+    def reject(name, candidate=fill, claimed=profile):
+        try:
+            check(candidate, claimed)
+        except ValueError as error:
+            controls[name] = str(error)
+        else:
+            raise AssertionError('owner corruption accepted: ' + name)
+    reject('missing_role', {**fill, 'rows': fill['rows'][:-1]})
+    first = fill['rows'][0]
+    j = next(i for i, r in enumerate(fill['rows'][1:], 1) if r[0] == first[0])
+    def mutate(index, row):
+        rows = list(fill['rows']); rows[index] = row
+        return {**fill, 'rows': rows}
+    duplicate = list(fill['rows'][j]); duplicate[1] = first[1]
+    reject('duplicate_helper', mutate(j, duplicate))
+    collision = list(fill['rows'][j]); collision[2:5] = first[2:5]
+    reject('same_call_family_collision', mutate(j, collision))
+    overflow = list(first); overflow[5] = 49
+    reject('capacity_overflow', mutate(0, overflow))
+    wrong = dict(profile); wrong['1'] = wrong.get('1', 0) + 1
+    reject('changed_paid_profile', claimed=wrong)
+    exact = moment.run(base, base / 'baseline')
+    claim = read(P / 'CLAIM.json')
+    assert {str(k): v for k, v in profile.items()} == {str(k): v for k, v in claim['profile'].items()}, 'claimed complete profile'
+    assert all(sha(P / name) == digest for name, digest in {**word_pins, **allocation_pins}.items()), 'input drift'
+    result.update(status='PASS_CAP_FILL_LITERAL_OWNERS_AND_EXACT_MOMENT', providers=word_records,
+                  controls=controls, moment=exact, allocation_sha256=allocation_pins,
+                  scope='Recounted local frames, exact whole-owner geometry and directed moment; algebra/native/global/outer admission remains separately required.')
+    (out / 'RESULT.json').write_text(json.dumps(result, sort_keys=True, indent=2) + '\n')
+    print(result['status'], exact['target_decimal'], exact['gain_decimal'])
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-extension-cap-fill/check_cap.py b/research/paired-extension-cap-fill/check_cap.py
new file mode 100644
index 0000000000..c1569e8ebc
--- /dev/null
+++ b/research/paired-extension-cap-fill/check_cap.py
@@ -0,0 +1,77 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Fractions-only certificate that the literal allocation attains the fixed-capacity packing optimum.
+
+certificates/RELAX-CAP.json stores the 9-pattern optimal basis of the fractional relaxation of PR2917's
+unchanged inventory (bins 672/448/448/448 per replica of capacity 8/16/32/48, all 1,163 count-vector
+patterns, one idle child per bin, the complete per-call local profile paid). tools/relax_exact.py checks,
+with exact rationals only: primal feasibility of the basis (so the cap is at least its root) and the sign of
+every pattern's reduced cost at the upper end of the root bracket (weak duality: the cap is at most that
+end). This script then checks that the literal complete profile of allocation/PROFILE.json EQUALS the
+basic solution's profile summed over the 74 replicas (666 calls x local + 74 x idle), and that its exact
+root bracket equals the cap bracket. Hence no allocation of these words, under these capacities and this
+relaxation, can have a larger complex endpoint. It is not a bound over changed words or other templates.
+Marius-Paul Dumitrean, with substantial AI assistance (Claude Code). The relaxation model and root
+arithmetic are ours (research/t37-word-level-census-r12 lineage); the moment model is the shared
+complete-profile moment used by PR2857/PR2917.
+"""
+import gzip, json, sys
+from fractions import Fraction as Q
+from pathlib import Path
+P = Path(__file__).resolve().parent
+sys.path.insert(0, str(P / 'tools'))
+import relax_exact as RE
+import root as R
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if raw[:2] == b'\x1f\x8b' else raw)
+
+def main():
+    if not __debug__:
+        raise SystemExit('refusing python -O')
+    cert = read(P / 'certificates/RELAX-CAP.json')
+    words = [read(P / f'data/WORD-{t}.json.gz') for t in ('base', 'extra')]
+    for w in words:
+        assert {k: v for k, v in w['report']['local_profile'].items()} == cert['local_per_call'], 'certificate local profile = actual words'
+        assert {k: v for k, v in w['report']['width_inventory'].items()} == cert['inventory_per_call'], 'certificate inventory = actual words'
+    r = RE.verify_basis(cert['local_per_call'], cert['inventory_per_call'], cert['basis_patterns'])
+    assert r['status'] == 'PASS_EXACT_RELAXATION_CAP' and r['patterns'] == 1163
+    assert Q(r['cap_lower']) == Q(cert['cap_lower']) and Q(r['cap_upper']) == Q(cert['cap_upper'])
+    T, calls = 74, 666
+    expected = {}
+    for k, v in cert['local_per_call'].items():
+        expected[int(k)] = expected.get(int(k), 0) + calls * v
+    for k, v in r['idle_per_replica'].items():
+        n = T * Q(v)
+        assert n.denominator == 1, 'integral idle multiplicity at T74'
+        expected[int(k)] = expected.get(int(k), 0) + int(n)
+    profile = {int(k): v for k, v in read(P / 'allocation/PROFILE.json').items()}
+    assert profile == expected, 'literal complete profile equals the fractional optimum profile'
+    lo, hi = R.kappa_from_profile(profile, T)
+    assert (lo, hi) == (Q(cert['cap_lower']), Q(cert['cap_upper'])), 'literal root bracket equals the cap bracket'
+    # rejection controls: a perturbed basis and a perturbed profile must fail
+    controls = {}
+    try:
+        bad = [dict(e) for e in cert['basis_patterns']]; bad[0] = dict(bad[0]); bad[0]['widths'] = list(bad[0]['widths']) + [4]
+        RE.verify_basis(cert['local_per_call'], cert['inventory_per_call'], bad)
+    except Exception as error:
+        controls['perturbed_basis_pattern'] = str(error)[:120]
+    else:
+        raise AssertionError('perturbed basis accepted')
+    # a finer split of one idle rank-3 child into rank 1 + rank 2 (same rank mass) lowers the root strictly
+    # (concavity) and is not the optimum's profile
+    finer = dict(profile); finer[3] -= 1; finer[1] += 1; finer[2] += 1
+    assert sum(r * n for r, n in finer.items()) == sum(r * n for r, n in profile.items())
+    if not R.kappa_from_profile(finer, T)[1] < lo:
+        raise AssertionError('a finer idle split must fall strictly below the cap')
+    if finer == expected:
+        raise AssertionError('profile-equality check must reject a perturbed profile')
+    controls['finer_split_strictly_below_cap_and_rejected'] = 'PASS'
+    out = dict(status='PASS_LITERAL_ALLOCATION_ATTAINS_FIXED_INVENTORY_CAP', cap_lower=str(lo), cap_upper=str(hi),
+               tight_patterns=r['tight_patterns'], strict_patterns=r['strict_patterns'], idle_per_replica=r['idle_per_replica'],
+               profile={str(k): v for k, v in sorted(profile.items())}, controls=controls)
+    print(json.dumps(out, sort_keys=True))
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-extension-cap-fill/construction/T37-FLOW.json.gz b/research/paired-extension-cap-fill/construction/T37-FLOW.json.gz
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diff --git a/research/paired-extension-cap-fill/construction/T37-MODEL.json b/research/paired-extension-cap-fill/construction/T37-MODEL.json
new file mode 100644
index 0000000000..1f5dfa6783
--- /dev/null
+++ b/research/paired-extension-cap-fill/construction/T37-MODEL.json
@@ -0,0 +1 @@
+{"T":37,"catalogue":"tight","chronology":"pr2833-t37","constraints":78830,"flow_variables":94492,"groups":333,"nonzeros":361705,"pattern_variables":703,"patterns_per_cap":{"16":2,"32":4,"48":2,"8":1},"variables":95195,"workers":1}
\ No newline at end of file
diff --git a/research/paired-extension-cap-fill/construction/T37-PATTERNS.json b/research/paired-extension-cap-fill/construction/T37-PATTERNS.json
new file mode 100644
index 0000000000..cd4b0b3ecf
--- /dev/null
+++ b/research/paired-extension-cap-fill/construction/T37-PATTERNS.json
@@ -0,0 +1 @@
+{"T":37,"catalogue":"tight","chronology":"pr2833-t37","gain_vs_PR2917_claim_exact_lower":"9112592454726837520000000000000000000001000000000000000000000001/10000000000000000000000000000000000000000000000000000000000000000000000","gain_vs_PR2917_claim_float":9.112592454726837e-07,"gain_vs_PR2917_root_lower_float":9.112592454726837e-07,"gap_to_relaxation_cap":1e-25,"headline_floor24_minus":"17224999064432745643569999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000","idle":{"1":8658,"3":2997,"5":3441,"48":13579},"kappa_lower":"1722499906443274564357/1000000000000000000000000","kappa_lower_decimal":"0.001722499906443274564357","kappa_upper":"17224999064432745643571/10000000000000000000000000","kappa_upper_decimal":"0.0017224999064432745643571","mode":"milp","profile":{"1":813186,"2":213120,"3":96237,"4":36630,"5":12099,"8":2664,"48":13579},"relaxation_cap_lower":"1722499906443274564357/1000000000000000000000000","relaxation_cap_upper":"17224999064432745643571/10000000000000000000000000","relaxation_cap_upper_decimal":"0.0017224999064432745643571","target":[[8,[0,0,0,1,0],24864],[16,[0,0,0,2,0],3552],[16,[0,0,1,0,1],13024],[32,[0,0,0,0,3],3441],[32,[0,0,2,0,2],3811],[32,[0,1,0,0,3],666],[32,[1,0,0,0,3],8658],[48,[0,0,0,0,0],13579],[48,[0,0,0,0,5],2997]],"widths":[4,5,7,8,9]}
\ No newline at end of file
diff --git a/research/paired-extension-cap-fill/construction/T37-SOLVER.json b/research/paired-extension-cap-fill/construction/T37-SOLVER.json
new file mode 100644
index 0000000000..38938d4a67
--- /dev/null
+++ b/research/paired-extension-cap-fill/construction/T37-SOLVER.json
@@ -0,0 +1 @@
+{"T":37,"candidate":true,"catalogue":"tight","chronology":"pr2833-t37","hint_fill":null,"hint_flow":"../../../r12/vendor/pr2857/research/shared-kernel-repacking/allocation/construction/FLOW.json.gz","hint_zeros":true,"max_time_seconds":900,"seconds":267.91080689430237,"seed":7,"status":"OPTIMAL","workers":1}
\ No newline at end of file
diff --git a/research/paired-extension-cap-fill/construction/controls.py b/research/paired-extension-cap-fill/construction/controls.py
new file mode 100644
index 0000000000..08ee9f4653
--- /dev/null
+++ b/research/paired-extension-cap-fill/construction/controls.py
@@ -0,0 +1,75 @@
+#!/usr/bin/env python3
+"""controls.py -- independent re-verification of a produced allocation directory exactly the way #2917's check_allocation.py does:
+fresh load of the vendored PR2839 engine from #2917's package, owner.check(T, ORDER, FILL, DISPATCH, PROFILE(claimed), PLAN, TEMPLATE, PROVIDERS),
+the five semantic rejection controls (missing role, duplicate helper, same-call family collision, capacity overflow, changed paid profile),
+the 82-buffer physical display (live + 408 + 8 + 82 + 2), and #2917's own exact dyadic moment auditor tools/audit_allocation_moment.run
+(candidate = the directory, source = #2917's allocation/baseline = PR2908's pinned claim), plus root.py's bracket.
+Usage: python controls.py OUT_DIR [--chronology pr2833-t37|pr2917-t74|pr2833-t74]   (writes OUT_DIR/CONTROLS.json)"""
+import os, sys
+os.environ['PYTHONDONTWRITEBYTECODE'] = '1'
+sys.dont_write_bytecode = True
+import argparse, gzip, hashlib, json, pathlib, types, collections
+from fractions import Fraction as Q
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import root as R
+import relax as X
+import fill17 as F
+
+def load(name, path):
+    m = types.ModuleType(name); m.__file__ = str(path); sys.modules[name] = m
+    exec(compile(path.read_bytes(), str(path), 'exec'), m.__dict__); return m
+
+ap = argparse.ArgumentParser(); ap.add_argument('out', type=pathlib.Path); ap.add_argument('--chronology', default=None); a = ap.parse_args()
+out = a.out.resolve()
+assert hashlib.sha256(F.ENGINE.read_bytes()).hexdigest() == F.ENGINE_SHA
+owners = load('c1_owners', F.ENGINE)
+moment = load('c1_moment', F.PKG17 / 'tools/audit_allocation_moment.py')
+order, fill, raw_dispatch = F.read(out / 'ORDER.json'), F.read(out / 'FILL.json.gz'), F.read(out / 'DISPATCH.json')
+profile = F.read(out / 'PROFILE.json'); providers_raw = F.read(out / 'PROVIDERS.json')
+providers = {k: {'widths': v['widths'], 'actual_paid_profile': {int(r): n for r, n in v['actual_paid_profile'].items()}} for k, v in providers_raw.items()}
+# the provider registry must be exactly #2917's (same widths per id, same local profile)
+reg = F.read(F.PKG17 / 'allocation/PROVIDERS.json')
+assert {k: (v['widths'], {int(r): n for r, n in v['actual_paid_profile'].items()}) for k, v in reg.items()} == {k: (v['widths'], v['actual_paid_profile']) for k, v in providers.items()}, 'PROVIDERS differ from #2917'
+dispatch = {(s, r): p for s, r, p in raw_dispatch}; assert len(dispatch) == len(raw_dispatch)
+chron = a.chronology or json.load(open(out / 'OWNER-CHECK.json'))['chronology']
+template, plan, c_order, c_dispatch, T = F.load_chronology(chron)
+assert order == c_order and raw_dispatch == c_dispatch, 'ORDER/DISPATCH are not the %s chronology' % chron
+assert len(order) // 9 == T
+def check(candidate=fill, claimed=profile):
+    return owners.check(T, order, candidate, dispatch, claimed, plan, template, providers)
+result, _, _ = check()
+assert result['roles'] == 9 * T * 408
+physical = result['live'] + 408 + 8 + 82 + 2
+controls = {}
+def reject(name, candidate=fill, claimed=profile):
+    try:
+        check(candidate, claimed)
+    except ValueError as e:
+        controls[name] = str(e)
+    else:
+        raise AssertionError('owner corruption accepted: ' + name)
+reject('missing_role', {**fill, 'rows': fill['rows'][:-1]})
+first = fill['rows'][0]
+j = next(i for i, r in enumerate(fill['rows'][1:], 1) if r[0] == first[0])
+def mutate(index, row):
+    rows = list(fill['rows']); rows[index] = row; return {**fill, 'rows': rows}
+duplicate = list(fill['rows'][j]); duplicate[1] = first[1]; reject('duplicate_helper', mutate(j, duplicate))
+collision = list(fill['rows'][j]); collision[2:5] = first[2:5]; reject('same_call_family_collision', mutate(j, collision))
+overflow = list(first); overflow[5] = 49; reject('capacity_overflow', mutate(0, overflow))
+wrong = dict(profile); wrong['1'] = wrong.get('1', 0) + 1; reject('changed_paid_profile', claimed=wrong)
+# #2917's own exact dyadic moment auditor (source = its allocation/baseline = PR2908's pinned claim/profile/order)
+exact = moment.run(out, F.PKG17 / 'allocation/baseline')
+prof = {int(k): v for k, v in profile.items()}
+k_lo, k_hi = R.kappa_from_profile(prof, T)
+inv = collections.Counter(providers['gauge44']['widths'])
+rel = X.relax(providers['gauge44']['actual_paid_profile'], dict(inv))
+res = dict(status='PASS_C1_INDEPENDENT_RECHECK', chronology=chron, T=T, engine=result, physical=physical, controls=controls, moment=exact,
+           root_bracket=[str(k_lo), str(k_hi)], root_lower_decimal=R.mpmath_str(k_lo, 25), relaxation_cap=[rel['cap_lower'], rel['cap_upper']],
+           gain_vs_PR2917_claim=str(Q(exact['target']) - F.PR2917_KAPPA), gain_vs_PR2917_claim_float=float(Q(exact['target']) - F.PR2917_KAPPA),
+           target_vs_PR2917_claim_decimal=str(Q(exact['target']) - F.PR2917_KAPPA), headline_target=exact['target_decimal'],
+           fill_sha256=hashlib.sha256((out / 'FILL.json.gz').read_bytes()).hexdigest(), files_sha256={p.name: hashlib.sha256(p.read_bytes()).hexdigest() for p in sorted(out.iterdir()) if p.is_file()})
+(out / 'CONTROLS.json').write_text(json.dumps(res, sort_keys=True, indent=1, default=str) + '\n')
+print(json.dumps({k: res[k] for k in ['status', 'chronology', 'T', 'physical', 'root_lower_decimal', 'gain_vs_PR2917_claim_float', 'headline_target']}, indent=1))
+print('engine', result['roles'], result['idle'], 'rank_mass', result['rank_mass'])
+print('controls', {k: v for k, v in controls.items()})
+print('moment auditor', exact['status'], 'lower', exact['lower'], 'upper', exact['upper'], 'target', exact['target_decimal'][:40], 'gain vs PR2908', exact['gain_decimal'][:30])
diff --git a/research/paired-extension-cap-fill/construction/double.py b/research/paired-extension-cap-fill/construction/double.py
new file mode 100644
index 0000000000..7bb063b346
--- /dev/null
+++ b/research/paired-extension-cap-fill/construction/double.py
@@ -0,0 +1,48 @@
+#!/usr/bin/env python3
+"""double.py -- if #2917's T74 chronology is the exact interleaving of two copies of PR2833's T37 chronology
+(order74[2k] = order37[k], order74[2k+1] = (stage, replica+37), dispatch copied), a T37 fill doubles into a T74 fill
+on #2917's OWN chronology: row (t,h,o,c,p,z) -> (2t,h,o,c,p,z) and (2t+1,h,o+37,c,p,z).  Verified by the vendored engine.
+Usage: python double.py T37_DIR OUT_DIR"""
+import os, sys
+os.environ['PYTHONDONTWRITEBYTECODE'] = '1'
+sys.dont_write_bytecode = True
+import collections, hashlib, json, pathlib, types, time
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import root as R, relax as X, fill17 as F
+src, out = pathlib.Path(sys.argv[1]).resolve(), pathlib.Path(sys.argv[2]).resolve()
+out.mkdir(parents=True, exist_ok=False)
+owner = types.ModuleType('frozen_owner'); exec(compile(F.ENGINE.read_bytes(), 'frozen_owner', 'exec'), owner.__dict__)
+t37 = F.load_chronology('pr2833-t37'); t74 = F.load_chronology('pr2917-t74')
+order37, disp37 = t37[2], {(s, r): p for s, r, p in t37[3]}
+template, plan, order74, dispatch74, T = t74
+disp74 = {(s, r): p for s, r, p in dispatch74}
+ok_order = all(order74[2 * k] == order37[k] and order74[2 * k + 1] == [order37[k][0], order37[k][1] + 37] for k in range(333))
+ok_disp = all(disp74[(s, r)] == disp37[(s, r)] and disp74[(s, r + 37)] == disp37[(s, r)] for s, r in map(tuple, order37))
+print('order74 == interleave(order37, order37+37):', ok_order, '; dispatch copied:', ok_disp)
+assert ok_order and ok_disp
+fill37 = F.read(src / 'FILL.json.gz')
+providers = F.load_providers(F.PKG17 / 'allocation/PROVIDERS.json')
+assert F.read(src / 'PROVIDERS.json')['gauge44']['widths'] == providers['gauge44']['widths']
+rows = []
+for t, h, o, c, p, z in fill37['rows']:
+    rows.append([2 * t, h, o, c, p, z]); rows.append([2 * t + 1, h, o + 37, c, p, z])
+fill = {'columns': fill37['columns'], 'dispatch_overrides': [], 'method': fill37.get('method', '') + ' | doubled from the T37 fill onto #2917 T74 chronology (order74 = interleave of two T37 copies; double.py)', 'rows': sorted(rows)}
+t0 = time.time()
+result, _, _ = owner.check(T, order74, fill, disp74, None, plan, template, providers)
+print('engine PASS in %.1f s' % (time.time() - t0), result['roles'], result['idle'], 'rank_mass', result['rank_mass'], 'live', result['live'])
+profile = {int(k): v for k, v in result['profile'].items()}
+prof37 = {int(k): v for k, v in F.read(src / 'PROFILE.json').items()}
+assert profile == {r: 2 * n for r, n in prof37.items()}, 'profile is not 2x the T37 profile'
+inv = collections.Counter(providers['gauge44']['widths'])
+rel = X.relax(providers['gauge44']['actual_paid_profile'], dict(inv))
+k_lo, k_hi, pr = F.price(profile, T, rel)
+prov_out = {pid: {'actual_paid_profile': {str(r): n for r, n in providers[pid]['actual_paid_profile'].items()}, 'widths': providers[pid]['widths']} for pid in providers}
+payload_sha = {}
+for n, obj in [('ORDER.json', order74), ('FILL.json.gz', fill), ('DISPATCH.json', dispatch74), ('PROFILE.json', {str(k): v for k, v in sorted(profile.items())}), ('PROVIDERS.json', prov_out)]:
+    F.save(out / n, obj); payload_sha[n] = hashlib.sha256(json.dumps(obj, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+check = dict(result, status='PASS_VENDORED_PR2839_OWNER_ENGINE_CHECK', solver='DOUBLED_FROM_T37_FILL ' + str(src), chronology='pr2917-t74', T=T, calls=len(order74),
+             physical=result['live'] + 408 + 8 + 82 + 2, physical_formula='live + 408 helpers + 8 centres + 82 private buffers + 2 guards',
+             inventory={pid: dict(sorted(inv.items())) for pid in providers}, local=providers['gauge44']['actual_paid_profile'], engine_sha256=F.ENGINE_SHA, payload_sha256=payload_sha, **pr)
+F.save(out / 'OWNER-CHECK.json', check)
+print('physical', check['physical'], 'KAPPA', pr['kappa_lower_decimal'], '..', pr['kappa_upper_decimal'], 'cap', rel['cap_upper_decimal'], 'gap %.3e' % pr['gap_to_relaxation_cap'], 'gain vs PR2917 claim %.6e' % pr['gain_vs_PR2917_claim_float'])
+print('payload sha', payload_sha)
diff --git a/research/paired-extension-cap-fill/construction/fill17.py b/research/paired-extension-cap-fill/construction/fill17.py
new file mode 100644
index 0000000000..01775cdaff
--- /dev/null
+++ b/research/paired-extension-cap-fill/construction/fill17.py
@@ -0,0 +1,552 @@
+#!/usr/bin/env python3
+"""fill17.py -- lane C's fill.py (r12) adapted to PR #2917's words: literal owner allocation for #2917's exact
+per-provider widths (allocation/PROVIDERS.json) under a chosen chronology, with the integer pattern mix of relax.py,
+CP-SAT (single thread), edge-colouring realization, the vendored PR2839 owner engine (sha 77a84872..., the same file
+#2917 ships in allocation/vendor/) and root.py's exact bracket.  Also replays/prices any literal fill (--check-fill).
+
+Chronologies:
+  pr2833-t37 : PR2833 T37 owners chronology (333 calls) as used by PR2857/lane C (template/plan from PR2857 sources)
+  pr2833-t74 : PR2833 borrow-fill chronology (666 calls)
+  pr2917-t74 : #2917's own allocation/ORDER.json + DISPATCH.json (666 calls; = PR2908's, 'inherited chronology')
+Template and plan payloads are byte-identical across the packages (decompressed sha 514e5931..., 163431bf...).
+
+Usage (AGI venv = OR-Tools 9.15; num_search_workers MUST be 1 on this machine):
+  $AGI -B fill17.py --work OUT/x --chronology pr2833-t37 --catalogue tight --hint-flow PR2857/FLOW.json.gz --hint-zeros --seed 7 --seconds 900
+  $AGI -B fill17.py --work OUT/x --chronology pr2917-t74 --catalogue tight --hint-fill PR2917/allocation/FILL.json.gz --hint-zeros
+  $AGI -B fill17.py --work OUT/x --chronology pr2917-t74 --check-fill PR2917/allocation/FILL.json.gz   (replay + price)
+  --mix-only : stop after the pattern mix and its exact kappa (fill-independent)
+  --mix-file PATTERNS.json : use a given target mix (list of [cap, counts, n]) instead of the milp
+Outputs: PATTERNS.json, MODEL.json, SOLVER.json, FLOW.json.gz, ORDER.json, FILL.json.gz, DISPATCH.json, PROFILE.json,
+  PROVIDERS.json (= #2917's allocation format), OWNER-CHECK.json (engine result, physical stock, exact bracket, cap, gains).
