diff --git a/research/owned-relation-independent-validation/.gitattributes b/research/owned-relation-independent-validation/.gitattributes
new file mode 100644
index 0000000000..fc5763a274
--- /dev/null
+++ b/research/owned-relation-independent-validation/.gitattributes
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+      "sha256": "727b0999f3afd17b8756efdc2eec96e5d76f9fcab111db9031814b7fbfbd0d54",
+      "git_blob": "8c3ce2187fd20e3d470d42181f2b9850278af8f1"
+    },
+    {
+      "path": "git-evidence/tree/e4370e0bff125a6575ed3c073d24aa1a984323d1",
+      "bytes": 969,
+      "sha256": "b706afd4ac83f0df442f7da0cc70b26e3d8da71d5e1c343731e5d2d90f2bd44a",
+      "git_blob": "0e9fcca56e932b4b6f13b46965456346b2fc57ed"
+    },
+    {
+      "path": "git-evidence/tree/e6ae7fb7f6eee1465b54989e937f0bc80b1c3a76",
+      "bytes": 740,
+      "sha256": "238db5571e898c6db4c20eb31642a341a1c02eaa11dd232663959608263252f5",
+      "git_blob": "3ff895b2ed63c2db6159fa47071b6d7ff382bbb7"
+    },
+    {
+      "path": "git-evidence/tree/e9c70b9927d6e9233633e4e88108f831e7c5c5d9",
+      "bytes": 14144,
+      "sha256": "22369b51a2b61cb47fb424394c7a9fac4f8ef81a1e29f4e9a6805892dbbba7e9",
+      "git_blob": "df81143d27491882d65cf288ba2fc4f783727669"
+    },
+    {
+      "path": "SOURCE-GUARDS.json",
+      "bytes": 17029,
+      "sha256": "7b9b7817296dafd13a0a57d1df5727479522d9392802ca715f2a1430eff14cd1",
+      "git_blob": "cac9ce93ab8d476f20c9dfbd4e24cb6c762a1a0d"
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/README.md b/research/owned-relation-independent-validation/README.md
new file mode 100644
index 0000000000..45e466532d
--- /dev/null
+++ b/research/owned-relation-independent-validation/README.md
@@ -0,0 +1,60 @@
+# Independent conditional validation of PR5377
+
+Exact Ali Romman [PR5377](https://github.com/CrocSwap/integer-mult-bounds/pull/5377) head `c448d13c71908647f968b06cddb795ce7d288139` supports **κ = 60447/20000000 = .00302235**, an exact conditional gain `2871/5000000000 = .0000005742` over selected PR4610's `.0030217758`. This package supplies independent physical and cost checks, a constructive extension of the selected precision/storage prescription, and the complete frozen registered author cold receipt. It preserves the same five framework assumptions and changes no selected record. No unconditional or formal-kernel theorem is claimed.
+
+This is an independent audit. Construction credit remains with Ali Romman and the predecessors below. The physical engine uses reverse free-word propagation plus a separate all-column forward check. The cost engine reconstructs the literal controller invoice and uses newly written directed rational logarithm/exponential enclosures. It imports no submitted interval or native evaluator. It explicitly reuses the pinned independently transcribed PR5241 outer ledger function.
+
+## Result and evidence
+
+The author makes L230 private in each of 16 backward LOCAL calls and prepares `h230 = h324 - h326 - h328 + h333`. A same-frame snapshot replaces one rank-eight center; a proved zero row permits physical identity in place of one rank-one paid transition. One rank-nine productive helper is surrendered per such call. The two forward calls retain the original 408-helper contract. All retained arbitrary main/helper columns and the complete owned return are checked. The controller proof supplies separate helper banks for all 18 calls.
+
+The complete invoice has 64,372 paid jobs and 10,912 productive fields, with target/paid rank masses 239,742/238,990. Its changed terms are minus 16 H1 and minus 16 H8 paid jobs and minus 16 H9 productive targets. The moment gain is `16*(1 + 8^t - 9^t)>0` for `0<t<1`. Added scalar work costs 46 primitive allowances per backward occurrence. Owned fields earn no productive credit.
+
+The independent cost engine establishes a strict crossing enclosure **(.00302238736347, .00302238736348)**, with negative derivative on `[0,.05]` and negative moment on `[.05,1]`. This is a sharp ceiling for this exact complete paid/target profile and moment model. It does not optimize over other relations, controllers, helper inventories or physical words, or assert that the endpoint has funded compiler/outer slack. The conditional claim `.00302235` uses tested saving `.00302236`, uniform gap `1/700000000`, compiler grid `j=44836`, and `N=2^31385200000000`. Both charged tails, completion/splitting, integer threshold and all 54 strict plus 4 functional outer predicates pass.
+
+Read the complete [physical report](evidence/physical/PHYSICAL-REVIEW.md), [cost/specialization report](evidence/cost/REPORT.md), and [third constructive extension review](evidence/cold/PHYSICAL-EXTENSION-REVIEW.md). They supply the full same-frame/zero/operator/owned-boundary argument and a constructive finite-template extension. Expanded `W,P,O,R,G,N` are freshly defined for the changed construction: each suspended backward LOCAL occurrence has three distinct owned banks, each forward occurrence one, plus separately charged query/completion/compiler banks. The source prescription uses these new constants and a new eventual threshold. The raw `181098496 < 10^9` allowance is not an expanded storage/precision bound. No enormous uniform word is materialized.
+
+The retained assumptions are exactly `native_all_columns`, `owned_erasure`, `compiler`, `precision_tape`, and `analytic_recovery`. Full source native phase foundations, ordinary BIT stock/conversion and upstream analytic/recovery are authenticated reuse. The changed physical implication and new template constants are reviewed here; those generic foundations are not discharged.
+
+## Frozen sources and guards
+
+[SOURCES.json](SOURCES.json) uses only canonical base `1ec1119972c9aefe42525172d07b332fcff81cb4` and pins its selected record and task catalogue as provenance. Candidate head and canonical main are sibling children of source base `7c472563474e60185e6ca101a17622133d047e56`. The unmerged candidate head is retained evidence, not a canonical ancestor or a live input requiring an unavailable side commit.
+
+`capsule/` preserves all 9 author package files, all 9 original registered live input paths, and all 14 original source-manifest rows including provenance. Historical author-base `capsule/certificates/selected-result.json` has blob `c35482cd9035843b15a634cc8276a7e1e40e8395`. The canonical record used for comparison is separately retained at `engines/physical/pinned/selected-current.json` and `engines/cost/frozen/selected-initial.txt`, blob `b288ae44032fd84dd5564243422836cbcd29835e`. These roles and bytes differ. Package SOURCES pins the canonical record.
+
+[CAPSULE.json](CAPSULE.json) inventories all frozen source/script/report/receipt bytes and is SHA256-pinned in verify.py. [SOURCE-GUARDS.json](SOURCE-GUARDS.json) maps 63 actual source copies/aliases to exact original commits, paths and blobs. `git-evidence/` contains raw commit/tree objects: the verifier checks their object hashes, traverses every declared Merkle path, and compares the copied blob without Git or network. This includes the complete original author payload and original source guards, plus the independently reused ledger. Byte authentication is separate from mathematical acceptance. No original compressed source or report was normalized or repaired.
+
+Publication history and working bytes require the separate repository preflight. Package replay has no dependency on reaching the side head from a clean Git checkout; its full inputs and raw evidence are committed inside this package.
+
+## Reproduce and coverage
+
+From repository root with standard-library Python3.12:
+
+```sh
+python3 -B scripts/research_package.py --package research/owned-relation-independent-validation --check-only
+python3 -B scripts/research_package.py --package research/owned-relation-independent-validation
+python3 -B scripts/check_research_commit.py --package research/owned-relation-independent-validation --check-source-history
+```
+
+After extracting a checked committed export into a fresh Git-free directory:
+
+```sh
+python3 -I -B research/owned-relation-independent-validation/verify.py
+python3 -I -O -B research/owned-relation-independent-validation/verify.py
+```
+
+`--integrity-only` checks the full inventory, Merkle paths and frozen cold receipts without running mathematical engines. Full replay runs unchanged independent engines from private temporary directories with read-only source inputs and fresh bytecode namespaces. Every stable mathematical result field must equal its frozen original receipt; runtime seconds alone are excluded. The cost receipt predates additional provenance captures: its original 12 source hashes must match and the current 24-file map is authenticated separately. All inputs are rechecked after execution.
+
+Fresh controls include the physical engine's wrong-relation and wrong-snapshot checks; the cost engine's old BIT, closed uniform gap, unfunded endpoint and closed epsilon checks; an actual altered-WORD-byte inventory rejection; and a private copied receipt falsely crediting 16 surrendered rank-nine outputs, rejected by the literal census. No source guard is bypassed or mutant repinned. All checks remain active under optimized Python.
+
+The **frozen author cold execution** is [VALIDATION.json](evidence/cold/VALIDATION.json), [the full bounded resource receipt](evidence/cold/BOUNDED-REGISTERED-RUN.json), stdout/stderr and pre/post 24-file hashes. A separately owned registered run executed the unmodified author normal and optimized commands in 94.344 seconds, peak sampled descendant RSS 153572KiB, 12 controls per mode, no changed scientific byte. Both commands compared freshly reconstructed complete RESULT and decompressed WORD against exact committed artifacts. This package authenticates that full evidence and freshly reruns the independent engines. It does not claim that hosted package CI reruns the author cold commands.
+
+Frozen reports describe their original review stage, including gates then outstanding. The completed cold receipt supplies that subsequent gate; original report bytes remain unchanged. Package/CI success is conditional finite evidence, not a maintainer's selected-frontier update.
+
+## Open next questions
+
+[TASK.json](TASK.json) records structured questions about a changed profile beyond this ceiling and independent discharge of the retained foundations. For the former, specify a new independent helper contract and complete invoice before synthesis. For the latter, select one named generic contract and pinned source proof as a separate review. Neither question requests another equivalent root evaluation or unsupported construction search.
+
+## Credit and license
+
+Ali Romman supplied the new relation/word; Cao Yifan supplied final PR4610; Cinna Davis supplied the p16 controller/helper lineage; zxv supplied native/compiler/precision machinery; Jacob Alan Sussman supplied mixed-target recursion; Chris R/Clear1nsight supplied PR5241 independent admission. All attributed native, BIT, phase, physical and analytic predecessors remain credited in exact retained sources. New review by Chris R / Clear1nsight, with substantial OpenAI Codex assistance; no independent human review or new construction authorship claimed. New work is Apache-2.0 under the repository license.
diff --git a/research/owned-relation-independent-validation/REGISTERED-REPLAY.stderr.log b/research/owned-relation-independent-validation/REGISTERED-REPLAY.stderr.log
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/research/owned-relation-independent-validation/REGISTERED-REPLAY.stdout.log b/research/owned-relation-independent-validation/REGISTERED-REPLAY.stdout.log
new file mode 100644
index 0000000000..270e6fc958
--- /dev/null
+++ b/research/owned-relation-independent-validation/REGISTERED-REPLAY.stdout.log
@@ -0,0 +1,85 @@
+CHECK Exact immutable capsule/Merkle source guards; independent reverse/all-column physical engine and new rational complete-cost engine; complete stable-result comparisons and semantic/source mutation controls; frozen full author cold receipt authentication.
+{
+  "cold_frozen_receipt": {
+    "controls": 24,
+    "fresh_here": false,
+    "seconds": 94.34425078798085,
+    "source_files_unchanged": 24,
+    "status": "PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED"
+  },
+  "fixed_profile_root": [
+    "302238736347/100000000000000",
+    "75559684087/25000000000000"
+  ],
+  "framework_assumptions": 5,
+  "gain_over_selected4610": "2871/5000000000",
+  "head": "c448d13c71908647f968b06cddb795ce7d288139",
+  "independent_engines": {
+    "cost": {
+      "complete_stable_result_equal": true,
+      "seconds": 17.20837299298728,
+      "source_hashes": 24,
+      "status": "PASS_INDEPENDENT_SCALAR_CENSUS_MOMENT_COMPILER_OUTER_SCREEN"
+    },
+    "physical": {
+      "complete_stable_result_equal": true,
+      "seconds": 2.924,
+      "source_hashes": 16,
+      "status": "PASS_BOUNDED_INDEPENDENT_PHYSICAL_DELTA"
+    }
+  },
+  "inventory_files": 126,
+  "kappa": "60447/20000000",
+  "raw_merkle_source_paths": 63,
+  "seconds": 21.862,
+  "selected_record_changed": false,
+  "status": "PASS_INDEPENDENT_PR5377_CONDITIONAL_VALIDATION",
+  "wrapper_controls": [
+    "altered source byte rejected by actual inventory guard",
+    "unearned16rank9productive-targets rejected by literal census",
+    "fresh physical engine executes its intrinsic wrong-relation and wrong-snapshot controls"
+  ]
+}
+CHECK Same checks with assertions disabled; child interpreter inherits optimization; no submitted author replay rerun.
+{
+  "cold_frozen_receipt": {
+    "controls": 24,
+    "fresh_here": false,
+    "seconds": 94.34425078798085,
+    "source_files_unchanged": 24,
+    "status": "PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED"
+  },
+  "fixed_profile_root": [
+    "302238736347/100000000000000",
+    "75559684087/25000000000000"
+  ],
+  "framework_assumptions": 5,
+  "gain_over_selected4610": "2871/5000000000",
+  "head": "c448d13c71908647f968b06cddb795ce7d288139",
+  "independent_engines": {
+    "cost": {
+      "complete_stable_result_equal": true,
+      "seconds": 17.90116847102763,
+      "source_hashes": 24,
+      "status": "PASS_INDEPENDENT_SCALAR_CENSUS_MOMENT_COMPILER_OUTER_SCREEN"
+    },
+    "physical": {
+      "complete_stable_result_equal": true,
+      "seconds": 2.973,
+      "source_hashes": 16,
+      "status": "PASS_BOUNDED_INDEPENDENT_PHYSICAL_DELTA"
+    }
+  },
+  "inventory_files": 126,
+  "kappa": "60447/20000000",
+  "raw_merkle_source_paths": 63,
+  "seconds": 22.624,
+  "selected_record_changed": false,
+  "status": "PASS_INDEPENDENT_PR5377_CONDITIONAL_VALIDATION",
+  "wrapper_controls": [
+    "altered source byte rejected by actual inventory guard",
+    "unearned16rank9productive-targets rejected by literal census",
+    "fresh physical engine executes its intrinsic wrong-relation and wrong-snapshot controls"
+  ]
+}
+PASS_REGISTERED_RESEARCH_PACKAGE research/owned-relation-independent-validation outcome=completed
diff --git a/research/owned-relation-independent-validation/REPLAY.json b/research/owned-relation-independent-validation/REPLAY.json
new file mode 100644
index 0000000000..2752721ff3
--- /dev/null
+++ b/research/owned-relation-independent-validation/REPLAY.json
@@ -0,0 +1,97 @@
+{
+  "status": "PASS_REGISTERED_NORMAL_AND_OPTIMIZED_INDEPENDENT_ENGINES",
+  "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]",
+  "platform": "Linux-7.0.0-38-generic-x86_64-with-glibc2.39",
+  "command": [
+    "python3",
+    "-B",
+    "scripts/research_package.py",
+    "--package",
+    "research/owned-relation-independent-validation"
+  ],
+  "normal": {
+    "cold_frozen_receipt": {
+      "controls": 24,
+      "fresh_here": false,
+      "seconds": 94.34425078798085,
+      "source_files_unchanged": 24,
+      "status": "PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED"
+    },
+    "fixed_profile_root": [
+      "302238736347/100000000000000",
+      "75559684087/25000000000000"
+    ],
+    "framework_assumptions": 5,
+    "gain_over_selected4610": "2871/5000000000",
+    "head": "c448d13c71908647f968b06cddb795ce7d288139",
+    "independent_engines": {
+      "cost": {
+        "complete_stable_result_equal": true,
+        "seconds": 17.20837299298728,
+        "source_hashes": 24,
+        "status": "PASS_INDEPENDENT_SCALAR_CENSUS_MOMENT_COMPILER_OUTER_SCREEN"
+      },
+      "physical": {
+        "complete_stable_result_equal": true,
+        "seconds": 2.924,
+        "source_hashes": 16,
+        "status": "PASS_BOUNDED_INDEPENDENT_PHYSICAL_DELTA"
+      }
+    },
+    "inventory_files": 126,
+    "kappa": "60447/20000000",
+    "raw_merkle_source_paths": 63,
+    "seconds": 21.862,
+    "selected_record_changed": false,
+    "status": "PASS_INDEPENDENT_PR5377_CONDITIONAL_VALIDATION",
+    "wrapper_controls": [
+      "altered source byte rejected by actual inventory guard",
+      "unearned16rank9productive-targets rejected by literal census",
+      "fresh physical engine executes its intrinsic wrong-relation and wrong-snapshot controls"
+    ]
+  },
+  "optimized": {
+    "cold_frozen_receipt": {
+      "controls": 24,
+      "fresh_here": false,
+      "seconds": 94.34425078798085,
+      "source_files_unchanged": 24,
+      "status": "PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED"
+    },
+    "fixed_profile_root": [
+      "302238736347/100000000000000",
+      "75559684087/25000000000000"
+    ],
+    "framework_assumptions": 5,
+    "gain_over_selected4610": "2871/5000000000",
+    "head": "c448d13c71908647f968b06cddb795ce7d288139",
+    "independent_engines": {
+      "cost": {
+        "complete_stable_result_equal": true,
+        "seconds": 17.90116847102763,
+        "source_hashes": 24,
+        "status": "PASS_INDEPENDENT_SCALAR_CENSUS_MOMENT_COMPILER_OUTER_SCREEN"
+      },
+      "physical": {
+        "complete_stable_result_equal": true,
+        "seconds": 2.973,
+        "source_hashes": 16,
+        "status": "PASS_BOUNDED_INDEPENDENT_PHYSICAL_DELTA"
+      }
+    },
+    "inventory_files": 126,
+    "kappa": "60447/20000000",
+    "raw_merkle_source_paths": 63,
+    "seconds": 22.624,
+    "selected_record_changed": false,
+    "status": "PASS_INDEPENDENT_PR5377_CONDITIONAL_VALIDATION",
+    "wrapper_controls": [
+      "altered source byte rejected by actual inventory guard",
+      "unearned16rank9productive-targets rejected by literal census",
+      "fresh physical engine executes its intrinsic wrong-relation and wrong-snapshot controls"
+    ]
+  },
+  "full_log": "REGISTERED-REPLAY.stdout.log",
+  "stderr": "REGISTERED-REPLAY.stderr.log",
+  "scope": "Fresh narrow independent engines with complete stable-result comparison to full frozen original result bytes; full frozen author cold receipt authenticated, not rerun."
+}
diff --git a/research/owned-relation-independent-validation/SOURCE-GUARDS.json b/research/owned-relation-independent-validation/SOURCE-GUARDS.json
new file mode 100644
index 0000000000..cac9ce93ab
--- /dev/null
+++ b/research/owned-relation-independent-validation/SOURCE-GUARDS.json
@@ -0,0 +1,384 @@
+{
+  "schema_version": 1,
+  "description": "Raw Git commit/tree Merkle paths authenticate exported source bytes without Git; source-history publication preflight separately binds canonical package provenance. The side head is retained byte evidence, not a canonical ancestor.",
+  "rows": [
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/TASK.json",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/TASK.json",
+      "git_blob": "f5df24ffe3bc51288ab57d55494b1db8684d7de9"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/native.py",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/native.py",
+      "git_blob": "b8249ed7ba981a798ba282a6aeabd81a600bda36"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/price.py",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/price.py",
+      "git_blob": "6077adf74c1a154e5f790411f774a52745eb5281"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/WORD.json.gz",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/WORD.json.gz",
+      "git_blob": "5e79bd826c6ca1e782766ea0ae28a61d136303d1"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/RESULT.json",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/RESULT.json",
+      "git_blob": "27b4e5470812c2b9feaa54fbfe867b3fb68def68"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/README.md",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/README.md",
+      "git_blob": "777f4e1d5114e35ba6de2a8e818b790b16aca655"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/SOURCES.json",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/SOURCES.json",
+      "git_blob": "9854abbb4f66f20aad8ab5016ede8319cd47519c"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/verify.py",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/verify.py",
+      "git_blob": "b19f7d0ca4a6e61a0a75595bbc413f9341e84717"
+    },
+    {
+      "local": "capsule/research/kappa-owned-relation-20261023/VERIFY.json",
+      "commit": "c448d13c71908647f968b06cddb795ce7d288139",
+      "path": "research/kappa-owned-relation-20261023/VERIFY.json",
+      "git_blob": "8098df4c806a6c6e9e2be7253ba4101744dab08d"
+    },
+    {
+      "local": "capsule/research/higher-moment-strictification/verify.py",
+      "commit": "7c472563474e60185e6ca101a17622133d047e56",
+      "path": "research/higher-moment-strictification/verify.py",
+      "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699"
+    },
+    {
+      "local": "capsule/research/joint-helper-lattice/CONTROLLER.json",
+      "commit": "7c472563474e60185e6ca101a17622133d047e56",
+      "path": "research/joint-helper-lattice/CONTROLLER.json",
+      "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5"
+    },
+    {
+      "local": "capsule/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+      "commit": "7c472563474e60185e6ca101a17622133d047e56",
+      "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+      "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb"
+    },
+    {
+      "local": "capsule/research/kappa-rebuild/architecture/mixed_target_probe.py",
+      "commit": "7c472563474e60185e6ca101a17622133d047e56",
+      "path": "research/kappa-rebuild/architecture/mixed_target_probe.py",
+      "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e"
+    },
+    {
+      "local": "capsule/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "commit": "7c472563474e60185e6ca101a17622133d047e56",
+      "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e"
+    },
+    {
+      "local": "capsule/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+      "commit": "7c472563474e60185e6ca101a17622133d047e56",
+      "path": "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+      "git_blob": "ac77b78547d6dbf2e6bd102e1047c5b16c1bca88"
+    },
+    {
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diff --git a/research/owned-relation-independent-validation/SOURCES.json b/research/owned-relation-independent-validation/SOURCES.json
new file mode 100644
index 0000000000..eeb3af8971
--- /dev/null
+++ b/research/owned-relation-independent-validation/SOURCES.json
@@ -0,0 +1,18 @@
+{
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+      "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038"
+    },
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+      "usage": "provenance",
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+}
diff --git a/research/owned-relation-independent-validation/TASK.json b/research/owned-relation-independent-validation/TASK.json
new file mode 100644
index 0000000000..cdaf24f08c
--- /dev/null
+++ b/research/owned-relation-independent-validation/TASK.json
@@ -0,0 +1,106 @@
+{
+  "schema_version": 1,
+  "task_id": "independent-moment",
+  "priority_revision": 7,
+  "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+  "original_card": {
+    "id": "independent-moment",
+    "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-mixed-fourth-entry/README.md",
+      "research/staged-fourth-mixture-ceiling/README.md",
+      "research/r437-two-window-carrier/README.md"
+    ],
+    "methods": [
+      "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.",
+      "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls."