+"""
+import os, sys
+os.environ['PYTHONDONTWRITEBYTECODE'] = '1'
+sys.dont_write_bytecode = True
+import argparse, collections, gzip, hashlib, json, pathlib, time, types
+from fractions import Fraction as Q
+import numpy as np
+from scipy.sparse import coo_matrix, csr_matrix
+from scipy.sparse.csgraph import maximum_bipartite_matching
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import root as R
+import relax as X
+
+SCR = pathlib.Path('S')
+PKG17 = SCR / 'r13/vendor/pr2917/research/paired-helper-extension'
+PKG57 = SCR / 'r12/vendor/pr2857/research/shared-kernel-repacking'
+P33 = SCR / 'r12/vendor/pr2833/research/gmx-t74-borrow43-handoff'
+ENGINE = PKG17 / 'allocation/vendor/independent_owners.py'
+ENGINE_SHA = '77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461'
+PR2917_KAPPA = Q('17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000')
+PR2917_ROOT_LOWER = Q('1721588647197801880605/1000000000000000000000000')   # floor of its root at 24 digits (CLAIM complex_lower = 344317729439560376121/2e23)
+PRIVATE_BUFFERS = 82
+HELPERS = 408
+CENTRES = 8
+GUARDS = 2
+
+
+def read(p):
+    b = pathlib.Path(p).read_bytes()
+    return json.loads(gzip.decompress(b) if b[:2] == b'\x1f\x8b' else b)
+
+
+def save(p, x):
+    b = json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+    if str(p).endswith('.gz'):
+        b = bytearray(gzip.compress(b, mtime=0))
+        b[9] = 255
+        b = bytes(b)
+    pathlib.Path(p).write_bytes(b)
+
+
+def log(*a):
+    print(*a, flush=True)
+
+
+def load_chronology(name):
+    if name == 'pr2833-t37':
+        template = read(PKG57 / 'sources/PR2833-T37-TEMPLATE.json.gz')
+        plan = read(PKG57 / 'sources/PR2833-PLAN.json.gz')
+        owners = read(PKG57 / 'sources/PR2833-T37-OWNERS.json.gz')
+        T = 37
+        timecalls = {}
+        for r in owners:
+            key, call = r['time'], (r['stage'], r['replica'])
+            assert key not in timecalls or timecalls[key] == call
+            timecalls[key] = call
+        assert set(timecalls) == set(range(9 * T))
+        order = [list(timecalls[t]) for t in range(9 * T)]
+        dispatch = read(PKG57 / 'sources/PR2833-T37-DISPATCH.json')
+    elif name == 'pr2833-t74':
+        template = read(PKG57 / 'sources/PR2833-T37-TEMPLATE.json.gz')
+        plan = read(PKG57 / 'sources/PR2833-PLAN.json.gz')
+        order = read(P33 / 'new/borrow-fill/ORDER.json')
+        dispatch = read(P33 / 'new/borrow-fill/DISPATCH.json')
+        T = 74
+    elif name == 'pr2917-t74':
+        template = read(PKG17 / 'allocation/vendor/TEMPLATE.json.gz')
+        plan = read(PKG17 / 'allocation/vendor/PLAN.json.gz')
+        order = read(PKG17 / 'allocation/ORDER.json')
+        dispatch = read(PKG17 / 'allocation/DISPATCH.json')
+        T = 74
+    else:
+        raise SystemExit('unknown chronology ' + name)
+    assert {(s, r) for s, r, p in dispatch} == set(map(tuple, order)) and len(order) == 9 * T and len(dispatch) == 9 * T
+    return template, plan, order, dispatch, T
+
+
+def load_providers(path, local_override=None):
+    providers = read(path)
+    out = {}
+    for pid, v in providers.items():
+        widths = [int(w) for w in v['widths']]
+        assert len(widths) == HELPERS
+        local = {int(k): int(n) for k, n in v['actual_paid_profile'].items()}
+        if local_override is not None:
+            local = dict(local_override)
+        local = {k: n for k, n in sorted(local.items()) if n}
+        assert sum(r * n for r, n in local.items()) - sum(widths) == 1856, 'local mass - width mass != 1856 for ' + pid
+        out[pid] = {'widths': widths, 'actual_paid_profile': local}
+    return out
+
+
+def integer_pattern_mix(inv_by_call, T, bins_per_replica, cap_root, catalogue, tight):
+    widths = sorted({w for inv in inv_by_call for w in inv})
+    bins = {c: n * T for c, n in bins_per_replica.items()}
+    demand = collections.Counter()
+    for inv in inv_by_call:
+        for w, n in inv.items():
+            demand[w] += n
+    from scipy.optimize import milp, Bounds, LinearConstraint
+    pats = X.patterns(bins_per_replica, widths)
+    if catalogue == 'tight':
+        keep = {(t['capacity'], tuple(t['widths'].count(w) for w in widths)) for t in tight}
+        for cap in bins:
+            for i, w in enumerate(widths):
+                if w <= cap:
+                    keep.add((cap, tuple(int(j == i) for j in range(len(widths)))))
+            keep.add((cap, tuple(0 for _ in widths)))
+        pats = [p for p in pats if (p[0], p[1]) in keep]
+    elif catalogue == 'tightonly':
+        keep = {(t['capacity'], tuple(t['widths'].count(w) for w in widths)) for t in tight}
+        pats = [p for p in pats if (p[0], p[1]) in keep]
+    caps = sorted(bins)
+    b = float(cap_root)
+    c = np.array([X.Hfloat(r, b) for cap, counts, r in pats])
+    A = np.zeros((len(caps) + len(widths), len(pats)))
+    for j, (cap, counts, r) in enumerate(pats):
+        A[caps.index(cap), j] = 1.0
+        for i, n in enumerate(counts):
+            A[len(caps) + i, j] = n
+    rhs = np.array([float(bins[cap]) for cap in caps] + [float(demand[w]) for w in widths])
+    res = milp(c, integrality=np.ones(len(pats)), bounds=Bounds(0, np.inf), constraints=LinearConstraint(A, rhs, rhs), options={'time_limit': 120, 'mip_rel_gap': 0})
+    assert res.x is not None, 'integer pattern mix infeasible: ' + str(res.message)
+    xi = np.rint(res.x).astype(np.int64)
+    assert np.max(np.abs(xi - res.x)) < 1e-6 and np.all(A @ xi == rhs)
+    target = {(pats[j][0], pats[j][1]): int(xi[j]) for j in range(len(pats)) if xi[j]}
+    return target, widths
+
+
+def color_pattern(n, q, counts, WID):
+    slots = [w for j, w in enumerate(WID) for _ in range(q[j])]
+    if not slots:
+        assert not counts
+        return [[] for _ in range(n)]
+    times = sorted({t for t, w in counts})
+    K = len(times)
+    assert K >= len(slots)
+    ti = {t: j for j, t in enumerate(times)}
+    A = np.zeros((K, K), dtype=np.int64)
+    slot_by_w = collections.defaultdict(list)
+    for j, w in enumerate(slots):
+        slot_by_w[w].append(j)
+    for w, js in slot_by_w.items():
+        atslot = 0
+        remaining = n
+        for t in times:
+            needed = counts.get((t, w), 0)
+            while needed:
+                take = min(needed, remaining)
+                A[ti[t], js[atslot]] += take
+                needed -= take
+                remaining -= take
+                if remaining == 0:
+                    atslot += 1
+                    remaining = n
+        assert atslot == len(js)
+    assert all(v <= n for v in A.sum(axis=1))
+    j = len(slots)
+    remaining = n
+    for r in range(K):
+        needed = n - int(A[r].sum())
+        while needed:
+            assert j < K
+            take = min(needed, remaining)
+            A[r, j] += take
+            needed -= take
+            remaining -= take
+            if remaining == 0:
+                j += 1
+                remaining = n
+    assert np.all(A.sum(axis=0) == n) and np.all(A.sum(axis=1) == n)
+    output = []
+    for color in range(n):
+        matching = maximum_bipartite_matching(csr_matrix(A > 0), perm_type='column')
+        assert len(matching) == K and min(matching) >= 0 and len(set(map(int, matching))) == K
+        output.append([(times[r], slots[int(c)]) for r, c in enumerate(matching) if c < len(slots)])
+        A[np.arange(K), matching] -= 1
+    assert not A.any()
+    return output
+
+
+def pattern_name(WID, counts):
+    return '+'.join(str(w) for w, k in zip(WID, counts) for _ in range(k)) or 'empty'
+
+
+def fill_to_bins(fill, order, disp, providers):
+    """literal fill rows -> {bin: [(t, w)]} using the provider widths (helper column = 0-based index, as the engine reads it)."""
+    bybin = collections.defaultdict(list)
+    for t, h, o, c, p, z in fill['rows']:
+        w = providers[disp[tuple(order[t])]]['widths'][h]
+        bybin[o, c, p].append((t, w))
+    return bybin
+
+
+def price(profile, T, rel):
+    k_lo, k_hi = R.kappa_from_profile(profile, T)
+    cap_hi = Q(rel['cap_upper'])
+    return k_lo, k_hi, dict(kappa_lower=str(k_lo), kappa_upper=str(k_hi), kappa_lower_decimal=R.mpmath_str(k_lo, 25), kappa_upper_decimal=R.mpmath_str(k_hi, 25),
+                            headline_floor24_minus=str(Q(int(k_lo * 10 ** 24), 10 ** 24) - Q(1, 10 ** 46) - Q(1, 10 ** 70)),
+                            relaxation_cap_lower=rel['cap_lower'], relaxation_cap_upper=rel['cap_upper'], relaxation_cap_upper_decimal=rel['cap_upper_decimal'],
+                            gap_to_relaxation_cap=float(cap_hi - k_lo), gain_vs_PR2917_claim_float=float(k_lo - PR2917_KAPPA), gain_vs_PR2917_root_lower_float=float(k_lo - PR2917_ROOT_LOWER),
+                            gain_vs_PR2917_claim_exact_lower=str(k_lo - PR2917_KAPPA))
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter)
+    ap.add_argument('--work', type=pathlib.Path, required=True)
+    ap.add_argument('--chronology', choices=['pr2833-t37', 'pr2833-t74', 'pr2917-t74'], default='pr2833-t37')
+    ap.add_argument('--providers', type=pathlib.Path, default=PKG17 / 'allocation/PROVIDERS.json')
+    ap.add_argument('--local', help='JSON per-call local profile overriding PROVIDERS (both providers)')
+    ap.add_argument('--catalogue', choices=['all', 'tight', 'tightonly'], default='tight')
+    ap.add_argument('--mix-file', type=pathlib.Path, help='PATTERNS.json-style target list [[cap, counts, n], ...] to use instead of the milp')
+    ap.add_argument('--mix-only', action='store_true')
+    ap.add_argument('--seconds', type=int, default=600)
+    ap.add_argument('--workers', type=int, default=1)
+    ap.add_argument('--seed', type=int, default=124)
+    ap.add_argument('--hint-flow', type=pathlib.Path, help='FLOW.json.gz of the same chronology/T (e.g. PR2857 allocation/construction/FLOW.json.gz for pr2833-t37)')
+    ap.add_argument('--hint-fill', type=pathlib.Path, help='literal FILL.json.gz of the same chronology (e.g. #2917 allocation/FILL.json.gz for pr2917-t74); converted to X/Z hints')
+    ap.add_argument('--hint-zeros', action='store_true')
+    ap.add_argument('--reuse-flow', type=pathlib.Path)
+    ap.add_argument('--solver', choices=['cp', 'highs-lp', 'highs-mip'], default='cp', help='cp = CP-SAT; highs-lp = LP relaxation feasibility only (fractional flow); highs-mip = scipy milp')
+    ap.add_argument('--check-fill', type=pathlib.Path, help='replay: owner-check and price this literal fill under the chronology (no solve)')
+    ap.add_argument('--method', default='r13 lane C1: relax.py integer pattern mix + CP-SAT chronological flow + edge-colouring realization (fill17.py)')
+    a = ap.parse_args()
+    assert a.workers == 1, 'num_search_workers must be 1 on this machine (3 deadlocks)'
+    out = a.work.resolve()
+    out.mkdir(parents=True, exist_ok=False)
+    t0 = time.time()
+    assert hashlib.sha256(ENGINE.read_bytes()).hexdigest() == ENGINE_SHA, 'owner engine pin'
+    owner = types.ModuleType('frozen_owner')
+    exec(compile(ENGINE.read_bytes(), 'frozen_owner', 'exec'), owner.__dict__)
+    template, plan, order, dispatch, T = load_chronology(a.chronology)
+    local_override = {int(k): int(v) for k, v in json.loads(a.local).items()} if a.local else None
+    providers = load_providers(a.providers, local_override)
+    disp = {(s, r): p for s, r, p in dispatch}
+    inv_by_call = [collections.Counter(providers[disp[tuple(sr)]]['widths']) for sr in order]
+    calls_by_pid = collections.Counter(disp[tuple(sr)] for sr in order)
+    locals_ = {pid: providers[pid]['actual_paid_profile'] for pid in providers}
+    # relaxation cap (call-weighted average inventory; the local profile is the same for both providers here)
+    avg_inv = collections.Counter()
+    for inv in inv_by_call:
+        for w, n in inv.items():
+            avg_inv[w] += Q(n, len(order))
+    loc0 = next(iter(locals_.values()))
+    assert all(l == loc0 for l in locals_.values()), 'providers differ in local profile; relax.py needs one profile'
+    rel = X.relax(loc0, avg_inv)
+    cap_lo, cap_hi = Q(rel['cap_lower']), Q(rel['cap_upper'])
+    log('CHRONOLOGY', a.chronology, 'T', T, 'calls', len(order), 'calls per provider', dict(calls_by_pid))
+    log('INVENTORY', {pid: dict(sorted(collections.Counter(providers[pid]['widths']).items())) for pid in providers}, 'LOCAL', loc0)
+    log('RELAX cap', rel['cap_lower_decimal'], rel['cap_upper_decimal'], 'tight', rel['tight_patterns'], 'idle/replica', rel['idle_per_replica'])
+    live = 896 * T
+    physical = live + HELPERS + CENTRES + PRIVATE_BUFFERS + GUARDS
+
+    if a.check_fill:
+        fill = read(a.check_fill)
+        result, _, _ = owner.check(T, order, fill, disp, None, plan, template, providers)
+        profile = {int(k): v for k, v in result['profile'].items()}
+        k_lo, k_hi, pr = price(profile, T, rel)
+        bybin = fill_to_bins(fill, order, disp, providers)
+        pat_hist = collections.Counter()
+        win = owner.windows(template, order, T)
+        for (o, c), (cap, lo, hi) in win.items():
+            for port in range(112):
+                rs = bybin.get((o, c, port), [])
+                pat_hist['%d:%s' % (cap, '+'.join(str(w) for w in sorted(w for t, w in rs)) or 'empty')] += 1
+        assert result['live'] == live
+        check = dict(result, status='PASS_VENDORED_PR2839_OWNER_ENGINE_CHECK', mode='check-fill', fill=str(a.check_fill), chronology=a.chronology, T=T,
+                     physical=result['live'] + HELPERS + CENTRES + PRIVATE_BUFFERS + GUARDS, physical_expected=physical, pattern_histogram=dict(sorted(pat_hist.items())), **pr)
+        save(out / 'OWNER-CHECK.json', check)
+        save(out / 'PROFILE.json', dict(sorted(profile.items())))
+        log('CHECK-FILL PASS roles', result['roles'], 'idle', result['idle'], 'physical', check['physical'])
+        log('PATTERNS', dict(sorted(pat_hist.items())))
+        log('KAPPA', pr['kappa_lower_decimal'], '..', pr['kappa_upper_decimal'], 'cap', rel['cap_upper_decimal'], 'gap %.3e' % pr['gap_to_relaxation_cap'], 'gain vs PR2917 claim %.4e' % pr['gain_vs_PR2917_claim_float'])
+        return
+
+    bins_per_replica = X.BINS
+    if a.mix_file:
+        mf = read(a.mix_file)
+        WID = [int(w) for w in mf['widths']]
+        target = {(int(cap), tuple(int(k) for k in counts)): int(n) for cap, counts, n in mf['target']}
+    else:
+        target, WID = integer_pattern_mix(inv_by_call, T, bins_per_replica, (cap_lo + cap_hi) / 2, a.catalogue, rel['tight_pattern_list'])
+    idle_mix = collections.Counter()
+    for (cap, counts), n in target.items():
+        r = cap - sum(w * k for w, k in zip(WID, counts))
+        assert r >= 0
+        if r:
+            idle_mix[r] += n
+    profile_mix = collections.Counter(idle_mix)
+    for pid, ncalls in calls_by_pid.items():
+        for r, n in locals_[pid].items():
+            profile_mix[r] += n * ncalls
+    mix_lo, mix_hi, mix_pr = price(dict(profile_mix), T, rel)
+    log('PATTERN MIX', {('%d:%s' % (cap, pattern_name(WID, counts))): n for (cap, counts), n in sorted(target.items())})
+    log('MIX kappa bracket', mix_pr['kappa_lower_decimal'], mix_pr['kappa_upper_decimal'], 'idle', dict(sorted(idle_mix.items())), 'gap to cap %.3e' % mix_pr['gap_to_relaxation_cap'], 'gain vs PR2917 %.4e' % mix_pr['gain_vs_PR2917_claim_float'])
+    save(out / 'PATTERNS.json', dict(mode='milp' if not a.mix_file else 'file', catalogue=a.catalogue, T=T, chronology=a.chronology, widths=WID,
+                                     target=[[cap, list(counts), n] for (cap, counts), n in sorted(target.items())], idle=dict(sorted(idle_mix.items())),
+                                     profile=dict(sorted(profile_mix.items())), **mix_pr))
+    if a.mix_only:
+        return
+
+    # ---- chronology windows and the flow model (PR2857 discover_original.py, all bins active)
+    win = owner.windows(template, order, T)
+    family = lambda b: b[0] * 896 + (2 * plan['pairs'][str(b[1])] + plan['sides'][str(b[1])]) * 112 + b[2]
+    fw = collections.defaultdict(list)
+    for (o, c), (cap, lo, hi) in win.items():
+        fw[family((o, c, 0))].append((lo, hi, c))
+    for ww in fw.values():
+        for i, (lo, hi, c) in enumerate(ww):
+            assert all(max(lo, l) >= min(hi, h) for l, h, d in ww[i + 1:]), 'overlapping same-family windows'
+    need = {t: collections.Counter(inv_by_call[t]) for t in range(len(order))}
+    pats = collections.defaultdict(list)
+    for (cap, counts) in target:
+        pats[cap].append(counts)
+    groups = collections.defaultdict(list)
+    for (o, c), (cap, lo, hi) in win.items():
+        for port in range(112):
+            groups[cap, tuple(range(max(0, lo + 1), min(len(order), hi + 1)))].append((o, c, port))
+    G = sorted(groups)
+    groupof = {b: gi for gi, g in enumerate(G) for b in groups[g]}
+    edge, lb, ub, rl, ru = [], [], [], [], []
+    Xv, Zv = {}, {}
+
+    def cr(l, u=None):
+        j = len(rl)
+        rl.append(l)
+        ru.append(l if u is None else u)
+        return j
+
+    def cv(u):
+        j = len(lb)
+        lb.append(0)
+        ub.append(u)
+        return j
+
+    def put(r, v, n):
+        if n:
+            edge.append((r, v, n))
+    callrow = {(t, w): cr(n) for t, cnt in need.items() for w, n in cnt.items() if n}
+    globalrow = {key: cr(n) for key, n in target.items()}
+    for gi, (cap, ts) in enumerate(G):
+        nb = len(groups[G[gi]])
+        br = cr(nb)
+        for q in pats[cap]:
+            xv = cv(nb)
+            Xv[gi, q] = xv
+            put(br, xv, 1)
+            put(globalrow[cap, q], xv, 1)
+            residual = {w: q[j] for j, w in enumerate(WID) if q[j]}
+            wr = {w: cr(0) for w in residual}
+            for w, n in residual.items():
+                put(wr[w], xv, -n)
+            for t in ts:
+                tr = cr(-nb, 0)
+                put(tr, xv, -1)
+                for w in residual:
+                    if (t, w) not in callrow:
+                        continue
+                    zv = cv(min(nb, need[t][w]))
+                    Zv[gi, q, t, w] = zv
+                    put(tr, zv, 1)
+                    put(wr[w], zv, 1)
+                    put(callrow[t, w], zv, 1)
+    modelinfo = dict(T=T, chronology=a.chronology, groups=len(G), variables=len(lb), pattern_variables=len(Xv), flow_variables=len(Zv), constraints=len(rl), nonzeros=len(edge), workers=a.workers,
+                     catalogue=a.catalogue, patterns_per_cap={str(cap): len(ps) for cap, ps in pats.items()})
+    save(out / 'MODEL.json', modelinfo)
+    log('MODEL', modelinfo)
+    rr = np.fromiter((e[0] for e in edge), np.int32)
+    cc = np.fromiter((e[1] for e in edge), np.int32)
+    vv = np.fromiter((e[2] for e in edge), np.float64)
+    mat = coo_matrix((vv, (rr, cc)), shape=(len(rl), len(lb))).tocsr()
+    del edge
+    t1 = time.time()
+    if a.reuse_flow:
+        saved = read(a.reuse_flow)
+        value = np.zeros(len(lb), dtype=np.int64)
+        for gi, q, n in saved['x']:
+            value[Xv[gi, tuple(q)]] = n
+        for gi, q, t, w, n in saved['z']:
+            value[Zv[gi, tuple(q), t, w]] = n
+        status = 'EXACT_FLOW_REPLAY'
+    elif a.solver == 'highs-lp':
+        from scipy.optimize import milp, Bounds, LinearConstraint
+        r = milp(np.zeros(len(lb)), integrality=np.zeros(len(lb)), bounds=Bounds(np.array(lb, dtype=float), np.array(ub, dtype=float)), constraints=LinearConstraint(mat, np.array(rl, dtype=float), np.array(ru, dtype=float)), options={'time_limit': a.seconds, 'disp': True})
+        status = 'LP_RELAXATION_' + ('FEASIBLE' if r.x is not None else 'INFEASIBLE_OR_FAILED') + ': ' + str(r.message)
+        log('LP RELAXATION', status, '%.1f s' % (time.time() - t1))
+        save(out / 'SOLVER.json', dict(status=status, solver='highs-lp', seconds=time.time() - t1, chronology=a.chronology, T=T, catalogue=a.catalogue, mix_file=str(a.mix_file) if a.mix_file else None))
+        return
+    elif a.solver == 'highs-mip':
+        from scipy.optimize import milp, Bounds, LinearConstraint
+        r = milp(np.zeros(len(lb)), integrality=np.ones(len(lb)), bounds=Bounds(np.array(lb, dtype=float), np.array(ub, dtype=float)), constraints=LinearConstraint(mat, np.array(rl, dtype=float), np.array(ru, dtype=float)), options={'time_limit': a.seconds, 'mip_rel_gap': 0, 'disp': True})
+        status = str(r.message)
+        value = None if r.x is None else np.rint(r.x).astype(np.int64)
+    else:
+        from ortools.sat.python import cp_model
+        model = cp_model.CpModel()
+        vs = [model.NewIntVar(int(l), int(u), '') for l, u in zip(lb, ub)]
+        for j, (l, u) in enumerate(zip(rl, ru)):
+            b, e = mat.indptr[j:j + 2]
+            ind = mat.indices[b:e]
+            co = mat.data[b:e]
+            model.AddLinearConstraint(cp_model.LinearExpr.WeightedSum([vs[int(k)] for k in ind], [int(k) for k in co]), int(l), int(u))
+        hinted = {}
+        if a.hint_flow:
+            saved = read(a.hint_flow)
+            for gi, q, n in saved['x']:
+                if (gi, tuple(q)) in Xv:
+                    hinted[Xv[gi, tuple(q)]] = min(int(n), int(ub[Xv[gi, tuple(q)]]))
+            for gi, q, t, w, n in saved['z']:
+                if (gi, tuple(q), t, w) in Zv:
+                    hinted[Zv[gi, tuple(q), t, w]] = min(int(n), int(ub[Zv[gi, tuple(q), t, w]]))
+            log('HINT from flow', a.hint_flow, 'variables', len(hinted), 'of', len(vs))
+        if a.hint_fill:
+            hf = read(a.hint_fill)
+            bybin = fill_to_bins(hf, order, disp, providers)
+            hx = collections.Counter()
+            hz = collections.Counter()
+            missing = collections.Counter()
+            for gi_, g_ in enumerate(G):
+                for b in groups[g_]:
+                    rs = bybin.get(b, [])
+                    q = tuple(sum(1 for t, w in rs if w == ww) for ww in WID)
+                    if (gi_, q) not in Xv:
+                        missing['%d:%s' % (G[gi_][0], pattern_name(WID, q))] += 1
+                        continue
+                    hx[gi_, q] += 1
+                    for t, w in rs:
+                        hz[gi_, q, t, w] += 1
+            for k, n in hx.items():
+                hinted[Xv[k]] = min(n, int(ub[Xv[k]]))