+    ],
+    "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.",
+    "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+    "allowed_variations": [
+      "Reconstruct either a source ledger or a numeric enclosure with a different method."
+    ],
+    "scope_change_triggers": [
+      "Importing the primary function and calling its output independent verification.",
+      "Calling an aggregate histogram or source archive an independently accepted physical supplier."
+    ],
+    "overlap_terms": [
+      "independent moment",
+      "rank histogram",
+      "exact enclosure",
+      "2979",
+      "rank7 joint endframes",
+      "paired extraction",
+      "joint lowering",
+      "4088",
+      "4091",
+      "4067",
+      "staged544-mixed-fourth-entry",
+      "staged-fourth-mixture-ceiling",
+      "r437-two-window-carrier"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.",
+        "evidence": "research/staged544-mixed-fourth-entry/README.md",
+        "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.",
+        "status": "author-checked",
+        "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.",
+        "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+        "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.",
+        "status": "author-checked",
+        "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.",
+        "evidence": "research/r437-two-window-carrier/README.md",
+        "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.",
+        "status": "author-checked",
+        "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Independently validate exact PR5377 head: local changed owned relation and full boundaries, complete literal invoice, new directed rational enclosures and fixed-profile ceiling, same-premise finite-template specialization, and frozen registered author cold receipt.",
+  "scope_change_reason": "Explicit donor assignment requests complete conditional verification of the new owned-relation candidate. Numerical independent-moment work is combined with separately authored physical and applicability reports; the card alone would stop after its chosen numerical implication.",
+  "bottleneck_link": "Independent reconstruction prevents a surrendered owned helper from receiving productive credit and binds the improved paid profile to actual physical and same-premise conditional coverage.",
+  "budget_minutes": 60,
+  "stop_rule": "One exact-head packet, narrow independent replays and recorded cold evidence; no construction search, selected-record change or historical suites.",
+  "outcome": "completed",
+  "evidence": "README.md; evidence/physical and evidence/cost complete reports; evidence/cold/VALIDATION.json and full logs/receipts; registered fresh independent engine replay",
+  "author": "Chris R / Clear1nsight, with substantial OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance; no independent human or formal-kernel acceptance claimed.",
+  "open_questions": [
+    {
+      "question": "Can another admissible owned relation change the complete paid profile beyond this fixed-profile ceiling?",
+      "why_it_matters": "The present scalar root caps this exact invoice only; more digits do not create another construction improvement.",
+      "first_step": "Name a changed independent helper contract and derive its fully charged paid/target profiles before synthesis.",
+      "blocked_by": "Physical all-column proof, disjoint ownership, charged storage and a new independent moment check."
+    },
+    {
+      "question": "Can the retained five framework assumptions be independently discharged?",
+      "why_it_matters": "This conditional audit does not establish an unconditional multiplication theorem.",
+      "first_step": "Take one explicitly retained native/owned/compiler/precision/analytic contract and its pinned source proof as a separate review task.",
+      "blocked_by": "Full physical implementation and all-size analytic/recovery foundations; no formal-kernel proof claimed."
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/VERIFY.json b/research/owned-relation-independent-validation/VERIFY.json
new file mode 100644
index 0000000000..b8840092f8
--- /dev/null
+++ b/research/owned-relation-independent-validation/VERIFY.json
@@ -0,0 +1,28 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 150,
+      "checks": "Exact immutable capsule/Merkle source guards; independent reverse/all-column physical engine and new rational complete-cost engine; complete stable-result comparisons and semantic/source mutation controls; frozen full author cold receipt authentication."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 150,
+      "checks": "Same checks with assertions disabled; child interpreter inherits optimization; no submitted author replay rerun."
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/capsule/certificates/selected-result.json b/research/owned-relation-independent-validation/capsule/certificates/selected-result.json
new file mode 100644
index 0000000000..c35482cd90
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/certificates/selected-result.json
@@ -0,0 +1,85 @@
+{
+  "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit",
+  "kappa": "60403/20000000",
+  "decimal": "0.00302015",
+  "source_prs": [
+    4470,
+    4447,
+    4441,
+    4440,
+    4416,
+    4433,
+    4359,
+    4268,
+    3945,
+    4085,
+    2979,
+    4076,
+    4088,
+    1673,
+    1758,
+    1786,
+    23,
+    555,
+    589
+  ],
+  "source_manifest": "certificates/frontier4470-source.json",
+  "certificate": "certificates/frontier4470/CLAIM.json",
+  "certificate_sha256": "d962932a6971b8f0054462c59f4ad699dcf3d1fbf886e1f856a6fa9e97491232",
+  "proof": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md",
+  "proof_supplements": {
+    "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c",
+    "notes/batched-complex-rows.tex": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c",
+    "notes/compact-control-movement.tex": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6",
+    "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+    "notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a",
+    "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "references/semantic-bulk/pr23/semantic-bulk-17-note.tex": "652242b05174bb776ffc6165af170df9c8cf220dbd0fc26c24d778f320dbabc8",
+    "research/e8-bit-carrier-skeleton/code/bit/export_records.py": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3",
+    "research/e8-bit-carrier-skeleton/code/nine/geometry.py": "36eeda3184bd009e89462b65c8725d10860c444f8da8f1f87e5f6e50120011ca",
+    "research/e8-bit-p111-tuned/code/gen_p3.py": "438b83f10d70ceca7cf78049420204b7de2dc61682f913c50a62596106ad84cd",
+    "research/e8-bit-p111-tuned/code/xcheck_p.py": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e",
+    "research/e8-bit-p111-tuned/tune/EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "research/e8-bit-p111-tuned/tune/apply.py": "806ae4cb2648e4f05dcf56bd089891fd3ba33a6ee5fe76d3329e322c6770c1a1",
+    "research/e8-bit-p111-tuned/tune/wlib.py": "a37fdf3cdf5f62945c2a90193401c0e9edc9dd3cda8d8cb36a3b9c329ebe4dbc",
+    "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "docs/research/pr-intake-evidence/pr4359/PROOF-REVIEW.md": "7d67bb814285f7634029fbd378c6457156545f0b38858cc1c6ec34b68cd9d162",
+    "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md": "5c111dd56beb53dc44ab727d96e1af03aaf50f3023d4342e2b0a89ede6cf585b",
+    "docs/research/pr-intake-evidence/pr4416/PROOF-REVIEW.md": "2c2bbe6fe1bab44778192118f27e59a0d23dbe02c47aa8a42845093f1ce46f49"
+  },
+  "review": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md",
+  "validation": "docs/research/pr-intake-evidence/pr4470/VALIDATION.json",
+  "integration": "docs/research/pr-intake-evidence/pr4470/INTEGRATION.json",
+  "reproduce": "make frontier4470-verify",
+  "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized.",
+  "previous_kappa": "23/10000",
+  "previous_record": "certificates/checkpoints/frontier4359.json",
+  "audited_source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363",
+  "source_certificate": "research/joint-helper-lattice/RESULT.json",
+  "source_certificate_sha256": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21",
+  "replay_mode": "fresh changed-construction replay with exact-source prior foundation review reuse",
+  "contributors": "docs/research/community-joint4470-contributors.md",
+  "assumptions": [
+    {
+      "id": "native_all_columns",
+      "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity."
+    },
+    {
+      "id": "owned_erasure",
+      "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts."
+    },
+    {
+      "id": "compiler",
+      "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract."
+    },
+    {
+      "id": "precision_tape",
+      "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template."
+    },
+    {
+      "id": "analytic_recovery",
+      "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework."
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/capsule/docs/research/agent-task-catalog.json b/research/owned-relation-independent-validation/capsule/docs/research/agent-task-catalog.json
new file mode 100644
index 0000000000..f126dd2e2d
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/docs/research/agent-task-catalog.json
@@ -0,0 +1,1242 @@
+{
+  "schema_version": 1,
+  "priority_revision": 7,
+  "priority_log": "docs/research/research-priority-log.md",
+  "assessed_on": "2026-10-20",
+  "status": "Research suggestions, not reservations or assertions that these questions are unclaimed. Check current main and live PRs.",
+  "tracks": [
+    {
+      "id": "bit-mechanisms",
+      "weight": 20,
+      "tasks": [
+        {
+          "id": "bit-helper-contract",
+          "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/r439-bsection-stars-seed01/README.md",
+            "research/r439-copy-path-sharing-barrier/README.md"
+          ],
+          "methods": [
+            "Derive a replacement interface lemma and price its implementation.",
+            "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement."
+          ],
+          "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/r439-bsection-stars-seed01/verify.py"
+            ],
+            "expected": "PASS_R439_BSECTION_STARS",
+            "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.",
+          "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.",
+          "allowed_variations": [
+            "Choose one helper-star or quartet instance; narrow to one boundary implication."
+          ],
+          "scope_change_triggers": [
+            "Changing only source count or scalar addition count without an interface argument."
+          ],
+          "overlap_terms": [
+            "H2_D_frame0_targets_from_helpers",
+            "K_equals_D",
+            "helper-star"
+          ]
+        },
+        {
+          "id": "bit-new-register-model",
+          "question": "Can an explicitly larger or nonabelian register model escape the scoped three-register obstruction?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/bit-three-register-lower-bound/README.md",
+            "certificates/selected-result.json",
+            "research/bit-gl3-mixed-targets-length10/README.md",
+            "docs/research/community-efficient1000-review.md"
+          ],
+          "methods": [
+            "Construct the smallest exact identity in a newly specified legal operation alphabet.",
+            "Derive a target-specific relaxation bound for that same explicit alphabet."
+          ],
+          "acceptance_gate": "Name the changed hypothesis, all counted roles and a uniform identity; finite column tests alone do not certify it. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read Model section 1 of the three-register bound and identify the exact excluded free operations.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "First compare the alphabet, role count and length with the fully replayed #1974 census and #2027 mixed-root tariff. Identify a changed premise and a legal native implementation; then price one smallest completed instance before searching larger words.",
+          "bottleneck_link": "A small-width completed saving changes the bit primitive; a finite-address identity alone is insufficient.",
+          "allowed_variations": [
+            "Choose a fixed larger register count or a specified nonabelian operation family."
+          ],
+          "scope_change_triggers": [
+            "Remaining inside the already-excluded three-register abelian model.",
+            "Repeating the two-register GL3 census or a covered three-register length without changing a hypothesis; a formal group-algebra word without native conversion is a partial result."
+          ],
+          "overlap_terms": [
+            "three-register",
+            "nonabelian",
+            "group algebra"
+          ]
+        },
+        {
+          "id": "r437-carrier-integration",
+          "question": "Can the paid R437 two-window carrier improvement be admitted by the actual pooled compiler and physical caller?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/r437-two-window-carrier/README.md",
+            "research/r437-reverse-row-coefficient/README.md"
+          ],
+          "methods": [
+            "Close one compiler/request, caller or precision/stock implication for the pinned paid exchange.",
+            "Falsify that exact interface with an arbitrary-dirty-state or chronology counterexample."
+          ],
+          "acceptance_gate": "Pin the complete source and destination contracts, exact paid and scalar deltas, and all remaining assumptions. A local moment gain is not a physical or all-size supplier admission.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4067 paid profile and open integration obligations; #4147 covers the reverse row coefficient. Three additional ADDs per call and all helpers remain charged. This is not a selected supplier.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Choose one unclaimed obligation: pooled compiler codebook/request alignment, actual physical caller, or precision/stock envelope using the already reported reverse coefficient. Pin the input and receiver, preserve dirty/source windows, and test one binding with a rejection control. Stop at unresolved dependencies; do not rederive the coefficient or quote the local moment as a completed bound.",
+          "bottleneck_link": "The exchange changes the paid profile; integration must establish that its gain survives the complete caller.",
+          "allowed_variations": [
+            "One compiler rebind, one actual caller boundary, or one precision/stock implication."
+          ],
+          "scope_change_triggers": [
+            "Ignoring added ADDs, retaining an obsolete reverse coefficient, or declaring global admission from the local histogram."
+          ],
+          "overlap_terms": [
+            "R437",
+            "two-window carrier",
+            "4067",
+            "4147",
+            "pooled compiler",
+            "request alignment",
+            "reverse row coefficient"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4067: source-bound two-window carrier with (2,2) to (1,3) paid exchange and fixed OQ4 host.",
+              "evidence": "research/r437-two-window-carrier/README.md",
+              "remaining": "Pooled compiler/request rebind, physical caller and precision/stock admission.",
+              "status": "author-checked",
+              "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4147: reverse row coefficient follow-up.",
+              "evidence": "research/r437-reverse-row-coefficient/README.md",
+              "remaining": "Use the exact coefficient in a caller-bound precision/stock proof rather than repeat the arithmetic.",
+              "status": "author-checked",
+              "source_commit": "72e7bb797adf82aeb525a399f56ab8adbab8e93c",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        }
+      ]
+    },
+    {
+      "id": "complex-mechanisms",
+      "weight": 20,
+      "tasks": [
+        {
+          "id": "p104-side-correction",
+          "question": "Can a changed P104 producer/consumer contract escape the scoped slot, chart and completion obstructions with a favorable full bill?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/p104-literal-slot-defect/README.md",
+            "research/p104-uniform-commutation-gap/README.md",
+            "research/p104-uniform-encoding-gap/README.md",
+            "research/p104-source-chart-shortcut/README.md",
+            "research/p104-fiber-tag-seam/README.md"
+          ],
+          "methods": [
+            "Construct one side-correction word at an explicit chronological cut with the needed frames still available.",
+            "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget."
+          ],
+          "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the named successor obstructions before extending #2981 static flags. Distinguish literal-slot action, commutation, uniform encoding, source-chart shortcut and fiber-tag seam scopes; none excludes all P104 mechanisms.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Name one hypothesis changed from these exact interfaces. Write a literal producer-to-consumer timeline and an arbitrary-dirty-input positive/control pair, then charge acquisition, coefficients, completion, hosting and restoration. Stop if the same slot/fiber mismatch persists or the favorable full budget already fails. A scoped independent audit remains useful; another static count is not a new completion.",
+          "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.",
+          "allowed_variations": [
+            "One correction factorization, one chronological cut, or one explicit hosting obstruction.",
+            "A changed correction schedule with an updated full bill and native frame contract."
+          ],
+          "scope_change_triggers": [
+            "Recompiling the already certified low-rank channel without closing a new obligation.",
+            "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.",
+            "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.",
+            "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful.",
+            "Repeating a static cover, source-chart shortcut or fiber-tag seam without changing the hypothesis responsible for its obstruction."
+          ],
+          "overlap_terms": [
+            "P104",
+            "I-G/2",
+            "side correction",
+            "native channel",
+            "1972",
+            "1991",
+            "2586",
+            "endpoint transport",
+            "physical dual",
+            "relay composition",
+            "2981",
+            "joint unit flags",
+            "acquisition delivery",
+            "static nesting",
+            "4133",
+            "4136",
+            "4140",
+            "4153",
+            "4154",
+            "p104-literal-slot-defect",
+            "p104-uniform-commutation-gap",
+            "p104-uniform-encoding-gap",
+            "p104-source-chart-shortcut",
+            "p104-fiber-tag-seam"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4133: literal-slot defect",
+              "evidence": "research/p104-literal-slot-defect/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4136: uniform commutation gap",
+              "evidence": "research/p104-uniform-commutation-gap/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4140: uniform encoding gap",
+              "evidence": "research/p104-uniform-encoding-gap/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance",
+              "evidence": "research/p104-source-chart-shortcut/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4154: fiber-tag seam mismatch",
+              "evidence": "research/p104-fiber-tag-seam/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "complex-rank-shape-decoder",
+          "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/complex-decoder-field-extension-seed44/README.md",
+            "research/complex-frame-pair-decoders/README.md",
+            "research/selected-k8-unrestricted-ends/README.md",
+            "research/eisenstein-reduction-copy-floor/README.md"
+          ],
+          "methods": [
+            "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.",
+            "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration."
+          ],
+          "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).",
+          "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.",
+          "allowed_variations": [
+            "One masked, overcomplete or block decoder family with exact labels and supports.",
+            "A scoped lower bound on effective rank for one alphabet.",
+            "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": [
+            "Repacking idle remainders of an unchanged word (covered by the packing ceiling).",
+            "Repeating the eight-term all-pairs search inside its proved scope.",
+            "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+            "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "rank shape",
+            "block climb",
+            "masked decoder",
+            "overcomplete",
+            "effective rank"
+          ]
+        },
+        {
+          "id": "complex-new-helper-inventory",
+          "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/heterogeneous-owner-assembly/README.md",
+            "certificates/selected-result.json",
+            "research/selected-k8-unrestricted-ends/README.md"
+          ],
+          "methods": [
+            "Propose a changed helper inventory and derive an optimistic exact moment.",
+            "Design a small completed instance and independently verify its endpoint and rank bill."
+          ],
+          "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+          "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+          "allowed_variations": [
+            "Narrow to one changed boundary or helper type with explicit counts.",
+            "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": [
+            "Mixing only providers already inside the pinned catalogue.",
+            "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "helper inventory",
+            "heterogeneous-owner",
+            "mutable leaver"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "recursive-interfaces",
+      "weight": 20,
+      "tasks": [
+        {
+          "id": "joint-query-controller",
+          "question": "Can the installed QQ16 caller win a complete matched protocol bill, or can a changed demand eliminate actual paid work?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/qq16-caller-install/README.md"
+          ],
+          "methods": [
+            "Derive the matched whole-caller physical bill for installed and baseline protocols.",
+            "Change the actual demanded observations and prove a cheaper legal producer/consumer contract."
+          ],
+          "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.",
+          "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+          "allowed_variations": [
+            "One paid query, one changed first pair, or one precisely specified affine helper state.",
+            "A counterexample or lower bound for that exact proposed repair.",
+            "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain."
+          ],
+          "scope_change_triggers": [
+            "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.",
+            "Treating cover-map counts as zero-cost physical address operations.",
+            "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.",
+            "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.",
+            "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.",
+            "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving."
+          ],
+          "overlap_terms": [
+            "QQ16",
+            "joint-query",
+            "changing-chart controller",
+            "selected observation",
+            "1969",
+            "2540",
+            "early record",
+            "output-bank retention",
+            "complete native decoder",
+            "2965",
+            "producer defect",
+            "dirty-helper range",
+            "F17 consumer",
+            "4166",
+            "qq16-caller-install"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.",
+              "evidence": "research/qq16-caller-install/README.md",
+              "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.",
+              "status": "author-checked",
+              "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "centre-path-sharing",
+          "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.",
+            "Prove a lower bound on copied information per call for the selected decoder contract."
+          ],
+          "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).",
+          "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.",
+          "allowed_variations": [
+            "One sharing pattern across a fixed number of calls.",
+            "One reduced copied-total contract for the existing decoder.",
+            "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": [
+            "Removing copies without a replacement contract for the decoder's copied totals.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "centre path",
+            "copied totals",
+            "private temporary",
+            "shared centre",
+            "batching"
+          ]
+        },
+        {
+          "id": "coverage-law-change",
+          "question": "Can a template or call contract leave two or more unpaid coordinates per live family?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/idle-axis-hosting/PROOF.md",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "State a replacement for the coverage identity (mass = 72W + 64N) and the contract change that realizes it, with its implementation cost.",
+            "Find an obstruction: show which data-endpoint obligation forces exactly one unpaid coordinate in the current template."
+          ],
+          "acceptance_gate": "An explicit replacement identity, verified on a small complete instance with dirty inputs, priced with ceiling.ceiling(unpaid=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Explain where the single unpaid coordinate per family comes from in the hosted template; propose one change and price it. Ideal budget: two unpaid coordinates per family is 3.77x (levers.py).",
+          "bottleneck_link": "The deficit is one coordinate per family minus the centre charge; doubling unpaid coordinates per family scales it directly.",
+          "allowed_variations": [
+            "One template change or one endpoint-contract change.",
+            "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": [
+            "Counting a coordinate as unpaid while leaving it unadvanced in the data endpoint.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "coverage identity",
+            "unpaid coordinate",
+            "deficit law",
+            "W - 64N"
+          ]
+        },
+        {
+          "id": "connector-alphabet-change",
+          "question": "Does one explicit extension of the connector alphabet offer a favorable completed budget?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/universal-connector-boundary/README.md",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Construct and charge a legal extra operation on a minimal instance.",
+            "Prove a target-specific bound after adding one specified operation family."
+          ],
+          "acceptance_gate": "State which fixed-alphabet premise changes and charge its implementation; do not declare it free. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/universal-connector-boundary/verify.py"
+            ],
+            "expected": "PASS_UNIVERSAL_CONNECTOR_BOUNDARY",
+            "inspect": "Reproduce the 945-pairing control, then read Exact interface to list the allowed calls.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Add exactly one legally priced operation and test a tiny dirty-input instance before enumerating larger cases.",
+          "bottleneck_link": "A new legal connector operation could change recursive interface cost; a larger census in the same alphabet is a separate side result.",
+          "allowed_variations": [
+            "Choose one additional operation and a small source count for its first counterexample."
+          ],
+          "scope_change_triggers": [
+            "Keeping the alphabet and only increasing the source count; record this as a changed assignment.",
+            "Extending a source-count census without naming a supplier/interface decision it could change; audit #2973 pruning concerns before relying on the affected predecessor exclusions."
+          ],
+          "overlap_terms": [
+            "universal connector",
+            "source-toggle",
+            "connector alphabet"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "adversarial-audit",
+      "weight": 15,
+      "tasks": [
+        {
+          "id": "selected-stock-envelope",
+          "question": "What explicit uniform stock envelope does the actual selected stopped producer supply at one bootstrap stage?",
+          "starting_points": [
+            "research/selected-bootstrap-stock-audit/README.md",
+            "research/bootstrap-cutoff-time-space-split/README.md",
+            "certificates/selected-result.json",
+            "docs/research/community-efficient1000-review.md",
+            "research/stock-margin-chain/README.md"
+          ],
+          "methods": [
+            "Derive a source-bound reserve recurrence at the actual selected atom widths, separating parent stock from completed inner borrowing.",
+            "Find an exact missing implication or counterexample to a proposed selected-stage stock envelope."
+          ],
+          "acceptance_gate": "Bind every coefficient and depth factor to the selected producer and state the width domain. Compare a proved envelope with the sufficient cutoff guard; a large numerical headroom or a historical m=120 coefficient is not a selected m=73 proof.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #2972 stock-margin chain and the selected stock audit. The new source archive reports the remaining cutoff comparisons, but leaves every actual stock coefficient unresolved; it is not an independently validated reserve envelope.",
+            "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+          },
+          "first_experiment": "Choose one actual selected producer/stage and derive its parent reserve and depth coefficient from source. Check whether newer handoffs already cover that exact obligation. Stop with the missing implementation lemma if it cannot be bounded; do not rerun #2972 cutoff/headroom arithmetic as a new contribution.",
+          "bottleneck_link": "This reduces a concrete inherited implementation obligation without confusing unchanged kappa arithmetic with a completed theorem.",
+          "allowed_variations": [
+            "One stage or one explicit reserve/depth implication.",
+            "An independently checked same-domain proof repair, retaining all remaining assumptions."
+          ],
+          "scope_change_triggers": [
+            "Importing the historical 57604 or 252 allowance without a selected-producer binding.",
+            "Calling a conditional fit lemma a full outer-proof adoption.",
+            "Replacing an actual selected stock coefficient with cutoff comparisons or a conditional fit inequality."
+          ],
+          "overlap_terms": [
+            "selected stock",
+            "stock envelope",
+            "bootstrap cutoff",
+            "1956",
+            "1965",
+            "1990",
+            "2972",
+            "stock-margin-chain",
+            "actual_stock_coefficient"
+          ],
+          "existing_checks": [
+            {
+              "scope": "Retained stock audit identifies missing actual selected-stage coefficients; later cutoff-chain arithmetic does not supply them.",
+              "evidence": "docs/research/research-family-status.md#revision-6-handoffs-source-archives-awaiting-independent-validation",
+              "remaining": "Derive one actual reserve/depth coefficient from the selected producer.",
+              "status": "reviewed",
+              "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "supplier-boundary-audit",
+          "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged544-mixed-fourth-entry/README.md",
+            "research/scatter-boundary-decision/README.md"
+          ],
+          "methods": [
+            "Trace one hypothesis through the source, checker and complete caller.",
+            "Construct one semantically invalid but superficially well-formed fixture and test rejection."
+          ],
+          "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.",
+          "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.",
+          "allowed_variations": [
+            "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage."
+          ],
+          "scope_change_triggers": [
+            "Reporting the historical timing-only diagnostic as a new current acceptance bug.",
+            "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.",
+            "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass."
+          ],
+          "overlap_terms": [
+            "owner boundary",
+            "bridge omission",
+            "hosting",
+            "2977",
+            "scatter export",
+            "duplicate index",
+            "parity semantics",
+            "4088",
+            "3801",
+            "staged544-mixed-fourth-entry",
+            "scatter-boundary-decision"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.",
+              "evidence": "research/staged544-mixed-fourth-entry/README.md",
+              "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.",
+              "status": "author-checked",
+              "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #3801: successor scatter-boundary decision package.",
+              "evidence": "research/scatter-boundary-decision/README.md",
+              "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.",
+              "status": "author-checked",
+              "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "uniform-transfer-audit",
+          "question": "Does one quantified step of the proposed #4100 all-size construction hold at its actual caller?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/unconditional-batched-crt/README.md"
+          ],
+          "methods": [
+            "Prove one missing implication with explicit quantified hypotheses.",
+            "Find an exact counterexample at the claimed interface boundary."
+          ],
+          "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read PROOF.md and AUDIT.md in #4100. Select one distinct obligation: CRT total repair, native/free-algebra lifting, precision/conditioning, or complete fixed-tape cost. This is an author-submitted proof, not an accepted unconditional theorem.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Check live handoffs; name one proposition, its caller, quantified domain and dependency closure. Independently prove the implication or exhibit a precise gap/counterexample. Prioritize CRT.md total repair or COMPLEX.md free-algebra lift only if unclaimed. Stop at the chosen obligation; do not substitute finite samples or root arithmetic for an all-size proof, or launch the complete package by default.",
+          "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.",
+          "allowed_variations": [
+            "One CRT repair, native lift, precision/conditioning or tape-cost proposition, with its exact caller."
+          ],
+          "scope_change_triggers": [
+            "Replacing a quantified obligation with another finite smoke test.",
+            "Treating archive intake, an author PASS receipt or a finite composed fixture as discharge of the universal hypotheses."
+          ],
+          "overlap_terms": [
+            "uniform transfer",
+            "all-size",
+            "precision",
+            "4100",
+            "unconditional-batched-crt"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4100: proposed unconditional construction and finite checks, without independent acceptance.",
+              "evidence": "research/unconditional-batched-crt/README.md",
+              "remaining": "Independent proof audit of one caller-bound all-size implication; all other premises remain explicit.",
+              "status": "author-checked",
+              "source_commit": "337d04939571a637aeab54a0f58f54fde811663a",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "census-pruning-audit",
+          "question": "Does the reported word-census parity-pruning error invalidate a specific exclusion we still rely on, and what bounded repair is justified?",
+          "starting_points": [
+            "research/f7-weight-parity-census-correction/README.md",
+            "docs/research/research-family-status.md"
+          ],
+          "methods": [
+            "Independently reconstruct the tiny counterexample and trace one affected exclusion to its exact pruning code.",
+            "Compare corrected and unpruned enumeration on a small exhaustive domain, then audit the changed pruning implication."
+          ],
+          "acceptance_gate": "Pin the old and proposed corrected engines, distinguish a disproved pruning rule from a disproved final bound, and state exactly which downstream exclusions need revalidation. #2973 is an author-checked source archive; neither its new f(7) claim nor all old conclusions are automatically accepted or rejected.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #2973 error description and MATH.md; manually reconstruct the prefix states of 01021323 before running any large census.",
+            "scope": "Source-binding orientation only; no full enumeration or mathematical validation."
+          },
+          "first_experiment": "Reconstruct the eight prefix states of 01021323 and compare bit-0 versus Hamming-weight parity budgets independently. Trace the reported false prune to one pinned predecessor (#2542, #2634 or #2691), then test a small exhaustive domain. Stop after a source-impact handoff or corrected-prune proof; a full seven-label replay needs a separate resource budget and a named research decision it can change.",
+          "bottleneck_link": "An unsound exclusion can wrongly close a mechanism; correcting its dependency boundary is more useful than extending the same census.",
+          "allowed_variations": [
+            "One predecessor pruning rule, one independently exhaustive small domain, or one downstream dependency audit."
+          ],
+          "scope_change_triggers": [
+            "Launching a larger census before validating the prune and explaining which active decision it changes.",
+            "Treating a small-domain counterexample to the old rule as a counterexample to every reported seven-label bound."
+          ],
+          "overlap_terms": [
+            "2973",
+            "2542",
+            "2634",
+            "2691",
+            "weight parity",
+            "bit-0",
+            "01021323",
+            "census pruning"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "independent-verification",
+      "weight": 10,
+      "tasks": [
+        {
+          "id": "independent-moment",
+          "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged544-mixed-fourth-entry/README.md",
+            "research/staged-fourth-mixture-ceiling/README.md",
+            "research/r437-two-window-carrier/README.md"
+          ],
+          "methods": [
+            "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.",
+            "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls."
+          ],
+          "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.",
+          "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+          "allowed_variations": [
+            "Reconstruct either a source ledger or a numeric enclosure with a different method."
+          ],
+          "scope_change_triggers": [
+            "Importing the primary function and calling its output independent verification.",
+            "Calling an aggregate histogram or source archive an independently accepted physical supplier."
+          ],
+          "overlap_terms": [
+            "independent moment",
+            "rank histogram",
+            "exact enclosure",
+            "2979",
+            "rank7 joint endframes",
+            "paired extraction",
+            "joint lowering",
+            "4088",
+            "4091",
+            "4067",
+            "staged544-mixed-fourth-entry",
+            "staged-fourth-mixture-ceiling",
+            "r437-two-window-carrier"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.",
+              "evidence": "research/staged544-mixed-fourth-entry/README.md",
+              "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.",
+              "status": "author-checked",
+              "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.",
+              "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+              "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.",
+              "status": "author-checked",
+              "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.",
+              "evidence": "research/r437-two-window-carrier/README.md",
+              "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.",
+              "status": "author-checked",
+              "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "formal-interface-lemma",
+          "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/gate-operand-parity-lean/README.md",
+            "research/staged544-certified-endpoint/README.md",
+            "research/unconditional-batched-crt/README.md"
+          ],
+          "methods": [
+            "Formalize a missing boundary lemma identified by the selected review.",
+            "Audit a formal theorem-to-certificate binding independently."
+          ],
+          "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Inventory the gate-operand parity lemma (#3807) and certified endpoint arithmetic (#3857). Neither is a full multiplication proof. For #4100, audit the compact-switch statement and its hypotheses before formalizing it.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.",
+          "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.",
+          "allowed_variations": [
+            "Narrow to one formal lemma or one theorem-to-certificate binding."
+          ],
+          "scope_change_triggers": [
+            "Formalizing already-covered arithmetic and claiming the full multiplication theorem."
+          ],
+          "overlap_terms": [
+            "hyperplane end",
+            "formal interface",
+            "Lean binding",
+            "3807",
+            "3857",
+            "4100",
+            "gate-operand-parity-lean",
+            "staged544-certified-endpoint",
+            "unconditional-batched-crt"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #3807: scoped gate-operand parity formalization.",
+              "evidence": "research/gate-operand-parity-lean/README.md",
+              "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.",
+              "status": "author-checked",
+              "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #3857: certified real-power moment/endpoint arithmetic.",
+              "evidence": "research/staged544-certified-endpoint/README.md",
+              "remaining": "Uniform algorithmic implications, not another endpoint digit.",
+              "status": "author-checked",
+              "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4100: compact-switch formalization proposed as future validation.",
+              "evidence": "research/unconditional-batched-crt/README.md",
+              "remaining": "Audit the statement and assumptions before a formal proof campaign.",
+              "status": "author-checked",
+              "source_commit": "337d04939571a637aeab54a0f58f54fde811663a",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        }
+      ]
+    },
+    {
+      "id": "verifier-engineering",
+      "weight": 8,
+      "tasks": [
+        {
+          "id": "replay-runtime",
+          "question": "Can one measured replay bottleneck be sped up without dropping coverage?",
+          "starting_points": [
+            "scripts/run_isolated_tests.py",
+            "scripts/verify_replay_coverage.py",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Profile one isolated replay and optimize the measured bottleneck.",
+            "Design source-bound reuse with explicit dependency invalidation and negative controls."
+          ],
+          "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the selected reproduction command and choose a single replay stage for profiling.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.",
+          "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.",
+          "allowed_variations": [
+            "Profile one stage or design one source-bound cache boundary."
+          ],
+          "scope_change_triggers": [
+            "Skipping coverage or comparing different fixtures to claim speedup."
+          ],
+          "overlap_terms": [
+            "replay runtime",
+            "cache invalidation",
+            "isolated tests"
+          ]
+        },
+        {
+          "id": "portable-replay",
+          "question": "Can one reproducible environment or artifact-comparison failure be repaired?",
+          "starting_points": [
+            "research/gzip-container-reproducibility/README.md",
+            "docs/ci-verification.md"
+          ],
+          "methods": [
+            "Reproduce one portability failure and add a minimal cross-environment fix.",
+            "Audit one canonical-payload comparison for omitted proof-relevant fields."
+          ],
+          "acceptance_gate": "Preserve immutable source hashes and proof-relevant content; a different compressed byte stream alone is not a mathematical mismatch.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the gzip-container reproducibility examples and distinguish frozen source bytes from regenerated payloads.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Reproduce one specific mismatch or audit one canonical comparison for omitted proof-relevant fields.",
+          "bottleneck_link": "Portable exact checks prevent environment failures from blocking valid contributions.",
+          "allowed_variations": [
+            "One interpreter/version mismatch or one payload field comparison."
+          ],
+          "scope_change_triggers": [
+            "Removing immutable-source pins because generated compressed bytes differ."
+          ],
+          "overlap_terms": [
+            "gzip container",
+            "reproducibility",
+            "canonical payload"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "consolidation",
+      "weight": 5,
+      "tasks": [
+        {
+          "id": "overlap-receipt",
+          "question": "What exact content and credit of a small named PR set has already been retained?",
+          "starting_points": [
+            "docs/research/pr-ledger.md",
+            "CONTRIBUTORS.md"
+          ],
+          "methods": [
+            "Compare exact heads and retained artifacts to write a source-bound disposition receipt.",
+            "Audit an existing receipt for missing content or predecessor attribution."
+          ],
+          "acceptance_gate": "Separate complete integration, partial retention and changed heads; make no autonomous closures.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read one small PR set in the ledger and identify exact reviewed heads and unresolved content.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Compare that set to retained artifacts; produce a complete or explicitly partial disposition receipt.",
+          "bottleneck_link": "Reliable overlap evidence preserves credit and prevents repeated review of already-retained material.",
+          "allowed_variations": [
+            "One small related PR family or one existing integration receipt."
+          ],
+          "scope_change_triggers": [
+            "Treating matching titles or one shared blob as proof of full incorporation."
+          ],
+          "overlap_terms": [
+            "overlap receipt",
+            "partial integration",
+            "attribution"
+          ]
+        },
+        {
+          "id": "scope-navigation",
+          "question": "Can one misleading historical-current claim or missing research cross-reference be corrected?",
+          "starting_points": [
+            "docs/research/current-status.md",
+            "docs/research/pr-ledger.md",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Trace one confusing path from onboarding to its authoritative source.",
+            "Index one tightly related family of obstructions with explicit excluded and open hypotheses."
+          ],
+          "acceptance_gate": "Produce evidence-backed navigation, preserve historical records and avoid a duplicate global survey.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Follow one link from the selected record to its review and compare a potentially stale historical claim.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Repair one confusing path or produce a scoped map of one related obstruction family.",
+          "bottleneck_link": "Clear navigation lowers entry cost for central research; a global survey without a concrete fix is not required.",
+          "allowed_variations": [
+            "One historical-current ambiguity or one bounded family index."
+          ],
+          "scope_change_triggers": [
+            "Rewriting frozen scientific packages just to change their historical wording."
+          ],
+          "overlap_terms": [
+            "current status",
+            "historical checkpoint",
+            "scope navigation"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "incumbent-optimization",
+      "weight": 2,
+      "tasks": [
+        {
+          "id": "selected-packing",
+          "question": "Does a named residual packing task have meaningful uncovered headroom after its exact fixed-inventory ceiling?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged-fourth-mixture-ceiling/README.md",
+            "research/staged544-mixed-fourth-entry/README.md"
+          ],
+          "methods": [
+            "Check a fixed-inventory ceiling and source equivalence before any explicitly bounded residual search.",
+            "Price a genuinely changed word/interface under a newly applicable model."
+          ],
+          "acceptance_gate": "Check live overlap and exact model/source binding first. Distinguish a chronological construction from a pooled optimum. State the applicable fixed-inventory ceiling and remaining headroom; changed words or interfaces require a new fully charged model. Do not launch a residual search without an explicit scope and time cap.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4091 fixed-word pooled ceiling and #4088 later 1090-call literal fill. Bind the unchanged local invoices/capacities/stock before transferring the ceiling; its earlier 1080-call residual-bin recipe is historical.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Default to a bounded headroom/source-equivalence check. Only start residual search with an explicit unclaimed domain, time cap and reason the tiny remaining gain matters. Otherwise hand off or select a changed-word mechanism. A changed word or interface needs a fresh cost model, not the old ceiling. Stop at the fixed-inventory cap; do not extend by new random seeds.",
+          "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",
+            "4091",
+            "4088",
+            "staged-fourth-mixture-ceiling",
+            "staged544-mixed-fourth-entry"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4091: pooled optimum at one-third staging for pinned fixed words; not a chronological fill.",
+              "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+              "remaining": "Independent scope/source check; any residual optimization is explicitly bounded and optional.",
+              "status": "author-checked",
+              "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4088: later 1090-call literal fill improves the earlier 1080-call witness.",
+              "evidence": "research/staged544-mixed-fourth-entry/README.md",
+              "remaining": "Complete admission remains separate; old residual-bin instructions must not be copied blindly.",
+              "status": "author-checked",
+              "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "scalar-to-moment",
+          "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged544-a2-graph-rewrite/README.md",
+            "research/staged544-separated-a2/README.md",
+            "research/staged544-a2-composition-audit/README.md",
+            "research/staged544-a1858-contraction-audit/README.md"
+          ],
+          "methods": [
+            "Derive the changed legal frame itinerary and exact child histogram.",
+            "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+          ],
+          "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.",
+          "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+          "allowed_variations": [
+            "One existing scalar simplification and one proposed frame-path change."
+          ],
+          "scope_change_triggers": [
+            "Submitting only another scalar count as completion of a paid-profile task."
+          ],
+          "overlap_terms": [
+            "scalar simplification",
+            "paid profile",
+            "R439",
+            "3998",
+            "4019",
+            "4112",
+            "4152",
+            "staged544-a2-graph-rewrite",
+            "staged544-separated-a2",
+            "staged544-a2-composition-audit",
+            "staged544-a1858-contraction-audit"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #3998: consecutive A2 scalar contraction",
+              "evidence": "research/staged544-a2-graph-rewrite/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4019: separated A2 sites with unchanged recursive histogram",
+              "evidence": "research/staged544-separated-a2/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "f408e09df300b575235f7f77f81948071397e16d",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4112: composition audit",
+              "evidence": "research/staged544-a2-composition-audit/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4152: A1858 contraction audit",
+              "evidence": "research/staged544-a1858-contraction-audit/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        }
+      ]
+    }
+  ],
+  "selection_context": {
+    "refreshed_on": "2026-10-22",
+    "kappa": "60403/20000000",
+    "source_pr": 4470,
+    "record": "certificates/selected-result.json",
+    "review": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md",
+    "orientation_command": "python3 -B scripts/research_selected_baseline.py",
+    "scope": "Metadata refresh only. Revision-7 weights and cards remain historical suggestions pending separate strategic reassessment; check current contracts and overlap before adopting them."
+  }
+}
diff --git a/research/owned-relation-independent-validation/capsule/research/free-word-tensor-lift-audit/PROOF.md b/research/owned-relation-independent-validation/capsule/research/free-word-tensor-lift-audit/PROOF.md
new file mode 100644
index 0000000000..69c337a770
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/free-word-tensor-lift-audit/PROOF.md
@@ -0,0 +1,174 @@
+# Source-bound free-operator tensor lift
+
+This audit affirms one specific premise in PR4100's `COMPLEX.md`, lines 62–89:
+the retained four PR4088 words cancel in a free group algebra before any
+particular native operator is substituted. The premise is true for the exact
+source exports checked here. This is a local algebra and source-binding result;
+it supplies no new paid profile, numerical allowance, encoded implementation,
+physical hosting theorem, outer release or selected-frontier improvement.
+
+## Exact source and contract
+
+The audited text is `research/unconditional-batched-crt/COMPLEX.md`, Git blob
+`c3be56fbfdb4fb29c1ace88cbcdfa7475fb6e343`, SHA256
+`853e1295850862752e4f854aa9e8b28f9ca6eaa9306e2af110b7b77526d1b5e1`.
+It is identical at retained PR4100 head
+`337d04939571a637aeab54a0f58f54fde811663a` and canonical main
+`12fa8c5c844be21bfefb38a19503fbd867a11244`.
+
+Its stated source is PR4088 head
+`72d7efc181edb21806a878f174847c96dd410ab0`, package
+`research/staged544-mixed-fourth-entry`. This audit exports the exact four
+`inputs/{THREE,FOUR}-{base,extra}.json.gz` files, retained `vendor/audit_core.py`,
+`vendor/audit_verify.py`, source `verify.py`, `PROOF.md` and `NOTICE.md`.
+`SOURCE-PINS.json` records every original commit, path, length, Git blob and
+SHA256. Every file is authenticated before the retained checker is executed.
+No native runner, owner fill, solver, NumPy or historical outer engine is run.
+
+Each word has 632 live registers, 91 arbitrary dirty private registers,
+72 abstract unary generators and 36 listed initial correction terms. The
+forward common-label contract on the 723-register direct sum is
+
+`(x,y,h,b) -> (x,y+x,h,b)`.
+
+The dual contract is `(x,y,h,b) -> (x-y,y,h,b)`. In particular every private
+buffer is an independent input, returns identically, and has no leakage into
+live outputs. Neither contract assumes zero private inputs or a product state.
+
+## What the retained checker actually computes
+
+In `audit_core.py`, lines 297–391, a register value is a sparse dictionary
+
+`(initial_input, reduced_signed_operator_word) -> Fraction`.
+
+`program` includes every declared initial correction, precondition,
+compensation, A and cut gate, chronologically inserted B warp, B gate,
+restoration and cleanup gate. `_left` and `_right` cancel only adjacent inverse
+letters; `_axpy` adds exact rational coefficients and removes exact zeros.
+There is no commutation, finite-order relation, numerical operator matrix,
+Fourier-character evaluation or univariate minimal-polynomial reduction.
+
+`audit_verify.semantics` runs all 723 independent symbols forward and dual,
+compares an independent direction of pullback, and checks both cleanup-boundary
+contracts. Every emitted provider passes. Each endpoint consists of exactly
+835 nonzero terms: the 723 diagonal terms and 112 intended shear terms. Every
+surviving operator word is empty.
+
+That is a universal algebraic identity, rather than an identity inferred from
+one operator realization. The source's use of the word “symbolic” is justified
+by these actual data structures, reductions and endpoint predicates.
+
+## All positive tensor multiplicities
+
+Let `F` be the free group on symbols `g_1,...,g_72`, and let `A=Q[F]` be its
+rational group algebra. The finite word program is a product of elementary
+723-by-723 matrices over `A`. A correction `c*g_word*x_source` is an off-diagonal
+entry of one such elementary matrix. Scalar ADD and SCALE entries belong to
+`Q*1_A`.
+
+Let `K` be any characteristic-zero field (in particular `Q[i]`) and let `V`
+be any finite-dimensional vector space over `K`. Choose arbitrary invertible `K`-linear operators
+`G_k` on `V`. All tensor products below are over `K`. For every positive integer `f`, define
+
+`rho_f(g_k) = G_k tensor ... tensor G_k` (f factors).
+
+The assignment of free generators extends uniquely to a group homomorphism
+`F -> GL(V tensor f)`: inverses map to tensor products of inverses, and
+
+`(G H) tensor f = (G tensor f)(H tensor f)`.
+
+Extend this map rationally from `A` into the `K`-linear endomorphisms of
+`V tensor f`. This extension is a unital rational algebra
+homomorphism because multiplication of finite formal sums distributes and
+because the group map preserves products. In particular
+
+`rho_f(sum_w c_w*w) = sum_w c_w*rho_f(w)`.
+
+Apply this homomorphism entrywise to the certified elementary-matrix product.
+It preserves each elementary action, the order of events and the product.
+Since the certified endpoint has only rational multiples of empty words, its
+image is exactly the same register-level shear with each scalar multiplied
+by the identity of `V tensor f`. This proves the endpoint for every positive
+`f` and every input in the 723-register direct sum of `V tensor f`, including
+arbitrarily correlated live/private data.
+
+The number of register roles remains 723. We are changing the internal space
+of each role; we are not taking a tensor power of the 723-by-723 register matrix.
+The latter operation would create a different program with 723^f roles.
+
+The dual pass treats `d_k=G_k^(-T)` as separate free generators. The same
+argument applies, and `(G_k^(-T)) tensor f = (G_k tensor f)^(-T)` in the product
+basis. Native frame labels can be replaced by their tensor powers if the
+separately supplied directed native recipe identities are exact. This audit
+does not reprove or rerun those native recipe identities.