+            for k, n in hz.items():
+                if k in Zv:
+                    hinted[Zv[k]] = min(n, int(ub[Zv[k]]))
+            log('HINT from fill', a.hint_fill, 'bins hinted', sum(hx.values()), 'bins with non-catalogue patterns (unhinted)', sum(missing.values()), dict(missing.most_common(12)), 'variables', len(hinted))
+        if hinted:
+            for j, v in hinted.items():
+                model.AddHint(vs[j], v)
+            if a.hint_zeros:
+                for j in range(len(vs)):
+                    if j not in hinted:
+                        model.AddHint(vs[j], 0)
+            log('HINT total', len(hinted), '(+ zeros for the rest)' if a.hint_zeros else '')
+        solver = cp_model.CpSolver()
+        solver.parameters.num_search_workers = a.workers
+        solver.parameters.max_time_in_seconds = a.seconds
+        solver.parameters.random_seed = a.seed
+        solver.parameters.log_search_progress = True
+        result = solver.Solve(model)
+        status = solver.StatusName(result)
+        value = np.array([solver.Value(v) for v in vs], dtype=np.int64) if result in (cp_model.OPTIMAL, cp_model.FEASIBLE) else None
+        log(solver.ResponseStats())
+    solve_seconds = time.time() - t1
+    log('SOLVER', status, '%.1f s' % solve_seconds)
+    save(out / 'SOLVER.json', dict(status=status, seconds=solve_seconds, workers=a.workers, seed=a.seed, max_time_seconds=a.seconds, candidate=value is not None, chronology=a.chronology, T=T, catalogue=a.catalogue,
+                                   hint_flow=str(a.hint_flow) if a.hint_flow else None, hint_fill=str(a.hint_fill) if a.hint_fill else None, hint_zeros=a.hint_zeros))
+    if value is None:
+        log('NO FEASIBLE FLOW (status %s)' % status)
+        raise SystemExit(2)
+    assert not (np.any(value < lb) or np.any(value > ub) or np.any(mat @ value < rl) or np.any(mat @ value > ru))
+    xc = collections.defaultdict(collections.Counter)
+    zc = collections.defaultdict(collections.Counter)
+    for (gi, q), v in Xv.items():
+        if value[v]:
+            xc[gi][q] = int(value[v])
+    for (gi, q, t, w), v in Zv.items():
+        if value[v]:
+            zc[gi, q][t, w] = int(value[v])
+    save(out / 'FLOW.json.gz', {'x': [[gi, list(q), n] for gi, c in xc.items() for q, n in c.items()], 'z': [[gi, list(q), t, w, n] for (gi, q), c in zc.items() for (t, w), n in c.items()]})
+    gc = collections.Counter()
+    for gi, c in xc.items():
+        for q, n in c.items():
+            gc[G[gi][0], q] += n
+    assert dict(gc) == target, 'global integer pattern counts differ'
+    for gi in range(len(G)):
+        assert sum(xc[gi].values()) == len(groups[G[gi]]), 'window class bin count'
+    call_count = collections.defaultdict(collections.Counter)
+    for (gi, q), c in zc.items():
+        by_w = collections.Counter()
+        by_t = collections.Counter()
+        for (t, w), n in c.items():
+            assert t in G[gi][1] and q[WID.index(w)] > 0, 'ineligible time/width flow'
+            by_w[w] += n
+            by_t[t] += n
+            call_count[t][w] += n
+        assert all(by_w[w] == q[j] * xc[gi][q] for j, w in enumerate(WID)), 'pattern-width supply'
+        assert all(n <= xc[gi][q] for n in by_t.values()), 'more than one role per bin/time'
+    assert all(call_count[t] == need[t] for t in range(len(order))), 'flow call width demand'
+    slots = []
+    for gi, (cap, ts) in enumerate(G):
+        bins = groups[G[gi]]
+        offset = 0
+        for q, n in sorted(xc[gi].items()):
+            res = color_pattern(n, q, zc[gi, q], WID)
+            assert len(res) == n
+            for b, it in zip(bins[offset:offset + n], res):
+                z = 0
+                for t, w in sorted(it):
+                    slots.append((t, w, *b, z))
+                    z += w
+                assert z <= cap
+            offset += n
+        assert offset == len(bins)
+    available = {t: collections.defaultdict(list) for t in range(len(order))}
+    for t in available:
+        for h, w in enumerate(providers[disp[tuple(order[t])]]['widths']):
+            available[t][w].append(h)
+    final = []
+    for t, w, o, c, p, z in sorted(slots):
+        final.append([t, available[t][w].pop(), o, c, p, z])
+    assert not any(v for d in available.values() for v in d.values())
+    fill = {'columns': ['time', 'helper', 'owner_replica', 'child', 'port', 'offset'], 'dispatch_overrides': [], 'method': a.method, 'rows': sorted(final)}
+    result, _, _ = owner.check(T, order, fill, disp, None, plan, template, providers)
+    profile = {int(k): v for k, v in result['profile'].items()}
+    assert collections.Counter(profile) == profile_mix, 'realized profile differs from the pattern-mix profile'
+    assert result['live'] == live
+    k_lo, k_hi, pr = price(profile, T, rel)
+    payload_sha = {}
+    prov_out = {pid: {'actual_paid_profile': {str(r): n for r, n in providers[pid]['actual_paid_profile'].items()}, 'widths': providers[pid]['widths']} for pid in providers}
+    for n, obj in [('ORDER.json', order), ('FILL.json.gz', fill), ('DISPATCH.json', dispatch), ('PROFILE.json', {str(k): v for k, v in sorted(profile.items())}), ('PROVIDERS.json', prov_out)]:
+        save(out / n, obj)
+        payload_sha[n] = hashlib.sha256(json.dumps(obj, sort_keys=True, separators=(',', ':')).encode()).hexdigest()
+    check = dict(result, status='PASS_VENDORED_PR2839_OWNER_ENGINE_CHECK', solver=status, solve_seconds=solve_seconds, total_seconds=time.time() - t0, chronology=a.chronology, T=T, calls=len(order),
+                 physical=result['live'] + HELPERS + CENTRES + PRIVATE_BUFFERS + GUARDS, physical_formula='live + 408 helpers + 8 centres + 82 private buffers + 2 guards',
+                 inventory={pid: dict(sorted(collections.Counter(providers[pid]['widths']).items())) for pid in providers}, local=loc0, engine_sha256=ENGINE_SHA, catalogue=a.catalogue,
+                 pattern_mix={('%d:%s' % (cap, pattern_name(WID, counts))): n for (cap, counts), n in sorted(target.items())}, payload_sha256=payload_sha, seed=a.seed, **pr)
+    save(out / 'OWNER-CHECK.json', check)
+    log('OWNER_CHECK_PASS', out, 'roles', result['roles'], 'idle', result['idle'], 'physical', check['physical'])
+    log('KAPPA', pr['kappa_lower_decimal'], '..', pr['kappa_upper_decimal'], 'cap', rel['cap_upper_decimal'], 'gap %.3e' % pr['gap_to_relaxation_cap'], 'gain vs PR2917 claim %.4e' % pr['gain_vs_PR2917_claim_float'])
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-extension-cap-fill/data/WORD-base.json.gz b/research/paired-extension-cap-fill/data/WORD-base.json.gz
new file mode 100644
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diff --git a/research/paired-extension-cap-fill/evidence/ADAPTER-DERIVATION.json b/research/paired-extension-cap-fill/evidence/ADAPTER-DERIVATION.json
new file mode 100644
index 0000000000..4bcbc9f4f8
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/ADAPTER-DERIVATION.json
@@ -0,0 +1,124 @@
+{
+  "status": "PASS_CHECKED_82_BUFFER_ADAPTER_DERIVATION_R13",
+  "parent_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "parent_manifest_sha256": "9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f",
+  "source_commit": "paired-helper-extension-pr2908",
+  "source_profile": "paired-extension",
+  "upstream_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "source_files": 632,
+  "comparisons": {
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+      "head": "51309592971e3b5be935599eed2a95404dc7781e",
+      "sha256": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf"
+    },
+    "pr2917": {
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+      "head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+      "sha256": "e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac"
+    }
+  },
+  "retained_receipt_sha256": "eec93526dafc5d6fb8f6b4318efb57b15209b7a31bbd670d470b1a65de244720",
+  "buffer_count": 82,
+  "physical_overhead": 500,
+  "changes": {
+    "prepare_extension_native.py": {
+      "source": "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/pr2908/tools/prepare_channel_native.py",
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+      "after_sha256": "a64ff448b62a93108ed6db64dfbed71d86bbbe4dec36f78731d6e995e39772cf",
+      "replacements": [
+        {
+          "old": "SOURCE_SHA='56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83'",
+          "new": "SOURCE_SHA='98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1'"
+        },
+        {
+          "old": "SOURCE_FILES=610",
+          "new": "SOURCE_FILES=632"
+        },
+        {
+          "old": "SOURCE_COMMIT='two-sided-helper408-pr2894'",
+          "new": "SOURCE_COMMIT='paired-helper-extension-pr2908'"
+        },
+        {
+          "old": "OLD_RECEIPT_SHA='dd36443f2789ffa6deca7210c76ada781e2b9b7e622a546b366f51a475faff3e'",
+          "new": "OLD_RECEIPT_SHA='eec93526dafc5d6fb8f6b4318efb57b15209b7a31bbd670d470b1a65de244720'"
+        },
+        {
+          "old": "len(can['zero_buffers'])==73",
+          "new": "len(can['zero_buffers'])==82"
+        }
+      ]
+    },
+    "admit_extension.py": {
+      "source": "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/pr2908/tools/admit_channel408.py",
+      "before_sha256": "a62c21eac4e0df502cbfb78c88b19a763fd351cde3c11c0588874f84db6992bf",
+      "after_sha256": "682a9e90994d86a248f48c76bc05bdef71751414ab6d6c78fc6e1ac64e835308",
+      "replacements": [
+        {
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+          "new": "    'paired-extension': dict(commit='paired-helper-extension-pr2908',manifest='98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1',helpers=408,source_file_count=632,upstream_head='51309592971e3b5be935599eed2a95404dc7781e'),"
+        },
+        {
+          "old": "COMPARISONS = {",
+          "new": "COMPARISONS = {\n    'pr2908': dict(pr=2908,head='51309592971e3b5be935599eed2a95404dc7781e',sha256='2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf',field='kappa'),\n    'pr2917': dict(pr=2917,head='224bd5e56041c40078ff6b5fa7393733a215de5c',sha256='e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac',field='kappa'),"
+        },
+        {
+          "old": "ap.add_argument('--source-profile', choices=['channel408'], default='channel408')",
+          "new": "ap.add_argument('--source-profile', choices=['paired-extension'], default='paired-extension')"
+        },
+        {
+          "old": "ap.add_argument('--comparison-profile', choices=['pr2894'], default='pr2894')",
+          "new": "ap.add_argument('--comparison-profile', choices=['pr2908','pr2917'], default='pr2908')"
+        },
+        {
+          "old": "zero_buffers_allocated_and_cleared=73",
+          "new": "zero_buffers_allocated_and_cleared=82"
+        },
+        {
+          "old": "len(c.get('zero_buffers',[]))==73, 'helper408 physical ABI including all 73 private buffers'",
+          "new": "len(c.get('zero_buffers',[]))==82, 'paired extension physical ABI including all 82 private buffers'"
+        },
+        {
+          "old": "896*T+expected_helpers+8+73+2, 'complete physical cost including all actual helpers and 73 buffers'",
+          "new": "896*T+expected_helpers+8+82+2, 'complete physical cost including all actual helpers and 82 buffers'"
+        }
+      ]
+    },
+    "extension_blocknorm.py": {
+      "source": "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/pr2908/tools/channel_blocknorm.py",
+      "before_sha256": "b53ebd53e3948f658c6da4f487a9ea10c9cb0a6acf2435750a32d6efeb9869c0",
+      "after_sha256": "d3893ef2265b1027f90b33832a3631b7a664bfdcac47962b83149d904bb7578f",
+      "replacements": [
+        {
+          "old": "len(allocated)==73, 'all73 private zero buffers released'",
+          "new": "len(allocated)==82, 'all82 private zero buffers released'"
+        },
+        {
+          "old": "'zero_buffers_allocated_and_cleared':73",
+          "new": "'zero_buffers_allocated_and_cleared':82"
+        },
+        {
+          "old": "r['zero_buffers_returned_to_zero']==73",
+          "new": "r['zero_buffers_returned_to_zero']==82"
+        },
+        {
+          "old": "physical==live+8+408+73+2",
+          "new": "physical==live+8+408+82+2"
+        },
+        {
+          "old": "'zero_buffers':[live+416,live+489], 'coefficient':[live+489,live+491]",
+          "new": "'zero_buffers':[live+416,live+498], 'coefficient':[live+498,live+500]"
+        },
+        {
+          "old": "len(mp)==73 and set(mp.values())==set(range(*ns['zero_buffers'])), '73distinct private Z slots'",
+          "new": "len(mp)==82 and set(mp.values())==set(range(*ns['zero_buffers'])), '82distinct private Z slots'"
+        },
+        {
+          "old": "T=len(order)//9; live=896*T; physical=live+490",
+          "new": "T=len(order)//9; live=896*T; physical=live+500"
+        }
+      ]
+    }
+  }
+}
diff --git a/research/paired-extension-cap-fill/evidence/ADMISSION-RESULT.json b/research/paired-extension-cap-fill/evidence/ADMISSION-RESULT.json
new file mode 100644
index 0000000000..7ac29da97c
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/ADMISSION-RESULT.json
@@ -0,0 +1,382 @@
+{
+  "actual_expected_helpers": 408,
+  "comparison_claim_sha256": "e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac",
+  "comparison_head": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+  "comparison_kappa": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "comparison_pr": 2917,
+  "complex_lower": "1722499906443274564357/1000000000000000000000000",
+  "dispatch_sha256": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "external_input_sha256": {
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/adapters/extension_blocknorm.py": "d3893ef2265b1027f90b33832a3631b7a664bfdcac47962b83149d904bb7578f",
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/parent-export/pr2894/vendor/pr2857/vendor/pr2839/lift_parent.py": "9a1edd7d4ab4a2f2ac8d15b42b7e40f93653d65026bac59e4c1ce80b486bd60e",
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/parent-export/pr2894/vendor/pr2857/vendor/pr2839/reconstruct_replica.py": "5472811c24aef3852dc7e189dff5060076a6c0b25bfde928da50dcfe9b5bdc15",
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/parent-export/pr2894/vendor/pr2857/vendor/pr2839/replica_parent.py": "48bdbf28f59d80edb266803ec61bf5e22e8fb5e5a0e2b88004b6039147589bd4",
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/pr2917/CLAIM.json": "e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac",
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/wt-r13pub/research/paired-extension-cap-fill/allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/wt-r13pub/research/paired-extension-cap-fill/allocation/FILL.json.gz": "e045aa613f8fba06d81313f5e1c2cbec9ee94552163b8d1eb9205bf2fa7f2285",
+    "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/wt-r13pub/research/paired-extension-cap-fill/allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1"
+  },
+  "fill_sha256": "e045aa613f8fba06d81313f5e1c2cbec9ee94552163b8d1eb9205bf2fa7f2285",
+  "gain": "113907405684085469/125000000000000000000000",
+  "kappa": "17224999064432745643569999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017224999064432745643569999999999999999999998999999999999999999999999",
+  "native_receipt_sha256": "9a2e23c80436cf257c6f21fa4bd3f796fdb569bf30005ca2c2bb16d8f2094969",
+  "order_sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "package_manifest_sha256": "b690eab49b010091973a4e7d1b8d58306200fd09f4c2281bbeeec57aa1b077d5",
+  "patches": [
+    {
+      "after_sha256": "52f8b4cec2dab69cbe590e1fd0f7a68e1b35de5a540bd22fd2adfce07a92b46b",
+      "before_sha256": "faf283eb4edd2e6a1ccb40b3cb3ba30ae54338eaf5ea0a10d84d11d7939502af",
+      "path": "new/rebind.py",
+      "replacements": [
+        [
+          "physical=spec['expected']['live'] + 8 + R + 2)",
+          "physical=spec['expected']['live'] + 8 + R + 2 + max(len(rd(d / 'CANONICAL-WORD.json.gz').get('zero_buffers', [])) for d in locs.values()))"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "99bef04f24a99088e5c0c9b8f6bbc8386669d8315b8f572d6bbfb932c5d51145",
+      "before_sha256": "7edb4732b34e5814b27650a55c938626cb50d68f06397744dd4fe451437e90e0",
+      "path": "geometry_controls.py",
+      "replacements": [
+        [
+          " i['complete_invocation_sweeps']=i['bridge_sweeps']=333",
+          " i['complete_invocation_sweeps']-=1;i['bridge_sweeps']-=1"
+        ],
+        [
+          " o,i=copy.deepcopy(owner),copy.deepcopy(invoice);fn(o,i);oh=digest(o);i['owner_audit_sha256']=oh",
+          " o,i=copy.deepcopy(owner),copy.deepcopy(invoice);fn(o,i);assert (o,i)!=(owner,invoice), 'geometry mutant must change actual receipts';oh=digest(o);i['owner_audit_sha256']=oh"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "6cfefe80c02a6c0f243f50ca9e146e1ab1440b84a033d8a71d42be5a5fa27f6b",
+      "before_sha256": "c43680a2da390f79925547a5ee1919d8a76637cccf98e2c8164b6f667fbc3183",
+      "path": "verify_release.py",
+      "replacements": [
+        [
+          "Fraction(1, 10 ** 3046) - Fraction(1, 10 ** 3022)",
+          "Fraction(1, 10 ** (spec['outer_refinement']['endpoint_digits'] + 46)) - Fraction(1, 10 ** (spec['outer_refinement']['endpoint_digits'] + 22))"
+        ],
+        [
+          "epsilon=1-(1025/1024)e-3080",
+          "epsilon=1-(1025/1024)e-{spec['outer_refinement']['endpoint_digits']+80}"
+        ],
+        [
+          "at the one 3000-digit rejection call",
+          "at the one {spec['outer_refinement']['endpoint_digits']}-digit rejection call"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98",
+      "before_sha256": "9e12909c73d3b3a31a45d801ae76c034510d6306400412e474df79bc4f1dc67e",
+      "path": "outer/check_ledger.py",
+      "replacements": [
+        [
+          "assert (m,W)==(73,66304)",
+          "T=spec['geometry']['replicas']\nassert type(T) is int and T>0\nassert m==73 and W==896*T and W==BJ['live']"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+      "before_sha256": "08ca58abff11bdfba721dc56ab8acf06ec1b7c48a8699a0955cf35324680aca7",
+      "path": "code/witness.py",
+      "replacements": [
+        [
+          "   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))",
+          "   import time as _wr_time\n   _wr_path=Path(os.environ['WITNESS_RECORD'])\n   _wr_lock=_wr_path.with_name(_wr_path.name+'.append.lock')\n   _wr_deadline=_wr_time.monotonic()+60\n   _wr_fd=None\n   while _wr_fd is None:\n    try:_wr_fd=os.open(_wr_lock,os.O_CREAT|os.O_EXCL|os.O_WRONLY)\n    except FileExistsError:\n     if _wr_time.monotonic()>=_wr_deadline:raise TimeoutError('discovery record lock timeout; existing lock preserved')\n     _wr_time.sleep(.005)\n   try:\n    with _wr_path.open('a',encoding='utf-8',newline='\\n')as _wr_out:\n     _wr_out.write(json.dumps([key,got],default=str)+chr(10))\n     _wr_out.flush()\n   finally:\n    os.close(_wr_fd)\n    _wr_lock.unlink()"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "680b6de474a8226777c5a17191470b21cd5cc524cc22921d12dff6cef25c43ee",
+      "before_sha256": "b0d5f4217b4699c37609dc7c3633d570acbccd205840777d38f891846b4b918c",
+      "path": "verify.py",
+      "replacements": [
+        [
+          "run('lift-parent',P/'lift_parent.py','--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')",
+          "run('lift-parent',P/'lift_parent.py','--package',P,'--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "0d8cc021d2401d047aaec79060ec2ea28ba06f12eca8dbf4c60c78bb31975c4e",
+      "before_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+      "path": "code/witness.py",
+      "replacements": [
+        [
+          "PAYLOAD==1<<(192+(GEO['dimension']+1)//2+2*CALLS+4).bit_length()",
+          "PAYLOAD==1<<(128+(GEO['dimension']+1)//2+18+1330+1+4).bit_length()"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+      "before_sha256": "bb213d0af12218ff7c9c572717e522d8bbeeb2856b87a253f4a7f44e0fd71f15",
+      "path": "code/invoice_allcold.py",
+      "replacements": [
+        [
+          "    required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4",
+          "    from blocknorm_certificate import certify\n    blocknorm=certify(template, {pid:base/'providers'/pid for pid in template['local_providers']})\n    assert blocknorm['status'] == 'PASS_TENSOR_BLOCK_NORM_CERTIFICATE'\n    assert localbits <= 128, 'actual native scalar/Horner prefix exceeds charged local reserve'\n    required_prefix=localbits+input_l2_bits+blocknorm['max_active_depth']+blocknorm['stock_l2_bits']+1+4"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+      "before_sha256": "02502a217fe8c9e10229075b50745518beac512c48db20e64c3e06514a4da5b5",
+      "path": "independent_core.py",
+      "replacements": [
+        [
+          "    payload = 1 << (192 + (M+1)//2 + 2*len(c['order']) + 4).bit_length()",
+          "    require(localbits <= 128, 'measured native prefix exceeds local reserve')\n    payload = 1 << (128 + (M+1)//2 + 18 + 1330 + 1 + 4).bit_length()"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "d598a2ac1e2e8eaee14a8c285e0277a7ae44ca6a15bd2b5cfc67fb40844fb387",
+      "before_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+      "path": "code/invoice_allcold.py",
+      "replacements": [
+        [
+          "        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,",
+          "        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,blocknorm=blocknorm,"
+        ],
+        [
+          "        primitive_arithmetic_margin_bits=4,controller_audit_sha256=",
+          "        tensor_block_norm=blocknorm,partial_cover_margin_bits=1,physical_stock_l2_bits=blocknorm['stock_l2_bits'],primitive_arithmetic_margin_bits=4,controller_audit_sha256="
+        ],
+        [
+          "Sum every actual invocation and bridge sweep and take the maximum local scalar/Horner prefix over both orientations of the fixed provider.",
+          "All invocations and bridge sweeps remain charged. Bound completed-boundary energy by at most eighteen active steps per owner replica, using exact tensor-isomorphic whole-family helper unitaries. Add the full group-indexed physical-stock sup-to-l2 factor and one partial-cover margin, then the maximum local scalar/Horner prefix."