+
+## The distinction that must be retained
+
+This algebra homomorphism is linear on formal sums. Therefore
+
+`rho_f(g-I) = G tensor f - I`,
+
+not `(G-I) tensor f`. Likewise `rho_f(c*g)=c*(G tensor f)`, not
+`(c*G) tensor f = c^f*(G tensor f)`. A role SCALE or bridge coefficient must
+remain scalar, while a constant phase already inside a unary generator is
+part of that generator and therefore occurs in every tensor factor.
+
+For an exact small counterexample, take `G=[[1,1],[0,1]]` and `f=2`.
+Then `(G tensor G-I)` sends `e_2 tensor e_2` to
+`e_1 tensor e_1 + e_1 tensor e_2 + e_2 tensor e_1`; whereas
+`(G-I) tensor (G-I)` sends it only to `e_1 tensor e_1`. Their difference is
+nonzero over `Q` (and over the supplemental field F101).
+The code checks a distinct noncommuting 72-generator family as well, and rejects
+both the whole-difference and whole-scalar tensorization rules.
+
+## Independent evidence and its scope
+
+`independent.py` imports or executes no retained implementation. It reconstructs
+the literal sequence from the four exported words and, for each of the 723
+outputs separately, pulls the output functional backward through that sequence
+over exact `Q[F_72]`. The reverse traversal appends words on the right; a stack
+reduces only adjacent inverse letters. All four forward and all four dual
+contracts match exactly: 5784 output-functional checks, 6680 endpoint terms and
+zero surviving nonempty words. Its controls preserve a nontrivial commutator,
+a fourth power and the two distinct terms of `g-I`.
+
+This implementation is independent of the source engine; the format and
+endpoint contract were read from the same credited source. Agreement is
+supplemental to inspection of the finite exact computations, not a substitute
+for proving what the reductions mean.
+
+`verify.py` also reconstructs and executes the literal events directly on dense
+vectors over F101, with 72 distinct invertible 2-by-2 matrices. The first two do
+not commute. It substitutes their tensor powers at `f=1,2,3` in both orientations
+of all four providers, yielding 24 direct fixtures; all 723 registers are given
+deterministic dirty values. These finite-field experiments are controls, not
+the proof for every rational input or unbounded f. Erasing the actual listed
+correction generators fails at 20 registers; tensorizing the actual role SCALE
+coefficients fails at the reported registers. Exact inverse and product
+compatibility controls also pass.
+
+## Remaining obligations and credit
+
+This positive result discharges only the source's formal free-operator premise
+and its algebraic implication to per-role tensor multiplicity. The physical
+lowering of native monomials, directed native recipes, placement, common cover,
+hosted slices, analytic bounds, coefficient precision, fixed-tape inventory,
+recovery and complete ordinary/outer release are outside this audit. The source
+construction makes additional written claims about these interfaces; this audit
+neither verifies nor refutes those claims.
+No paid-rank saving, all-size multiplication theorem, independent human
+acceptance or new kappa is claimed.
+
+The tensor-lift proposal and current construction are credited to Cinna Davis,
+the PR4100 author; this audit does not claim to invent the representation argument.
+Cinna Davis's PR4088 supplies the four literal providers and source integration.
+Sagar Thakrar's PR3687 exact free-operator engine and roger-sato's PR3693
+all-dirty/reverse audit are reused explicitly. Retained lineage includes Rohan
+Arun/PR4076, Dugongue/David Ganz/PR4085 and PR3945, Nick Petalas, Ross
+Richardson/PR3605, dataisfire/PR3734, ChaloupeMusic/Erwan Secousses, Marius-Paul
+Dumitrean, zxv and the earlier geometry/native/compiler/owner contributors.
+The byte-identical source notice and source-file notices remain in `source/`.
+
+The formal and F101 implementations were separately written by one Codex agent. A second Codex agent independently reviewed them and supplied the exact rational signed-permutation oracle in `independent_real.py`; see `INDEPENDENT-REVIEW.md`. None is a human or formal-kernel acceptance.
+
+`mutation_controls.py` also produces exact actual-program counterexamples in `MUTATIONS.json`: erasing the first correction generator yields `(I-G59)x273` in output115; dropping the first nonidentity scale yields `-3*x119` in output119. Both baseline output functionals pass first. Every actual correction word has length one, so a multi-letter correction reorder is inapplicable rather than counted as an executed control.
diff --git a/research/owned-relation-independent-validation/capsule/research/higher-moment-strictification/verify.py b/research/owned-relation-independent-validation/capsule/research/higher-moment-strictification/verify.py
new file mode 100644
index 0000000000..4b24a50961
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/higher-moment-strictification/verify.py
@@ -0,0 +1,421 @@
+#!/usr/bin/env python3
+"""Higher-moment strictification and a polynomial-logarithm compiler bound.
+
+New arithmetic is independent of predecessor interval code. The unchanged
+invoice replay and two outer ledgers are credited, byte-pinned oracles.
+zxv with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+import argparse
+import ast
+from collections import Counter
+from contextlib import redirect_stdout
+from fractions import Fraction as Q
+from functools import lru_cache
+from hashlib import sha256, sha1
+import io
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+GRID = 2**192
+C = Q('0.00268648')
+KAPPA = Q('0.00268647')
+T = {5:420, 6:270, 7:840, 8:1395, 9:3195,
+     25:448, 41:448, 57:448, 121:224}
+P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300,
+     8:1464, 16:448, 32:448, 48:448}
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def down(x):
+    return Q((x*GRID).__floor__(), GRID)
+
+
+def up(x):
+    return Q(-((-x*GRID).__floor__()), GRID)
+
+
+def rounded(lo, hi):
+    return down(lo), up(hi)
+
+
+def mul(a, b):
+    products = [x*y for x in a for y in b]
+    return rounded(min(products), max(products))
+
+
+def scale(a, x):
+    return mul(a, (x, x))
+
+
+def divide(a, b):
+    need(b[0] > 0, 'positive interval denominator')
+    return mul(a, rounded(1/b[1], 1/b[0]))
+
+
+@lru_cache(None)
+def log_bounds(n):
+    """Exact atanh series, binary reduction; round only the final interval."""
+    need(isinstance(n, int) and n >= 1, 'positive integer logarithm')
+
+    def series(x):
+        u = (x-1)/(x+1)
+        term, total = u, Q(0)
+        for j in range(80):
+            total += 2*term/(2*j+1)
+            term *= u*u
+        tail = 2*term/(161*(1-u*u))
+        return total, total+tail
+
+    k = n.bit_length()-1
+    a, b = series(Q(2))
+    c, d = series(Q(n, 2**k))
+    return rounded(k*a+c, k*b+d)
+
+
+def exp_point(x):
+    """Outward fixed-point Taylor enclosure, with binary scaling/squaring."""
+    need(abs(x) < 16, 'bounded exponential argument')
+    if x < 0:
+        a, b = exp_point(-x)
+        return rounded(1/b, 1/a)
+    divisions = 0
+    while x > Q(1, 2):
+        x /= 2
+        divisions += 1
+    term = total = (Q(1), Q(1))
+    for j in range(1, 65):
+        term = scale(term, x/j)
+        total = rounded(total[0]+term[0], total[1]+term[1])
+    following = scale(term, x/65)
+    # Every remaining ratio is <= 1/132. Twice the next term is safe.
+    result = rounded(total[0], total[1]+2*following[1])
+    for _ in range(divisions):
+        result = mul(result, result)
+    return result
+
+
+def exp_interval(a):
+    return exp_point(a[0])[0], exp_point(a[1])[1]
+
+
+@lru_cache(None)
+def power(n, exponent):
+    return exp_interval(scale(log_bounds(n), exponent))
+
+
+def moment(histogram, exponent):
+    low = high = Q(0)
+    for n, count in histogram.items():
+        a, b = power(n, exponent)
+        low += count*a
+        high += count*b
+    return rounded(low, high)
+
+
+def display(a):
+    unit = 10**30
+
+    def fixed(n):
+        sign = '-' if n < 0 else ''
+        s = str(abs(n)).rjust(31, '0')
+        return sign+s[:-30]+'.'+s[-30:]
+
+    return {'lower': fixed((a[0]*unit).__floor__()),
+            'upper': fixed(-((-a[1]*unit).__floor__()))}
+
+
+def encoded(x):
+    if isinstance(x, Q):
+        return str(x)
+    if isinstance(x, dict):
+        return {str(k): encoded(v) for k, v in x.items()}
+    if isinstance(x, (list, tuple)):
+        return [encoded(v) for v in x]
+    return x
+
+
+def source_environment(path):
+    env = {'__file__': str(path), '__name__': 'pinned_source_oracle'}
+    exec(compile(path.read_bytes(), str(path), 'exec'), env)
+    return env
+
+
+def authenticate():
+    result = {}
+    for row in json.loads((HERE/'VENDOR.json').read_text())['files']:
+        path = HERE/'vendor'/Path(row['path']).relative_to(
+            'research/higher-moment-strictification/vendor')
+        digest = sha256(path.read_bytes()).hexdigest()
+        need(digest == row['sha256'], 'changed source: '+row['path'])
+        raw = path.read_bytes()
+        need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()
+             == row['git_blob'], 'changed Git source blob')
+        result[row['path']] = digest
+    return result
+
+
+def invoice_oracle():
+    """Run #4426 unchanged, rebinding only its two file-location globals."""
+    path = HERE/'vendor/invoice-review/verify.py'
+    env = source_environment(path)
+    env.update(ROOT=path.parent, PHASES='DATA-PHASES.json')
+    output = io.StringIO()
+    with redirect_stdout(output):
+        env['main']()
+    result = json.loads(output.getvalue())
+    need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle')
+    need({int(k): v for k, v in result['targets'].items()} == T
+         and {int(k): v for k, v in result['paid'].items()} == P,
+         'exact literal-word invoice')
+    return result
+
+
+def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)):
+    t = 1-C
+    need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks')
+    need(t+u >= 1, 'tail moment exponent at least one')
+    target, paid = moment(T, t), moment(P, t)
+    alpha = divide(paid, target)
+    gamma = divide(moment(P, t+u), mul(power(cutoff, u), target))
+    delta = divide((Q(sum(T.values())*floor),)*2,
+                   mul(power(cutoff, C), target))
+    limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500))
+    for name, bounds, limit in zip(('alpha', 'gamma', 'delta'),
+                                  (alpha, gamma, delta), limits):
+        need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit')
+    a, g, d = limits
+    bound = 1/(1+v*(1-a))+2*g**v+2*d**v
+    need(bound < 1, 'complete charged normalized moment')
+    old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2,
+                       mul(power(cutoff, C), target))
+    old_lower = alpha[0]**v+2*old_gamma[0]**v
+    need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power')
+    return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor,
+            'paid_moment_exponent': t+u, 'tail_offset_u': u,
+            'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma),
+            'delta': display(delta), 'rational_upper_limits': limits,
+            'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2),
+            'old_rank_one_gamma': display(old_gamma),
+            'old_rank_one_bound_lower': display((old_lower, old_lower)),
+            'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v),
+            'maximum_paid': str(cutoff)+'^'+str(v),
+            'productive_fields_before_uniform_compiler': '7688^'+str(v),
+            'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v),
+            'materialized_product_or_uniform_word': False}
+
+
+def uniform_rank(v):
+    t, p, theta = 1-C, 13, Q(6, 7)
+    gap = (C-KAPPA)/7
+    uniform_saving = C-gap
+    need(10**7 < 15**6, 'theta upper bound')
+    need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality')
+    eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t)
+    need(eta[0] > theta**p, 'exit contraction below complement capacity')
+    base = exp_interval(scale(log_bounds(121), v*C))
+    need(base[1] < 2**p, 'entire ordinary base range fits')
+    # Integer grid: gap*H is integral, avoiding enormous rational powers.
+    step = gap.denominator
+    need(gap.numerator == 1, 'chosen rational gap grid')
+
+    def passes(j):
+        H = step*j
+        return (H+1)**p < 2**j
+
+    lo, hi = 1, 2
+    while not passes(hi):
+        lo, hi = hi, 2*hi
+    while hi-lo > 1:
+        mid = (lo+hi)//2
+        if passes(mid):
+            hi = mid
+        else:
+            lo = mid
+    H = step*hi
+    need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison')
+    need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails')
+    return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap,
+            'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta),
+            'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)),
+            'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H),
+            'integer_test': {'left_base': H+1, 'left_exponent': p,
+                             'right_base': 2, 'right_exponent': hi},
+            'grid_step': step, 'previous_grid_point_rejected': True,
+            'smaller_logarithmic_power_rejected': True}
+
+
+def power_majorant_comparison(v, uniform_saving):
+    """Retain #4416's older power proof, changing only the new unit's ranks."""
+    t, z, h = 1-C, 1-uniform_saving, Q(1, 7)
+    z0 = (t+z)/2
+    delta = z0-t
+    B, debt = (4+7*h)*v, 1+7*v*(1-z0)
+    ratio = (delta*B+debt)/(h*delta)
+    H0 = -((-ratio.numerator)//ratio.denominator)
+    ratio = H0*(1-z0)/(z-z0)
+    H1 = ratio.numerator//ratio.denominator+1
+    need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold')
+    need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected')
+    need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0),
+         'strict power-majorant comparison and previous-rank control')
+    return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h,
+            'scope': 'Tail transformation alone, retaining the older power majorant.'}
+
+
+def outer_ledger(uniform_saving):
+    d = (C-KAPPA)/7
+    params = {'kappa': KAPPA, 'tested_saving': C,
+              'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d,
+              'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'),
+              'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10,
+              'stop': d, 'layout': d, 'd': d}
+    env = source_environment(HERE/'vendor/outer_endpoint.py')
+    row = env['ledger'](params)
+    need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3,
+         'complete first outer ledger')
+    need(all(v > 0 for group in ('strict_checks', 'functional_checks')
+             for v in row[group].values()), 'all outer predicates')
+    frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer']
+    need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger')
+    parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes())
+    function = next(n for n in parsed.body
+                    if isinstance(n, ast.FunctionDef) and n.name == 'ledger')
+    constants = [n for n in parsed.body if isinstance(n, ast.Assign)
+                 and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_')
+                         for t in n.targets)]
+    eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a'))
+    grid = 10**10
+    backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA
+    need(backoff > 0, 'strict derived oracle grid backoff')
+    oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8),
+              'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff,
+              'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2),
+              'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16),
+              'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'],
+              'online': Q('0.001730970419199163702738'),
+              'old': Q('0.001730970419199163702738')}
+    code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[]))
+    exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle)
+    second = oracle['ledger']('higher_moment_smaller_ranks')
+    need(second['kappa'] == KAPPA and second['margins'] == row['margins'],
+         'all nine rows match both ledgers')
+    need(len(second['strict_checks']) == 63 and
+         all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates')
+    controls = {}
+    for name, updates in [('closed_epsilon', {'epsilon': Q(1)}),
+                          ('missing_layout', {'layout': Q(0)}),
+                          ('unfunded_kappa', {'kappa': C}),
+                          ('closed_uniform_gap', {'complex_uniform_saving': params['b']}),
+                          ('insufficient_BIT', {'bit_saving': Q('0.0023')})]:
+        bad = env['ledger'](dict(params, **updates))
+        failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0)
+        need(failed, 'outer control rejected: '+name)
+        controls[name] = failed
+    for name, options in [('old_per_axis_scan', {'old_scan': True}),
+                          ('group_equals_dimension', {'beta_': eps})]:
+        bad = oracle['ledger']('reject_'+name, **options)
+        failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0)
+        need(failed, 'legacy control rejected: '+name)
+        controls[name] = failed
+    return {'ledger': row, 'legacy_63_checks': second['strict_checks'],
+            'legacy_grid': grid, 'legacy_backoff': backoff,
+            'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA,
+            'rejected_controls': controls}
+
+
+def finite_controls():
+    def tensor(histogram):
+        out = Counter()
+        for k, n in histogram.items():
+            for h, b in histogram.items():
+                out[k*h] += n*b
+        return out
+
+    def split(histogram, cutoff):
+        out = Counter()
+        for k, n in histogram.items():
+            q, r = divmod(k, cutoff)
+            out[cutoff] += q*n
+            if r:
+                out[r] += n
+        return +out
+
+    target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1})
+    padded, completion = Counter(), Counter()
+    for k, n in target.items():
+        padded[max(k, 9)] += n
+        if k < 9:
+            completion[9-k] += n
+    final = split(paid+completion, 4)
+    mass = lambda x: sum(k*n for k, n in x.items())
+    need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass')
+    need(min(padded) > max(final), 'exact toy separation')
+    need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory')
+    # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension.
+    invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1]
+    need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting')
+    return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13,
+            'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2',
+                                             'sigma': '3/4', 'actual_charge': 100,
+                                             'invalid_upper': display((invalid, invalid))}}
+
+
+def verify():
+    sources = authenticate()
+    invoice = invoice_oracle()
+    tail = tail_certificate()
+    rank = uniform_rank(tail['tensor_power'])
+    endpoint = outer_ledger(rank['uniform_saving'])
+    controls = finite_controls()
+    rejected = []
+    for name, updates, expected in [
+        ('too_short_product', {'v': 100}, 'complete charged normalized moment'),
+        ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'),
+        ('lost_separation', {'floor': 10}, 'strict finite ranks'),
+    ]:
+        try:
+            tail_certificate(**updates)
+        except ValueError as error:
+            need(str(error) == expected, 'wrong rejection: '+name)
+            rejected.append({'mutation': name, 'failed_at': str(error)})
+        else:
+            raise ValueError('accepted mutation: '+name)
+    old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler']
+    return encoded({'schema': 'higher-moment-native-strictification/1',
+                    'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA,
+                    'invoice_oracle': invoice, 'strictification': tail,
+                    'uniform_rank': rank, 'outer': endpoint,
+                    'tail_only_power_majorant': power_majorant_comparison(
+                        tail['tensor_power'], rank['uniform_saving']),
+                    'finite_controls': controls, 'rejected_mutations': rejected,
+                    'predecessor_H': old['H1'],
+                    'rank_exponent_reduction_factor': Q(old['H1'], rank['H']),
+                    'tensor_power_reduction_factor': Q(6240, tail['tensor_power']),
+                    'source_sha256': sources,
+                    'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(),
+                    'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'})
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--out', type=Path)
+    args = parser.parse_args()
+    result = verify()
+    if args.out:
+        need(not args.out.exists(), 'new output path required')
+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    else:
+        need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt')
+    print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'],
+                      'uniform_rank': result['uniform_rank']['N'],
+                      'strict_moment_gap': result['strictification']['strict_moment_gap'],
+                      'kappa': result['kappa']}))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/capsule/research/joint-helper-lattice/CONTROLLER.json b/research/owned-relation-independent-validation/capsule/research/joint-helper-lattice/CONTROLLER.json
new file mode 100644
index 0000000000..49a2f06758
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/joint-helper-lattice/CONTROLLER.json
@@ -0,0 +1,5224 @@
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+    ],
+    [
+      "ADD",
+      31,
+      29,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      30,
+      14,
+      false
+    ],
+    [
+      "ADD",
+      28,
+      30,
+      -1
+    ],
+    [
+      "ADD",
+      31,
+      29,
+      1
+    ],
+    [
+      "LOCAL",
+      31,
+      15,
+      true
+    ],
+    [
+      "LOCAL",
+      32,
+      15,
+      false
+    ],
+    [
+      "IDLE",
+      7,
+      [
+        17,
+        19,
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      8,
+      [
+        19,
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      9,
+      [
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      10,
+      [
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      11,
+      [
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      12,
+      [
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      13,
+      [
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      14,
+      [
+        31,
+        32
+      ]
+    ],
+    [
+      "ADD",
+      30,
+      28,
+      1
+    ],
+    [
+      "ADD",
+      29,
+      31,
+      -1
+    ],
+    [
+      "ADD",
+      28,
+      26,
+      1
+    ],
+    [
+      "ADD",
+      27,
+      29,
+      -1
+    ],
+    [
+      "ADD",
+      26,
+      24,
+      1
+    ],
+    [
+      "ADD",
+      25,
+      27,
+      -1
+    ],
+    [
+      "ADD",
+      24,
+      22,
+      1
+    ],
+    [
+      "ADD",
+      23,
+      25,
+      -1
+    ],
+    [
+      "ADD",
+      22,
+      20,
+      1
+    ],
+    [
+      "ADD",
+      21,
+      23,
+      -1
+    ],
+    [
+      "ADD",
+      20,
+      18,
+      1
+    ],
+    [
+      "ADD",
+      19,
+      21,
+      -1
+    ],
+    [
+      "ADD",
+      18,
+      16,
+      1
+    ],
+    [
+      "ADD",
+      17,
+      19,
+      -1
+    ],
+    [
+      "ADD",
+      16,
+      14,
+      1
+    ],
+    [
+      "ADD",
+      15,
+      17,
+      -1
+    ],
+    [
+      "ADD",
+      14,
+      12,
+      1
+    ],
+    [
+      "ADD",
+      13,
+      15,
+      -1
+    ],
+    [
+      "ADD",
+      12,
+      10,
+      1
+    ],
+    [
+      "ADD",
+      11,
+      13,
+      -1
+    ],
+    [
+      "ADD",
+      10,
+      8,
+      1
+    ],
+    [
+      "ADD",
+      9,
+      11,
+      -1
+    ],
+    [
+      "ADD",
+      8,
+      6,
+      1
+    ],
+    [
+      "ADD",
+      7,
+      9,
+      -1
+    ],
+    [
+      "ADD",
+      6,
+      4,
+      1
+    ],
+    [
+      "ADD",
+      5,
+      7,
+      -1
+    ],
+    [
+      "ADD",
+      4,
+      2,
+      1
+    ],
+    [
+      "ADD",
+      3,
+      5,
+      -1
+    ],
+    [
+      "ADD",
+      2,
+      0,
+      1
+    ],
+    [
+      "ADD",
+      1,
+      3,
+      -1
+    ],
+    [
+      "SIGNED_SWAP",
+      0,
+      1
+    ],
+    [
+      "SIGNED_SWAP",
+      2,
+      3
+    ],
+    [
+      "SIGNED_SWAP",
+      4,
+      5
+    ],
+    [
+      "SIGNED_SWAP",
+      6,
+      7
+    ],
+    [
+      "SIGNED_SWAP",
+      8,
+      9
+    ],
+    [
+      "SIGNED_SWAP",
+      10,
+      11
+    ],
+    [
+      "SIGNED_SWAP",
+      12,
+      13
+    ],
+    [
+      "SIGNED_SWAP",
+      14,
+      15
+    ],
+    [
+      "SIGNED_SWAP",
+      16,
+      17
+    ],
+    [
+      "SIGNED_SWAP",
+      18,
+      19
+    ],
+    [
+      "SIGNED_SWAP",
+      20,
+      21
+    ],
+    [
+      "SIGNED_SWAP",
+      22,
+      23
+    ],
+    [
+      "SIGNED_SWAP",
+      24,
+      25
+    ],
+    [
+      "SIGNED_SWAP",
+      26,
+      27
+    ],
+    [
+      "SIGNED_SWAP",
+      28,
+      29
+    ],
+    [
+      "SIGNED_SWAP",
+      30,
+      31
+    ]
+  ],
+  "prefix_pairs": 7
+}
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py b/research/owned-relation-independent-validation/capsule/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py
new file mode 100644
index 0000000000..5a55034ec9
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py
@@ -0,0 +1,351 @@
+#!/usr/bin/env python3
+"""Independent literal native replay with arbitrary dirty cleanup buffers.
+
+The retained emitter supplies words; this module imports no retained evaluator.
+Free warp symbols distinguish primal and inverse-transpose operators. Physical
+phase receipts are authenticated inherited evidence, not regenerated here.
+Apache-2.0. Substantial OpenAI assistance.
+"""
+from collections import Counter, defaultdict
+from fractions import Fraction
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import ast
+import gzip
+import json
+
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[2]
+CORE = ROOT / "research/kappa-native-resume/native-source/rebased-core"
+PACKET = ROOT / "research/kappa-native-resume/causal-controller/sources/research/joint-query/certificate.json.gz"
+TAGS = ("THREE-base", "THREE-extra", "FOUR-base", "FOUR-extra")
+Q = Fraction
+
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == ".gz" else raw)
+
+
+def digest(path):
+    return sha256(path.read_bytes()).hexdigest()
+
+
+def authenticate():
+    pins = read(HERE / "SOURCES.json")
+    for relative, expected in pins.items():
+        need(digest(ROOT / relative) == expected, "Changed retained source: " + relative)
+    return pins
+
+
+def emit_original(canonical):
+    """Reuse only the pinned source's pure writer; no source verifier executes."""
+    source = CORE / "sources/bw_emit.py"
+    names = {"basis", "reg", "dual", "scalar", "lregs", "expand", "emit", "primitive_bound"}
+    tree = ast.parse(source.read_text())
+    functions = [n for n in tree.body if isinstance(n, ast.FunctionDef) and n.name in names]
+    need({n.name for n in functions} == names, "Exact writer function inventory")
+    context = dict(c=canonical, frames=canonical["frames"], v=112, R=408, h=9, n=632, Q=Q)
+    exec(compile(ast.Module(body=functions, type_ignores=[]), str(source), "exec"), context)
+    return {"forward": context["emit"](False), "backward": context["emit"](True)}
+
+
+def span(basis):
+    points = {0}
+    for vector in basis:
+        need(isinstance(vector, int) and 0 <= vector < 512, "Nine-dimensional frame")
+        points |= {v ^ vector for v in tuple(points)}
+    return frozenset(points)
+
+
+def identity(role):
+    return {(role, ()): Q(1)}
+
+
+def add(destination, source, coefficient):
+    for key, value in tuple(source.items()):
+        value = destination.get(key, Q(0)) + coefficient * value
+        if value:
+            destination[key] = value
+        else:
+            destination.pop(key, None)
+
+
+def warp(row, operator, backward):
+    symbol = (1 if operator > 0 else -1) * (abs(operator) + (10**6 if backward else 0))
+    out = {}
+    for (variable, word), coefficient in row.items():
+        moved = word[1:] if word and word[0] == -symbol else (symbol,) + word
+        key = variable, moved
+        out[key] = out.get(key, Q(0)) + coefficient
+    return {k: v for k, v in out.items() if v}
+
+
+def expected(role, R, backward, clean):
+    out = identity(role)
+    name, i = role
+    if name != "L":
+        return out
+    target = i < 112 if backward else 112 <= i < 224
+    if not target:
+        return out
+    port = i if backward else i - 112
+    source_offset = 112 if backward else 0
+    sign = -1 if backward else 1
+    add(out, identity(("L", source_offset + port)), Q(sign))
+    if clean:
+        for query in R:
+            if port in query:
+                for j, value in query.items():
+                    add(out, identity(("L", source_offset + j)), -sign * query[port] * value / 4)
+    return out
+
+
+def replay(program, canonical, R, backward, clean, omit_cleanup_last=False):
+    """All L inputs and all Z inputs are independent, including dirty outputs."""
+    n = 2 * canonical["v"] + canonical["R"]
+    need(n == 632, "Retained compact width")
+    rows = {("L", i): identity(("L", i)) for i in range(n)}
+    current = {("L", i): frame for i, frame in enumerate(canonical["start"])}
+    center_indices = set()
+    for event in program:
+        if event[0] == "scalar":
+            op = event[1]
+            for register in op[1:3] if op[0] in ("add", "copy") else op[1:2]:
+                if register[0] == "C":
+                    center_indices.add(register[1])
+        elif event[0] == "center":
+            center_indices.add(event[1])
+    need(center_indices <= set(range(8)), "Known center workspace indices")
+    for i in center_indices:
+        rows["C", i] = identity(("C", i))
+        current["C", i] = None
+    spaces = [span(vectors) for vectors in canonical["frames"]]
+    dimensions = [len(s).bit_length() - 1 for s in spaces]
+    need(dimensions[1] == 9, "Cleanup uses the full native frame")
+    live = set()
+    profile = Counter()
+    counts = Counter()
+    scalar_primitives = 0
+    cleanup_start = next(i for i, event in enumerate(program) if event == ["phase", "full_frame_cleanup"])
+    last_scalar = max(i for i, event in enumerate(program) if event[0] == "scalar" and i > cleanup_start)
+    for position, event in enumerate(program):
+        kind = event[0]
+        counts[kind] += 1
+        if kind in ("climb", "center"):
+            if kind == "climb":
+                _, part, index, old, new, rank = event
+                role = "L", index
+                need(spaces[old] < spaces[new], "Non-nested or empty paid climb")
+            else:
+                _, index, old, new, rank = event
+                role = "C", index
+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], "Center residual is not nested")
+            need(current[role] == old and rank == abs(dimensions[new] - dimensions[old]), "Paid edge source/rank")
+            current[role] = new
+            profile[rank] += 1
+        elif kind == "zero_buffer":
+            _, action, index = event
+            role = "Z", index
+            if action == "alloc":
+                need(role not in rows and role not in live, "Cleanup buffer duplicate")
+                rows[role] = identity(role)
+                current[role] = 1
+                live.add(role)
+            else:
+                need(action == "free" and role in live and current[role] == 1, "Cleanup buffer retirement")
+                live.remove(role)
+        elif kind == "warp":
+            _, role, operator, old, new = event
+            role = tuple(role)
+            need(current[role] == old, "Warp entrance frame")
+            rows[role] = warp(rows[role], operator, backward)
+            current[role] = new
+        elif kind == "scalar":
+            op, frame = event[1:]
+            target = tuple(op[1])
+            if op[0] == "clear":
+                need(target[0] == "C", "A borrowed input was cleared")
+                rows[target] = {}
+                current[target] = frame
+                scalar_primitives += 1
+                continue
+            need(current[target] == frame, "Scalar target frame")
+            if op[0] in ("add", "copy"):
+                source = tuple(op[2])
+                need(current[source] == frame, "Scalar source frame")
+                if op[0] == "copy":
+                    need(target[0] == "C", "Copy overwrites borrowed state")
+                    rows[target] = dict(rows[source])
+                    scalar_primitives += 1
+                    continue
+                coefficient = Q(op[3], op[4])
+                need(target != source, "Self-ADD is not a reversible shear")
+                numerator, denominator = abs(coefficient.numerator), coefficient.denominator
+                need(numerator and denominator & (denominator - 1) == 0, "Non-dyadic ADD")
+                scalar_primitives += 3 + numerator.bit_length() - 1 + numerator.bit_count() + denominator.bit_length() - 1
+                if not (omit_cleanup_last and position == last_scalar):
+                    add(rows[target], rows[source], coefficient)
+            else:
+                need(op[0] == "scale", "Unknown scalar event")
+                coefficient = Q(op[2], op[3])
+                numerator, denominator = abs(coefficient.numerator), coefficient.denominator
+                need(numerator and numerator & (numerator - 1) == 0 and denominator & (denominator - 1) == 0,
+                     "Nonunit dyadic SCALE")
+                scalar_primitives += abs(numerator.bit_length() - denominator.bit_length()) + int(coefficient < 0)
+                if not (omit_cleanup_last and position == last_scalar):
+                    rows[target] = {k: coefficient * v for k, v in rows[target].items()}
+        else:
+            need(kind in ("phase", "adapter", "residual_adapter"), "Unknown native event")
+    need(not live and [current["L", i] for i in range(n)] == canonical["final"], "Retired fields/final frames")
+    need(dict(profile) == {int(k): v for k, v in canonical["local_profile"].items()}, "Complete paid profile")
+    mismatches = []
+    for role, actual in rows.items():
+        wanted = {} if role[0] == "C" else expected(role, R, backward, clean)
+        if actual != wanted:
+            mismatches.append({"role": list(role), "unequal_coefficients": sum(actual.get(k, 0) != wanted.get(k, 0) for k in set(actual) | set(wanted))})
+    if not omit_cleanup_last:
+        need(not mismatches, "Native dirty-buffer operator mismatch: " + repr(mismatches[:3]))
+    else:
+        need(mismatches, "Missing-cleanup negative control unexpectedly accepted")
+    buffer_count = sum(role[0] == "Z" for role in rows)
+    return dict(direction="backward" if backward else "forward", clean_J=clean,
+                independent_borrowed_input_fields=632+buffer_count, original_data_fields=224,
+                expected_restored_helpers=408, expected_restored_arbitrary_cleanup_buffers=buffer_count,
+                explicitly_owned_C_fields_cleared=len(center_indices), event_counts=dict(counts),
+                paid_profile=dict(sorted(profile.items())), paid_rank_mass=sum(k*v for k,v in profile.items()),
+                conservative_real_scalar_primitive_allowance=2*scalar_primitives,
+                all_scalar_frames_checked=True, dyadic_coefficients_and_unit_scales_checked=True,
+                free_warp_operator_endpoint_matches=not mismatches,
+                negative_control_omitted_last_cleanup_scalar=omit_cleanup_last,
+                mismatch_examples=mismatches[:3])
+
+
+def liveness(canonical):
+    times = defaultdict(list)
+    for i, event in enumerate(canonical["cleanup"]):
+        for role in event[1:3] if event[0] == "add" else event[1:2]:
+            role = tuple(role) if isinstance(role, list) else ("L", role)
+            times[role].append(i)
+    full = [i for i, f in enumerate(canonical["final"]) if f == 1]
+    candidates = []
+    for z in canonical["zero_buffers"]:
+        begin, end = min(times["Z", z]), max(times["Z", z])
+        possible = [i for i in range(112) if all(t < begin or t > end for t in times["L", i])]
+        candidates.append(dict(buffer=z, first_use=begin, last_use=end,
+                               noninterfering_same_call_X_candidates=possible,
+                               noninterfering_full_frame_L_candidates=[i for i in full if all(t < begin or t > end for t in times["L", i])]))
+    return dict(full_frame_live_roles=len(full), full_frame_roles_unused_in_cleanup=[i for i in full if not times["L", i]],
+                same_call_X_outputs_touched=sum(bool(times["L", i]) for i in range(112)),
+                buffers_with_no_noninterfering_same_call_X=sum(not row["noninterfering_same_call_X_candidates"] for row in candidates),
+                buffers_with_no_noninterfering_full_frame_L=sum(not row["noninterfering_full_frame_L_candidates"] for row in candidates),
+                intervals=candidates,
+                conclusion="Arbitrary-buffer restoration does not establish a legal same-call completed-output alias.",
+                external_same_frame_bank_requirement=91,
+                external_bank_hosting_constructed=False)
+
+
+def find_aliases(canonical):
+    """Injective lifetime-safe matching; no native L access during its Z span."""
+    options = {row["buffer"]: row["noninterfering_full_frame_L_candidates"]
+               for row in liveness(canonical)["intervals"]}
+    owner = {}
+
+    def augment(z, seen):
+        for role in options[z]:
+            if role in seen:
+                continue
+            seen.add(role)
+            if role not in owner or augment(owner[role], seen):
+                owner[role] = z
+                return True
+        return False
+
+    for z in sorted(options, key=lambda z: (len(options[z]), z)):
+        augment(z, set())
+    bindings = {z: role for role, z in owner.items()}
+    need(len(set(bindings.values())) == len(bindings), "Alias must be injective")
+    need(all(role in options[z] for z, role in bindings.items()), "Interfering alias")
+    return bindings
+
+
+def alias_program(program, bindings):
+    """Replace only Z register operands, retaining every native/scalar event."""
+    out = []
+
+    def mapped(role):
+        return ["L", bindings[role[1]]] if role[0] == "Z" and role[1] in bindings else list(role)
+
+    for event in program:
+        if event[0] == "zero_buffer" and event[2] in bindings:
+            continue
+        if event[0] == "scalar":
+            op = event[1].copy()
+            op[1] = mapped(op[1])
+            if op[0] in ("add", "copy"):
+                op[2] = mapped(op[2])
+            out.append(["scalar", op, event[2]])
+        elif event[0] == "warp":
+            out.append([event[0], mapped(event[1]), *event[2:]])
+        else:
+            out.append(event)
+    return out
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--output", type=Path, default=HERE / "RESULT.json")
+    args = parser.parse_args()
+    pins = authenticate()
+    R = [{int(k): Q(v) for k, v in row.items()} for row in read(PACKET)["R_rows"]]
+    providers = {}
+    for tag in TAGS:
+        providers[tag] = {}
+        for clean in (False, True):
+            folder = "converted" if clean else "sources"
+            canonical = read(CORE / folder / (tag + "-CANONICAL.json.gz"))
+            programs = read(CORE / folder / (tag + "-NATIVE-WORD.json.gz")) if clean else emit_original(canonical)
+            checks = [replay(programs[direction], canonical, R, direction == "backward", clean)
+                      for direction in ("forward", "backward")]
+            bindings = find_aliases(canonical)
+            aliases = {direction: alias_program(program, bindings) for direction, program in programs.items()}
+            aliased_checks = [replay(aliases[direction], canonical, R, direction == "backward", clean)
+                              for direction in ("forward", "backward")]
+            need(len(bindings) == 53, "Expected source-bound 53-field lifetime match")
+            for original, aliased in zip(checks, aliased_checks):
+                need(original["paid_profile"] == aliased["paid_profile"] and
+                     original["conservative_real_scalar_primitive_allowance"] == aliased["conservative_real_scalar_primitive_allowance"],
+                     "Aliasing changes the charged operation list")
+            providers[tag]["clean_J" if clean else "ordinary"] = dict(checks=checks, liveness=liveness(canonical),
+                lifetime_alias_bindings={str(z): role for z, role in sorted(bindings.items())},
+                aliased_checks=aliased_checks,
+                eliminated_cleanup_fields=len(bindings), remaining_cleanup_fields=91-len(bindings),
+                aliased_word_sha256={direction: sha256(json.dumps(program, sort_keys=True, separators=(",", ":")).encode()).hexdigest()
+                                     for direction, program in aliases.items()})
+        print("PASS all arbitrary cleanup inputs", tag, flush=True)
+    canonical = read(CORE / "converted/THREE-base-CANONICAL.json.gz")
+    programs = read(CORE / "converted/THREE-base-NATIVE-WORD.json.gz")
+    controls = [replay(programs[direction], canonical, R, direction == "backward", True, True)
+                for direction in ("forward", "backward")]
+    result = dict(schema="literal-native-dirty-buffers/1", status="PASS_NATIVE_ARBITRARY_DIRTY_BUFFER_REPLAY",
+                  new_multiplication_kappa=False, physical_phase_generation_rerun=False,
+                  phase_evidence="Pinned inherited exact native phase receipts; unchanged native edges.",
+                  source_hashes=pins, verifier_sha256=digest(Path(__file__)), providers=providers,
+                  negative_controls=controls,
+                  lifetime_safe_local_full_frame_aliases_per_word=53,
+                  remaining_external_bank_fields_per_word=38,
+                  all_91_local_output_alias_claim=False, external_bank_placement_and_cost_closed=False)
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    args.output.write_text(json.dumps(result, indent=2) + "\n")
+    print(result["status"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-interface-round2-20261022/price_profile.py b/research/owned-relation-independent-validation/capsule/research/kappa-interface-round2-20261022/price_profile.py
new file mode 100644
index 0000000000..1d93e43d1c
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-interface-round2-20261022/price_profile.py
@@ -0,0 +1,147 @@
+"""Complete p16 price and finite compiler for a changed native profile.
+
+Adapted from Cinna Davis's PR4470 arithmetic, retaining zxv's paid tensor
+completion/logarithmic majorant and Jacob Alan Sussman's mixed-job flow.
+Apache-2.0. Substantial OpenAI Codex assistance. Native admission is separate.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import importlib.util
+import json
+import math
+import sys
+sys.dont_write_bytecode=True
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+
+def need(ok,why):
+    if not ok:raise ValueError(why)
+
+def load(path,name):
+    spec=importlib.util.spec_from_file_location(name,path)
+    m=importlib.util.module_from_spec(spec);sys.modules[name]=m;spec.loader.exec_module(m)
+    return m
+
+def encode(x):
+    if isinstance(x,Q):return str(x)
+    if isinstance(x,dict):return {str(k):encode(v) for k,v in x.items()}
+    if isinstance(x,(list,tuple)):return [encode(v) for v in x]
+    return x
+
+def read(path):
+    import gzip
+    b=path.read_bytes();return json.loads(gzip.decompress(b) if path.suffix=='.gz' else b)
+
+def assemble(local):
+    H={int(k):v for k,v in local['helpers'].items()};N={int(k):v for k,v in local['paid'].items()}
+    sys.path.insert(0,str(ROOT/'research/joint-helper-lattice'))
+    J=load(ROOT/'research/joint-helper-lattice/verify.py','round2_pinned_controller')
+    sys.path.insert(0,str(ROOT/'research/query-thinned-controllers'))
+    C=load(ROOT/'research/query-thinned-controllers/controller.py','round2_controller_engine')
+    word=J.controller16(C)
+    T,P=Counter(),Counter();full=thin=0
+    for e in word['physical_events']:
+        if e[0]=='LOCAL':full+=1;T.update(H);P.update(N)
+        elif e[0]=='QUERY_SHEAR':thin+=1;P[1]+=112
+        elif e[0]=='IDLE':P[8*len(e[2])]+=224
+    for term in word['diagonal']:T[1+8*sum(term[1:])]+=112
+    need(full==18 and thin==15 and sum(H.values())==408,'Complete retained p16 call and input inventory')
+    return H,N,T,P,word
+
+def run(local,kappa=None):
+    H,N,T,P,word=assemble(local)
+    E=load(ROOT/'research/higher-moment-strictification/verify.py','round2_exact_intervals')
+    other=load(ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','round2_second_intervals')
+    def margin(c):
+        t,p=E.moment(T,1-c),E.moment(P,1-c)
+        return t[0]-p[1],t[1]-p[0]
+    old_upper=Q('.0030201659771')
+    need(margin(old_upper)[0]>0,'Changed complete invoice strictly beats old raw root upper endpoint')
+    # Binary search on a fixed rational grid; all final signs use exact intervals.
+    lo,hi=0,100000000
+    grid=10**10
+    while hi-lo>1:
+        mid=(lo+hi)//2
+        if margin(Q(mid,grid))[0]>0:lo=mid
+        else:hi=mid
+    root_low,root_high=Q(lo,grid),Q(hi,grid)
+    need(margin(root_low)[0]>0 and margin(root_high)[1]<0,'Strict changed-profile rational root enclosure')
+    if kappa is None:kappa=Q((root_low*10**8).__floor__()-3,10**8)
+    tested=kappa+Q(1,10**8)
+    need(Q('.003020165')<kappa<tested<root_low,'New multiplication saving with compiler headroom')
+    t,u,v,c,b=1-tested,Q(1,5),1024,20,21
+    target,paid=E.moment(T,t),E.moment(P,t)
+    tl,th=other.moment(T,tested);pl,ph=other.moment(P,tested)
+    need(tl>ph and max(tl,target[0])<=min(th,target[1]) and max(pl,paid[0])<=min(ph,paid[1]),'Two independently implemented rational moment engines agree')
+    alpha=E.divide(paid,target)
+    gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target))
+    delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,tested),target))
+    alpha_gap=Q(1,10**9);g=d=Q(97,100)
+    need(alpha[1]<1-alpha_gap and gamma[1]<g and delta[1]<d,'All original and productive-completion tails charged')
+    need(g**128<Q(1,16) and d**128<Q(1,16),'Both strict tail decay blocks')
+    normalized=1/(1+v*alpha_gap)+Q(4,2**32)
+    need(normalized<1 and c**64<b**63,'Paid completion, splitting and rounding fit')
+    theta,power=Q(63,64),1000
+    eta=E.scale(E.power(145,-v*tested),t)
+    need(2*(20**v)**64<=(145**v)**63 and eta[0]>theta**power,'Shifted exits and complement capacity')
+    need(E.power(145,v*tested)[1]<2**power,'Compiler initial range')
+    gap=(tested-kappa)/7;need(gap.numerator==1,'Explicit finite integer grid')
+    step=gap.denominator
+    def wins(j):return (step*j+1)**power<2**j
+    left,right=1,2
+    while not wins(right):left,right=right,2*right
+    while right-left>1:
+        mid=(left+right)//2
+        if wins(mid):right=mid
+        else:left=mid
+    height=step*right
+    need(height>8*v and wins(right) and not wins(right-1),'Strict finite uniform-rank integer bound')
+    local_scalar=max(x['real_scalar_allowance'] for x in local['native'].values())
+    routes=(sum(N.values())+2*408+688)*1000
+    need(local_scalar+routes<10**7,'Complete scalar and fixed monomial routing bound')
+    scalar_upper=18*10**7+15*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program']) for k in ('left','right')))
+    need(scalar_upper<10**9,'Raw controller scalar bound')
+    bit=read(ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']
+    atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599');admitted=Q(bit['admitted'])
+    need(atom==Q('.004') and atom>ordinary>admitted>tested and atom<1-ordinary,'Source ordinary BIT admission and stock')
+    L=load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','round2_outer_ledger')
+    params={'kappa':kappa,'tested_saving':tested,'complex_uniform_saving':kappa+6*gap,
+            'b':kappa+5*gap,'a':kappa+4*gap,'q':kappa+3*gap,'bit_saving':admitted,
+            'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap}
+    outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom)
+    need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Whole outer predicate inventory')
+    need(all(x>0 for key in ('strict_checks','functional_checks') for x in outer[key].values()),'All outer inequalities strictly positive')
+    controls={}
+    for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':tested}),('closed_epsilon',{'epsilon':Q(1)})]:
+        bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items() if x<=0]
+        need(failed,'Reject unsupported outer patch '+name);controls[name]=failed
+    return encode({'status':'PASS_CHANGED_PROFILE_ARITHMETIC_NATIVE_ADMISSION_SEPARATE','kappa':kappa,
+        'gain_over_PR4535':kappa-Q('.003020165'),'raw_root_interval':[root_low,root_high],
+        'margin_at_old_root_upper':margin(old_upper),'local_helpers':H,'local_paid':N,'targets':T,'paid':P,
+        'productive_fields':sum(T.values()),'paid_calls':sum(P.values()),'rank_mass_surplus':sum(r*n for r,n in T.items())-sum(r*n for r,n in P.items()),
+        'strictification':{'tested':tested,'power':v,'cutoff':c,'floor':b,'tail_offset':u,'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'normalized_paid_upper':normalized},
+        'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'gap':gap,'uniform_saving':params['complex_uniform_saving'],'H':height,'N':'2^'+str(height),'integer_test_exponent':right,'word_materialized':False},
+        'nonrecursive':{'local_scalar':local_scalar,'local_routes':routes,'raw_scalar_upper':scalar_upper},
+        'ordinary_BIT':bit,'outer':outer,'negative_controls':controls,
+        'scope':'Exact changed-profile arithmetic only. Requires separately admitted changed native programs, paid transports and absolute phases. Retained compiler/native/precision/tape/analytic/recovery assumptions.'})
+
+if __name__=='__main__':
+    ap=argparse.ArgumentParser();ap.add_argument('--native',type=Path,required=True);ap.add_argument('--kappa');ap.add_argument('--out',type=Path,default=HERE/'ARITHMETIC.json');args=ap.parse_args()
+    result=run(read(args.native),Q(args.kappa) if args.kappa else None)
+    result['native_receipt_sha256']=sha256(args.native.read_bytes()).hexdigest()
+    # Pin all loaded project source modules and the non-module controller/stock
+    # records read by the inherited engines. Standard-library files are outside
+    # the repository and are recorded instead by the replay's Python version.