+        ]
+      ]
+    },
+    {
+      "after_sha256": "e051aaa166e01263780d5ae03699690670b597fed6593af4c37a7e978825eb85",
+      "before_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+      "path": "independent_core.py",
+      "replacements": [
+        [
+          "    prefix = localbits + (M + 1) // 2 + len(c['order']) + c['bridges'] + 4",
+          "    bn=c['blocknorm']\n    require(bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['max_active_depth']==18 and bn['stock_l2_bits']<=1330, 'independent tensor block certificate')\n    prefix = localbits + (M + 1) // 2 + bn['max_active_depth'] + bn['stock_l2_bits'] + 1 + 4"
+        ],
+        [
+          "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4)",
+          "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], active_block_depth=18,stock_l2=bn['stock_l2_bits'],partial_cover=1,margin=4),blocknorm=bn"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "393323f150d0bb686419804d51cf43d0f58450d2a1e7929725acdd26fdbb3640",
+      "before_sha256": "2286f00e462ff28abbb3f396095463482a1e063213b9526a7225275980c77eaf",
+      "path": "audit_mixed.py",
+      "replacements": [
+        [
+          "pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)",
+          "import blocknorm_certificate as BN;ctx['blocknorm']=BN.certify_context(ctx,roles,dirs,source_parent=parent);pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "3ef9b2a2fa0dcf2d53884e205b7ac20ae6ef47d173b0d8a5bc97fb2a445fc143",
+      "before_sha256": "f25e1e870df5d5a16a1e367b3df8843cb01644ab4b75895d7939af81e4fcb833",
+      "path": "code/assemble.py",
+      "replacements": [
+        [
+          " assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+CALLS+CALLS+4",
+          " bn=invoice['blocknorm']\n assert bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['replicas']==REPLICAS\n assert bn['max_active_depth']==bn['boundary_depth_bits']==18 and bn['active_calls_per_block']==bn['bridges_per_block']==9\n assert bn['block_width_families']==896 and bn['physical_families']==invoice['physical'] and bn['live_families']==invoice['live']\n assert bn['partial_cover_bits']==1 and bn['input_l2_bits']==37 and bn['local_reserve_bits']==128 and bn['retained_payload_bits']==PAYLOAD\n localbits=max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())\n assert bn['local_actual_prefix_bits']==localbits and localbits<=128\n assert invoice['global_prefix_bits']==bn['actual_prefix_bits']==localbits+37+18+bn['stock_l2_bits']+1+4\n assert bn['required_reserve_bits']==128+37+18+bn['stock_l2_bits']+1+4<PAYLOAD\n expected_endpoint=dict(all_arbitrary_columns=632,helper_to_data_response_zero=True,centres_first_clear_and_terminal_zero=8,zero_buffers_allocated_and_cleared=82,coefficient_work_contract='unchanged audited clear-before-and-after Horner macro')\n assert bn['endpoint_replay']=={pid:{o:expected_endpoint for o in ('forward','backward')} for pid in invoice['providers']}"
+        ],
+        [
+          " stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']",
+          " stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']\n assert bn['physical_stock_bits']==stock.bit_length() and bn['stock_l2_bits']==(stock.bit_length()+1)//2<=1330"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "b7a6a7dbca02aec52d7807ed3104362b0fab1014d2f624b5fe638a3f30f65133",
+      "before_sha256": "d7675ff0b0994b29541d37eaa3010c5f39bb1447700c9f8e750522bf8c951f56",
+      "path": "code/assembly_controls.py",
+      "replacements": [
+        [
+          "        i['global_prefix_bits'] = 1 + 37 + CALLS + CALLS + 4",
+          "        i['global_prefix_bits'] = 1 + 37 + 18 + i['blocknorm']['stock_l2_bits'] + 1 + 4"
+        ],
+        [
+          "        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),",
+          "        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),\n        ('missing_blocknorm', lambda o,i:i.pop('blocknorm')),\n        ('understated_active_depth',lambda o,i:i['blocknorm'].__setitem__('max_active_depth',17)),\n        ('understated_full_stock_norm',lambda o,i:i['blocknorm'].__setitem__('stock_l2_bits',10)),\n        ('missing_partial_cover_margin',lambda o,i:i['blocknorm'].__setitem__('partial_cover_bits',0)),\n        ('forged_helper_response',lambda o,i:i['blocknorm']['endpoint_replay'][next(iter(i['providers']))]['forward'].__setitem__('helper_to_data_response_zero',False)),"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "9612cc95bfa2a36a9d9cbdcedc557f28f52e83f20f113ab21d0d54cf9c190be2",
+      "before_sha256": "1d965b7a329b98008fcc67e73d03dcf6e75f0f33c2858a39f1182bb3d0ed0ea1",
+      "path": "freeze_spec.py",
+      "replacements": [
+        [
+          "spec['expected']['assembly_controls_rejected'] = 32 + sum(",
+          "spec['expected']['assembly_controls_rejected'] = 37 + sum("
+        ]
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+    {
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+      "path": "replay.py",
+      "replacements": [
+        [
+          "len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==114",
+          "len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==119"
+        ]
+      ]
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+          "['replay.py','freeze_spec.py','audit_mixed.py','independent_core.py','geometry_controls.py','audit_fast.py','blocknorm_certificate.py']"
+        ],
+        [
+          "controls=dict(admission=114,bit=12,controller=15,independent_owner=8,geometry=6)",
+          "controls=dict(admission=119,bit=12,controller=15,independent_owner=8,geometry=6)"
+        ]
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+  "scope": "Conditional finite construction and modern outer arithmetic. Exact inherited theorem obligations remain. Both native providers explicitly reused from authenticated fresh five-stage runs.",
+  "source_commit": "paired-helper-extension-pr2908",
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+        "-B",
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+        "--out",
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+        "-B",
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+        "--package",
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+        "--owners",
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+        "--out",
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+        "-B",
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+        "-B",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/candidate/layout/packing74/replay.py",
+        "--data",
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+        "--work",
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+        "--local",
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+        "-B",
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+        "-B",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/candidate/package/outer/independent_check.py"
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+        "-B",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/candidate/package/verify_release.py",
+        "--main",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs",
+        "--work",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/candidate/release",
+        "--native-cache",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/native/native-cache",
+        "--jobs",
+        "2"
+      ],
+      "exit_code": 0,
+      "log_sha256": "e01086be77ae2169e978708e1f7417f1ea2195ed3fc21579102986f1b2115778",
+      "name": "release",
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+}
diff --git a/research/paired-extension-cap-fill/evidence/ADMISSION-STAGES.json b/research/paired-extension-cap-fill/evidence/ADMISSION-STAGES.json
new file mode 100644
index 0000000000..1fb125ef62
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/ADMISSION-STAGES.json
@@ -0,0 +1,113 @@
+[
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+      "-B",
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+      "--out",
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+      "-B",
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+      "--package",
+      "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/candidate/package",
+      "--owners",
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+      "--out",
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+      "--data",
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+      "--work",
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+      "--local",
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+      "--discover"
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+      "-B",
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+      "-B",
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+      "-B",
+      "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/candidate/package/verify_release.py",
+      "--main",
+      "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs",
+      "--work",
+      "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/candidate/release",
+      "--native-cache",
+      "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/native/native-cache",
+      "--jobs",
+      "2"
+    ],
+    "exit_code": 0,
+    "log_sha256": "e01086be77ae2169e978708e1f7417f1ea2195ed3fc21579102986f1b2115778",
+    "name": "release",
+    "script_sha256": "6cfefe80c02a6c0f243f50ca9e146e1ab1440b84a033d8a71d42be5a5fa27f6b",
+    "seconds": 201.28864574991167
+  }
+]
diff --git a/research/paired-extension-cap-fill/evidence/ENVIRONMENT.json b/research/paired-extension-cap-fill/evidence/ENVIRONMENT.json
new file mode 100644
index 0000000000..e9e5c00ae3
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/ENVIRONMENT.json
@@ -0,0 +1,13 @@
+{
+  "assertions_enabled": true,
+  "dependency_versions": {
+    "gmpy2": "2.3.2",
+    "mpmath": "1.3.0",
+    "numpy": "2.4.5",
+    "psutil": "7.2.1",
+    "scipy": "1.16.1",
+    "sympy": "1.14.0"
+  },
+  "executable": "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r12/env312/bin/python",
+  "python": "3.12.13"
+}
diff --git a/research/paired-extension-cap-fill/evidence/FULL-NATIVE-RECEIPT.json b/research/paired-extension-cap-fill/evidence/FULL-NATIVE-RECEIPT.json
new file mode 100644
index 0000000000..da3f62881b
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/FULL-NATIVE-RECEIPT.json
@@ -0,0 +1,113 @@
+{
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+        "local/INDEPENDENT-LOCAL-REPLAY.json": "a28c61fa107cb671881e5784dd3600f5803ac9bb74f7f771686b98dfe69c1d4c",
+        "local/LOCAL-CHECKS.json": "267fcd623066776956ed1e2483b7d98dde9fc44c5984f752d1042807d8937e90",
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+        "local/RESIDUAL-ADAPTERS.json": "3dabb2399852c6ee81b0f350682f41bd3a2d9497f1ffbcad0f8cd50f71fac834",
+        "local/SCALAR-FRAME-AUDIT.json": "7d675605dba1e616f7fd94372f7815b78a1d0e3d6dfe0afc2ef7419fc7a7b2d0",
+        "local/WARP-RECIPE-CHECKS.json": "e6eafe0ad31b7ae2eac010bfeabf3e549b910f23c837676cc8698b0f33c5daf6",
+        "local/WRAPPER-CHECKS.json": "b1b66e6a7e134fb26b0b7799dfe5388b327bd207fd402ed9b0cbfc420c824d40"
+      },
+      "word_sha256": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f"
+    }
+  },
+  "retained_parent_receipt_sha256": "fbf2590a39e8080a6267d77a41ba95ec9c0216c562ac51459145ddab0d945fa4",
+  "retained_reuse_receipt_sha256": "eec93526dafc5d6fb8f6b4318efb57b15209b7a31bbd670d470b1a65de244720",
+  "reused_retained_native_count": 2,
+  "reused_retained_parent": true,
+  "source_commit": "paired-helper-extension-pr2908",
+  "status": "PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE"
+}
diff --git a/research/paired-extension-cap-fill/evidence/FULL-NATIVE-RESULT.json b/research/paired-extension-cap-fill/evidence/FULL-NATIVE-RESULT.json
new file mode 100644
index 0000000000..ed15370462
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/FULL-NATIVE-RESULT.json
@@ -0,0 +1,41 @@
+{
+  "environment_sha256": "c6faaaa9b538ddbf0ea3c624bbe2f1c7e4074f8cb504d4bee0f3353f1e7f32a1",
+  "native_receipt_sha256": "9a2e23c80436cf257c6f21fa4bd3f796fdb569bf30005ca2c2bb16d8f2094969",
+  "preparer_sha256": "a64ff448b62a93108ed6db64dfbed71d86bbbe4dec36f78731d6e995e39772cf",
+  "scope": "Fresh changed base/extra native chains; two unchanged retained native chains and16-stage parent admission explicitly reused by exact full-tree receipts. No owner/controller/outer admission yet.",
+  "seconds": 24.331681123003364,
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
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+        "-B",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/source/new/fastnative/run_native.py",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/source/new/borrow/words/BORROW-WORD-43base.json.gz",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/native/fresh-base"
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+      "log_sha256": "9375151c96b6d5ef6321b7e7c65bd417ade58dd8f9041af72e48008cfaf695d3",
+      "name": "fresh-current-base",
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+        "-B",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/source/new/fastnative/run_native.py",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/source/new/borrow/words/BORROW-WORD-43extra.json.gz",
+        "/private/tmp/claude-501/-Users-mdumitrean-Desktop-dev-aigent-math-prime/c80ebb8e-fc28-4d1d-b7ef-b214d4660f98/scratchpad/r13pub-build/runs/fresh1/native/fresh-extra"
+      ],
+      "exit_code": 0,
+      "log_sha256": "bced1d285ea7c60ee09fd60df7bb91e908020ef19ff86aa34ab1d6489924846c",
+      "name": "fresh-current-extra",
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+      "seconds": 24.258154874667525
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+  "status": "PASS_TWO_FRESH_SHARED_KERNEL_NATIVE_CHAINS_AUTHENTICATED_PARENT_REUSE"
+}
diff --git a/research/paired-extension-cap-fill/evidence/FULL-REPLAY-RESULT.json b/research/paired-extension-cap-fill/evidence/FULL-REPLAY-RESULT.json
new file mode 100644
index 0000000000..b5d68cd21c
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/FULL-REPLAY-RESULT.json
@@ -0,0 +1,73 @@
+{
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+  "explicit_retained_reuse": false,
+  "fresh_retained_bootstrap": true,
+  "gain": "113907405684085469/125000000000000000000000",
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+  "native_receipt_sha256": "9a2e23c80436cf257c6f21fa4bd3f796fdb569bf30005ca2c2bb16d8f2094969",
+  "scope": "Conditional finite supplier/outer result; inherited all-size theorem obligations remain.",
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+      "stage": "complete-admission"
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+  "status": "PASS_CAP_FILL_COMPLETE_REPLAY"
+}
diff --git a/research/paired-extension-cap-fill/evidence/FULL-REPLAY-STAGES.json b/research/paired-extension-cap-fill/evidence/FULL-REPLAY-STAGES.json
new file mode 100644
index 0000000000..cab512fca7
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/FULL-REPLAY-STAGES.json
@@ -0,0 +1,62 @@
+[
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diff --git a/research/paired-extension-cap-fill/evidence/RELEASE-RECEIPT.json b/research/paired-extension-cap-fill/evidence/RELEASE-RECEIPT.json
new file mode 100644
index 0000000000..30f1cde388
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/RELEASE-RECEIPT.json
@@ -0,0 +1,7 @@
+{
+  "status": "PASS_RELEASE",
+  "kappa_decimal": "0.0017224999064432745643569999999999999999999998999999999999999999999999",
+  "manifest_sha256": "b690eab49b010091973a4e7d1b8d58306200fd09f4c2281bbeeec57aa1b077d5",
+  "proof": "Supplier: the package's own unchanged `verify.py` (retained PR1297 provider and parent admission, owner reconstruction, parent lift, strict T74 admission, geometry controls): `PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION`, native reuse {'base': 'e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e', 'extra': '7b0e9fbda32749aabc7e156d9fe09bceb0624a178628fe69e5dfea783462f905'}; its complex endpoint 1722499906443274564357/1000000... brackets the ledger's b = 172249990644327456435699999999999999999999999999999999999999999999999999999999999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000. Outer (PR1673 capped phase-cell fusion): regenerated exact ledger (63 strict inequalities: the 62 retained rows plus the explicit main-binding row gaussian_above_main, the fixed-grid maximum kappa = C - 1/F - B asserted, 17 rejecting controls incl. the old g-factor union row, the old linear and old-theta chirp guards, the old 2*beta tag test, epsilon at 1 or at the r0 slack and beta outside its window, larger endpoint rejected by the native moment), independent balance derivation, the exact union-schedule simulation, the (retained, not used for kappa) structured-boundary displacement-rank check, the gauge-free identity/symbol/circuit checks, PR1786's finite prime/underflow controls and 19 exact evidence replays all pass. Conditional kappa 0.0017224999064432745643569999999999999999999998999999999999999999999999 (union schedule outer/UNION-SCHEDULE.md; explicit Strassen boundary tau=45/16 (the structured boundary of outer/STRUCTURED-BOUNDARY.md is not used); gauge-free interiors outer/GAUGEFREE-INTERIORS.md; fine source-prime padding PR1786 at the free point epsilon=1-(1025/1024)e-104, outer/FINE-PADDING-COMPOSITION.md; fixed-grid maximum of PR2180/PR2161 (dataisfire), outer/PROOF-GRID-MAX.md; exact-integer coarse exponential PR2168/PR2184 (dataisfire) at the one 24-digit rejection call).",
+  "seconds": 201.2
+}
diff --git a/research/paired-extension-cap-fill/evidence/RETAINED-BOOTSTRAP-RECEIPT.json b/research/paired-extension-cap-fill/evidence/RETAINED-BOOTSTRAP-RECEIPT.json
new file mode 100644
index 0000000000..1e63b80567
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/RETAINED-BOOTSTRAP-RECEIPT.json
@@ -0,0 +1,113 @@
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+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/CLIFFORD-RECIPES.json": "8cecbc37fa1b75526beb20cd7fd0e7099b8799f66d6968e755ba26de7ee6514b",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/CLIFFORD-REVIEW.json": "f3144957ef10615c4b1b179645d9770bd9ccfb366ef2276c84e3a7de2ad9d10e",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/FULL-WORD.json.gz": "10b73d24b63de4dc73d30110eb1cbfe893d0df6a6907ee164beca5d686003a01",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/INDEPENDENT-LOCAL-REPLAY.json": "e8d26813d722d00e12d15f8e95710558f59f6cec8cfc3a8c4ab26ce12e7b3790",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/LOCAL-CHECKS.json": "77a424b5ddebfb877ad89a66f659b3d101e2d90a650d5ea3ca4017ecf785794a",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/LOCAL-PROGRAMS.json.gz": "d96fc56ee439dc031cf323f9a3bc43af9f2c9832ef4b6db5dc3296f10981b32f",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/RESIDUAL-ADAPTERS.json": "53c2a9d31a75c8aa34f314d67afb8c5b16026aa31e745b1ba13d5103f55c4f35",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/SCALAR-FRAME-AUDIT.json": "01120bd4d6aa424252ce0cab9264944760e8bc6344973e5911364e0ac66bcfd0",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/WARP-RECIPE-CHECKS.json": "a4ece0cf2599112f18aecbd9b34934a3fd72534875861587a32d1f3ee991a9f5",
+    "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac/local/WRAPPER-CHECKS.json": "00c62303b0981544f84bacef519b0917212dbe90b11853e10f0bb3074b4aa156",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/CACHE.json": "e0172a1c1cdab1d9d2a9f4c3d11c06c705f242453a59c7c8de184e67f850f7f0",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/STEPS.json": "81f954d54f98c43dcc4787c3c6c199c841f71a66acd87e92253e5b3a4a34f7d9",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/CANONICAL-WORD.json.gz": "4e3a387e199459a7a9977401b618c2daf426ac6e2fbd3d9153cd0344eacef29d",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/CLIFFORD-RECIPES.json": "b50d092a779f0202eed697391211d0e54ff8dd596ffa373cbfae504175e99b9e",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/CLIFFORD-REVIEW.json": "d51725595d267d521dec5a8be7bd1a0adad7c2daa128d48b74419d2524fdb999",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/FULL-WORD.json.gz": "2d818c32f4118553b5fd8e051b38a4fdc8e2e9c8b7666d9233912cf82244389e",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/INDEPENDENT-LOCAL-REPLAY.json": "d507570359c70e493fc0ad29702eb464138a028c3cadec281e6ca54c5289a84e",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/LOCAL-CHECKS.json": "77a424b5ddebfb877ad89a66f659b3d101e2d90a650d5ea3ca4017ecf785794a",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/LOCAL-PROGRAMS.json.gz": "d96fc56ee439dc031cf323f9a3bc43af9f2c9832ef4b6db5dc3296f10981b32f",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/RESIDUAL-ADAPTERS.json": "cb24ff72025d5d6a91e41507f4e80460b0600605236a0904c70f72134b3ca53f",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/SCALAR-FRAME-AUDIT.json": "c62f64be2fb206fc6937612447e4ee298ede8c2344e9b1d5750f76e42d8878d2",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/WARP-RECIPE-CHECKS.json": "87e4406b4f4f2f70c79a48b8f2bace2be5c81498e84909b54062c357a6d4bfa0",
+    "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7/local/WRAPPER-CHECKS.json": "00c62303b0981544f84bacef519b0917212dbe90b11853e10f0bb3074b4aa156",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/CACHE.json": "479b1ac5b3c9414d0c44146a098b696679a52e52c19c86d6199ea6c8006c8404",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/STEPS.json": "d554e7927fe9b2131debaa6d824e494a5e968418f239f3d1a41dc28289c1b42d",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/ledgers.log": "2f40f12c67d436dde2ea415ea3e033ec60a9d43cc71427dcc1bf987962da34d7",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local-replay.log": "dd643a58258431c3b07d3b06d9060c49677fa23b4fafc9f10988ed1f6867bd9a",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/CANONICAL-WORD.json.gz": "f69c0ca2c217eab87a231b67e548cd6491286314b1215e19f0b1d7463afd5e91",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/CLIFFORD-RECIPES.json": "f1b5a509e39293f5d7ffea7b269fd9e5443e625a9286a022caa1fd4b62af8063",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/CLIFFORD-REVIEW.json": "6dbfb579f109f83ac628f45fb1dd4e36659a4a203f4f67f191d5ef5fb7e6d247",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/FULL-WORD.json.gz": "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/INDEPENDENT-LOCAL-REPLAY.json": "70b4b787a5a4529452a58e9ac48826e848748a35b95a9b20c5358f4355705058",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/LOCAL-CHECKS.json": "e52e7feece9cb22e83c1d687c0f98731f8d50b7e8c863732ec662c89453fbcd4",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/LOCAL-PROGRAMS.json.gz": "81d4aefacaa27f2f215e7d35559d5a079ca521f4ca2eb9a9c6a6bd7062179bff",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/RESIDUAL-ADAPTERS.json": "89e5779ba4fcc1b1a76bed05c9b36600bc1dc3c6efd7e623865692ec715c30c5",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/SCALAR-FRAME-AUDIT.json": "33a19b67f00f01d9d3f29799f0077b478e4ec9664959cf16b14e854ebd354b42",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/local/WRAPPER-CHECKS.json": "fc7e24778302326fdacfd08dd3d5e63483cf4539cd5022a6c77f016752fac1a3",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/native.log": "1ed4bd0f8530755f5cb8612d440eae3dafe2feee6cf716dc1ba9b89df4df4eea",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/phases.log": "9b47f563030974b2c71528ea6dc19f02fe5a9ca7a7ee373e27508b9170806c4b",
+    "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e/wrappers.log": "74b13cf8570ca2f32ce0018575b1b73e95af77a28e59d09556fec59260bdbba5"
+  },
+  "fresh_current_provider_count": 2,
+  "fresh_retained_native_count": 2,
+  "fresh_retained_parent": true,
+  "manifest_sha256": "c8ec4d1b7be08d2ad30730a07392ad9cb6d0222f2c35bef43c9a80a39b16e41f",
+  "providers": {
+    "base": {
+      "complete_native_files": {
+        "STEPS.json": "81f954d54f98c43dcc4787c3c6c199c841f71a66acd87e92253e5b3a4a34f7d9",
+        "local/CANONICAL-WORD.json.gz": "4e3a387e199459a7a9977401b618c2daf426ac6e2fbd3d9153cd0344eacef29d",
+        "local/CLIFFORD-RECIPES.json": "b50d092a779f0202eed697391211d0e54ff8dd596ffa373cbfae504175e99b9e",
+        "local/CLIFFORD-REVIEW.json": "d51725595d267d521dec5a8be7bd1a0adad7c2daa128d48b74419d2524fdb999",
+        "local/FULL-WORD.json.gz": "2d818c32f4118553b5fd8e051b38a4fdc8e2e9c8b7666d9233912cf82244389e",
+        "local/INDEPENDENT-LOCAL-REPLAY.json": "d507570359c70e493fc0ad29702eb464138a028c3cadec281e6ca54c5289a84e",
+        "local/LOCAL-CHECKS.json": "77a424b5ddebfb877ad89a66f659b3d101e2d90a650d5ea3ca4017ecf785794a",
+        "local/LOCAL-PROGRAMS.json.gz": "d96fc56ee439dc031cf323f9a3bc43af9f2c9832ef4b6db5dc3296f10981b32f",
+        "local/RESIDUAL-ADAPTERS.json": "cb24ff72025d5d6a91e41507f4e80460b0600605236a0904c70f72134b3ca53f",
+        "local/SCALAR-FRAME-AUDIT.json": "c62f64be2fb206fc6937612447e4ee298ede8c2344e9b1d5750f76e42d8878d2",
+        "local/WARP-RECIPE-CHECKS.json": "87e4406b4f4f2f70c79a48b8f2bace2be5c81498e84909b54062c357a6d4bfa0",
+        "local/WRAPPER-CHECKS.json": "00c62303b0981544f84bacef519b0917212dbe90b11853e10f0bb3074b4aa156"
+      },
+      "word_sha256": "dda9878455b3a3bec64ca16b1ac7789bbf5ffb603d5713b8df8644485e85b1b7"
+    },
+    "extra": {
+      "complete_native_files": {
+        "STEPS.json": "89eb86ad5210fa244ed7922bf964ea6e97a8180567e9c20947800ca5c27c7e99",
+        "local/CANONICAL-WORD.json.gz": "16aa445c0fb4525c39c7dfa34c8b645847cdaa8ba0fa7dc3a1ef0bca5b97f3e7",
+        "local/CLIFFORD-RECIPES.json": "8cecbc37fa1b75526beb20cd7fd0e7099b8799f66d6968e755ba26de7ee6514b",
+        "local/CLIFFORD-REVIEW.json": "f3144957ef10615c4b1b179645d9770bd9ccfb366ef2276c84e3a7de2ad9d10e",
+        "local/FULL-WORD.json.gz": "10b73d24b63de4dc73d30110eb1cbfe893d0df6a6907ee164beca5d686003a01",
+        "local/INDEPENDENT-LOCAL-REPLAY.json": "e8d26813d722d00e12d15f8e95710558f59f6cec8cfc3a8c4ab26ce12e7b3790",
+        "local/LOCAL-CHECKS.json": "77a424b5ddebfb877ad89a66f659b3d101e2d90a650d5ea3ca4017ecf785794a",
+        "local/LOCAL-PROGRAMS.json.gz": "d96fc56ee439dc031cf323f9a3bc43af9f2c9832ef4b6db5dc3296f10981b32f",
+        "local/RESIDUAL-ADAPTERS.json": "53c2a9d31a75c8aa34f314d67afb8c5b16026aa31e745b1ba13d5103f55c4f35",
+        "local/SCALAR-FRAME-AUDIT.json": "01120bd4d6aa424252ce0cab9264944760e8bc6344973e5911364e0ac66bcfd0",
+        "local/WARP-RECIPE-CHECKS.json": "a4ece0cf2599112f18aecbd9b34934a3fd72534875861587a32d1f3ee991a9f5",
+        "local/WRAPPER-CHECKS.json": "00c62303b0981544f84bacef519b0917212dbe90b11853e10f0bb3074b4aa156"
+      },
+      "word_sha256": "bbe6bcba59e45e827a8e932ee4b23650d56ed4a0b8e0875c14f23c36b9e47eac"
+    }
+  },
+  "retained_parent_receipt_sha256": "fbf2590a39e8080a6267d77a41ba95ec9c0216c562ac51459145ddab0d945fa4",
+  "retained_reuse_receipt_sha256": null,
+  "reused_retained_native_count": 0,
+  "reused_retained_parent": false,
+  "source_commit": "pr2833-dirtentry",
+  "status": "PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE"
+}
diff --git a/research/paired-extension-cap-fill/evidence/RUNTIME-PATCHES.json b/research/paired-extension-cap-fill/evidence/RUNTIME-PATCHES.json
new file mode 100644
index 0000000000..7995d777e7
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/RUNTIME-PATCHES.json
@@ -0,0 +1,225 @@
+[
+  {
+    "after_sha256": "52f8b4cec2dab69cbe590e1fd0f7a68e1b35de5a540bd22fd2adfce07a92b46b",
+    "before_sha256": "faf283eb4edd2e6a1ccb40b3cb3ba30ae54338eaf5ea0a10d84d11d7939502af",
+    "path": "new/rebind.py",
+    "replacements": [
+      [
+        "physical=spec['expected']['live'] + 8 + R + 2)",
+        "physical=spec['expected']['live'] + 8 + R + 2 + max(len(rd(d / 'CANONICAL-WORD.json.gz').get('zero_buffers', [])) for d in locs.values()))"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "99bef04f24a99088e5c0c9b8f6bbc8386669d8315b8f572d6bbfb932c5d51145",
+    "before_sha256": "7edb4732b34e5814b27650a55c938626cb50d68f06397744dd4fe451437e90e0",
+    "path": "geometry_controls.py",
+    "replacements": [
+      [
+        " i['complete_invocation_sweeps']=i['bridge_sweeps']=333",
+        " i['complete_invocation_sweeps']-=1;i['bridge_sweeps']-=1"
+      ],
+      [
+        " o,i=copy.deepcopy(owner),copy.deepcopy(invoice);fn(o,i);oh=digest(o);i['owner_audit_sha256']=oh",
+        " o,i=copy.deepcopy(owner),copy.deepcopy(invoice);fn(o,i);assert (o,i)!=(owner,invoice), 'geometry mutant must change actual receipts';oh=digest(o);i['owner_audit_sha256']=oh"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "6cfefe80c02a6c0f243f50ca9e146e1ab1440b84a033d8a71d42be5a5fa27f6b",
+    "before_sha256": "c43680a2da390f79925547a5ee1919d8a76637cccf98e2c8164b6f667fbc3183",
+    "path": "verify_release.py",
+    "replacements": [
+      [
+        "Fraction(1, 10 ** 3046) - Fraction(1, 10 ** 3022)",
+        "Fraction(1, 10 ** (spec['outer_refinement']['endpoint_digits'] + 46)) - Fraction(1, 10 ** (spec['outer_refinement']['endpoint_digits'] + 22))"
+      ],
+      [
+        "epsilon=1-(1025/1024)e-3080",
+        "epsilon=1-(1025/1024)e-{spec['outer_refinement']['endpoint_digits']+80}"
+      ],
+      [
+        "at the one 3000-digit rejection call",
+        "at the one {spec['outer_refinement']['endpoint_digits']}-digit rejection call"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98",
+    "before_sha256": "9e12909c73d3b3a31a45d801ae76c034510d6306400412e474df79bc4f1dc67e",
+    "path": "outer/check_ledger.py",
+    "replacements": [
+      [
+        "assert (m,W)==(73,66304)",
+        "T=spec['geometry']['replicas']\nassert type(T) is int and T>0\nassert m==73 and W==896*T and W==BJ['live']"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+    "before_sha256": "08ca58abff11bdfba721dc56ab8acf06ec1b7c48a8699a0955cf35324680aca7",
+    "path": "code/witness.py",
+    "replacements": [
+      [
+        "   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))",
+        "   import time as _wr_time\n   _wr_path=Path(os.environ['WITNESS_RECORD'])\n   _wr_lock=_wr_path.with_name(_wr_path.name+'.append.lock')\n   _wr_deadline=_wr_time.monotonic()+60\n   _wr_fd=None\n   while _wr_fd is None:\n    try:_wr_fd=os.open(_wr_lock,os.O_CREAT|os.O_EXCL|os.O_WRONLY)\n    except FileExistsError:\n     if _wr_time.monotonic()>=_wr_deadline:raise TimeoutError('discovery record lock timeout; existing lock preserved')\n     _wr_time.sleep(.005)\n   try:\n    with _wr_path.open('a',encoding='utf-8',newline='\\n')as _wr_out:\n     _wr_out.write(json.dumps([key,got],default=str)+chr(10))\n     _wr_out.flush()\n   finally:\n    os.close(_wr_fd)\n    _wr_lock.unlink()"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "680b6de474a8226777c5a17191470b21cd5cc524cc22921d12dff6cef25c43ee",
+    "before_sha256": "b0d5f4217b4699c37609dc7c3633d570acbccd205840777d38f891846b4b918c",
+    "path": "verify.py",
+    "replacements": [
+      [
+        "run('lift-parent',P/'lift_parent.py','--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')",
+        "run('lift-parent',P/'lift_parent.py','--package',P,'--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "0d8cc021d2401d047aaec79060ec2ea28ba06f12eca8dbf4c60c78bb31975c4e",
+    "before_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+    "path": "code/witness.py",
+    "replacements": [
+      [
+        "PAYLOAD==1<<(192+(GEO['dimension']+1)//2+2*CALLS+4).bit_length()",
+        "PAYLOAD==1<<(128+(GEO['dimension']+1)//2+18+1330+1+4).bit_length()"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+    "before_sha256": "bb213d0af12218ff7c9c572717e522d8bbeeb2856b87a253f4a7f44e0fd71f15",
+    "path": "code/invoice_allcold.py",
+    "replacements": [
+      [
+        "    required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4",
+        "    from blocknorm_certificate import certify\n    blocknorm=certify(template, {pid:base/'providers'/pid for pid in template['local_providers']})\n    assert blocknorm['status'] == 'PASS_TENSOR_BLOCK_NORM_CERTIFICATE'\n    assert localbits <= 128, 'actual native scalar/Horner prefix exceeds charged local reserve'\n    required_prefix=localbits+input_l2_bits+blocknorm['max_active_depth']+blocknorm['stock_l2_bits']+1+4"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+    "before_sha256": "02502a217fe8c9e10229075b50745518beac512c48db20e64c3e06514a4da5b5",
+    "path": "independent_core.py",
+    "replacements": [
+      [
+        "    payload = 1 << (192 + (M+1)//2 + 2*len(c['order']) + 4).bit_length()",
+        "    require(localbits <= 128, 'measured native prefix exceeds local reserve')\n    payload = 1 << (128 + (M+1)//2 + 18 + 1330 + 1 + 4).bit_length()"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "d598a2ac1e2e8eaee14a8c285e0277a7ae44ca6a15bd2b5cfc67fb40844fb387",
+    "before_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+    "path": "code/invoice_allcold.py",
+    "replacements": [
+      [
+        "        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,",
+        "        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,blocknorm=blocknorm,"
+      ],
+      [
+        "        primitive_arithmetic_margin_bits=4,controller_audit_sha256=",
+        "        tensor_block_norm=blocknorm,partial_cover_margin_bits=1,physical_stock_l2_bits=blocknorm['stock_l2_bits'],primitive_arithmetic_margin_bits=4,controller_audit_sha256="
+      ],
+      [
+        "Sum every actual invocation and bridge sweep and take the maximum local scalar/Horner prefix over both orientations of the fixed provider.",
+        "All invocations and bridge sweeps remain charged. Bound completed-boundary energy by at most eighteen active steps per owner replica, using exact tensor-isomorphic whole-family helper unitaries. Add the full group-indexed physical-stock sup-to-l2 factor and one partial-cover margin, then the maximum local scalar/Horner prefix."