+    paths={Path(__file__).resolve(),ROOT/'research/joint-helper-lattice/CONTROLLER.json',
+           ROOT/'research/query-thinned-controllers/RESULT.json'}
+    for module in tuple(sys.modules.values()):
+        name=getattr(module,'__file__',None)
+        if name:
+            path=Path(name).resolve()
+            if path.is_relative_to(ROOT) and path.is_file():paths.add(path)
+    result['source_sha256']={p.relative_to(ROOT).as_posix():sha256(p.read_bytes()).hexdigest() for p in sorted(paths)}
+    args.out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+    print(json.dumps({k:result[k] for k in ('status','kappa','gain_over_PR4535','raw_root_interval','paid_calls','compiler')},indent=2))
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/README.md b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/README.md
new file mode 100644
index 0000000000..777f4e1d51
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/README.md
@@ -0,0 +1,249 @@
+# Conditional kappa 0.00302235 from one owned helper relation
+
+This construction gives **conditional kappa = 60447/20000000 = 0.00302235**.
+The gain over Cao Yifan's final
+[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)
+value, 0.0030217758, is **2871/5000000000 = 0.0000005742**.
+The construction changes the complete paid profile. It does not obtain the
+gain by taking more digits of the old root.
+
+One helper becomes owned storage in each backward call. A prepared relation
+then makes one paid rank-eight center equal to an earlier saved value. The same
+relation makes one later rank-one job act on zero. Both jobs can be removed,
+with the rank-nine helper credit also removed. All other independent outputs
+and all main interfaces keep their source operators.
+
+[WORD.json.gz](WORD.json.gz) is the complete emitted word.
+[RESULT.json](RESULT.json) records the exact native checks, the two source
+identities, both full profiles, completion, compiler and outer calculations.
+[SOURCES.json](SOURCES.json) pins every external input by Git blob and SHA256.
+The proof below explains why the changed word has the stated contract.
+
+## Source and scope
+
+The base is canonical main
+[7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56).
+The native source is the final PR #4610 word at
+[20bb93cd990d2ff683e4d0fc56b87a42cd5d3296](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz).
+Its decompressed SHA256 is
+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.
+The comparison value and old crossing come from its
+[final compiler arithmetic](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json).
+All consumed bytes are already in the recorded main base.
+
+This is one instance of the current `complex-new-helper-inventory` priority.
+The [scoped claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737)
+reserves only the relation and two replacements below.
+[Discussion #5355](https://github.com/CrocSwap/integer-mult-bounds/discussions/5355)
+retains all 632 independent inputs and all eight centers.
+[Discussion #4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930)
+retains every original helper endpoint. This construction removes the
+independent L230 job in backward calls. It does not claim those broader scopes.
+The selected certificate is unchanged. A fresh check at 20:20 UTC found that
+Discussion #5355 had released its original-input scope without a saving.
+Canonical main still had the recorded base commit.
+
+## Exact replacement proof
+
+All indices below are zero-based indices in the frozen backward program.
+Let `h_r` be the source logical input of helper `Lr`. The five helpers in
+
+```math
+\Delta=h_{230}-h_{324}+h_{326}+h_{328}-h_{333}
+```
+
+all start in frame 0 and finish in frame 1, of rank nine. The new backward
+contract has 224 independent main fields and 407 independent helper fields.
+L230 is private. Clear it, then use four same-frame ADDs to prepare
+
+```math
+h_{230}=h_{324}-h_{326}-h_{328}+h_{333}.
+```
+
+The other helper inputs remain arbitrary and independent. This preparation
+sets Delta to zero for every input. It uses no recursive job. It removes one
+rank-nine productive target; the dependent field receives no output credit.
+
+Run the original source program on unrestricted inputs. Let `q` be the
+logical row of L92 just after event 11205, a paid climb into frame 254.
+The separate predecessor row engine gives these exact identities:
+
+| Source position | Exact logical row |
+| --- | --- |
+| C0 at the rank-eight center, event 11332 | `q + Delta/4` |
+| L92 at the rank-one climb, event 15584 | `-Delta/4` |
+
+These identities are over rational coefficients and free native operator
+words. They hold for every value of every source input and for every invertible
+interpretation of the native symbols. They do not use numerical samples or an
+assumed relation between distinct native maps.
+
+For every positive tensor width f, substitute each native generator by its
+source operator tensor power and each inverse by the inverse tensor power.
+This defines a representation of the free group. Keep the rational scalar
+coefficients outside the substitution. The two row identities therefore hold
+at every such width. In particular, Delta/4 remains a scalar linear form; it
+is not a tensor power of that sum. This uses the termwise argument recorded in
+the [free-word tensor audit](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/free-word-tensor-lift-audit/PROOF.md),
+which credits Cinna Davis's proposal and ToikY's scoped audit. Physical frame
+realization and the complete all-size compiler retain their source contracts.
+
+Immediately after event 11205, clear a new private field C1 in frame 254 and
+COPY L92 into it. C1 is not written until the replacement of event 11332. At
+that event, clear owned C0, set its frame to 254, COPY C1 into C0, then clear C1.
+The copy coefficient is exactly one. Under Delta = 0, the copied field is the
+same physical value as the old center output: the logical rows and the exact
+frame gauge are equal. The old C0 input can be erased because C0 is owned.
+This removes one rank-eight recursive job.
+
+At event 15584, L92 is exactly zero in every input column. The physical
+identity therefore has the same result as the old rank-one frame change.
+`zero_retag` records this fact. It performs no physical write and is accepted
+only when the full exact row is empty and the current frame is 254. It then
+records frame 1. This removes one rank-one recursive job. It does not erase a
+main input or replace a nonzero transform with a free frame change.
+
+Every other event stays in source order. Clear private L230 at return. The
+source clears C0, and the new program has already cleared C1. The original
+linear endpoint identity, restricted by the prepared relation, gives all 224
+main outputs and all 407 retained helper outputs. The literal new-word replay
+checks these outputs separately, with all 631 retained inputs and all three
+owned entry fields initially arbitrary. It also checks every scalar frame,
+paid rank, native frame transition and final frame.
+
+The 4,429 source frames, 72 native maps, all remaining paid operators, and main
+adapters are unchanged. The source
+[absolute-phase certificate](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz)
+is authenticated and reused. Same-frame COPY and identity on zero introduce no
+phase recipe. The source's amplitude and Clifford-lowering checks are not
+rerun by this package. The new free-word identities prove equivalence for the
+source operators with their full phases, not just their projective classes.
+
+## Complete cost and conditional compiler
+
+The forward word is unchanged. Each backward call has these counts:
+
+```text
+paid:    {1:2200, 2:412, 3:510, 4:127, 5:40, 8:7}
+helpers: {4:28, 7:7, 8:47, 9:325}
+```
+
+The full p16/a7 controller contains 16 backward calls, two forward calls and
+15 query shears. Thus the complete difference is **minus 16 H1 and 16 H8 paid
+jobs, and minus 16 H9 productive targets**. It includes every idle and main
+target. There are 64,372 paid jobs and 10,912 productive fields. Their rank
+masses are 238,990 and 239,742; the surplus remains 752.
+
+For every real `0 < t < 1`, the complete target-minus-paid moment increases by
+
+```math
+16(1+8^t-9^t)>0.
+```
+
+For a direct proof, both `(1/9)^t > 1/9` and `(8/9)^t > 8/9`; multiply their
+sum by `9^t`. The improvement is strict throughout the required range.
+
+The backward word has 158,214 real scalar operations under the source macro
+allowance, exactly 46 more than its source. Its maximum formal prefix L1 norm
+is 169, with maximum denominator 64; both equal the source bounds. The forward
+bounds remain 457 and 32. One extra physical private slot holds C1. L230 uses
+an existing slot. The route bound also charges two routes for each of the two
+new owned lifetimes. The local scalar-plus-route bound stays below 10^7, and
+the complete raw nonrecursive bound stays **181,098,496 < 10^9**. Preparation,
+COPY, CLEAR and storage therefore do not introduce an unpaid recursive cost.
+
+Two rational interval engines check the complete moment. Its unique crossing
+in `0 < kappa < 1` lies in
+**(0.00302238736347, 0.00302238736348)**. The verifier proves the moment decreases
+on `[0,0.05]` and remains negative on `[0.05,1]`. This is a ceiling for this
+fixed complete profile, not an optimum over circuits or helper relations.
+The claimed kappa leaves more than **0.00000003736347** raw headroom.
+
+The separately tested saving is 0.00302236. The paid/target ratio is below
+`0.999999971483293515393313955730`, with reserve `1e-9`. Both charged tails are
+below `0.97`. The source power 1024, cutoff 20, floor 21, tail offset 1/5,
+complement factor 63/64 and logarithm power 1000 still pass. The compiler gap
+is `1/700000000`, with `j=44836`, `H=31385200000000` and `N=2^31385200000000`.
+The exact integer test `(H+1)^1000 < 2^44836` passes; the preceding grid integer
+fails. The uniform complex saving is `2115651/700000000`. All 54 strict outer
+predicates and four functional predicates pass, using the retained ordinary
+BIT saving 0.0034.
+
+## Verification and reproduction
+
+Use Python 3.12 or 3.14, with the standard library only. From the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023 --check-only
+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023
+```
+
+The registered commands run normal and optimized Python. The direct command,
+also used for a Git-free export, is:
+
+```sh
+python3 -B research/kappa-owned-relation-20261023/verify.py
+python3 -O -B research/kappa-owned-relation-20261023/verify.py
+```
+
+Each prints status
+`PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION`.
+The verifier reconstructs the word and compares its bytes and exact result with
+the published artifacts. `--write` is a separate authoring command. It changes
+only this package's word and result after all checks pass.
+
+Fresh checks cover both source words, both candidate words, every independent
+entry column and owned return, the two unrestricted source identities, retained
+phase bindings, the p16 rational Laurent factorization, both scalar boundary
+programs, two complete invoice counts, two rational interval engines, the fixed
+profile ceiling, completion, compiler, BIT conversion and all outer predicates.
+The emitted word replaces the old single `canonical.local_profile` metadata
+field with explicit `paid_profiles` for the two directions.
+
+Seven native controls reject a wrong relation sign, omitted input clear, wrong
+snapshot, wrong zero frame, wrong paid rank, wrong copy gauge, and omitted
+output clear. Five cost/outer controls reject the lost helper's output credit,
+old BIT stock, closed uniform gap, unfunded endpoint and closed epsilon.
+
+Normal and optimized registered replays passed on CPython 3.12.14. The direct
+author check also passed on CPython 3.14. Source metadata and pins passed.
+The optional full-history preflight is not claimed in the shallow checkout.
+The publication handoff records export and committed-byte checks.
+
+The full source phase lowering, BIT native replay, Lean, Docker, physical tape
+execution, numerical precision execution, analytic decomposition and integer
+recovery are not rerun here. The complete bound retains those predecessor
+contracts, including permitted owned erasure, whole-job normalizers, mixed
+productive-target recursion and all-size closure. The expanded compiled word
+is specified by a finite algorithm, not materialized. This is a conditional
+construction with exact finite evidence, not an unconditional multiplication
+theorem, a practical timing result or independent human acceptance.
+
+## Credit
+
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+Cao Yifan's [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)
+supplies the exact source word, phase evidence and previous compiler value.
+Cinna Davis's [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470)
+supplies the p16 controller and helper-interface lineage. The source code keeps
+credit for Dugongue's transported frames, zxv's native and finite-compiler
+work, Jacob Alan Sussman's mixed-target recursion and their predecessors.
+The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py)
+and [literal native source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-rebuild/complex/native_extensions.py)
+are pinned as provenance for the adapted checks.
+
+zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283)
+supplies the related cache contract and the explicit handoff to find actual
+matching rows and their lifetimes. Its standalone cache example is not part of
+this word. The new contribution is the five-helper relation, its actual cache
+and zero identities, the full owned-field replacement and the complete positive
+bill. No priority is claimed for the general cache or paid-history ideas.
+
+## Open next questions
+
+Independent review should first check the three source rows and the physical
+COPY/zero argument above, then the retained all-size and phase premises.
+A later construction could test a different helper relation, but it must claim
+a disjoint scope and pay every lost target and owned field. This package does
+not classify such relations. [TASK.json](TASK.json) records the first steps,
+relevance and blockers for both questions.
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/RESULT.json b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/RESULT.json
new file mode 100644
index 0000000000..27b4e54708
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/RESULT.json
@@ -0,0 +1,373 @@
+{
+  "arithmetic": {
+    "compiler": {
+      "H": 31385200000000,
+      "N": "2^31385200000000",
+      "eta": {
+        "lower": "0.000000203927056311365991628189",
+        "upper": "0.000000203927056311365991628190"
+      },
+      "gap": "1/700000000",
+      "integer_test_exponent": 44836,
+      "logarithm_power": 1000,
+      "theta": "63/64",
+      "uniform_saving": "2115651/700000000",
+      "word_materialized": false
+    },
+    "fixed_profile_ceiling": {
+      "decreasing_through": "1/20",
+      "derivative_upper": {
+        "lower": "-195778.630038840116414999953237565269",
+        "upper": "-195778.630038840116414999953237565268"
+      },
+      "remaining_interval_moment_upper": {
+        "lower": "-6836.549542075249598033582799619360",
+        "upper": "-6836.549542075249598033582799619359"
+      }
+    },
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+    "full_forward": 2,
+    "gain_over_PR4610": "2871/5000000000",
+    "kappa": "60447/20000000",
+    "kappa_decimal": ".00302235",
+    "margin_at_previous_kappa": {
+      "lower": "0.151161494385402651700356241377",
+      "upper": "0.151161494385402651700356241378"
+    },
+    "margin_at_previous_root_upper": {
+      "lower": "0.151143999513185007311808491175",
+      "upper": "0.151143999513185007311808491176"
+    },
+    "negative_controls": {
+      "closed_epsilon": [
+        "epsilon_below_one",
+        "global_gamma_power_slack",
+        "actual_logarithmic_gamma_guard",
+        "source_axis_superpolynomial",
+        "gaussian_above_main",
+        "new_semantic_guard_with_C1_one"
+      ],
+      "closed_uniform": [
+        "new_complex_uniform_saving_above_b"
+      ],
+      "old_BIT": [
+        "actual_bit_above_effective"
+      ],
+      "unearned_helper_credit": "Rejected by the independent complete census",
+      "unfunded_endpoint": [
+        "main_transform_above_kappa",
+        "global_coordinate_router_above_kappa",
+        "fused_gaussian_above_kappa",
+        "group_bit_router_above_kappa",
+        "boundary_algebraic_matrix_above_kappa"
+      ]
+    },
+    "nonrecursive": {
+      "additional_private_slots": 1,
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+      "local_scalar": 158214,
+      "owned_slots_backward": 3,
+      "raw_budget": 1000000000,
+      "raw_scalar_upper": 181098496
+    },
+    "ordinary_BIT": {
+      "admitted": "17/5000",
+      "after_cover": "69/20000",
+      "atom": "1/250",
+      "before_cover": "3459/1000000",
+      "ordinary_saving": "8590884599/2500000000000",
+      "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+    },
+    "outer": {
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+        "actual_new_BIT_stock_sublinear": "174299999253/175000000000",
+        "fixed_halo_explicit_metadata_branch": "13475000001/175000000",
+        "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000",
+        "new_semantic_group_guard": "3/700000000"
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+        "fused_gaussian": "23139910838329/7656250000000000",
+        "global_coordinate_router": "2115649/700000000",
+        "group_bit_router": "1480954993653053/490000000000000000",
+        "group_scans": "349999999/350000000",
+        "main_transform": "23139899966943/7656250000000000",
+        "microbox_face_corrections": "13475000001/175000000",
+        "polynomial_products": "699999999/700000000",
+        "sparse_union_movement": "3133491473404443/7656250000000000"
+      },
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+        "a": "2115649/700000000",
+        "b": "42313/14000000",
+        "beta": "699999997/700000000",
+        "bit_saving": "17/5000",
+        "cap_xi": "6961616462466943/7656250000000000",
+        "complex_uniform_saving": "2115651/700000000",
+        "d": "1/700000000",
+        "epsilon": "699999999/700000000",
+        "kappa": "60447/20000000",
+        "lambda_": "199395529/200000000",
+        "lambda_prime": "10904443/10937500",
+        "layout": "1/700000000",
+        "q": "33057/10937500",
+        "r0": "1/7000000000",
+        "stop": "1/700000000",
+        "tested_saving": "75559/25000000"
+      },
+      "strict_checks": {
+        "actual_bit_above_effective": "264351/700000000",
+        "actual_logarithmic_gamma_guard": "1/700000000",
+        "actual_logarithmic_group_guard": "694633553939307/3828125000000000",
+        "alpha_logarithm_absorption": "1/7000000000",
+        "boundary_algebraic_matrix_above_kappa": "43716943/7656250000000000",
+        "cap_above_band": "3133491462466943/7656250000000000",
+        "cap_below_cell": "694633526595557/7656250000000000",
+        "cap_below_phase_cell_power": "8350883537533057/7656250000000000",
+        "complex_above_effective": "1/700000000",
+        "complex_below_one_over_32": "395187/14000000",
+        "complex_endpoint": "1/350000000",
+        "epsilon_below_one": "1/700000000",
+        "epsilon_positive": "699999999/700000000",
+        "fine_prime_halo_umbrella": "7/2",
+        "fused_gaussian_above_kappa": "43650829/7656250000000000",
+        "gaussian_above_main": "5435693/3828125000000000",
+        "global_coordinate_router_above_kappa": "1/175000000",
+        "global_gamma_power_slack": "9/7000000000",
+        "group_below_dimension": "1/350000000",
+        "group_bit_router_above_kappa": "3493653053/490000000000000000",
+        "group_gauge_power_slack": "43414597087027/239257812500000",
+        "group_key_fits_record": "1/350000000",
+        "group_positive": "699999997/700000000",
+        "group_scans_above_kappa": "697884353/700000000",
+        "halo_covers_generic_inverse_radius": "5",
+        "improvement_over_user_baseline": "645689790400418148631/500000000000000000000000",
+        "lambda_above_internal": "1/1400000000",
+        "lambda_above_sigma": "3/1400000000",
+        "lambda_above_tau": "1/1400000000",
+        "lambda_prime_above_lambda": "1/1400000000",
+        "lambda_prime_above_leaf": "27957687/9800000000000000",
+        "leaf_saving_above_effective": "13957687/9800000000000000",
+        "main_transform_above_kappa": "32779443/7656250000000000",
+        "membership_arithmetic_fits_record": "1/700000000",
+        "microbox_face_corrections_above_kappa": "53897884359/700000000",
+        "microbox_halo_volume": "55300000003/700000000",
+        "new_complex_uniform_saving_above_b": "1/700000000",
+        "new_semantic_guard_with_C1_one": "1/700000000",
+        "polynomial_products_above_kappa": "348942177/350000000",
+        "positive_layout_slack": "1/700000000",
+        "q_below_effective": "1/700000000",
+        "q_below_internal": "1/700000000",
+        "q_below_leaf": "27957687/9800000000000000",
+        "q_positive": "33057/10937500",
+        "short_record_fallback": "13957687/14000000",
+        "source_axis_superpolynomial": "1/700000000",
+        "sparse_union_movement_above_kappa": "3110351606216943/7656250000000000",
+        "stop_below_one": "699999999/700000000",
+        "stop_positive": "1/700000000",
+        "strassen_integer_power_gap": "1951441519231",
+        "support_router_span": "3/700000000",
+        "theta_positive_polynomial_power": "2",
+        "union_header_fits_record": "3/700000000",
+        "union_tag_work_per_visit_fits_record": "3/700000000"
+      }
+    },
+    "paid": {
+      "1": 41282,
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+      "2": 7416,
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+      "3": 9180,
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+      "72": 224,
+      "8": 128
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+    "paid_calls": 64372,
+    "productive_fields": 10912,
+    "query_shears": 15,
+    "rank_mass_surplus": 752,
+    "raw_headroom": [
+      "3736347/100000000000000",
+      "934087/25000000000000"
+    ],
+    "raw_root_interval": [
+      "302238736347/100000000000000",
+      "75559684087/25000000000000"
+    ],
+    "strictification": {
+      "alpha": {
+        "lower": "0.999999971483293515393313955729",
+        "upper": "0.999999971483293515393313955730"
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+      "cutoff": 20,
+      "delta": {
+        "lower": "0.957459689758527661921334851512",
+        "upper": "0.957459689758527661921334851513"
+      },
+      "floor": 21,
+      "gamma": {
+        "lower": "0.956310980726438847618396606911",
+        "upper": "0.956310980726438847618396606912"
+      },
+      "normalized_paid_upper": "2097152001953127/2097154147483648",
+      "power": 1024,
+      "reserve": "1/1000000000",
+      "tail_offset": "1/5",
+      "tested": "75559/25000000"
+    },
+    "targets": {
+      "145": 224,
+      "17": 448,
+      "25": 448,
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+      "7": 126,
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+    }
+  },
+  "candidate_native": {
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+        "8": 47,
+        "9": 325
+      },
+      "independent_owned_entry_columns": 3,
+      "independent_persistent_columns": 631,
+      "max_denominator": 64,
+      "max_formal_prefix_l1": "169",
+      "owned_outputs_zero": true,
+      "paid": {
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+        "3": 510,
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+        "5": 40,
+        "8": 7
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+      "real_scalar_allowance": 158214,
+      "zero_identities": 1
+    },
+    "forward": {
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+      },
+      "independent_owned_entry_columns": 1,
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+      "max_denominator": 32,
+      "max_formal_prefix_l1": "457",
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+      "paid": {
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+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
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+      "zero_identities": 0
+    }
+  },
+  "independent_source_identities": {
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+    "center_replaced": 11332,
+    "copy_coefficient": "1",
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+    "snapshot_terms_before_substitution": 61,
+    "source_event_indices_are_zero_based": true,
+    "zero_identity_at": 15584,
+    "zero_site_row": "-Delta/4"
+  },
+  "native_negative_controls": {
+    "missing_owned_input_clear": "Every independent main/helper endpoint: 0",
+    "uncleared_owned_output": "Every owned entry column is erased at return",
+    "under_or_overstated_paid_rank": "Exact paid rank and frame",
+    "wrong_copy_gauge": "Exact scalar destination frame",
+    "wrong_relation_sign": "Every independent main/helper endpoint: 0",
+    "wrong_snapshot_source": "Zero identity requires an identically zero full row",
+    "wrong_zero_input_frame": "Zero identity requires an identically zero full row"
+  },
+  "phase_inheritance": {
+    "absolute_phase_receipt_reused": "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+    "all_retained_paid_events_and_warps_from_source": true,
+    "new_gaussian_operators": 0,
+    "new_native_maps": 0,
+    "new_operations": "Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.",
+    "source_amplitudes_and_phase_lowering_freshly_replayed": false
+  },
+  "scope": "Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.",
+  "source_native": {
+    "backward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
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+      "max_denominator": 64,
+      "max_formal_prefix_l1": "169",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158168,
+      "zero_identities": 0
+    },
+    "forward": {
+      "helpers": {
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+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "max_denominator": 32,
+      "max_formal_prefix_l1": "457",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158120,
+      "zero_identities": 0
+    }
+  },
+  "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION",
+  "word_payload_sha256": "645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35"
+}
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/SOURCES.json b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/SOURCES.json
new file mode 100644
index 0000000000..9854abbb4f
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/SOURCES.json
@@ -0,0 +1,90 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/free-word-tensor-lift-audit/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "69c337a7704ce589798269ab4b8606189c070c4e",
+      "sha256": "cc8ad3698a673fb225419a3636a39aa99a66c7a0676f12e329b1e76564fa1459"
+    },
+    {
+      "path": "research/higher-moment-strictification/verify.py",
+      "usage": "input",
+      "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699",
+      "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326"
+    },
+    {
+      "path": "research/joint-helper-lattice/CONTROLLER.json",
+      "usage": "input",
+      "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5",
+      "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f"
+    },
+    {
+      "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+      "usage": "input",
+      "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb",
+      "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7"
+    },
+    {
+      "path": "research/kappa-interface-round2-20261022/price_profile.py",
+      "usage": "provenance",
+      "git_blob": "1d93e43d1cb888d128c2faa2be83a96d85b84295",
+      "sha256": "adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb"
+    },
+    {
+      "path": "research/kappa-rebuild/architecture/mixed_target_probe.py",
+      "usage": "input",
+      "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e",
+      "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a"
+    },
+    {
+      "path": "research/kappa-rebuild/complex/native_extensions.py",
+      "usage": "provenance",
+      "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8",
+      "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+      "usage": "input",
+      "git_blob": "ac77b78547d6dbf2e6bd102e1047c5b16c1bca88",
+      "sha256": "6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b"
+    },
+    {
+      "path": "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json",
+      "usage": "input",
+      "git_blob": "0fdb65f946d557c13d8e2781b9151e2a8ddee5c3",
+      "sha256": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de"
+    },
+    {
+      "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py",
+      "usage": "input",
+      "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59",
+      "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15"
+    },
+    {
+      "path": "research/query-thinned-controllers/RESULT.json",
+      "usage": "input",
+      "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c",
+      "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f"
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/TASK.json b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/TASK.json
new file mode 100644
index 0000000000..f5df24ffe3
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/TASK.json
@@ -0,0 +1,80 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 7,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json",
+      "research/selected-k8-unrestricted-ends/README.md"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+    "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts.",
+      "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": [
+      "Mixing only providers already inside the pinned catalogue.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Make helper L230 owned in each backward call, prepare one five-helper relation, retain one exact frame-254 snapshot, remove one rank-eight center and one rank-one zero job, and debit one rank-nine target.",
+  "scope_change_reason": "This uses the current helper-inventory priority. It changes the independent input inventory and scalar word; all physical native maps and the p16 controller remain fixed.",
+  "bottleneck_link": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737",
+  "budget_minutes": 240,
+  "stop_rule": "Publish one exact complete-profile kappa improvement after native, ownership, phase-inheritance, compiler and cold-export checks.",
+  "outcome": "completed",
+  "evidence": "README.md, WORD.json.gz, RESULT.json and verify.py. The complete conditional kappa is 60447/20000000.",
+  "author": "Ali Romman",
+  "ai_assistance": "Substantial OpenAI Codex assistance in discovery, code, proof, verification and publication.",
+  "open_questions": [
+    {
+      "question": "Can a separate reviewer validate this one-relation restriction and the inherited physical transfer premises?",
+      "why_it_matters": "The new finite construction is exact, but the complete bound still uses the source phase and all-size contracts.",
+      "first_step": "Replay the three unrestricted source rows in native.py and check the COPY and zero-identity argument in README.md.",
+      "blocked_by": "Independent review has not yet occurred."