+      ]
+    ]
+  },
+  {
+    "after_sha256": "e051aaa166e01263780d5ae03699690670b597fed6593af4c37a7e978825eb85",
+    "before_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+    "path": "independent_core.py",
+    "replacements": [
+      [
+        "    prefix = localbits + (M + 1) // 2 + len(c['order']) + c['bridges'] + 4",
+        "    bn=c['blocknorm']\n    require(bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['max_active_depth']==18 and bn['stock_l2_bits']<=1330, 'independent tensor block certificate')\n    prefix = localbits + (M + 1) // 2 + bn['max_active_depth'] + bn['stock_l2_bits'] + 1 + 4"
+      ],
+      [
+        "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4)",
+        "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], active_block_depth=18,stock_l2=bn['stock_l2_bits'],partial_cover=1,margin=4),blocknorm=bn"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "393323f150d0bb686419804d51cf43d0f58450d2a1e7929725acdd26fdbb3640",
+    "before_sha256": "2286f00e462ff28abbb3f396095463482a1e063213b9526a7225275980c77eaf",
+    "path": "audit_mixed.py",
+    "replacements": [
+      [
+        "pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)",
+        "import blocknorm_certificate as BN;ctx['blocknorm']=BN.certify_context(ctx,roles,dirs,source_parent=parent);pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "3ef9b2a2fa0dcf2d53884e205b7ac20ae6ef47d173b0d8a5bc97fb2a445fc143",
+    "before_sha256": "f25e1e870df5d5a16a1e367b3df8843cb01644ab4b75895d7939af81e4fcb833",
+    "path": "code/assemble.py",
+    "replacements": [
+      [
+        " assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+CALLS+CALLS+4",
+        " bn=invoice['blocknorm']\n assert bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['replicas']==REPLICAS\n assert bn['max_active_depth']==bn['boundary_depth_bits']==18 and bn['active_calls_per_block']==bn['bridges_per_block']==9\n assert bn['block_width_families']==896 and bn['physical_families']==invoice['physical'] and bn['live_families']==invoice['live']\n assert bn['partial_cover_bits']==1 and bn['input_l2_bits']==37 and bn['local_reserve_bits']==128 and bn['retained_payload_bits']==PAYLOAD\n localbits=max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())\n assert bn['local_actual_prefix_bits']==localbits and localbits<=128\n assert invoice['global_prefix_bits']==bn['actual_prefix_bits']==localbits+37+18+bn['stock_l2_bits']+1+4\n assert bn['required_reserve_bits']==128+37+18+bn['stock_l2_bits']+1+4<PAYLOAD\n expected_endpoint=dict(all_arbitrary_columns=632,helper_to_data_response_zero=True,centres_first_clear_and_terminal_zero=8,zero_buffers_allocated_and_cleared=82,coefficient_work_contract='unchanged audited clear-before-and-after Horner macro')\n assert bn['endpoint_replay']=={pid:{o:expected_endpoint for o in ('forward','backward')} for pid in invoice['providers']}"
+      ],
+      [
+        " stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']",
+        " stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']\n assert bn['physical_stock_bits']==stock.bit_length() and bn['stock_l2_bits']==(stock.bit_length()+1)//2<=1330"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "b7a6a7dbca02aec52d7807ed3104362b0fab1014d2f624b5fe638a3f30f65133",
+    "before_sha256": "d7675ff0b0994b29541d37eaa3010c5f39bb1447700c9f8e750522bf8c951f56",
+    "path": "code/assembly_controls.py",
+    "replacements": [
+      [
+        "        i['global_prefix_bits'] = 1 + 37 + CALLS + CALLS + 4",
+        "        i['global_prefix_bits'] = 1 + 37 + 18 + i['blocknorm']['stock_l2_bits'] + 1 + 4"
+      ],
+      [
+        "        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),",
+        "        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),\n        ('missing_blocknorm', lambda o,i:i.pop('blocknorm')),\n        ('understated_active_depth',lambda o,i:i['blocknorm'].__setitem__('max_active_depth',17)),\n        ('understated_full_stock_norm',lambda o,i:i['blocknorm'].__setitem__('stock_l2_bits',10)),\n        ('missing_partial_cover_margin',lambda o,i:i['blocknorm'].__setitem__('partial_cover_bits',0)),\n        ('forged_helper_response',lambda o,i:i['blocknorm']['endpoint_replay'][next(iter(i['providers']))]['forward'].__setitem__('helper_to_data_response_zero',False)),"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "9612cc95bfa2a36a9d9cbdcedc557f28f52e83f20f113ab21d0d54cf9c190be2",
+    "before_sha256": "1d965b7a329b98008fcc67e73d03dcf6e75f0f33c2858a39f1182bb3d0ed0ea1",
+    "path": "freeze_spec.py",
+    "replacements": [
+      [
+        "spec['expected']['assembly_controls_rejected'] = 32 + sum(",
+        "spec['expected']['assembly_controls_rejected'] = 37 + sum("
+      ]
+    ]
+  },
+  {
+    "after_sha256": "cda0f3a63c5c92c0ff45f7f3a200567d7931fd421836e72ea3b8534f6ee24dcc",
+    "before_sha256": "3ec4330ede0db3c6daa453b0366817be9435c85c8c3213a0c35c442c96c1a955",
+    "path": "replay.py",
+    "replacements": [
+      [
+        "len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==114",
+        "len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==119"
+      ]
+    ]
+  },
+  {
+    "after_sha256": "d281f230c1b4defef003e3994ead92ac628d3b7eb715f1367efd900a6ececb79",
+    "before_sha256": "680b6de474a8226777c5a17191470b21cd5cc524cc22921d12dff6cef25c43ee",
+    "path": "verify.py",
+    "replacements": [
+      [
+        "['replay.py','freeze_spec.py','audit_mixed.py','independent_core.py','geometry_controls.py','audit_fast.py']",
+        "['replay.py','freeze_spec.py','audit_mixed.py','independent_core.py','geometry_controls.py','audit_fast.py','blocknorm_certificate.py']"
+      ],
+      [
+        "controls=dict(admission=114,bit=12,controller=15,independent_owner=8,geometry=6)",
+        "controls=dict(admission=119,bit=12,controller=15,independent_owner=8,geometry=6)"
+      ]
+    ]
+  }
+]
diff --git a/research/paired-extension-cap-fill/evidence/logs/admission-discovery.log.txt b/research/paired-extension-cap-fill/evidence/logs/admission-discovery.log.txt
new file mode 100644
index 0000000000..c634a1d121
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/admission-discovery.log.txt
@@ -0,0 +1,8 @@
+PASS bind
+PASS emit
+PASS audit
+PASS invoice
+PASS assembly
+PASS freeze
+PASS independent
+DISCOVERY 0.001719538002395023
diff --git a/research/paired-extension-cap-fill/evidence/logs/admission-outer-check_ledger.py.log.txt b/research/paired-extension-cap-fill/evidence/logs/admission-outer-check_ledger.py.log.txt
new file mode 100644
index 0000000000..7ec3104c8b
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/admission-outer-check_ledger.py.log.txt
@@ -0,0 +1,2 @@
+PASS_FINE_PRIME_PADDING_EXACT_ARITHMETIC
+struct_boundary_radix_union FINAL KAPPA 0.0017224999064432745643569999999999999999999998999999999999999999999999 positive checks 63 gain over online 0.0000029619040482515643569999999999999999999998999999999999999999999999
diff --git a/research/paired-extension-cap-fill/evidence/logs/admission-outer-independent_check.py.log.txt b/research/paired-extension-cap-fill/evidence/logs/admission-outer-independent_check.py.log.txt
new file mode 100644
index 0000000000..f1277acb7c
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/admission-outer-independent_check.py.log.txt
@@ -0,0 +1,43 @@
+{
+  "status": "PASS_INDEPENDENT_BALANCE_DERIVATION",
+  "source_sha256": "d173cb4c3016f46604de421787a4ca7376da833ce831b5a537282822197a7046",
+  "b": "172249990644327456435699999999999999999999999999999999999999999999999999999999999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "rows": {
+    "struct_boundary_radix_union": {
+      "epsilon": "4095999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999959/4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "cap": "185952767980839582630780313599999999999999999999999999999999999999999999999999999999999999999999999999995898468875191791287143068150000000000000000000000000000000000000000000000000000000000000000000000000000041/204800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "beta": "4095999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999877/4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "kappa": "17224999064432745643569999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+      "margin_above_kappa": "20480000000000000000000020479999999999999999999999999999995900468875191791287143068150000000000000000000000000000000000000000000000000000000000000000000000000000041/204800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "checked_cost_powers": 9,
+      "gap_to_q": "5000000000000000000000004999999999999999999999999999999999/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "epsilon_free_sweep_delta_gap_to_q": [
+        [
+          "1/10000000",
+          "1.7224999064432746e-10"
+        ],
+        [
+          "1/1000000000000",
+          "1.7224999064432746e-15"
+        ],
+        [
+          "1/1000000000000000000000000000000",
+          "1.7224999064432747e-33"
+        ],
+        [
+          "1/1000000000000000000000000000000000000000000000000000000000000",
+          "1.7224999064432745e-63"
+        ],
+        [
+          "41/4096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "1.7241820352581607e-107"
+        ],
+        [
+          "11/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "1.894749897087602e-107"
+        ]
+      ]
+    }
+  },
+  "scope": "Independent balance derivation and margin comparisons for this package's supplier endpoint; the supplier native admission is bound by verify_release.py; inherited all-size assumptions remain."
+}
diff --git a/research/paired-extension-cap-fill/evidence/logs/admission-owners.log.txt b/research/paired-extension-cap-fill/evidence/logs/admission-owners.log.txt
new file mode 100644
index 0000000000..bc065fcfd0
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/admission-owners.log.txt
@@ -0,0 +1 @@
+PASS_OWNER_VERIFY {5: 6882, 1: 17316, 48: 27158, 3: 5994} {1: 1626372, 2: 426240, 3: 192474, 4: 73260, 5: 24198, 8: 5328, 48: 27158}
diff --git a/research/paired-extension-cap-fill/evidence/logs/admission-parent-lift.log.txt b/research/paired-extension-cap-fill/evidence/logs/admission-parent-lift.log.txt
new file mode 100644
index 0000000000..19dae85e2e
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/admission-parent-lift.log.txt
@@ -0,0 +1 @@
+PASS_LITERAL_GENERAL_T_PARENT_PLAN_SPEC {"charged_prefix_bits": 2048, "dimension": 73, "pairs": 4, "parent_helpers": 504, "parent_idle": 149184, "parent_live": 111664, "parent_physical": 112178, "replicas": 74, "stages": 9}
diff --git a/research/paired-extension-cap-fill/evidence/logs/admission-rebind.log.txt b/research/paired-extension-cap-fill/evidence/logs/admission-rebind.log.txt
new file mode 100644
index 0000000000..0c0067ef21
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/admission-rebind.log.txt
@@ -0,0 +1 @@
+provider counts {'extra': 416, 'gauge44': 250} | new profile {'1': 1626372, '2': 426240, '3': 192474, '4': 73260, '5': 24198, '8': 5328, '48': 27158} | changed {'gauge44': ['artifact_semantic_sha256', 'artifact_sha256', 'orientation_program_sha256'], 'extra': ['artifact_semantic_sha256', 'artifact_sha256', 'orientation_program_sha256']}
diff --git a/research/paired-extension-cap-fill/evidence/logs/admission-release.log.txt b/research/paired-extension-cap-fill/evidence/logs/admission-release.log.txt
new file mode 100644
index 0000000000..39ae74c55e
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/admission-release.log.txt
@@ -0,0 +1,2 @@
+PYC-GUARD planted stale .pyc: tree guard rejected; plain interpreter ran 'authenticated source'; fresh-prefix interpreter ran 'authenticated source'
+PASS_RELEASE 0.0017224999064432745643569999999999999999999998999999999999999999999999
diff --git a/research/paired-extension-cap-fill/evidence/logs/complete-admission.log.txt b/research/paired-extension-cap-fill/evidence/logs/complete-admission.log.txt
new file mode 100644
index 0000000000..141fd180b1
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/complete-admission.log.txt
@@ -0,0 +1,8 @@
+PASS owners
+PASS parent-lift
+PASS rebind
+PASS discovery
+PASS outer-check_ledger.py
+PASS outer-independent_check.py
+PASS release
+PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE 0.0017224999064432745643569999999999999999999998999999999999999999999999
diff --git a/research/paired-extension-cap-fill/evidence/logs/derive-closed-adapters.log.txt b/research/paired-extension-cap-fill/evidence/logs/derive-closed-adapters.log.txt
new file mode 100644
index 0000000000..771586dca2
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/derive-closed-adapters.log.txt
@@ -0,0 +1 @@
+PASS_CHECKED_82_BUFFER_ADAPTER_DERIVATION_R13 98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1 632 {'prepare_extension_native.py': 'a64ff448b62a9310', 'admit_extension.py': '682a9e90994d86a2', 'extension_blocknorm.py': 'd3893ef2265b1027'}
diff --git a/research/paired-extension-cap-fill/evidence/logs/export-pr2833.log.txt b/research/paired-extension-cap-fill/evidence/logs/export-pr2833.log.txt
new file mode 100644
index 0000000000..1390231558
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/export-pr2833.log.txt
@@ -0,0 +1 @@
+{"head": "e9307b48d7d1b690939935ecef0f8e524e6d92f4", "manifest_entries": 541, "manifest_sha256": "c8ec4d1b7be08d2ad30730a07392ad9cb6d0222f2c35bef43c9a80a39b16e41f", "network_fetch": false, "source": "S/r13pub-build/runs/fresh1/pr2833", "status": "PASS_EXACT_PR2833_SOURCE_EXPORT"}
diff --git a/research/paired-extension-cap-fill/evidence/logs/export-pr2894.log.txt b/research/paired-extension-cap-fill/evidence/logs/export-pr2894.log.txt
new file mode 100644
index 0000000000..2bed900376
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/export-pr2894.log.txt
@@ -0,0 +1 @@
+PASS_PINNED_PR2894_EXPORT_RECIPE_ONLY
diff --git a/research/paired-extension-cap-fill/evidence/logs/four-kernel-stage.log.txt b/research/paired-extension-cap-fill/evidence/logs/four-kernel-stage.log.txt
new file mode 100644
index 0000000000..257be58c74
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/four-kernel-stage.log.txt
@@ -0,0 +1 @@
+{"derived_manifest_sha256": "54dc42f25c1d8b85adcf593c4bf6c0f83f7351388af857812790b8a0b4c3d869", "source_file_count": 547, "status": "PASS_SOURCE_BOUND_FOUR_KERNEL_OVERLAY_DERIVATION"}
diff --git a/research/paired-extension-cap-fill/evidence/logs/fresh-current-native.log.txt b/research/paired-extension-cap-fill/evidence/logs/fresh-current-native.log.txt
new file mode 100644
index 0000000000..820460ef57
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/fresh-current-native.log.txt
@@ -0,0 +1,3 @@
+PASS fresh-current-base
+PASS fresh-current-extra
+PASS_TWO_FRESH_SHARED_KERNEL_NATIVE_CHAINS_AUTHENTICATED_PARENT_REUSE
diff --git a/research/paired-extension-cap-fill/evidence/logs/fresh-retained-bootstrap.log.txt b/research/paired-extension-cap-fill/evidence/logs/fresh-retained-bootstrap.log.txt
new file mode 100644
index 0000000000..9308a84963
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/fresh-retained-bootstrap.log.txt
@@ -0,0 +1,6 @@
+PASS native-base
+PASS native-extra
+PASS native-retained-base
+PASS native-retained-extra
+PASS retained-parent
+PASS_PR2833_FRESH_NATIVE_PREPARATION
diff --git a/research/paired-extension-cap-fill/evidence/logs/paired-extension-stage.log.txt b/research/paired-extension-cap-fill/evidence/logs/paired-extension-stage.log.txt
new file mode 100644
index 0000000000..9ca3a42521
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/paired-extension-stage.log.txt
@@ -0,0 +1 @@
+PASS_SOURCE_BOUND_PAIRED_EXTENSION_OVERLAY 98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1 632
diff --git a/research/paired-extension-cap-fill/evidence/logs/parent-paired-stage.log.txt b/research/paired-extension-cap-fill/evidence/logs/parent-paired-stage.log.txt
new file mode 100644
index 0000000000..de80347a90
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/parent-paired-stage.log.txt
@@ -0,0 +1 @@
+PASS_SOURCE_BOUND_TWO_SIDED_HELPER408_OVERLAY 56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83 610
diff --git a/research/paired-extension-cap-fill/evidence/logs/preload-stage.log.txt b/research/paired-extension-cap-fill/evidence/logs/preload-stage.log.txt
new file mode 100644
index 0000000000..4fa79b5e48
--- /dev/null
+++ b/research/paired-extension-cap-fill/evidence/logs/preload-stage.log.txt
@@ -0,0 +1 @@
+{"derived_manifest_sha256": "4da246899e2c509dd8c6e5af34905c6124ca17671b188e11ac37e36adf449504", "source_file_count": 553, "status": "PASS_SOURCE_BOUND_PRELOAD_MOVE_OVERLAY_DERIVATION"}
diff --git a/research/paired-extension-cap-fill/reproduce.py b/research/paired-extension-cap-fill/reproduce.py
new file mode 100644
index 0000000000..c323d55c95
--- /dev/null
+++ b/research/paired-extension-cap-fill/reproduce.py
@@ -0,0 +1,147 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Exact Git exports, PR2917's declared source stages, fresh native chains and complete admission of the
+cap-attaining allocation of PR2917's unchanged words.
+
+The recipe is PR2917's reproduce.py (Mason Hale; PR2908 stage/native/release mechanisms of Jeremy Diviney
+and the credited upstream lineage) with three changes: PR2917's package is itself exported from its exact
+commit; the closed adapters are derived with the PR2917 headline as an additional comparator
+(tools/derive_adapters.py); and the admission uses this package's allocation/ and compares against PR2917.
+No network fetch is performed: the four commits below must be present in --repo (see README). Fresh
+retained bootstrap is the default; --retained explicitly reuses a completely authenticated cache.
+Marius-Paul Dumitrean, with substantial AI assistance (Claude Code).