+    },
+    {
+      "question": "Can a different helper relation give another complete positive bill?",
+      "why_it_matters": "This construction gives one positive instance, not an optimum for changed helper inventories.",
+      "first_step": "Claim a disjoint relation in Discussions, derive its exact rows, and include every lost target and owned-storage cost.",
+      "blocked_by": "Current active cache and paid-history scopes must be checked first."
+    }
+  ],
+  "coordination": {
+    "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737",
+    "distinct_scopes": [
+      "https://github.com/CrocSwap/integer-mult-bounds/discussions/5355",
+      "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930"
+    ],
+    "boundary": "The first scope retains 632 arbitrary inputs and eight centers. The second retains every original helper endpoint. This package removes the independent L230 job only in backward calls and claims only the stated relation and two event replacements."
+  }
+}
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/VERIFY.json b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/VERIFY.json
new file mode 100644
index 0000000000..8098df4c80
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/VERIFY.json
@@ -0,0 +1,38 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/higher-moment-strictification/verify.py",
+    "research/joint-helper-lattice/CONTROLLER.json",
+    "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+    "research/kappa-rebuild/architecture/mixed_target_probe.py",
+    "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+    "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+    "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json",
+    "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py",
+    "research/query-thinned-controllers/RESULT.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "The same checks remain active with Python assertions disabled."
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/WORD.json.gz b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/WORD.json.gz
new file mode 100644
index 0000000000..5e79bd826c
Binary files /dev/null and b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/WORD.json.gz differ
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/native.py b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/native.py
new file mode 100644
index 0000000000..b8249ed7ba
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/native.py
@@ -0,0 +1,299 @@
+"""One prepared helper removes two paid jobs in the PR4610 backward word.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+The source word is by Cao Yifan. The row convention and scalar allowance
+follow the credited native work of Cinna Davis and zxv.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha1, sha256
+from pathlib import Path
+import gzip
+import importlib.util
+import json
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'
+PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz'
+PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'
+RELATION = {230: 1, 324: -1, 326: 1, 328: 1, 333: -1}
+OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}
+NEW_PAID = dict(OLD_PAID)
+NEW_PAID[1] -= 1
+NEW_PAID[8] -= 1
+OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326}
+
+
+def need(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def encode(x):
+    if isinstance(x, Q):
+        return str(x)
+    if isinstance(x, dict):
+        return {str(k): encode(v) for k, v in x.items()}
+    if isinstance(x, (list, tuple)):
+        return [encode(v) for v in x]
+    return x
+
+
+def load(relative, name):
+    spec = importlib.util.spec_from_file_location(name, ROOT / relative)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+
+def authenticate():
+    pins = read(HERE / 'SOURCES.json')
+    for row in pins['files']:
+        if row['usage'] != 'input':
+            continue
+        p = ROOT
+        for part in Path(row['path']).parts:
+            p /= part
+            need(not p.is_symlink(), 'No source aliases')
+        raw = p.read_bytes()
+        need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path'])
+        need(sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob')
+    need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload')
+    return pins
+
+
+def span(basis):
+    out = {0}
+    for vector in basis:
+        need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate')
+        out |= {v ^ vector for v in tuple(out)}
+    need(len(out) == 2 ** len(basis), 'Independent frame basis')
+    return out
+
+
+def add(dst, src, q):
+    for k, v in tuple(src.items()):
+        value = dst.get(k, Q(0)) + q * v
+        if value:
+            dst[k] = value
+        else:
+            dst.pop(k, None)
+
+
+def allowance(g):
+    if g[0] in ('clear', 'copy'):
+        return 2
+    q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:])
+    n, d = abs(q.numerator), q.denominator
+    need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar')
+    if g[0] == 'scale':
+        need(n & (n - 1) == 0, 'Dyadic unit SCALE')
+        return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0))
+    need(g[0] == 'add', 'Known scalar operation')
+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)
+
+
+def construct(source):
+    c = source['canonical']
+    old = source['programs']['backward']
+    need(old[11205] == ['climb', 'warp_retimed', 92, 310, 254, 4], 'Snapshot source event')
+    need(old[11332] == ['center', 0, 0, 254, 8], 'Center source event')
+    need(old[15584] == ['climb', 'warp_retimed', 92, 254, 1, 1], 'Zero source event')
+    need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in RELATION), 'Five cold full-ended helpers')
+    word = [['scalar', ['clear', ['L', 230]], 0]]
+    word += [['scalar', ['add', ['L', 230], ['L', h], -q, 1], 0]
+             for h, q in RELATION.items() if h != 230]
+    for i, event in enumerate(old):
+        if i == 11332:
+            word += [['scalar', ['clear', ['C', 0]], 254],
+                     ['scalar', ['copy', ['C', 0], ['C', 1]], 254],
+                     ['scalar', ['clear', ['C', 1]], 254]]
+        elif i == 15584:
+            word.append(['zero_retag', ['L', 92], 254, 1])
+        else:
+            word.append(deepcopy(event))
+        if i == 11205:
+            word += [['scalar', ['clear', ['C', 1]], 254],
+                     ['scalar', ['copy', ['C', 1], ['L', 92]], 254]]
+    word.append(['scalar', ['clear', ['L', 230]], 1])
+    physical = deepcopy(c)
+    physical.pop('local_profile')
+    return {'schema': 'owned-helper-relation-word/1', 'canonical': physical,
+            'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID},
+            'owned': {'forward': [['C', 0]], 'backward': [['C', 0], ['C', 1], ['L', 230]]},
+            'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}}
+
+
+def replay(c, program, backward, specialized):
+    """Run every event on all independent entry columns and exact frames."""
+    owned = {('C', 0)} | ({('C', 1), ('L', 230)} if specialized else set())
+    roles = {('L', i) for i in range(632)} | owned
+    rows = {r: {(r, ()): Q(1)} for r in roles}
+    frames = {('L', i): f for i, f in enumerate(c['start'])}
+    frames.update({r: None for r in owned if r[0] == 'C'})
+    spaces = [span(b) for b in c['frames']]
+    paid = Counter()
+    cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0
+    for e in program:
+        kind, touched = e[0], None
+        if kind == 'scalar':
+            g, frame = e[1:]
+            dst = tuple(g[1]); touched = dst
+            need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame')
+            cost += allowance(g)
+            if g[0] == 'clear':
+                need(dst in owned, 'Only owned fields can be erased')
+                rows[dst] = {}; frames[dst] = frame
+            else:
+                need(frames[dst] == frame, 'Exact scalar destination frame')
+                if g[0] in ('add', 'copy'):
+                    src = tuple(g[2])
+                    need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame')
+                    if g[0] == 'copy':
+                        need(dst in owned and not rows[dst], 'COPY into cleared owned storage')
+                        rows[dst] = dict(rows[src])
+                    else:
+                        add(rows[dst], rows[src], Q(g[3], g[4]))
+                else:
+                    need(g[0] == 'scale', 'Known scalar operation')
+                    rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()}
+        elif kind == 'warp':
+            _, role, op, old, new = e
+            dst = tuple(role); touched = dst
+            need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input')
+            symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0))
+            rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q
+                         for (r, w), q in rows[dst].items()}
+            frames[dst] = new
+        elif kind in ('climb', 'center'):
+            if kind == 'climb':
+                _, _, i, old, new, rank = e
+                dst = ('L', i)
+                need(spaces[old] < spaces[new], 'Ascending paid climb')
+            else:
+                _, i, old, new, rank = e
+                dst = ('C', i)
+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center')
+            need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame')
+            frames[dst] = new; paid[rank] += 1
+        elif kind == 'zero_retag':
+            _, role, old, new = e
+            dst = tuple(role)
+            need(specialized and backward and dst == ('L', 92), 'Declared zero identity')
+            need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row')
+            need((old, new) == (254, 1), 'Declared zero frame change')
+            frames[dst] = new; zero_count += 1
+        else:
+            need(kind in ('phase', 'adapter'), 'Known inert source marker')
+        if touched is not None:
+            max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0)))
+            denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1))
+    need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame')
+    for i in range(632):
+        r = ('L', i)
+        if r in owned:
+            continue
+        expected = {(r, ()): Q(1)}
+        if i < 112 if backward else 112 <= i < 224:
+            expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1)
+        need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i))
+    need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return')
+    need(zero_count == int(specialized), 'Exactly one checked zero identity')
+    helpers = Counter()
+    for i in range(224, 632):
+        if ('L', i) in owned:
+            continue
+        a, b = c['start'][i], c['final'][i]
+        need(spaces[a] < spaces[b], 'Strict independent productive helper')
+        helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1
+    return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())),
+            'independent_persistent_columns': 631 if specialized else 632,
+            'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True,
+            'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1),
+            'max_denominator': denominator, 'zero_identities': zero_count}
+
+
+def independent_source_identities(source):
+    """Use the predecessor row engine on the unrestricted original word."""
+    v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'owned_relation_source_rows')
+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}
+    rows['C', 0] = v.identity(('C', 0))
+    delta = {(('L', i), ()): Q(q) for i, q in RELATION.items()}
+    saved = None
+    for index, e in enumerate(source['programs']['backward']):
+        if e[0] == 'scalar':
+            g = e[1]; dst = tuple(g[1])
+            if g[0] == 'clear': rows[dst] = {}
+            elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])])
+            elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()}
+            else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4]))
+        elif e[0] == 'warp':
+            dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True)
+        if index == 11205: saved = dict(rows['L', 92])
+        if index == 11332:
+            diff = dict(rows['C', 0]); v.add(diff, saved, -1)
+            need(diff == {k: q / 4 for k, q in delta.items()}, 'Independent exact center minus snapshot = Delta/4')
+        if index == 15584:
+            need(rows['L', 92] == {k: -q / 4 for k, q in delta.items()}, 'Independent exact zero-site row = -Delta/4')
+    need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints')
+    return {'source_event_indices_are_zero_based': True, 'snapshot_after': 11205,
+            'center_replaced': 11332, 'zero_identity_at': 15584,
+            'snapshot_terms_before_substitution': len(saved), 'copy_coefficient': '1',
+            'center_minus_snapshot': 'Delta/4', 'zero_site_row': '-Delta/4', 'relation': RELATION}
+
+
+def phase_inheritance(source, candidate):
+    receipt = read(ROOT / PHASE)
+    need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and
+         receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt')
+    physical = deepcopy(source['canonical']); physical.pop('local_profile')
+    need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged')
+    for direction, program in candidate['programs'].items():
+        old = source['programs'][direction]
+        for kind in ('warp', 'adapter', 'phase'):
+            need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence')
+        old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center'))
+        new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center'))
+        expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for i in (11332, 15584))
+        need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the two proved jobs are removed')
+    return {'new_gaussian_operators': 0, 'new_native_maps': 0,
+            'all_retained_paid_events_and_warps_from_source': True,
+            'absolute_phase_receipt_reused': PHASE,
+            'source_amplitudes_and_phase_lowering_freshly_replayed': False,
+            'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'}
+
+
+def controls(c, candidate):
+    controls = {}
+    base = candidate['programs']['backward']
+    variants = {}
+    bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad
+    variants['missing_owned_input_clear'] = deepcopy(base[1:])
+    bad = deepcopy(base)
+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63]
+    variants['wrong_snapshot_source'] = bad
+    bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0
+    variants['wrong_zero_input_frame'] = bad
+    bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1
+    variants['under_or_overstated_paid_rank'] = bad
+    bad = deepcopy(base)
+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0
+    variants['wrong_copy_gauge'] = bad
+    variants['uncleared_owned_output'] = deepcopy(base[:-1])
+    for name, program in variants.items():
+        try:
+            replay(c, program, True, True)
+        except ValueError as err:
+            controls[name] = str(err)
+        else:
+            raise ValueError('Control accepted: ' + name)
+    return controls
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/price.py b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/price.py
new file mode 100644
index 0000000000..6077adf74c
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/price.py
@@ -0,0 +1,196 @@
+"""Complete p16 bill and finite compiler for one owned helper relation.
+
+The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna
+Davis's PR4470 controller, zxv's completion and logarithmic majorant, and
+Jacob Alan Sussman's mixed-target recursion. Apache-2.0.
+Ali Romman, with substantial OpenAI Codex assistance.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from native import ROOT, read, load, need, encode, OLD_PAID, OLD_HELPERS
+
+KAPPA = Q('.00302235')
+TESTED = Q('.00302236')
+PREVIOUS = Q('.0030217758')
+OLD_ROOT_UPPER = Q('.00302177587078')
+
+
+def controller():
+    """Check the literal p16 word and both rational boundary programs."""
+    word = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json')
+    need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller')
+    zero = (0,) * 34
+    def plus(dst, src, q):
+        for k, v in src.items():
+            value = dst.get(k, Q(0)) + q * v
+            if value: dst[k] = value
+            else: dst.pop(k, None)
+    def shifted(row, term, sign=1):
+        return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row]
+    for side in ('left', 'right'):
+        matrix = [[Q(i == j) for j in range(32)] for i in range(32)]
+        for e in word['boundaries'][side + '_program']:
+            if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]]
+            elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]]
+            else:
+                need(e[0] == 'ADD', 'Boundary scalar opcode')
+                matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])]
+        need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program')
+    rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']]
+    for e in word['physical_events']:
+        if e[0] in ('LOCAL', 'QUERY_SHEAR'):
+            _, stage, pair, back = e
+            x, y = 2 * pair, 2 * pair + 1
+            if back: x, y = y, x
+            term = (1 if back else -1,) + (0,) * 33
+            for dst, src in zip(rows[y], shifted(rows[x], term)):
+                plus(dst, src, Q(-1 if back else 1))
+            if e[0] == 'LOCAL':
+                term = (0,) + tuple(int(s == stage) for s in range(33))
+                for r in (x, y): rows[r] = shifted(rows[r], term)
+        elif e[0] == 'IDLE':
+            term = (0,) + tuple(int(s in e[2]) for s in range(33))
+            for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term)
+        elif e[0] == 'ADD':
+            for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3]))
+        else:
+            need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode')
+            rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1)
+    out = [[{} for _ in range(32)] for _ in range(32)]
+    for i, row in enumerate(word['boundaries']['left']):
+        for k, q in enumerate(row):
+            if Q(q):
+                for j in range(32): plus(out[i][j], rows[k][j], Q(q))
+    expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)]
+    need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors')
+    return word
+
+
+def assemble(native, word):
+    T, P = Counter(), Counter()
+    orientations = Counter(); thin = 0
+    for e in word['physical_events']:
+        if e[0] == 'LOCAL':
+            direction = 'backward' if e[3] else 'forward'
+            orientations[direction] += 1
+            T.update(native[direction]['helpers']); P.update(native[direction]['paid'])
+        elif e[0] == 'QUERY_SHEAR': thin += 1; P[1] += 112
+        elif e[0] == 'IDLE': P[8 * len(e[2])] += 224
+    main = Counter()
+    for term in word['diagonal']:
+        need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole Gaussian main target')
+        main[1 + 8 * sum(term[1:])] += 112
+    T.update(main)
+    need(orientations == {'backward': 16, 'forward': 2} and thin == 15, 'Every actual call orientation')
+    # This second census uses the source invoice and the two local deltas.
+    check_T = Counter({int(r): n for r, n in word['invoice']['main'].items()})
+    check_T.update({r: 18 * n for r, n in OLD_HELPERS.items()}); check_T[9] -= 16
+    check_P = Counter({int(r): n for r, n in word['invoice']['whole_idle'].items()})
+    check_P.update({r: 18 * n for r, n in OLD_PAID.items()}); check_P[1] += 1680 - 16; check_P[8] -= 16
+    need(T == check_T and P == check_P, 'Independent full invoice substitution')
+    need(sum(T.values()) == 10912 and sum(P.values()) == 64372, 'Complete productive and paid counts')
+    need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Unchanged complete rank surplus')
+    return T, P
+
+
+def run(native):
+    word = controller(); T, P = assemble(native, word)
+    prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json')
+    need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing')
+    prior_T = Counter({int(r): n for r, n in prior['targets'].items()})
+    prior_P = Counter({int(r): n for r, n in prior['paid'].items()})
+    prior_T[9] -= 16; prior_P[1] -= 16; prior_P[8] -= 16
+    need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill')
+    E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals')
+    other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals')
+    def margin(c):
+        t, p = E.moment(T, 1 - c), E.moment(P, 1 - c)
+        return t[0] - p[1], t[1] - p[0]
+    need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint')
+    lo, hi, grid = 0, 10**12, 10**14
+    while hi - lo > 1:
+        mid = (lo + hi) // 2
+        if margin(Q(mid, grid))[0] > 0: lo = mid
+        else: hi = mid
+    root_low, root_high = Q(lo, grid), Q(hi, grid)
+    need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure')
+    need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom')
+    # The complete signed profile decreases on [0, .05], and stays negative
+    # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling.
+    signed = {r: T[r] - P[r] for r in T.keys() | P.keys()}
+    derivative, upper = None, None
+    for i in range(16):
+        l, r = Q(i, 320), Q(i + 1, 320); low = Q(0)
+        for rank, n in signed.items():
+            term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank))
+            low += n * term[0 if n > 0 else 1]
+        derivative = low if derivative is None else min(derivative, low)
+    for i in range(128):
+        l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560)
+        value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items())
+        upper = value if upper is None else max(upper, value)
+    need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1')
+    t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21
+    target, paid = E.moment(T, t), E.moment(P, t)
+    tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED)
+    need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree')
+    alpha = E.divide(paid, target)
+    gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target))
+    delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target))
+    reserve = Q(1, 10**9); g = d = Q(97, 100)
+    need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged')
+    need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks')
+    normalized = 1 / (1 + v * reserve) + Q(4, 2**32)
+    need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding')
+    theta, power = Q(63, 64), 1000
+    eta = E.scale(E.power(145, -v * TESTED), t)
+    need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')
+    need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range')
+    gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid')
+    step = gap.denominator
+    def wins(j): return (step * j + 1)**power < 2**j
+    left, right = 1, 2
+    while not wins(right): left, right = right, 2 * right
+    while right - left > 1:
+        mid = (left + right) // 2
+        if wins(mid): right = mid
+        else: left = mid
+    height = step * right
+    need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold')
+    local_scalar = max(x['real_scalar_allowance'] for x in native.values())
+    # The old route allowance is retained. Charge two additional owned field
+    # lifetimes at two routes each, even though L230 uses an existing slot.