+"""
+import argparse, hashlib, io, json, os, subprocess, sys, tarfile, time
+from fractions import Fraction as Q
+from pathlib import Path, PurePosixPath
+
+P = Path(__file__).resolve().parent
+PR2908 = ('51309592971e3b5be935599eed2a95404dc7781e', 'research/two-sided-helper-extraction',
+          '9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f')
+PR2917 = ('224bd5e56041c40078ff6b5fa7393733a215de5c', 'research/paired-helper-extension',
+          '55c46ddf2e3edc87dfe1ba3320947466d36980d457eb37f6cd6fba341dae0192')
+DERIVED_SOURCE = '98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1'
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def read(p):
+    return json.loads(p.read_bytes())
+
+def save(p, value):
+    p.write_text(json.dumps(value, indent=2, sort_keys=True) + '\n')
+
+def tree(p):
+    assert not any(f.is_symlink() for f in p.rglob('*'))
+    return {f.relative_to(p).as_posix(): sha(f) for f in p.rglob('*') if f.is_file() and f != p / 'MANIFEST.json'}
+
+def export(repo, head, package, manifest, out):
+    prefix = PurePosixPath(package)
+    raw = subprocess.run(['git', '-C', str(repo), 'archive', '--format=tar', head, str(prefix)],
+                         check=True, capture_output=True).stdout
+    out.mkdir()
+    with tarfile.open(fileobj=io.BytesIO(raw), mode='r:') as archive:
+        for member in archive.getmembers():
+            path = PurePosixPath(member.name)
+            assert not path.is_absolute() and '..' not in path.parts and '\\' not in member.name
+            if member.isdir() and (path == prefix or path in prefix.parents):
+                continue
+            assert path.is_relative_to(prefix) and (member.isfile() or member.isdir())
+            dest = out / path.relative_to(prefix)
+            if member.isdir():
+                dest.mkdir(parents=True, exist_ok=True)
+            else:
+                dest.parent.mkdir(parents=True, exist_ok=True)
+                dest.write_bytes(archive.extractfile(member).read())
+    assert sha(out / 'MANIFEST.json') == manifest, 'exact exported package manifest ' + package
+    assert tree(out) == read(out / 'MANIFEST.json'), 'complete exported inventory ' + package
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    for name in ('repo', 'work'):
+        ap.add_argument('--' + name, type=Path, required=True)
+    ap.add_argument('--retained', type=Path)
+    ap.add_argument('--jobs', type=int, default=1, choices=(1, 2, 3))
+    ap.add_argument('--dry-run', action='store_true')
+    args = ap.parse_args()
+    if not __debug__:
+        raise SystemExit('refusing python -O: the inherited validators rely on assertions')
+    work, repo = args.work.resolve(), args.repo.resolve()
+    assert not work.exists() and not work.is_relative_to(P) and not P.is_relative_to(work)
+    pins = read(P / 'MANIFEST.json')
+    assert tree(P) == pins, 'complete public package inventory'
+    work.mkdir(parents=True)
+    parent, extension = work / 'pr2908', work / 'pr2917'
+    export(repo, *PR2908, parent)
+    export(repo, *PR2917, extension)
+    for tag in ('base', 'extra'):
+        assert sha(P / f'data/WORD-{tag}.json.gz') == sha(extension / f'data/WORD-{tag}.json.gz'), 'unchanged PR2917 words'
+    upstream = work / 'parent-export/pr2894'
+    core = upstream / 'vendor/pr2857'
+    source = work / 'pr2833'
+    four, preload, channel, final = [work / n for n in ('source4', 'source-pm', 'source2908', 'source')]
+    native, candidate, adapters = [work / n for n in ('native', 'candidate', 'adapters')]
+    retained = args.retained.resolve() if args.retained else work / 'retained'
+    if args.retained:
+        assert not retained.is_relative_to(work) and not work.is_relative_to(retained)
+    py = [sys.executable, '-B']
+    recipe = [
+        ('export-pr2894', py + [parent / 'reproduce.py', '--repo', repo, '--work', work / 'parent-export', '--dry-run']),
+        ('export-pr2833', py + [upstream / 'tools/materialize_source.py', '--repo', repo, '--out', source]),
+    ]
+    if not args.retained:
+        recipe.append(('fresh-retained-bootstrap', py + [upstream / 'tools/prepare_retained.py', '--source', source, '--out', retained, '--jobs', '1']))
+    recipe += [
+        ('four-kernel-stage', py + [core / 'build_overlay.py', '--source', source, '--generator', core / 'shared_kernel.py', '--review', core / 'review_four_groups.py', '--candidate-dir', core / 'words', '--out', four]),
+        ('preload-stage', py + [upstream / 'vendor/pm/build_pm_overlay.py', '--overlay', four, '--pm-dir', upstream / 'vendor/pm', '--out', preload]),
+        ('parent-paired-stage', py + [parent / 'tools/build_channel_overlay.py', '--source', preload, '--local-package', parent, '--out', channel]),
+        ('paired-extension-stage', py + [extension / 'tools/build_extension.py', '--source', channel, '--local-package', extension, '--out', final]),
+        ('derive-closed-adapters', py + [P / 'tools/derive_adapters.py', '--parent-package', parent, '--source', final, '--retained-receipt', retained / 'NATIVE-RECEIPT.json', '--out', adapters,
+                                         '--buffers', '82', '--source-commit', 'paired-helper-extension-pr2908', '--source-profile', 'paired-extension', '--upstream-head', PR2908[0],
+                                         '--comparison', 'pr2917=' + str(extension / 'CLAIM.json')]),
+        ('fresh-current-native', py + [adapters / 'prepare_extension_native.py', '--source', final, '--retained-cache', retained / 'native-cache', '--retained-receipt', retained / 'NATIVE-RECEIPT.json', '--out', native, '--jobs', str(min(2, args.jobs))]),
+        ('complete-admission', py + [adapters / 'admit_extension.py', '--source', final, '--fill', P / 'allocation/FILL.json.gz', '--order', P / 'allocation/ORDER.json', '--dispatch', P / 'allocation/DISPATCH.json',
+                                     '--native-cache', native / 'native-cache', '--native-receipt', native / 'NATIVE-RECEIPT.json', '--work', candidate, '--replica-helper-dir', core / 'vendor/pr2839',
+                                     '--reconstructor', core / 'vendor/pr2839/reconstruct_replica.py', '--blocknorm-checker', adapters / 'extension_blocknorm.py',
+                                     '--comparison-claim', extension / 'CLAIM.json', '--source-profile', 'paired-extension', '--comparison-profile', 'pr2917', '--jobs', str(args.jobs)]),
+    ]
+    if args.dry_run:
+        save(work / 'PREFLIGHT.json', {'status': 'EXACT_EXPORTS_AND_RECIPE_ONLY_NOT_A_REPLAY', 'commands': [[n, list(map(str, c))] for n, c in recipe]})
+        print('PASS_PINNED_PR2908_PR2917_EXPORT_RECIPE_ONLY')
+        return
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONPYCACHEPREFIX=str(work / 'bytecode'),
+               OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1', PYTHONINTMAXSTRDIGITS='0')
+    for name in ('PYTHONOPTIMIZE', 'PYTHONPATH', 'WITNESS_SPEC', 'WITNESS_RECORD', 'WITNESS_DISCOVER'):
+        env.pop(name, None)
+    stages = []
+    for name, command in recipe:
+        log, start = work / (name + '.log'), time.monotonic()
+        with log.open('w') as stream:
+            result = subprocess.run(list(map(str, command)), env=env, cwd=work, stdin=subprocess.DEVNULL,
+                                    stdout=stream, stderr=subprocess.STDOUT)
+        stages.append({'stage': name, 'exit_code': result.returncode, 'seconds': time.monotonic() - start, 'log_sha256': sha(log)})
+        save(work / 'STAGES.json', stages)
+        assert result.returncode == 0, 'failed ' + name + '; see ' + str(log)
+        print('PASS', name, flush=True)
+    assert sha(final / 'MANIFEST.json') == DERIVED_SOURCE, 'derived source equals PR2917s'
+    admission = read(candidate / 'RESULT.json')
+    receipt = read(candidate / 'release/RELEASE-RECEIPT.json')
+    claim = read(P / 'CLAIM.json')
+    assert admission['status'] == 'PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE'
+    assert receipt['status'] == 'PASS_RELEASE'
+    assert Q(admission['kappa']) == Q(receipt['kappa_decimal']) == Q(claim['kappa'])
+    assert Q(admission['comparison_kappa']) == Q(read(extension / 'CLAIM.json')['kappa']) == Q(claim['baseline_kappa'])
+    assert admission['release_receipt_sha256'] == sha(candidate / 'release/RELEASE-RECEIPT.json')
+    assert admission['package_manifest_sha256'] == receipt['manifest_sha256']
+    assert admission['fill_sha256'] == sha(P / 'allocation/FILL.json.gz')
+    assert tree(P) == pins and tree(parent) == read(parent / 'MANIFEST.json') and tree(extension) == read(extension / 'MANIFEST.json')
+    save(work / 'RESULT.json', {'status': 'PASS_CAP_FILL_COMPLETE_REPLAY', 'kappa': admission['kappa'], 'gain': admission['gain'],
+                              'source_manifest_sha256': sha(final / 'MANIFEST.json'),
+                              'native_receipt_sha256': sha(native / 'NATIVE-RECEIPT.json'),
+                              'admission_result_sha256': sha(candidate / 'RESULT.json'),
+                              'explicit_retained_reuse': bool(args.retained), 'fresh_retained_bootstrap': not bool(args.retained),
+                              'stages': stages, 'scope': 'Conditional finite supplier/outer result; inherited all-size theorem obligations remain.'})
+    print('PASS_CAP_FILL_COMPLETE_REPLAY', admission['kappa'], flush=True)
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-extension-cap-fill/run_registered.py b/research/paired-extension-cap-fill/run_registered.py
new file mode 100644
index 0000000000..4412b7eabe
--- /dev/null
+++ b/research/paired-extension-cap-fill/run_registered.py
@@ -0,0 +1,83 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Bounded registered check: package pins, literal owners/controls/exact moment, the Fractions-only cap
+certificate, and binding of the stored complete native/admission/release receipts to the exact words,
+allocation and claim. It does not rerun the native or integrated outer replay (reproduce.py does).
+Structure adapted from Mason Hale's PR2917 run_registered.py. Marius-Paul Dumitrean, with substantial AI
+assistance (Claude Code).
+"""
+import hashlib, json, os, subprocess, sys, tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+
+P = Path(__file__).resolve().parent
+PR2917_HEAD = '224bd5e56041c40078ff6b5fa7393733a215de5c'
+DERIVED_SOURCE = '98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1'
+
+def read(p):
+    return json.loads(p.read_bytes())
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+def tree():
+    assert not any(f.is_symlink() for f in P.rglob('*'))
+    return {f.relative_to(P).as_posix(): sha(f) for f in P.rglob('*') if f.is_file() and f != P / 'MANIFEST.json'}
+
+def main():
+    if not __debug__:
+        raise SystemExit('refusing python -O: this check relies on assertions')
+    pins = read(P / 'MANIFEST.json')
+    assert tree() == pins, 'complete package inventory'
+    with tempfile.TemporaryDirectory(prefix='cap-fill-replay-') as tmp:
+        out = Path(tmp)
+        env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1')
+        for key in ('PYTHONOPTIMIZE', 'PYTHONPATH', 'WITNESS_SPEC', 'WITNESS_RECORD', 'WITNESS_DISCOVER'):
+            env.pop(key, None)
+        log = out / 'owners.log'
+        with log.open('w') as stream:
+            r = subprocess.run([sys.executable, '-B', str(P / 'check_allocation.py'), '--work', str(out / 'owners')],
+                               env=env, stdin=subprocess.DEVNULL, stdout=stream, stderr=subprocess.STDOUT)
+        if r.returncode:
+            print(log.read_text()[-8000:]); raise SystemExit(r.returncode)
+        r = subprocess.run([sys.executable, '-B', str(P / 'check_cap.py')], env=env, stdin=subprocess.DEVNULL,
+                           capture_output=True, text=True)
+        if r.returncode:
+            print(r.stdout[-4000:], r.stderr[-4000:]); raise SystemExit(r.returncode)
+        cap = json.loads(r.stdout.strip().splitlines()[-1])
+        owner = read(out / 'owners/RESULT.json')
+    claim = read(P / 'CLAIM.json')
+    admit = read(P / 'evidence/ADMISSION-RESULT.json')
+    release = read(P / 'evidence/RELEASE-RECEIPT.json')
+    native = read(P / 'evidence/FULL-NATIVE-RECEIPT.json')
+    baseline = read(P / 'allocation/baseline/CLAIM.json')
+    assert claim['status'] == 'CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE'
+    assert owner['status'] == 'PASS_CAP_FILL_LITERAL_OWNERS_AND_EXACT_MOMENT' and len(owner['controls']) == 5
+    assert cap['status'] == 'PASS_LITERAL_ALLOCATION_ATTAINS_FIXED_INVENTORY_CAP'
+    assert admit['status'] == 'PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE'
+    assert release['status'] == 'PASS_RELEASE'
+    k = Q(claim['kappa'])
+    assert Q(owner['moment']['target']) == k == Q(admit['kappa']) == Q(release['kappa_decimal'])
+    assert Q(cap['cap_lower']) == Q(claim['complex_lower']) == Q(admit['complex_lower'])
+    assert k == Q(claim['complex_lower']) - Q(1, 10 ** 46) - Q(1, 10 ** 70)
+    assert owner['profile'] == claim['profile'] == admit['profile'] == cap['profile']
+    assert owner['physical'] == claim['physical_families'] == 66804
+    assert release['manifest_sha256'] == admit['package_manifest_sha256'] == claim['admitted_package_manifest_sha256']
+    assert native['status'] == 'PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE'
+    assert native['fresh_current_provider_count'] == 2 and set(native['providers']) == {'base', 'extra'}
+    assert claim['release_receipt_sha256'] == admit['release_receipt_sha256'] == sha(P / 'evidence/RELEASE-RECEIPT.json')
+    assert claim['native_receipt_sha256'] == admit['native_receipt_sha256'] == sha(P / 'evidence/FULL-NATIVE-RECEIPT.json')
+    assert claim['source_manifest_sha256'] == native['manifest_sha256'] == admit['source_manifest_sha256'] == DERIVED_SOURCE
+    assert admit['comparison_pr'] == 2917 and admit['comparison_head'] == PR2917_HEAD == claim['baseline_head']
+    assert Q(claim['baseline_kappa']) == Q(admit['comparison_kappa']) == Q(baseline['kappa']) == Q(owner['moment']['previous'])
+    assert Q(claim['gain']) == Q(admit['gain']) == k - Q(baseline['kappa']) > 0
+    for tag in ('base', 'extra'):
+        assert native['providers'][tag]['word_sha256'] == sha(P / f'data/WORD-{tag}.json.gz')
+    assert admit['fill_sha256'] == sha(P / 'allocation/FILL.json.gz')
+    assert admit['order_sha256'] == sha(P / 'allocation/ORDER.json')
+    assert admit['dispatch_sha256'] == sha(P / 'allocation/DISPATCH.json')
+    assert tree() == pins
+    print('PASS_CAP_FILL_LOCAL_OWNER_MOMENT_CAP_AND_STORED_RELEASE', claim['kappa_decimal'][:40], 'gain', float(Q(claim['gain'])))
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-extension-cap-fill/tools/audit_allocation_moment.py b/research/paired-extension-cap-fill/tools/audit_allocation_moment.py
new file mode 100644
index 0000000000..e6a01a5e31
--- /dev/null
+++ b/research/paired-extension-cap-fill/tools/audit_allocation_moment.py
@@ -0,0 +1,82 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Independent dyadic interval moment auditor, atlas D020.
+Retained PR2908 arithmetic by Jeremy Diviney and its credited upstream authors;
+Mason Hale with OpenAI Codex assistance changes only the authenticated baseline.
+Marius-Paul Dumitrean (Claude Code assisted) again changes only the authenticated baseline: the PR2917 headline.
+Uses only Python integers/Fraction; imports no inherited numerical implementation.
+This authenticates a paid histogram and its root, not a physical realization.
+"""
+from fractions import Fraction as F
+from pathlib import Path
+from functools import lru_cache
+from collections import Counter
+import argparse,json,hashlib
+
+BITS=192
+SCALE=1<<BITS
+
+def need(c,m):
+    if not c:raise ValueError(m)
+def down(x):return F(x.numerator*SCALE//x.denominator,SCALE)
+def up(x):return F(-((-x.numerator*SCALE)//x.denominator),SCALE)
+@lru_cache(None)
+def log_bounds(q):
+    need(q>=1,'log domain');k=0
+    while q>2:q/=2;k+=1
+    def unit(y):
+        z=(y-1)/(y+1);z2=z*z;term=z;value=F(0)
+        for j in range(128):
+            value+=term/(2*j+1);term*=z2
+        remainder=2*term/(257*(1-z2))
+        return 2*value,2*value+remainder
+    l,u=unit(q);l2,u2=unit(F(2));return down(l+k*l2),up(u+k*u2)
+def exp_bounds(y):
+    need(0<=y<F(1,10),'small exponential domain');term=F(1);value=term
+    for j in range(1,25):term=term*y/j;value+=term
+    first=term*y/25;tail=first/(1-y/26)
+    return down(value),up(value+tail)
+def moment(profile,b,W):
+    need(0<=b<F(1,100),'saving domain');lo=hi=F(0)
+    for rank,count in profile.items():
+        need(0<rank<73 and count>0,'profile domain');l,u=log_bounds(F(73,rank));a=exp_bounds(b*l)[0];z=exp_bounds(b*u)[1];weight=F(rank*count,73*W);lo+=weight*a;hi+=weight*z
+    return down(lo),up(hi)
+def run(candidate,source):
+    import sys
+    if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0)
+    need(hashlib.sha256((source/'CLAIM.json').read_bytes()).hexdigest()=='e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac','exact pinned PR2917 full headline')
+    prof={int(k):v for k,v in json.loads((candidate/'PROFILE.json').read_bytes()).items()}
+    old={int(k):v for k,v in json.loads((source/'PROFILE.json').read_bytes()).items()}
+    W=896*(1+max(r for s,r in json.loads((candidate/'ORDER.json').read_bytes())))
+    oldW=896*(1+max(r for s,r in json.loads((source/'ORDER.json').read_bytes())))
+    need(sum(r*n for r,n in prof.items())==W*73-W*320//896,'new rank mass')
+    need(sum(r*n for r,n in old.items())==oldW*73-oldW*320//896,'old rank mass')
+    # No floating endpoint or inherited numerical implementation is used.
+    q=10**26;lo=0;hi=q//200
+    need(moment(prof,F(lo,q),W)[1]<1 and moment(prof,F(hi,q),W)[0]>1,'global root bracket')
+    while hi-lo>1:
+        mid=(lo+hi)//2;l,u=moment(prof,F(mid,q),W)
+        if u<1:lo=mid
+        elif l>1:hi=mid
+        else:raise ValueError('interval precision insufficient')
+    endpoint=F((lo//100),10**24)
+    target=endpoint-F(1,10**46)-F(1,10**70)
+    prior=F(json.loads((source/'CLAIM.json').read_bytes())['kappa'])
+    need(target>prior and target<F(lo,q),'strict frontier improvement and lower endpoint')
+    normalized_delta=Counter({r:n*oldW for r,n in prof.items()});normalized_delta.subtract({r:n*W for r,n in old.items()})
+    normalized_delta={r:n for r,n in normalized_delta.items()if n}
+    at_old=moment(prof,prior,W);need(at_old[1]<1,'new moment strictly below one at full previous headline')
+    # Positive root uniqueness: all charged ranks are strictly below m = 73,
+    # hence every nonzero summand increases strictly with the saving parameter.
+    need(log_bounds(F(1))==(0,0) and exp_bounds(F(0))==(1,1),'zero controls')
+    need(moment(prof,F(hi,q)+F(1,10**18),W)[0]>1,'overstated endpoint rejected')
+    wrong=dict(prof);wrong[32]=wrong.get(32,0)+1
+    need(moment(wrong,F(lo,q),W)[0]>1,'omitted rank charge rejected')
+    import decimal
+    with decimal.localcontext() as c:
+        c.prec=80
+        todec=lambda x:str(decimal.Decimal(x.numerator)/decimal.Decimal(x.denominator))
+        texttarget=todec(target);textgain=todec(target-prior)
+    return dict(status='PASS_SEPARATE_EXACT_RATIONAL_FRONTIER_MOMENT',lower=str(F(lo,q)),upper=str(F(hi,q)),outer_endpoint=str(endpoint),target=str(target),target_decimal=texttarget,previous=str(prior),gain=str(target-prior),gain_decimal=textgain,W=W,oldW=oldW,normalized_profile_delta=normalized_delta,new_moment_at_full_prior=[str(x)for x in at_old],profile_sha256=hashlib.sha256((candidate/'PROFILE.json').read_bytes()).hexdigest(),baseline_profile_sha256=hashlib.sha256((source/'PROFILE.json').read_bytes()).hexdigest(),baseline_claim_sha256=hashlib.sha256((source/'CLAIM.json').read_bytes()).hexdigest(),method='Independent 128-term atanh / degree24 exponential with explicit positive tails and outward 192-bit dyadic rounding',controls=['zero log/exp identities','overstated endpoint','added rank32 charge'],scope='Complete paid histogram and exact moment only; full native/physical/outer release is separate.')
+if __name__=='__main__':
+    p=argparse.ArgumentParser();p.add_argument('--candidate',type=Path,required=True);p.add_argument('--source',type=Path,required=True);p.add_argument('--out',type=Path,required=True);a=p.parse_args()
+    need(not a.out.exists(),'fresh output required');d=run(a.candidate,a.source);a.out.write_text(json.dumps(d,sort_keys=True,indent=2)+'\n',encoding='utf-8',newline='\n');print(json.dumps({k:d[k]for k in ['status','target_decimal','gain_decimal','lower','upper']}))
diff --git a/research/paired-extension-cap-fill/tools/derive_adapters.py b/research/paired-extension-cap-fill/tools/derive_adapters.py
new file mode 100644
index 0000000000..9e66ab8172
--- /dev/null
+++ b/research/paired-extension-cap-fill/tools/derive_adapters.py
@@ -0,0 +1,100 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Generalized PR2917 adapter derivation (Marius-Paul Dumitrean, Claude Code assisted; PR2917/PR2908 derivations by Mason Hale and Jeremy Diviney): PR2908's exact tools -> closed-profile adapters for an
+arbitrary derived overlay, buffer count B, source profile and comparator set. With B=82, commit
+'paired-helper-extension-pr2908', profile 'paired-extension' and comparisons=pr2908 the output is byte-identical to
+PR2917's tools/derive_adapters.py output (checked against its evidence/ADAPTER-DERIVATION.json), except the retained
+receipt binding, which is always sha256(--retained-receipt).
+usage: derive_adapters_r13.py --parent-package PR2908_PKG --source OVERLAY --retained-receipt FILE --out DIR
+       --buffers B --source-commit NAME --source-profile NAME --upstream-head HEX
+       [--comparison pr2917=/path/CLAIM.json ...]   (pr2908 is always derived from the parent package's CLAIM.json)
+"""
+from pathlib import Path
+import argparse, gzip, hashlib, json, sys
+PARENT_HEAD = '51309592971e3b5be935599eed2a95404dc7781e'
+PARENT_MANIFEST = '9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f'
+OLD_SOURCE = '56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83'
+OLD_RETAINED = 'dd36443f2789ffa6deca7210c76ada781e2b9b7e622a546b366f51a475faff3e'
+HEADS = {'pr2908': PARENT_HEAD, 'pr2917': '224bd5e56041c40078ff6b5fa7393733a215de5c'}
+sha = lambda b: hashlib.sha256(b).hexdigest()
+
+def need(p, msg):
+    if not p: raise ValueError(msg)
+
+def tree(p):
+    need(not any(f.is_symlink() for f in p.rglob('*')), 'no symlinks')
+    return {f.relative_to(p).as_posix(): sha(f.read_bytes()) for f in p.rglob('*') if f.is_file() and f != p / 'MANIFEST.json'}
+
+def derive(parent, source, out, retained_sha, B, commit, profile, upstream_head, claims):
+    manifest = json.loads((parent / 'MANIFEST.json').read_bytes()); need(tree(parent) == manifest, 'complete exact parent manifest inventory')
+    need(sha((parent / 'MANIFEST.json').read_bytes()) == PARENT_MANIFEST, 'exact PR2908 package manifest')
+    newsha = sha((source / 'MANIFEST.json').read_bytes())
+    files = json.loads((source / 'MANIFEST.json').read_bytes()); need(tree(source) == files, 'complete derived source inventory')
+    nfiles = len(files)
+    for tag in ('base', 'extra'):
+        w = json.loads(gzip.decompress((source / f'new/borrow/words/BORROW-WORD-43{tag}.json.gz').read_bytes()))
+        need(len(w['helper_final']) == B, f'declared {B}-buffer word ({tag}: {len(w["helper_final"])})')
+        need(len(set(range(224, 704)) - set(w['removed'])) == 408, '408 live helpers')
+    need(type(B) is int and 73 <= B <= 200, 'buffer count range')
+    need(len(retained_sha) == 64 and all(c in '0123456789abcdef' for c in retained_sha), 'retained receipt SHA256')
+    comps = [('pr2908', parent / 'CLAIM.json')] + [(k, Path(v)) for k, v in claims]
+    comp_entries = []
+    for name, path in comps:
+        claim = json.loads(path.read_bytes()); need('headline_kappa_source' not in claim and 'kappa' in claim, 'headline outer comparison ' + name)
+        need(name in HEADS, 'known comparator head ' + name)
+        comp_entries.append((name, int(name[2:]), HEADS[name], sha(path.read_bytes())))
+    out.mkdir(parents=True, exist_ok=False); changes = {}
+    def adapt(oldname, newname, pairs):
+        p = parent / 'tools' / oldname; body = p.read_text(); oldhash = sha(p.read_bytes()); applied = []
+        for old, new in pairs:
+            need(body.count(old) == 1, f'exact preimage occurrence {oldname}: {old[:120]}')
+            body = body.replace(old, new); applied.append({'old': old, 'new': new})
+        q = out / newname; q.write_text(body); compile(body, str(q), 'exec')
+        changes[newname] = {'source': str(p), 'before_sha256': oldhash, 'after_sha256': sha(q.read_bytes()), 'replacements': applied}
+    adapt('prepare_channel_native.py', 'prepare_extension_native.py', [
+        ("SOURCE_SHA='" + OLD_SOURCE + "'", "SOURCE_SHA='" + newsha + "'"),
+        ('SOURCE_FILES=610', 'SOURCE_FILES=' + str(nfiles)),
+        ("SOURCE_COMMIT='two-sided-helper408-pr2894'", "SOURCE_COMMIT='" + commit + "'"),
+        ("OLD_RECEIPT_SHA='" + OLD_RETAINED + "'", "OLD_RECEIPT_SHA='" + retained_sha + "'"),
+        ("len(can['zero_buffers'])==73", f"len(can['zero_buffers'])=={B}"),
+    ])
+    oldprofile = "    'channel408': dict(commit='two-sided-helper408-pr2894',manifest='" + OLD_SOURCE + "',helpers=408,source_file_count=610,upstream_head='18d03c447886895ef9abf888398178e0428533ca'),"
+    newprofile = "    '" + profile + "': dict(commit='" + commit + "',manifest='" + newsha + "',helpers=408,source_file_count=" + str(nfiles) + ",upstream_head='" + upstream_head + "'),"
+    comp_text = "COMPARISONS = {" + ''.join("\n    '" + n + "': dict(pr=" + str(pr) + ",head='" + h + "',sha256='" + s + "',field='kappa')," for n, pr, h, s in comp_entries)
+    choices = "['" + "','".join(n for n, *_ in comp_entries) + "']"
+    adapt('admit_channel408.py', 'admit_extension.py', [
+        (oldprofile, newprofile),
+        ("COMPARISONS = {", comp_text),
+        ("ap.add_argument('--source-profile', choices=['channel408'], default='channel408')", "ap.add_argument('--source-profile', choices=['" + profile + "'], default='" + profile + "')"),
+        ("ap.add_argument('--comparison-profile', choices=['pr2894'], default='pr2894')", "ap.add_argument('--comparison-profile', choices=" + choices + ", default='pr2908')"),
+        ('zero_buffers_allocated_and_cleared=73', f'zero_buffers_allocated_and_cleared={B}'),
+        ("len(c.get('zero_buffers',[]))==73, 'helper408 physical ABI including all 73 private buffers'", f"len(c.get('zero_buffers',[]))=={B}, 'paired extension physical ABI including all {B} private buffers'"),
+        ("896*T+expected_helpers+8+73+2, 'complete physical cost including all actual helpers and 73 buffers'", f"896*T+expected_helpers+8+{B}+2, 'complete physical cost including all actual helpers and {B} buffers'"),
+    ])
+    adapt('channel_blocknorm.py', 'extension_blocknorm.py', [
+        ("len(allocated)==73, 'all73 private zero buffers released'", f"len(allocated)=={B}, 'all{B} private zero buffers released'"),
+        ("'zero_buffers_allocated_and_cleared':73", f"'zero_buffers_allocated_and_cleared':{B}"),
+        ("r['zero_buffers_returned_to_zero']==73", f"r['zero_buffers_returned_to_zero']=={B}"),
+        ('physical==live+8+408+73+2', f'physical==live+8+408+{B}+2'),
+        ("'zero_buffers':[live+416,live+489], 'coefficient':[live+489,live+491]", f"'zero_buffers':[live+416,live+{416 + B}], 'coefficient':[live+{416 + B},live+{418 + B}]"),
+        ("len(mp)==73 and set(mp.values())==set(range(*ns['zero_buffers'])), '73distinct private Z slots'", f"len(mp)=={B} and set(mp.values())==set(range(*ns['zero_buffers'])), '{B}distinct private Z slots'"),
+        ('T=len(order)//9; live=896*T; physical=live+490', f'T=len(order)//9; live=896*T; physical=live+{418 + B}'),
+    ])
+    # The native address dimension and symplectic stock factor are deliberately retained (as in PR2917).
+    b = (out / 'extension_blocknorm.py').read_text(); a = (out / 'admit_extension.py').read_text()
+    need("require(d['m']==73" in b and 'Sp(72,2)' in b and 'range(1,37)' in b, 'retained native dimension and symplectic group')
+    need('assert m==73' in a, 'retained outer dimension')
+    receipt = {'status': f'PASS_CHECKED_{B}_BUFFER_ADAPTER_DERIVATION_R13', 'parent_head': PARENT_HEAD, 'parent_manifest_sha256': PARENT_MANIFEST,
+               'source_commit': commit, 'source_profile': profile, 'upstream_head': upstream_head, 'source_manifest_sha256': newsha, 'source_files': nfiles,
+               'comparisons': {n: dict(pr=pr, head=h, sha256=s) for n, pr, h, s in comp_entries}, 'retained_receipt_sha256': retained_sha,
+               'buffer_count': B, 'physical_overhead': 418 + B, 'changes': changes}
+    (out / 'ADAPTER-DERIVATION.json').write_text(json.dumps(receipt, indent=2) + '\n'); return receipt
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(); ap.add_argument('--parent-package', type=Path, required=True); ap.add_argument('--source', type=Path, required=True)
+    ap.add_argument('--retained-receipt', type=Path, required=True); ap.add_argument('--out', type=Path, required=True); ap.add_argument('--buffers', type=int, required=True)
+    ap.add_argument('--source-commit', required=True); ap.add_argument('--source-profile', required=True); ap.add_argument('--upstream-head', required=True)
+    ap.add_argument('--comparison', action='append', default=[], help='name=path/to/CLAIM.json (pr2917=...)'); a = ap.parse_args()
+    claims = [tuple(c.split('=', 1)) for c in a.comparison]
+    r = derive(a.parent_package.resolve(), a.source.resolve(), a.out.resolve(), sha(a.retained_receipt.read_bytes()), a.buffers, a.source_commit, a.source_profile, a.upstream_head, claims)
+    print(r['status'], r['source_manifest_sha256'], r['source_files'], {k: v['after_sha256'][:16] for k, v in r['changes'].items()})
diff --git a/research/paired-extension-cap-fill/tools/relax.py b/research/paired-extension-cap-fill/tools/relax.py
new file mode 100644
index 0000000000..97dfe35c43
--- /dev/null
+++ b/research/paired-extension-cap-fill/tools/relax.py
@@ -0,0 +1,329 @@
+#!/usr/bin/env python3
+"""relax.py -- changed-inventory, fixed-capacity fractional relaxation (upper bound on the complex endpoint)
+for an ARBITRARY per-call local profile and per-call helper-width inventory, with exact rational verification.
+
+Model (everything per replica; the fractional cap is independent of T):
+  * bins: every replica has 112 ports x 18 idle children; the child capacities (ranks) come from the
+    T37 template: 6 children of capacity 8, 4 of 16, 4 of 32, 4 of 48  -> bins {8:672, 16:448, 32:448, 48:448}.
+  * roles: every call hosts all its helpers; a helper of width w occupies w consecutive units of ONE bin;
+    the 9 calls of a replica supply 9*inventory[w] roles of width w per replica (the inventory is per call;
+    with two providers of different widths pass the call-weighted average, a Fraction is fine).
+  * pattern catalogue: every multiset of widths with sum <= capacity ("bounded count-vector enumeration");
+    the bin then pays ONE idle child of rank cap - used (rank 0 = nothing).
+  * CHRONOLOGY IS IGNORED: no source windows, no per-call family collisions, no "one role per bin per call",
+    no integrality.  A bin pattern count may be fractional.  Hence this is an UPPER bound on what any
+    actual fill of the same inventory can reach, and the bound is NOT a chronological witness.
+  * local profile is fixed and fully paid: 9 * local[r] children of rank r per replica.
+  Moment: M_x(b) = (9*sum_r local_r H_r(b) + sum_p x_p H_{r_p}(b)) / (73*896),  H_r(b) = r*(73/r)^b,
+  LP(b): min_x sum_p x_p H_{r_p}(b)  s.t.  sum_{p in cap c} x_p = bins[c],  sum_p n_w(p) x_p = 9*inv[w], x>=0.
+  cap = the root b of min_x M_x(b) = 1 (g(b) = min_x M_x(b) is increasing).
+
+Exact verification (same technique as PR2857's audit_relaxation.py, re-implemented):
+  1. float bisection with scipy/HiGHS locates b*; the optimal basis B (9 columns) is read off;
+  2. x_B = B^-1 rhs exactly (Fractions) -> the primal profile; root bracketed at 10^-25 with the package's
+     rational interval arithmetic (root.py): M(lo) < 1 < M(hi) -> cap >= lo (x_B is feasible);
+  3. dual y(b) = B^-T c_B(b) is an exact rational combination of the H_k(b): the Y matrix of the receipt;
+     every pattern's reduced cost at b = hi is bracketed with the H enclosures and must be > 0 (or identically 0
+     for the tight patterns)  -> by weak duality every feasible x has M_x(hi) >= M_{x_B}(hi) > 1  -> cap <= hi.
+  Reproduces PR2857: cap in [0.001720100805416885927944, 0.001720100805416885927945], 1163 patterns, 11 tight.
+
+Usage:
+  python -B relax.py --calibrate
+  python -B relax.py --inventory '{"4":26,"5":2,"7":62,"8":85,"9":233}' --local '{"1":2397,"2":640,"3":266,"4":128,"5":26,"8":8}'
+  python -B relax.py --delta-inventory '{"8":1,"9":-1}' --delta-local '{"1":3,"2":-2}'     # relative to PR2857
+  python -B relax.py --scenarios                      # the hypothetical table of ROUND.md (one/two 9->8, 8->7, removal)
+API: relax(local, inventory, bins=BINS) -> dict (cap_lower, cap_upper, active patterns, idle histogram, dual check, ...)
+"""
+from fractions import Fraction as Q
+from itertools import product
+import argparse, json, sys, os
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import root as R
+
+BINS = {8: 672, 16: 448, 32: 448, 48: 448}          # bins per replica (112 ports x children per capacity)
+LIVE = R.LIVE_PER_REPLICA                            # 896
+CALLS = R.CALLS_PER_REPLICA                          # 9
+PR2857_LOCAL = {1: 2394, 2: 642, 3: 266, 4: 128, 5: 26, 8: 8}
+PR2857_INV = {4: 26, 5: 2, 7: 62, 8: 84, 9: 234}
+PR2857_REALIZED_LOWER = Q('17200966286848326009728/10000000000000000000000000')
+PR2857_REALIZED_UPPER = Q('17200966286848326009729/10000000000000000000000000')
+PR2857_CAP_UPPER = Q('344020161083377185589/200000000000000000000000')      # 0.001720100805416885927945
+PR2848_KAPPA = Q('17186585083049300/10000000000000000000')                   # 0.0017186585083049300 (incumbent of PR2857's gain)
+
+
+def need(c, m):
+    if not c:
+        raise ValueError(m)
+
+
+def patterns(bins, widths):
+    out = []
+    for cap in sorted(bins):
+        for counts in product(*(range(cap // w + 1) for w in widths)):
+            used = sum(w * n for w, n in zip(widths, counts))
+            if used <= cap:
+                out.append((cap, counts, cap - used))
+    return out
+
+
+def Hfloat(r, b):
+    import math
+    return 0.0 if r == 0 else r * (73.0 / r) ** b
+
+
+def lp_min(pats, caps, widths, rhs, b):
+    """float LP at saving b: returns (optimal value, x, duals y)."""
+    import numpy as np
+    from scipy.optimize import linprog
+    c = np.array([Hfloat(r, b) for cap, counts, r in pats])
+    A = np.zeros((len(caps) + len(widths), len(pats)))
+    for j, (cap, counts, r) in enumerate(pats):
+        A[caps.index(cap), j] = 1.0
+        for i, n in enumerate(counts):
+            if n:
+                A[len(caps) + i, j] = n
+    res = linprog(c, A_eq=A, b_eq=np.array([float(v) for v in rhs]), bounds=(0, None), method='highs')
+    need(res.status == 0, 'LP infeasible or failed: ' + res.message)
+    return res.fun, res.x, res.eqlin.marginals, A
+
+
+def rat_inverse(Bm):
+    n = len(Bm)
+    M = [row[:] + [Q(int(i == j)) for j in range(n)] for i, row in enumerate(Bm)]
+    for col in range(n):
+        piv = next((r for r in range(col, n) if M[r][col] != 0), None)
+        need(piv is not None, 'singular basis')
+        M[col], M[piv] = M[piv], M[col]
+        f = M[col][col]
+        M[col] = [v / f for v in M[col]]
+        for r in range(n):
+            if r != col and M[r][col] != 0:
+                g = M[r][col]
+                M[r] = [a - g * bb for a, bb in zip(M[r], M[col])]
+    return [row[n:] for row in M]
+
+
+def rat_rank(cols):
+    """rank of a list of rational column vectors"""
+    rows = [list(c) for c in cols]
+    rank = 0
+    ncol = len(rows[0]) if rows else 0
+    for col in range(ncol):
+        piv = next((r for r in range(rank, len(rows)) if rows[r][col] != 0), None)
+        if piv is None:
+            continue
+        rows[rank], rows[piv] = rows[piv], rows[rank]
+        for r in range(len(rows)):
+            if r != rank and rows[r][col] != 0:
+                g = rows[r][col] / rows[rank][col]
+                rows[r] = [a - g * bb for a, bb in zip(rows[r], rows[rank])]
+        rank += 1
+    return rank
+
+
+def column(pat, caps, widths):
+    cap, counts, r = pat
+    return [Q(int(cap == c)) for c in caps] + [Q(n) for n in counts]
+
+
+def relax(local, inventory, bins=BINS, digits=25, verbose=False):
+    local = {int(r): Q(n) for r, n in local.items() if Q(n) != 0}
+    inventory = {int(w): Q(n) for w, n in inventory.items() if Q(n) != 0}
+    need(all(n > 0 for n in local.values()) and all(n > 0 for n in inventory.values()), 'positive local/inventory')
+    widths = sorted(inventory)
+    caps = sorted(bins)
+    pats = patterns(bins, widths)
+    rhs = [Q(bins[c]) for c in caps] + [CALLS * inventory[w] for w in widths]
+    local_rep = {r: CALLS * n for r, n in local.items()}
+    total_cap = sum(c * bins[c] for c in caps)
+    inv_mass = sum(w * inventory[w] for w in widths) * CALLS
+    local_mass = sum(r * n for r, n in local_rep.items())
+    idle_mass = total_cap - inv_mass
+    need(idle_mass >= 0, 'inventory exceeds bin capacity')
+    mass_ok = (local_mass + idle_mass == R.MASS_PER_REPLICA)
+
+    # --- 1. float bisection on b
+    import numpy as np
+    def gfloat(b):
+        val, x, y, A = lp_min(pats, caps, widths, rhs, b)
+        loc = sum(float(n) * Hfloat(r, b) for r, n in local_rep.items())
+        return (loc + val) / (73 * LIVE) - 1.0, x, y
+    lo, hi = 0.0, 0.01
+    g_lo, _, _ = gfloat(lo)
+    g_hi, _, _ = gfloat(hi)
+    need(g_lo < 0 < g_hi, 'root window [0, 0.01] does not bracket the cap')
+    for _ in range(64):
+        mid = (lo + hi) / 2
+        g, x, y = gfloat(mid)
+        if g < 0:
+            lo = mid
+        else:
+            hi = mid
+    b_star = (lo + hi) / 2
+    g, x, y, = gfloat(b_star)
+    val, x, y, A = lp_min(pats, caps, widths, rhs, b_star)
+
+    # --- 2. basis: support of x, completed by tight (zero reduced cost) columns to full rank
+    c = np.array([Hfloat(r, b_star) for cap, counts, r in pats])
+    rc = c - A.T @ y
+    order = sorted(range(len(pats)), key=lambda j: (0 if x[j] > 1e-9 else 1, abs(float(rc[j])), -float(x[j])))
+    basis = []
+    cols = []
+    for j in order:
+        if len(basis) == len(rhs):
+            break
+        if x[j] <= 1e-9 and abs(rc[j]) > 1e-7:
+            continue
+        col = column(pats[j], caps, widths)
+        if rat_rank(cols + [col]) > len(cols):
+            basis.append(j)
+            cols.append(col)
+    need(len(basis) == len(rhs), 'could not complete an optimal basis (degenerate LP); %d of %d' % (len(basis), len(rhs)))
+    Bm = [[cols[k][i] for k in range(len(basis))] for i in range(len(rhs))]   # rows = constraints
+    Binv = rat_inverse(Bm)
+    xB = [sum(Binv[k][i] * rhs[i] for i in range(len(rhs))) for k in range(len(basis))]
+    need(all(v >= 0 for v in xB), 'basis not primal feasible')
+    active = [(pats[j], xB[k]) for k, j in enumerate(basis) if xB[k] > 0]
+    idle = {}
+    for (cap, counts, r), n in active:
+        if r:
+            idle[r] = idle.get(r, 0) + n
+    full = dict(local_rep)
+    for r, n in idle.items():
+        full[r] = full.get(r, 0) + n
+    cap_lo, cap_hi = R.root_bracket(full, LIVE, digits, check_mass_T=1 if mass_ok else None)
+
+    # --- 3. exact dual in the H basis: y_j(b) = sum_k (B^-T)_{j,k} H_{r_k}(b)
+    ranks = sorted({r for cap, counts, r in pats if r})
+    # (B^-T)_{j,k} = Binv[k][j]
+    Y = {j: {} for j in range(len(rhs))}
+    for j in range(len(rhs)):
+        for k, pj in enumerate(basis):
+            r = pats[pj][2]
+            if r == 0 or Binv[k][j] == 0:
+                continue
+            Y[j][r] = Y[j].get(r, 0) + Binv[k][j]
+    Hhi = {r: R.H(r, cap_hi) for r in ranks}
+    tight = []
+    strict = 0
+    min_slack = None
+    for p in pats:
+        cap, counts, r = p
+        a = column(p, caps, widths)
+        coeff = {}
+        if r:
+            coeff[r] = Q(1)
+        for j in range(len(rhs)):
+            if a[j] == 0:
+                continue
+            for k, v in Y[j].items():
+                coeff[k] = coeff.get(k, 0) - a[j] * v
+        coeff = {k: v for k, v in coeff.items() if v != 0}
+        if not coeff:
+            tight.append(p)
+            continue
+        lower = sum(v * (Hhi[k][0] if v > 0 else Hhi[k][1]) for k, v in coeff.items())
+        need(lower > 0, 'dual sign failure for pattern %s (reduced-cost lower bound %s)' % (str(p), str(lower)))
+        strict += 1
+        min_slack = lower if min_slack is None else min(min_slack, lower)
+    dual_obj = sum(rhs[j] * sum(v * Hhi[k][0] for k, v in Y[j].items()) for j in range(len(rhs)))  # not needed for the proof, informational
+    dual_rows = ['cap%d' % c for c in caps] + ['w%d' % w for w in widths]
+    return dict(
+        status='PASS_EXACT_RELAXATION_CAP' if mass_ok else 'PASS_EXACT_RELAXATION_CAP_MASS_NOT_65088',
+        cap_lower=str(cap_lo), cap_upper=str(cap_hi), cap_lower_decimal=R.mpmath_str(cap_lo, digits), cap_upper_decimal=R.mpmath_str(cap_hi, digits),
+        patterns=len(pats), tight_patterns=len(tight), strict_patterns=strict, minimum_slack_lower=str(min_slack),
+        basis_patterns=[dict(capacity=pats[j][0], widths=[w for w, n in zip(widths, pats[j][1]) for _ in range(n)], count_per_replica=str(xB[k])) for k, j in enumerate(basis)],
+        tight_pattern_list=[dict(capacity=p[0], widths=[w for w, n in zip(widths, p[1]) for _ in range(n)]) for p in tight],
+        idle_per_replica={str(r): str(n) for r, n in sorted(idle.items())},
+        idle_mass_per_replica=str(idle_mass), local_mass_per_replica=str(local_mass), rank_mass_per_replica=str(local_mass + idle_mass), rank_mass_identity=mass_ok,
+        dual_Y={dual_rows[j]: {str(k): str(v) for k, v in sorted(Y[j].items())} for j in range(len(rhs))},
+        inventory_per_call={str(w): str(inventory[w]) for w in widths}, local_per_call={str(r): str(n) for r, n in sorted(local.items())}, bins_per_replica=bins,
+        delta_vs_PR2857_realized=dict(lower=str(cap_lo - PR2857_REALIZED_UPPER), upper=str(cap_hi - PR2857_REALIZED_LOWER), float=float(cap_lo - PR2857_REALIZED_LOWER)),
+        delta_vs_PR2857_cap=dict(float=float(cap_lo - PR2857_CAP_UPPER)),
+        assumptions='fixed capacities 8/16/32/48 (112 ports x 6/4/4/4 children per replica), all count-vector patterns with sum<=cap, one idle child of rank cap-used per bin, chronology/windows/collisions/integrality ignored, local profile fully paid; upper bound on any actual fill of this inventory, not a witness',
+    )
+
+
+def scenarios():
+    base_local, base_inv = PR2857_LOCAL, PR2857_INV
+    def mod(dl, di):
+        l = {r: base_local.get(r, 0) + dl.get(r, 0) for r in set(base_local) | set(dl)}
+        i = {w: base_inv.get(w, 0) + di.get(w, 0) for w in set(base_inv) | set(di)}
+        return {r: n for r, n in l.items() if n}, {w: n for w, n in i.items() if n}
+    table = [
+        ('PR2857 actual (calibration)', {}, {}),
+        ('one more 9->8 at PR2857 cost {1:+3,2:-2}', {1: 3, 2: -2}, {8: 1, 9: -1}),
+        ('one more 9->8 at PR2853 cost {1:+5,2:-3}', {1: 5, 2: -3}, {8: 1, 9: -1}),
+        ('one more 9->8 at minimal cost {1:+1,2:-1}', {1: 1, 2: -1}, {8: 1, 9: -1}),
+        ('two more 9->8 at PR2857 cost {1:+6,2:-4}', {1: 6, 2: -4}, {8: 2, 9: -2}),
+        ('four more 9->8 at PR2857 cost {1:+12,2:-8}', {1: 12, 2: -8}, {8: 4, 9: -4}),
+        ('one 8->7 at PR2857-like cost {1:+3,2:-2}', {1: 3, 2: -2}, {7: 1, 8: -1}),
+        ('one 8->7 at minimal cost {1:+1,2:-1}', {1: 1, 2: -1}, {7: 1, 8: -1}),
+        ('one 9->7 (two units) at cost {1:+6,2:-4}', {1: 6, 2: -4}, {7: 1, 9: -1}),
+        ('remove one width-9 helper, its 9 one-dim climbs vanish {1:-9}', {1: -9}, {9: -1}),
+        ('remove one width-9 helper paying {1:-7,2:-1}', {1: -7, 2: -1}, {9: -1}),
+        ('remove one width-8 helper {1:-8}', {1: -8}, {8: -1}),
+        ('remove one width-4 helper {1:-4}', {1: -4}, {4: -1}),
+        ('local only: +1 H1 -1 H2 per call (mass -1, inventory unchanged: NOT a legal word, derivative probe)', {1: 1, 2: -1}, {}),
+        ('local only: -1 H1 per call (mass -1, derivative probe)', {1: -1}, {}),
+        ('local only: 2 H1 -> 1 H2 per call (mass neutral)', {1: -2, 2: 1}, {}),
+        ('local only: 1 H3 -> 1 H1 + 1 H2 per call (mass neutral)', {3: -1, 1: 1, 2: 1}, {}),
+    ]
+    out = []
+    for name, dl, di in table:
+        l, i = mod(dl, di)
+        try:
+            r = relax(l, i)
+            row = dict(scenario=name, delta_local=dl, delta_inventory=di, cap_lower=r['cap_lower_decimal'], cap_upper=r['cap_upper_decimal'],
+                       gain_vs_PR2857_realized_float=r['delta_vs_PR2857_realized']['float'], gain_vs_PR2857_cap_float=r['delta_vs_PR2857_cap']['float'],
+                       tight=r['tight_patterns'], patterns=r['patterns'], idle_per_replica=r['idle_per_replica'], basis=r['basis_patterns'], rank_mass_identity=r['rank_mass_identity'], status=r['status'])
+        except Exception as e:  # noqa
+            row = dict(scenario=name, delta_local=dl, delta_inventory=di, error=str(e))
+        out.append(row)
+        print('%-95s cap<= %s  gain vs realized %+.4e  vs cap %+.4e  %s' % (name, row.get('cap_upper', '?'), row.get('gain_vs_PR2857_realized_float', float('nan')), row.get('gain_vs_PR2857_cap_float', float('nan')), row.get('error', '')), file=sys.stderr, flush=True)
+    return out
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter)
+    ap.add_argument('--calibrate', action='store_true')
+    ap.add_argument('--scenarios', action='store_true')
+    ap.add_argument('--inventory', help='JSON per-call {width: count}')
+    ap.add_argument('--local', help='JSON per-call {rank: count}')
+    ap.add_argument('--delta-inventory', help='JSON {width: +-count} relative to PR2857')
+    ap.add_argument('--delta-local', help='JSON {rank: +-count} relative to PR2857')
+    ap.add_argument('--digits', type=int, default=25)
+    ap.add_argument('--out')
+    a = ap.parse_args()
+    if a.calibrate:
+        r = relax(PR2857_LOCAL, PR2857_INV, digits=a.digits)
+        r['reproduces_PR2857_cap_lower'] = (Q(r['cap_lower']) == Q('215012600677110740993/125000000000000000000000'))
+        r['bracket_inside_PR2857_bracket'] = (Q(r['cap_lower']) >= Q('215012600677110740993/125000000000000000000000') and Q(r['cap_upper']) <= PR2857_CAP_UPPER)
+        r['reproduces_PR2857_cap_upper_at_24_digits'] = (relax(PR2857_LOCAL, PR2857_INV, digits=24)['cap_upper'] == str(PR2857_CAP_UPPER))
+        r['reproduces_PR2857_pattern_count_1163'] = (r['patterns'] == 1163)
+        r['reproduces_PR2857_11_tight_1152_strict'] = (r['tight_patterns'] == 11 and r['strict_patterns'] == 1152)
+        res = r
+    elif a.scenarios:
+        res = scenarios()
+    else:
+        local = dict(PR2857_LOCAL)
+        inv = dict(PR2857_INV)
+        if a.local:
+            local = {int(k): Q(v) for k, v in json.loads(a.local).items()}
+        if a.inventory:
+            inv = {int(k): Q(v) for k, v in json.loads(a.inventory).items()}
+        if a.delta_local:
+            for k, v in json.loads(a.delta_local).items():
+                local[int(k)] = local.get(int(k), 0) + Q(v)
+        if a.delta_inventory:
+            for k, v in json.loads(a.delta_inventory).items():
+                inv[int(k)] = inv.get(int(k), 0) + Q(v)
+        res = relax({k: v for k, v in local.items() if v}, {k: v for k, v in inv.items() if v}, digits=a.digits)
+    s = json.dumps(res, indent=1, sort_keys=True, default=str)
+    if a.out:
+        open(a.out, 'w').write(s)
+    print(s)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-extension-cap-fill/tools/relax_exact.py b/research/paired-extension-cap-fill/tools/relax_exact.py
new file mode 100644
index 0000000000..0be97756bb
--- /dev/null
+++ b/research/paired-extension-cap-fill/tools/relax_exact.py
@@ -0,0 +1,108 @@
+#!/usr/bin/env python3
+"""relax_exact.py -- Fractions-only verification of a stored optimal basis of the changed-inventory
+fixed-capacity fractional relaxation (relax.py), without scipy.
+
+relax.py locates the optimal basis with a float LP (scipy/HiGHS) and then certifies it exactly. This module
+performs only the exact part, from a stored list of basis patterns:
+  1. x_B = B^-1 rhs (exact rationals), x_B >= 0: the basic solution is feasible, so the cap is at least the
+     root of its complete profile (root.py bracket at 10^-digits);
+  2. the dual y(b) = B^-T c_B(b) is an exact rational combination of the H_k(b); every one of the capacity-
+     feasible patterns has reduced cost > 0 (or identically 0) at b = hi, so by weak duality every feasible x
+     has moment >= 1 at hi: the cap is at most hi.
+The bins, pattern catalogue, moment model and interval arithmetic are relax.py's / root.py's (imported).
+
+Marius-Paul Dumitrean, prepared with substantial AI assistance (Anthropic Claude, via Claude Code). Apache-2.0.
+"""
+from fractions import Fraction as Q
+import os, sys
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import root as R
+import relax as X
+
+
+def need(c, m):
+    if not c:
+        raise ValueError(m)
+
+
+def pattern_of(entry, widths, bins):
+    cap = int(entry['capacity'])
+    need(cap in bins, 'basis pattern capacity %r is not a bin capacity' % cap)
+    counts = tuple(list(entry['widths']).count(w) for w in widths)
+    need(sum(counts) == len(entry['widths']), 'basis pattern uses a width outside the inventory: %r' % (entry,))
+    used = sum(w * n for w, n in zip(widths, counts))
+    need(used <= cap, 'basis pattern exceeds its capacity')
+    return (cap, counts, cap - used)
+
+
+def verify_basis(local, inventory, basis_patterns, bins=X.BINS, digits=25):
+    local = {int(r): Q(n) for r, n in local.items() if Q(n) != 0}
+    inventory = {int(w): Q(n) for w, n in inventory.items() if Q(n) != 0}
+    need(all(n > 0 for n in local.values()) and all(n > 0 for n in inventory.values()), 'positive local/inventory')
+    widths = sorted(inventory)
+    caps = sorted(bins)
+    pats = X.patterns(bins, widths)
+    patset = set(pats)
+    rhs = [Q(bins[c]) for c in caps] + [X.CALLS * inventory[w] for w in widths]
+    local_rep = {r: X.CALLS * n for r, n in local.items()}
+    total_cap = sum(c * bins[c] for c in caps)
+    inv_mass = sum(w * inventory[w] for w in widths) * X.CALLS
+    local_mass = sum(r * n for r, n in local_rep.items())
+    idle_mass = total_cap - inv_mass
+    need(idle_mass >= 0, 'inventory exceeds bin capacity')
+    mass_ok = (local_mass + idle_mass == R.MASS_PER_REPLICA)
+    basis = [pattern_of(e, widths, bins) for e in basis_patterns]
+    need(len(basis) == len(rhs), 'basis must have exactly %d patterns' % len(rhs))
+    need(all(p in patset for p in basis), 'basis pattern outside the catalogue')
+    need(len(set(basis)) == len(basis), 'repeated basis pattern')
+    cols = [X.column(p, caps, widths) for p in basis]
+    need(X.rat_rank(cols) == len(rhs), 'basis columns are linearly dependent')
+    Bm = [[cols[k][i] for k in range(len(basis))] for i in range(len(rhs))]
+    Binv = X.rat_inverse(Bm)
+    xB = [sum(Binv[k][i] * rhs[i] for i in range(len(rhs))) for k in range(len(basis))]
+    need(all(v >= 0 for v in xB), 'basis not primal feasible (negative basic variable)')
+    for e, v in zip(basis_patterns, xB):
+        if 'count_per_replica' in e:
+            need(Q(e['count_per_replica']) == v, 'stored basic count differs from B^-1 rhs: %r' % (e,))
+    idle = {}
+    for p, n in zip(basis, xB):
+        if p[2] and n:
+            idle[p[2]] = idle.get(p[2], 0) + n
+    full = dict(local_rep)
+    for r, n in idle.items():
+        full[r] = full.get(r, 0) + n
+    cap_lo, cap_hi = R.root_bracket(full, X.LIVE, digits, check_mass_T=1 if mass_ok else None)
+    ranks = sorted({r for cap, counts, r in pats if r})
+    Y = {j: {} for j in range(len(rhs))}
+    for j in range(len(rhs)):
+        for k, p in enumerate(basis):
+            r = p[2]
+            if r == 0 or Binv[k][j] == 0:
+                continue
+            Y[j][r] = Y[j].get(r, 0) + Binv[k][j]
+    Hhi = {r: R.H(r, cap_hi) for r in ranks}
+    tight = strict = 0
+    min_slack = None
+    for p in pats:
+        a = X.column(p, caps, widths)
+        coeff = {}
+        if p[2]:
+            coeff[p[2]] = Q(1)
+        for j in range(len(rhs)):
+            if a[j] == 0:
+                continue
+            for k, v in Y[j].items():
+                coeff[k] = coeff.get(k, 0) - a[j] * v
+        coeff = {k: v for k, v in coeff.items() if v != 0}
+        if not coeff:
+            tight += 1
+            continue
+        lower = sum(v * (Hhi[k][0] if v > 0 else Hhi[k][1]) for k, v in coeff.items())
+        need(lower > 0, 'dual sign failure for pattern %s (reduced-cost lower bound %s)' % (str(p), str(lower)))
+        strict += 1
+        min_slack = lower if min_slack is None else min(min_slack, lower)
+    return dict(status='PASS_EXACT_RELAXATION_CAP' if mass_ok else 'PASS_EXACT_RELAXATION_CAP_MASS_NOT_65088',
+                cap_lower=str(cap_lo), cap_upper=str(cap_hi), patterns=len(pats), tight_patterns=tight,
+                strict_patterns=strict, minimum_slack_lower=str(min_slack), rank_mass_identity=mass_ok,
+                idle_per_replica={str(r): str(n) for r, n in sorted(idle.items())},
+                basic_counts=[str(v) for v in xB])
diff --git a/research/paired-extension-cap-fill/tools/root.py b/research/paired-extension-cap-fill/tools/root.py
new file mode 100644
index 0000000000..bd6dc2eb4e
--- /dev/null
+++ b/research/paired-extension-cap-fill/tools/root.py
@@ -0,0 +1,254 @@
+#!/usr/bin/env python3
+"""root.py -- exact (rational-bracketed) complex endpoint kappa from a complete global profile.
+
+The T-replica network has 9*T calls, live width W = 896*T, base m = 73.  A complete paid profile
+{rank: count} (local jumps of all calls + idle/remainder children of all bins) has the moment
+
+    M(b) = sum_r count_r * r * (73/r)^b / (73 * W)          (= audit_owners.moment(profile, b, W))
+
+which is increasing in b; the complex endpoint is the root M(b) = 1.  PR2857's headline is
+floor(root_lower, 24 digits) - 1e-46 - 1e-70; PR2853/PR2833's headlines are their roots - O(1e-3022).
+The rational interval arithmetic (log via atanh series, exp via Taylor, outward rounding at 10^-45)
+is the package's own, so the brackets coincide exactly with the independent audits.
+
+Rank-mass identity for a complete profile: sum_r r*count_r = 65088*T  (= (73-1)*896*T + 64*9*T).
+
+Usage:
+  python -B root.py --calibrate                      # PR2857 / PR2853 / PR2833 reproduction
+  python -B root.py --profile '{"1":805860,...}' --T 37 [--delta '{"1":9,"2":-9}'] [--digits 25]
+  python -B root.py --profile-file PROFILE.json --T 37 --table      # per-rank derivative table
+API:
+  kappa_from_profile(profile, T, digits=25) -> (lo, hi)  exact Fractions, M(lo)<1<M(hi) certified
+  delta_value(profile, T, delta)            -> dict with new bracket and exact gain interval
+  derivatives(profile, T)                   -> {rank: dkappa/dcount_r} (mpmath, 40 digits)
+"""
+from fractions import Fraction as Q
+from functools import lru_cache
+import argparse, json, sys
+
+M_BASE = 73
+LIVE_PER_REPLICA = 896
+CALLS_PER_REPLICA = 9
+MASS_PER_REPLICA = (M_BASE - 1) * LIVE_PER_REPLICA + 64 * CALLS_PER_REPLICA  # 65088
+SCALE = 10 ** 45
+
+
+def need(c, m):
+    if not c:
+        raise ValueError(m)
+
+
+@lru_cache(None)
+def logarithm(x):
+    """Rational enclosure of log(x), x >= 1 (package arithmetic, outward rounding 10^-45)."""
+    need(x >= 1, 'log argument')
+    k = 0
+    while x >= 2:
+        x /= 2
+        k += 1
+
+    def unit(y):
+        z = (y - 1) / (y + 1)
+        power = z
+        total = Q(0)
+        for j in range(100):
+            total += power / (2 * j + 1)
+            power *= z * z
+        total *= 2
+        tail = 2 * power / (201 * (1 - z * z))
+        return total, total + tail
+
+    lo, hi = unit(x)
+    l2, h2 = unit(Q(2))
+    lo += k * l2
+    hi += k * h2
+    return Q((lo * SCALE).__floor__(), SCALE), Q((hi * SCALE).__ceil__(), SCALE)
+
+
+def exponential(x):
+    need(0 <= x < 1, 'exp argument')
+    term = total = Q(1)
+    for j in range(1, 19):
+        term *= x / j
+        total += term
+    tail = term * x / 19 / (1 - x / 20)
+    return total, total + tail
+
+
+def H(rank, b):
+    """Enclosure of H_r(b) = r*(73/r)^b  (the moment of one rank-r child times 73)."""
+    l, h = logarithm(Q(M_BASE, rank))
+    return rank * exponential(b * l)[0], rank * exponential(b * h)[1]
+
+
+def moment(profile, b, W):
+    """Enclosure of sum_r count_r * r * (73/r)^b / (73*W); counts may be Fractions (>=0)."""
+    lo = hi = Q(0)
+    for rank, count in profile.items():
+        if count == 0:
+            continue
+        need(0 < rank < M_BASE and count > 0, 'child profile')
+        e0, e1 = H(rank, b)
+        lo += Q(count) * e0 / (M_BASE * W)
+        hi += Q(count) * e1 / (M_BASE * W)
+    return Q((lo * SCALE).__floor__(), SCALE), Q((hi * SCALE).__ceil__(), SCALE)
+
+
+def normalize(profile):
+    out = {}
+    for r, n in profile.items():
+        r = int(r)
+        n = Q(n) if not isinstance(n, int) else n
+        if n:
+            out[r] = out.get(r, 0) + n
+    return out
+
+
+def rank_mass(profile):
+    return sum(r * Q(n) for r, n in normalize(profile).items())
+
+
+def root_bracket(profile, W, digits=25, check_mass_T=None):
+    """Bisection on the grid 10^-digits: returns (lo, hi) with M(lo) < 1 < M(hi) certified."""
+    profile = normalize(profile)
+    if check_mass_T is not None:
+        need(rank_mass(profile) == MASS_PER_REPLICA * check_mass_T, 'rank-mass identity (incomplete profile?)')
+    G = 10 ** digits
+    low, high = 0, G // 100
+    need(moment(profile, Q(low, G), W)[1] < 1 < moment(profile, Q(high, G), W)[0], 'root initial interval')
+    while high - low > 1:
+        mid = (low + high) // 2
+        a, b = moment(profile, Q(mid, G), W)
+        if b < 1:
+            low = mid
+        elif a > 1:
+            high = mid
+        else:
+            raise ValueError('root interval precision exhausted at %d digits' % digits)
+    return Q(low, G), Q(high, G)
+
+
+def kappa_from_profile(profile, T, digits=25, strict_mass=True):
+    """Exact bracket of the complex endpoint for a complete global profile of a T-replica network."""
+    return root_bracket(profile, LIVE_PER_REPLICA * T, digits, T if strict_mass else None)
+
+
+def add_profiles(a, b, scale_b=1):
+    out = dict(normalize(a))
+    for r, n in normalize(b).items():
+        out[r] = out.get(r, 0) + scale_b * n
+        need(out[r] >= 0, 'negative count at rank %d' % r)
+        if out[r] == 0:
+            del out[r]
+    return out
+
+
+def delta_value(profile, T, delta, digits=25, strict_mass=True):
+    """Value (exact root brackets) of changing the complete profile by delta = {rank: +-count}."""
+    base = kappa_from_profile(profile, T, digits, strict_mass)
+    newp = add_profiles(profile, delta)
+    mass_ok = rank_mass(newp) == MASS_PER_REPLICA * T
+    new = kappa_from_profile(newp, T, digits, strict_mass and mass_ok)
+    return dict(base_lower=str(base[0]), base_upper=str(base[1]), new_lower=str(new[0]), new_upper=str(new[1]),
+                gain_lower=str(new[0] - base[1]), gain_upper=str(new[1] - base[0]),
+                gain_float=float((new[0] + new[1] - base[0] - base[1]) / 2), new_profile={str(r): str(n) for r, n in sorted(newp.items())},
+                new_rank_mass_identity=mass_ok, note=None if mass_ok else 'delta breaks the rank-mass identity: a derivative probe, not a complete legal profile (a legal word change moves local mass and inventory/idle mass together)')
+
+
+def derivatives(profile, T, b=None):
+    """dkappa/dcount_r (per single child of rank r) by the implicit function theorem, mpmath 40 digits."""
+    import mpmath
+    mpmath.mp.dps = 40
+    profile = normalize(profile)
+    W = LIVE_PER_REPLICA * T
+    if b is None:
+        lo, hi = kappa_from_profile(profile, T, strict_mass=False)
+        b = (lo + hi) / 2
+    b = mpmath.mpf(b.numerator) / b.denominator
+    dMdb = mpmath.mpf(0)
+    for r, n in profile.items():
+        dMdb += mpmath.mpf(n) * r * mpmath.power(mpmath.mpf(M_BASE) / r, b) * mpmath.log(mpmath.mpf(M_BASE) / r) / (M_BASE * W)
+    out = {}
+    for r in range(1, M_BASE):
+        dMdn = r * mpmath.power(mpmath.mpf(M_BASE) / r, b) / (M_BASE * W)
+        out[r] = -dMdn / dMdb
+    return out, b
+
+
+def fmt(x, nd=28):
+    return mpmath_str(x, nd)
+
+
+def mpmath_str(x, nd):
+    import mpmath
+    mpmath.mp.dps = nd + 5
+    return mpmath.nstr(mpmath.mpf(x.numerator) / x.denominator if isinstance(x, Q) else x, nd)
+
+
+CALIBRATION = {
+    'PR2857': dict(T=37, profile={1: 805860, 2: 213786, 3: 91775, 4: 42624, 5: 13098, 8: 2664, 9: 1, 48: 13379},
+                   expected_lower='17200966286848326009728/10000000000000000000000000',
+                   expected_upper='17200966286848326009729/10000000000000000000000000',
+                   headline='0.001720096628684832600972 - 1e-46 - 1e-70 (CLAIM.json)'),
+    'PR2853': dict(T=74, profile={1: 1616713, 2: 424908, 3: 183207, 4: 85249, 5: 26625, 6: 58, 7: 3, 8: 5328, 32: 47, 48: 26703},
+                   headline='0.00171937765869758665904733841726077218140089564514 (outer/OUTER-CLAIM.json, = C - 1e-3046 - 1e-3022)'),
+    'PR2833': dict(T=74, profile={1: 1603728, 2: 432900, 3: 183683, 4: 85248, 5: 26862, 8: 5328, 9: 1, 48: 26625},
+                   headline='0.00171865743716685595569345761432428040996497469293 (outer/OUTER-CLAIM.json)'),
+}
+
+
+def calibrate(digits=25):
+    results = {}
+    for name, c in CALIBRATION.items():
+        lo, hi = kappa_from_profile(c['profile'], c['T'], digits)
+        row = dict(T=c['T'], profile=c['profile'], lower=str(lo), upper=str(hi), lower_decimal=mpmath_str(lo, digits),
+                   upper_decimal=mpmath_str(hi, digits), headline=c['headline'], rank_mass=str(rank_mass(c['profile'])))
+        if 'expected_lower' in c:
+            row['reproduces_package_bracket'] = (lo == Q(c['expected_lower']) and hi == Q(c['expected_upper']))
+        else:
+            head = c['headline'].split(' ')[0]
+            row['headline_inside_bracket'] = (Q(head) >= lo - Q(1, 10 ** 22)) and (Q(head) <= hi)
+            dec = mpmath_str(lo, digits)
+            k = 0
+            while k < min(len(dec), len(head)) and dec[k] == head[k]:
+                k += 1
+            row['matches_headline_to_digits'] = k - 2  # decimals in common ('0.' excluded)
+        results[name] = row
+    return results
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter)
+    ap.add_argument('--calibrate', action='store_true')
+    ap.add_argument('--profile', help='JSON {rank: count}')
+    ap.add_argument('--profile-file')
+    ap.add_argument('--T', type=int, default=37)
+    ap.add_argument('--delta', help='JSON {rank: +-count} (complete-profile change, e.g. 9*T per-call units)')
+    ap.add_argument('--per-call-delta', help='JSON {rank: +-count per call}; multiplied by 9*T')
+    ap.add_argument('--digits', type=int, default=25)
+    ap.add_argument('--table', action='store_true', help='print per-rank derivative table')
+    ap.add_argument('--no-mass-check', action='store_true')
+    a = ap.parse_args()
+    if a.calibrate:
+        print(json.dumps(calibrate(a.digits), indent=1, sort_keys=True))
+        return
+    profile = json.loads(a.profile) if a.profile else json.load(open(a.profile_file))
+    profile = {int(k): (int(v) if str(v).lstrip('-').isdigit() else Q(v)) for k, v in profile.items()}
+    strict = not a.no_mass_check
+    lo, hi = kappa_from_profile(profile, a.T, a.digits, strict)
+    out = dict(T=a.T, W=LIVE_PER_REPLICA * a.T, lower=str(lo), upper=str(hi), lower_decimal=mpmath_str(lo, a.digits),
+               rank_mass=str(rank_mass(profile)))
+    if a.delta or a.per_call_delta:
+        d = {int(k): int(v) for k, v in json.loads(a.delta or a.per_call_delta).items()}
+        if a.per_call_delta:
+            d = {k: v * CALLS_PER_REPLICA * a.T for k, v in d.items()}
+        out['delta'] = delta_value(profile, a.T, d, a.digits, strict)
+    if a.table:
+        der, b = derivatives(profile, a.T)
+        out['derivative_per_child'] = {str(r): mpmath_str(v, 12) for r, v in der.items() if r in profile or r <= 9 or r == 48}
+        out['derivative_per_call_unit'] = {str(r): mpmath_str(v * CALLS_PER_REPLICA * a.T, 12) for r, v in der.items() if r in profile or r <= 9 or r == 48}
+    print(json.dumps(out, indent=1, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-extension-cap-fill/vendor/preload_move.py b/research/paired-extension-cap-fill/vendor/preload_move.py
new file mode 100644
index 0000000000..55b435035b
--- /dev/null
+++ b/research/paired-extension-cap-fill/vendor/preload_move.py
@@ -0,0 +1,133 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Declared preload-move stage: two more staged quartets on the PR2857 shared-kernel words.
+
+Preload re-synthesis (quartets (456,457,466,467) and (458,459,464,465)) by Jeremy Kothe
+(jeremykothe2), with AI assistance; the staged-kernel gate shapes, frame/inverse-cleanup
+conventions and the dirt-entry supplier are credited in CREDITS.md (PR2857 Lyy-iiis, PR2863
+Dugongue, PR2833 Jeremy Kothe, PR2853 philippeVV).
+
+apply(word, patch) takes the decoded PR2857 shared-kernel word and a DECLARED patch input
+that lists every changed gate. Every listed old gate must be present at its index, no
+other gate may change, the changed sections are limited to
+{A, B, compensation, start_extra, report, cleanup}, the frame/paid profile and width
+inventory are re-derived exactly from the changed word and must equal the declaration, and
+the inverse-reverse cleanup is re-derived. The inherited exact auditor (forward and dual
+free-operator replay over every input column) is the separate semantic check.
+No file, import, process or output is touched by apply().
+"""
+import copy, hashlib, json
+from collections import Counter
+
+SOURCE_CANONICAL = {
+ 'base': 'c0af0ef7ee6282e91f046d027983b35eaed7ebcb46489134d47e07724cf664bc',
+ 'extra': '61b20fbe78fdcbca0cde0597befcc254017ee206dad0724c576672aca690c66f',
+}
+ALLOWED_SECTIONS = {'A', 'B', 'compensation', 'start_extra', 'report', 'cleanup'}
+
+def require(ok, reason):
+ if not ok:raise ValueError(str(reason))
+
+def canon(w):return hashlib.sha256(json.dumps(w,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+
+def basis(vs):
+ piv={}
+ for a in vs:
+  while a:
+   bit=a.bit_length()-1
+   if bit in piv:a^=piv[bit]
+   else:piv[bit]=a;break
+ for k in sorted(piv):
+  for j in piv:
+   if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+ return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def restored_of(w):
+ n=2*w['report']['v']+w['report']['R']
+ return {g[1]-n for g in w['cleanup'] if g[1]>=n}|{g[2]-n for g in w['cleanup'] if g[0]=='add' and g[2]>=n}
+
+def derive_cleanup(w,restored):
+ v=w['report']['v'];n=2*v+w['report']['R'];full=list(basis([1<<i for i in range(w['report']['h'])]))
+ byp={}
+ for op,rec in enumerate(w['warps'],1):byp.setdefault(rec[0],[]).append((op,rec))
+ fw=list(w['A'])
+ for p in range(len(w['B'])+1):
+  for op,rec in byp.get(p,[]):fw.append(['warp',rec[1],op])
+  if p<len(w['B']):fw.append(w['B'][p])
+ fw+=w['restore'];buf=lambda r:r+n if r in restored else r;out=[]
+ for g in reversed([g for g in fw if g[0]=='warp' or not(v<=g[1]<2*v)]):
+  if g[0]=='warp':out.append(['warp',buf(g[1]),-g[2],full])
+  elif g[0]=='add':out.append(['add',buf(g[1]),buf(g[2]),-g[3],g[4],full])
+  else:out.append(['scale',buf(g[1]),g[3],g[2],full])
+ return out
+
+def frame_report(x):
+ """Exact paid profile and width inventory of a word, by the inherited frame rules."""
+ full=basis([1<<i for i in range(9)]);end=[full]*112+[basis([z for z in range(1,512) if(z&p).bit_count()%2==0]) for p in x['ports']]+[full]*480
+ for r,U in x['helper_final'].items():end[int(r)]=basis(U)
+ start=[(p,) for p in x['ports']]+[()]*(112+480)
+ for r,U in x['start_extra'].items():start[int(r)]=basis(U)
+ cur=start.copy();paid=Counter()
+ def climb(r,U):
+  U=basis(U);require(contained(cur[r],U),('nonmonotone frame',r,cur[r],U))
+  d=len(U)-len(cur[r])
+  if d:paid[d]+=1
+  cur[r]=U
+ def step(g):
+  if g[0]=='warp':require(cur[g[1]]==basis(g[3]),'A warp frame');cur[g[1]]=basis(g[4])
+  else:
+   for r in(g[1:3] if g[0]=='add' else g[1:2]):climb(r,g[-1])
+ for g in x['A']:step(g)
+ for r,U in zip(x['centers'],x['center_frames']):
+  require(cur[r]==basis(U),'centre frame')
+  for T in sorted({basis(x['target_levels'].get(str(g[1]-112),[])) for g in x['cut'] if g[2]==r},key=lambda t:-len(t)):
+   if basis(U)!=T:paid[len(U)-len(T)]+=1
+   U=T
+ bw={}
+ for rec in x['warps']:bw.setdefault(rec[0],[]).append(rec)
+ for p in range(len(x['B'])+1):
+  for rec in bw.get(p,[]):require(cur[rec[1]]==basis(rec[3]),'B warp frame');cur[rec[1]]=basis(rec[4])
+  if p<len(x['B']):step(x['B'][p])
+ for g in x['restore']:step(g)
+ live=set(range(704))-set(x['removed'])
+ for r in live:climb(r,end[r])
+ inv=Counter(len(end[r])-len(start[r]) for r in live if r>=224)
+ return {str(k):v for k,v in sorted(paid.items())},{str(k):v for k,v in sorted(inv.items())}
+
+def apply(word, patch):
+ """Return (changed word, ledger). Authenticates the decoded source first."""
+ require(patch.get('stage')=='preload-move','stage tag')
+ digest=canon(word);require(digest==patch['source_canonical_sha256'],'source canonical hash differs from the declared source')
+ require(patch['variant'] in SOURCE_CANONICAL and SOURCE_CANONICAL[patch['variant']]==digest,'unauthorized decoded source SHA256')
+ x=copy.deepcopy(word)
+ # A: replacements and insertions, both addressed by index in the SOURCE A (before any edit).
+ ops=patch['A_edits'];seen=set();byp={};repl={}
+ for e in ops:
+  if e['op']=='replace':
+   i=e['index'];require(i not in seen and i not in repl,('duplicate A replace',i));require(word['A'][i]==e['old'],('A old gate mismatch',i,word['A'][i]));repl[i]=e['new']
+  else:
+   require(e['op']=='insert' and 0<=e['before']<=len(word['A']),'A edit op');byp.setdefault(e['before'],[]).append(e['gate'])
+ A=[]
+ for p in range(len(word['A'])+1):
+  A.extend(copy.deepcopy(g) for g in byp.get(p,[]))
+  if p<len(word['A']):A.append(copy.deepcopy(repl.get(p,word['A'][p])))
+ x['A']=A
+ for name in ('B','compensation'):
+  idx=set()
+  for e in patch[name+'_edits']:
+   i=e['index'];require(i not in idx,(name,'duplicate index',i));idx.add(i);require(word[name][i]==e['old'],(name,'old gate mismatch',i,word[name][i]));x[name][i]=copy.deepcopy(e['new'])
+ for r,U in patch['start_extra_added'].items():
+  require(r not in x['start_extra'],('start_extra already declared',r));x['start_extra'][r]=list(U)
+ require(x['prelude_events']==word['prelude_events']+0 and len(x['A'])==len(word['A'])+len(patch['A_edits'])-len(repl),'A length bookkeeping')
+ profile,inventory=frame_report(x)
+ require(profile==patch['declared_local_profile'] and inventory==patch['declared_width_inventory'],('derived paid profile/width inventory differ from the declaration',profile,inventory))
+ x['report']['local_profile']=profile;x['report']['width_inventory']=inventory
+ t=copy.deepcopy(x);t['A']=t['A'][t['prelude_events']:];x['cleanup']=derive_cleanup(t,restored_of(x))
+ changed={k for k in word if word[k]!=x[k]}
+ require(changed<=ALLOWED_SECTIONS,('sections outside the declared stage',changed-ALLOWED_SECTIONS))
+ require(x['warps']==word['warps'] and x['helper_final']==word['helper_final'] and x['removed']==word['removed'] and x['prelude_events']==word['prelude_events'],'phase and buffer ABI unchanged')
+ require(canon(x)==patch['candidate_canonical_sha256'],'candidate canonical hash differs from the declaration')
+ ledger=dict(variant=patch['variant'],source_canonical_sha256=digest,candidate_canonical_sha256=canon(x),local_profile=profile,width_inventory=inventory,
+  changed_sections=sorted(changed),A_replaced=sorted(repl),A_inserted=sum(map(len,byp.values())),B_edits=len(patch['B_edits']),compensation_edits=len(patch['compensation_edits']),start_extra_added=sorted(patch['start_extra_added']))
+ return x,ledger