+    routes = (max(sum(x['paid'].values()) for x in native.values()) + 2 * 408 + 688 + 4) * 1000
+    need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit')
+    scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right')))
+    need(scalar_upper < 10**9, 'Complete raw nonrecursive bound')
+    bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']
+    atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted'])
+    need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock')
+    L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer')
+    params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap,
+              'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted,
+              'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap}
+    outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom)
+    need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')
+    need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict')
+    controls = {}
+    for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]:
+        bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0]
+        need(failed, 'Reject outer patch ' + name); controls[name] = failed
+    bad_native = {d: dict(x) for d, x in native.items()}
+    bad_native['backward']['helpers'] = OLD_HELPERS
+    try: assemble(bad_native, word)
+    except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census'
+    else: raise ValueError('Unowned helper credit was accepted')
+    return encode({'kappa': KAPPA, 'kappa_decimal': '.00302235', 'gain_over_PR4610': KAPPA - PREVIOUS,
+                   'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA],
+                   'margin_at_previous_kappa': E.display(margin(PREVIOUS)),
+                   'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)),
+                   'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)},
+                   'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752,
+                   'full_backward': 16, 'full_forward': 2, 'query_shears': 15,
+                   'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized},
+                   'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False},
+                   'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': 1, 'owned_slots_backward': 3},
+                   'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls})
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/verify.py b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/verify.py
new file mode 100644
index 0000000000..b19f7d0ca4
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-owned-relation-20261023/verify.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python3
+"""Replay the one-relation native word and its complete conditional kappa.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+Read README.md for the source credit and inherited proof obligations.
+"""
+from hashlib import sha256
+import argparse
+import gzip
+import json
+from pathlib import Path
+import sys
+sys.dont_write_bytecode = True
+import native as N
+import price
+
+
+def run():
+    N.authenticate()
+    source = N.read(N.ROOT / N.SOURCE)
+    candidate = N.construct(source)
+    c = candidate['canonical']
+    before, after = {}, {}
+    for direction in ('forward', 'backward'):
+        back = direction == 'backward'
+        before[direction] = N.replay(c, source['programs'][direction], back, False)
+        after[direction] = N.replay(c, candidate['programs'][direction], back, back)
+        N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Pinned source census')
+        N.need(after[direction]['paid'] == candidate['paid_profiles'][direction], 'Emitted direction-specific paid profile')
+        helpers = dict(N.OLD_HELPERS)
+        if back: helpers[9] -= 1
+        N.need(after[direction]['paid'] == (N.NEW_PAID if back else N.OLD_PAID) and after[direction]['helpers'] == helpers, 'Actual complete changed native census')
+    identities = N.independent_source_identities(source)
+    phase = N.phase_inheritance(source, candidate)
+    controls = N.controls(c, candidate)
+    arithmetic = price.run(after)
+    data = (json.dumps(candidate, sort_keys=True, separators=(',', ':')) + '\n').encode()
+    result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION',
+                       'source_payload_sha256': N.PAYLOAD, 'word_payload_sha256': sha256(data).hexdigest(),
+                       'source_native': before, 'candidate_native': after, 'independent_source_identities': identities,
+                       'phase_inheritance': phase, 'native_negative_controls': controls, 'arithmetic': arithmetic,
+                       'scope': 'Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.'})
+    return data, result
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--write', action='store_true', help='Write only this package word and result after all checks pass.')
+    ap.add_argument('--out', type=Path, help='Write a replay result to a separate path.')
+    args = ap.parse_args()
+    data, result = run()
+    if args.write:
+        (N.HERE / 'WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+        (N.HERE / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n', encoding='utf-8')
+    else:
+        N.need(gzip.decompress((N.HERE / 'WORD.json.gz').read_bytes()) == data, 'Exact literal published word')
+        N.need(N.read(N.HERE / 'RESULT.json') == result, 'Exact published replay result')
+    if args.out:
+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n', encoding='utf-8')
+    print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR4610', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-rebuild/architecture/mixed_target_probe.py b/research/owned-relation-independent-validation/capsule/research/kappa-rebuild/architecture/mixed_target_probe.py
new file mode 100644
index 0000000000..4fc05ab081
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-rebuild/architecture/mixed_target_probe.py
@@ -0,0 +1,291 @@
+#!/usr/bin/env python3
+"""Exact tariffs for productive helpers with heterogeneous target sizes.
+
+This is a conditional recursion-contract probe, not a new kappa claim.  The
+native helper adapters, main controller closure, scalar/precision charges,
+and the mixed-target outer theorem remain separate obligations.
+
+Apache-2.0. Substantial OpenAI assistance. The original pruned native profile
+and helper inventory come from the preserved kappa-function-composition work.
+Mixed-target balance follows Jacob Alan Sussman's PR4268 proposal; this file
+does not reprove or admit its all-size or integer-multiplication transfer.
+The rational elementary-function enclosure follows the independently retained
+productive_helper_forest.py recovery certificate, with fresh source identity.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from functools import lru_cache
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import json
+import math
+import sys
+
+sys.dont_write_bytecode = True
+HERE = Path(__file__).resolve().parent
+NATIVE = Counter({1:2453, 2:716, 3:224, 4:74, 5:48})
+HELPERS = Counter({5:28, 6:18, 7:56, 8:93, 9:213})
+OLD_PAIRS = [(56,9,7),(56,7,9),(18,9,6),(18,6,9),
+             (16,9,5),(16,5,9),(44,8,8)]
+OLD_MIDDLE = [(93,8),(56,7),(18,6),(28,5),(29,0)]
+
+def need(ok, message):
+    if not ok:
+        raise AssertionError(message)
+
+@lru_cache(None)
+def log_interval(r):
+    def odd_series(x):
+        z = (x-1)/(x+1)
+        n = 80
+        low = 2*sum((z**(2*j+1)/(2*j+1) for j in range(n)), Q(0))
+        high = low+2*z**(2*n+1)/((2*n+1)*(1-z*z))
+        return low, high
+    exponent = r.bit_length()-1
+    a,b = odd_series(Q(2))
+    c,d = odd_series(Q(r,2**exponent))
+    return exponent*a+c, exponent*b+d
+
+def exp_interval(x):
+    need(0 <= x < 1, 'Enclosure range')
+    term = total = Q(1)
+    n = 48
+    for j in range(1,n+1):
+        term *= x/j
+        total += term
+    following = term*x/(n+1)
+    return total, total+following/(1-x/(n+2))
+
+@lru_cache(None)
+def h_interval(r,c):
+    if r in (0,1):
+        return Q(r),Q(r)
+    a,b = log_interval(r)
+    low,_ = exp_interval(c*a)
+    _,high = exp_interval(c*b)
+    return Q(r)/high,Q(r)/low
+
+def moment(profile,c):
+    low=high=Q(0)
+    for r,n in profile.items():
+        a,b=h_interval(r,c)
+        low += n*(a if n >= 0 else b)
+        high += n*(b if n >= 0 else a)
+    return low,high
+
+def show(bounds):
+    scale=10**35
+    low,high=bounds
+    a=low.numerator*scale//low.denominator
+    b=-((-high.numerator*scale)//high.denominator)
+    def fixed(n):
+        sign='-' if n<0 else ''
+        s=str(abs(n)).rjust(36,'0')
+        return sign+s[:-35]+'.'+s[-35:]
+    return {'lower':fixed(a),'upper':fixed(b)}
+
+def split_rank(r,maximum):
+    """Least concave tariff partition with positive integers <= maximum."""
+    need(maximum>=1 and r>=0, 'Legal split')
+    q,remainder=divmod(r,maximum)
+    result=Counter()
+    if q:
+        result[maximum]+=q
+    if remainder:
+        result[remainder]+=1
+    return result
+
+def split_profile(profile,maximum):
+    result=Counter()
+    for r,n in profile.items():
+        for child,count in split_rank(r,maximum).items():
+            result[child]+=n*count
+    return result
+
+def add_scaled(target,source,multiple=1):
+    for key,value in source.items():
+        target[key]+=multiple*value
+
+def base_case(p,minimum,pairs=None,middle=None):
+    """Expand all role inventories; one fresh global field per unhosted role."""
+    need(p in (1,2), 'Only reconstructed p1 and p2 schedules are in scope')
+    need(2<=minimum<=41, 'Finite minimum-target menu')
+    calls=2*p+1
+    main_fields=224*p
+    main_rank=16*p+9
+    inventories=[Counter(HELPERS) for _ in range(calls)]
+    paid=split_profile(NATIVE,minimum-1)
+    paid=Counter({r:calls*n for r,n in paid.items()})
+    paid[1]+=8*calls  # same-width H completion, never waived
+    targets=Counter({main_rank:main_fields})
+    if p==1:
+        need(pairs is None and middle is None, 'p1 has no original idle bins')
+    else:
+        pairs=pairs if pairs is not None else [(224,0,0)]
+        middle=middle if middle is not None else [(224,0)]
+        need(sum(n for n,a,b in pairs)==224, 'Each pair window has 224 bins')
+        need(sum(n for n,a in middle)==224, 'Middle window has 224 bins')
+        for stages in [(0,1),(3,4)]:
+            for n,a,b in pairs:
+                need(a+b<=16 and a in (0,5,6,7,8,9) and b in (0,5,6,7,8,9), 'Pair capacities')
+                for stage,r in zip(stages,(a,b)):
+                    if r:
+                        inventories[stage][r]-=n
+                add_scaled(paid,split_rank(16-a-b,minimum-1),n)
+        for n,r in middle:
+            need(r in (0,5,6,7,8), 'Middle capacity')
+            if r:
+                inventories[2][r]-=n
+            add_scaled(paid,split_rank(8-r,minimum-1),n)
+    global_roles=Counter()
+    for inventory in inventories:
+        need(all(n>=0 for n in inventory.values()), 'No helper role used twice')
+        global_roles.update(inventory)
+    for r,n in global_roles.items():
+        if not n:
+            continue
+        target=max(r,minimum)
+        targets[target]+=n
+        add_scaled(paid,split_rank(target-r,minimum-1),n)
+    paid=+paid
+    targets=+targets
+    need(max(paid)<min(targets), 'Strict child/target separation')
+    signed=Counter(targets)
+    signed.subtract(paid)
+    rank_credit=sum(r*n for r,n in targets.items())
+    rank_bill=sum(r*n for r,n in paid.items())
+    need(rank_credit-rank_bill==224*p-8*calls, 'Complete displayed rank balance')
+    return {'p':p,'minimum_target_parameter':minimum,'targets':dict(sorted(targets.items())),
+            'paid':dict(sorted(paid.items())), 'signed':signed,
+            'global_helper_roles':dict(sorted(global_roles.items())),
+            'global_productive_fields':sum(global_roles.values()),
+            'pair_patterns':pairs,'middle_patterns':middle,
+            'rank_credit':rank_credit,'rank_bill':rank_bill,'rank_margin':rank_credit-rank_bill,
+            'strict_separation':{'maximum_child':max(paid),'minimum_target':min(targets)}}
+
+def serialize_case(case):
+    result={k:v for k,v in case.items() if k!='signed'}
+    result['targets_at_C']={}
+    for text in ('0.001745','0.004'):
+        c=Q(text)
+        allowance=moment(case['signed'],c)
+        row={'after_native_completion_before_main_closure':show(allowance)}
+        for debt in (112,224):
+            row[f'after_{debt}_H1_head_debt']=show((allowance[0]-debt,allowance[1]-debt))
+        # A head may be cut only when it is a literal private first transform.
+        # Target shrink is charged; this is the strongest favorable eligibility grant.
+        rank=16*case['p']+9
+        for count in (112,224):
+            delta=Counter({1:count,rank-1:count,rank:-count})
+            gain=moment(delta,c)
+            row[f'literal_{count}_H1_cut_gain_over_paying_heads']=show(gain)
+            loss=Counter({rank:count,rank-1:-count})
+            a,b=moment(loss,c)
+            row[f'after_cutting_{count}_literal_H1_heads_and_shrinking_targets']=show((allowance[0]-b,allowance[1]-a))
+        result['targets_at_C'][text]=row
+    return result
+
+def numerical_value(profile,c):
+    return sum(n*r**(1-c) for r,n in profile.items())
+
+def discover_pair_patterns(minimum,c):
+    """Optional small MILP; exact replay never relies on solver's optimal flag."""
+    import numpy as np
+    from scipy.optimize import milp, Bounds, LinearConstraint
+    widths=(0,5,6,7,8,9)
+    patterns=[(a,b) for a in widths for b in widths if a+b<=16]
+    h=lambda r:r**(1-c) if r else 0.0
+    sp=lambda r:sum(n*h(k) for k,n in split_rank(r,minimum-1).items())
+    value=lambda r:0.0 if not r else h(max(r,minimum))-sp(max(0,minimum-r))
+    gain=np.array([sp(16)-sp(16-a-b)-value(a)-value(b) for a,b in patterns])
+    rows=[np.ones(len(patterns))]
+    lower=[224.0]
+    upper=[224.0]
+    for side in (0,1):
+        for r in widths[1:]:
+            rows.append(np.array([float(pair[side]==r) for pair in patterns]))
+            lower.append(0.0)
+            upper.append(float(HELPERS[r]))
+    out=milp(c=-gain,integrality=np.ones(len(patterns)),bounds=Bounds(0,np.inf),
+             constraints=LinearConstraint(np.array(rows),lower,upper),
+             options={'time_limit':10,'mip_rel_gap':0})
+    need(out.x is not None, 'Discovery produced a candidate')
+    pairs=[(int(round(n)),a,b) for n,(a,b) in zip(out.x,patterns) if round(n)>0]
+    # Middle bins are independent single slots; choose positive-gain roles first.
+    candidates=sorted(((sp(8)-sp(8-r)-value(r),r) for r in (5,6,7,8)),reverse=True)
+    middle=[]
+    left=224
+    for gain,r in candidates:
+        if gain>1e-12:
+            n=min(HELPERS[r],left)
+            if n:
+                middle.append((n,r))
+                left-=n
+    if left:
+        middle.append((left,0))
+    return pairs,middle,{'status':int(out.status),'message':out.message,'not_an_exact_optimality_claim':True}
+
+def run(discover=False):
+    candidates=[]
+    for p in (1,2):
+        for minimum in range(2,26):
+            candidates.append(base_case(p,minimum))
+    candidates.append(base_case(2,9,OLD_PAIRS,OLD_MIDDLE))
+    discovery=[]
+    if discover:
+        for c in (.001745,.004):
+            for minimum in range(5,18):
+                pairs,middle,meta=discover_pair_patterns(minimum,c)
+                case=base_case(2,minimum,pairs,middle)
+                case['discovery_target']=str(c)
+                case['solver']=meta
+                discovery.append(case)
+        candidates.extend(discovery)
+    best={}
+    for p in (1,2):
+        for text in ('0.001745','0.004'):
+            c=Q(text)
+            rows=[case for case in candidates if case['p']==p]
+            ranked=sorted(rows,key=lambda case:-numerical_value(case['signed'],float(c)))
+            winner=ranked[0]
+            # Certify that this displayed winner beats all numerically distinct
+            # profiles in the finite scanned menu, not all possible schedules.
+            win=moment(winner['signed'],c)
+            for case in ranked[1:]:
+                if dict(case['signed'])!=dict(winner['signed']):
+                    need(win[0]>moment(case['signed'],c)[1], 'Exact finite-menu ordering')
+            best[f'p{p}_{text}']=serialize_case(winner)
+    controls={}
+    wrong=base_case(1,6)
+    wrong['targets'][6]+=1
+    controls['unearned_output_credit_rejected']=(sum(r*n for r,n in wrong['targets'].items())-wrong['rank_bill']!=wrong['rank_margin'])
+    controls['rank5_child_with_job5_rejected']=not(5<5)
+    need(all(controls.values()), 'Corruption controls')
+    return {'schema':'productive-helper-mixed-target-tariff/1',
+            'status':'PASS_CONDITIONAL_EXACT_ACCOUNTING',
+            'source_sha256':sha256(Path(__file__).read_bytes()).hexdigest(),
+            'native_profile':dict(NATIVE),'helper_inventory':dict(HELPERS),
+            'assumed_recursive_rule':'sum_paid n_r r^(1-C) < sum_targets W_k k^(1-C); max_paid_rank < min_target_rank',
+            'best_in_finite_menu':best,
+            'fixed_p2_minimum9':serialize_case(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)),
+            'discovery_candidates':[serialize_case(c) for c in discovery],
+            'controls':controls,
+            'not_proved':['native whole-helper adapters and arbitrary-input block diagonal contract',
+                          'correct main controller and all its heads/caches/cleanup',
+                          'literal eligibility of any displayed head-cut grant',
+                          'mixed-target all-size recursion in this native model',
+                          'finite-precision integer-multiplication transfer and scalar/stock costs'],
+            'new_kappa':False}
+
+def main():
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--discover',action='store_true')
+    parser.add_argument('--output',type=Path,default=HERE/'MIXED-TARGET-PROBE.json')
+    args=parser.parse_args()
+    result=run(args.discover)
+    args.output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+    print(json.dumps({'status':result['status'],'best':{k:v['targets_at_C'][k.split('_',1)[1]]['after_native_completion_before_main_closure'] for k,v in result['best_in_finite_menu'].items()}},sort_keys=True))
+
+if __name__=='__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-rebuild/complex/native_extensions.py b/research/owned-relation-independent-validation/capsule/research/kappa-rebuild/complex/native_extensions.py
new file mode 100644
index 0000000000..7f84894efc
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-rebuild/complex/native_extensions.py
@@ -0,0 +1,233 @@
+#!/usr/bin/env python3
+"""Native embedded query logger and common-frame H conjugation contacts.
+
+Apache-2.0. Substantial OpenAI assistance. These are fresh constructions with
+explicit arbitrary-input endpoints. An embedded cache output is not claimed
+as an independent clean helper output until a whole caller erases its defect.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import sys
+
+sys.dont_write_bytecode = True
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+import rebuild_native as N
+import power_two_balance as B
+
+B_SHA = '76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424'
+
+
+def common_frame_h(geo, offset, frame):
+    """H = diag(I,-I) S_L S_-K S_L, with all shear ADDs having coefficient ±1.
+
+    Balancing only the eight selected coordinates avoids scaling104 ordinary
+    coordinates. No private field and no recursive transport are introduced.
+    Precondition: ALL112 physical fields share the stated actual frame gauge.
+    """
+    A = geo['selected']
+    out = [['phase', 'fresh_common_frame_H']]
+    def scale(n, d):
+        out.extend(N.scalar(['scale', ['L', offset+a], n, d], frame) for a in A)
+    def left():
+        for k, a in enumerate(A):
+            for u, value in sorted(geo['L'][k].items()):
+                coefficient = 2*value
+                N.need(abs(coefficient) == 1, 'Balanced unit L coefficients')
+                out.append(N.scalar(['add', ['L', offset+a], ['L', offset+u], int(coefficient), 1], frame))
+    scale(2, 1); left(); scale(1, 4)
+    for k, a in enumerate(A):
+        for u, value in sorted(geo['L'][k].items()):
+            coefficient = -2*value
+            out.append(N.scalar(['add', ['L', offset+u], ['L', offset+a], int(coefficient), 1], frame))
+    scale(4, 1); left(); scale(-1, 2)
+    N.need(B.scalar_sum(out) == 10096, 'Exact common-frame H scalar allowance')
+    return out
+
+
+def embedded_cache_roles(canonical):
+    roles = [i for i in range(224, 632) if canonical['start'][i] == 0 and canonical['final'][i] == 1]
+    N.need(len(roles) == 213, '213 genuinely cold, full-ended native helper roles')
+    return roles[:8]
+
+
+def embedded_logger_suffix(canonical, geo, roles=None):
+    roles = embedded_cache_roles(canonical) if roles is None else list(roles)
+    N.need(len(roles) == len(set(roles)) == 8, 'Eight distinct embedded caches')
+    N.need(all(224 <= i < 632 and canonical['start'][i] == 0 and canonical['final'][i] == 1 for i in roles),
+           'Embedded logger only uses cold full-ended physical helper references')
+    out = [['phase', 'fresh_embedded_dirty_logger']]
+    for k, a in enumerate(geo['selected']):
+        r = roles[k]
+        out += [N.scalar(['scale', ['L', r], 2, 1], 1),
+                N.scalar(['add', ['L', r], ['L', a], 2, 1], 1)]
+        out += [N.scalar(['add', ['L', r], ['L', u], int(2*q), 1], 1)
+                for u, q in sorted(geo['L'][k].items())]
+        out.append(N.scalar(['scale', ['L', r], 1, 2], 1))
+    N.need(B.scalar_sum(out) == 3440, 'Embedded logger exact scalar bill')
+    return out
+
+
+def make_embedded_logger(canonical, base_word, geo):
+    word = B.make_balanced_h(canonical, base_word, geo)['forward']
+    return word+embedded_logger_suffix(canonical, geo)
+
+
+def make_wrapped_h(canonical, base_word, geo):
+    words = B.make_balanced_h(canonical, base_word, geo)
+    return {direction: common_frame_h(geo, 112, 0)+word+common_frame_h(geo, 0, 1)
+            for direction, word in words.items()}
+
+
+def literal_replay(v, c, program, backward=False):
+    """Second literal evaluator for new endpoints; all632 inputs arbitrary.
+
+    This checker has no endpoint-specific shortcut. It applies every scalar
+    and free-warp event and checks each contact's frame before comparing rows.
+    """
+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}
+    rows['C', 0] = v.identity(('C', 0))
+    current = {('L', i): f for i, f in enumerate(c['start'])}; current['C', 0] = None
+    spaces = [v.span(frame) for frame in c['frames']]
+    profile = Counter(); cost = 0; max_l1 = Q(1); witness = None; max_denominator = 1
+    for j, event in enumerate(program):
+        kind = event[0]; touched = None
+        if kind == 'scalar':
+            g, frame = event[1:]; target = tuple(g[1]); touched = target
+            cost += N.primitive_allowance(g)
+            if g[0] == 'clear':
+                N.need(target == ('C', 0), 'Only owned C0 can be cleared')
+                rows[target] = {}; current[target] = frame
+            else:
+                N.need(current[target] == frame, 'Exact scalar target frame')
+                if g[0] in ('add', 'copy'):
+                    source = tuple(g[2]); N.need(current[source] == frame, 'Exact scalar source frame')
+                    if g[0] == 'copy':
+                        N.need(target == ('C', 0), 'Only owned field overwritten by copy')
+                        rows[target] = dict(rows[source])
+                    else:
+                        N.need(target != source, 'Distinct reversible ADD arguments')
+                        v.add(rows[target], rows[source], Q(g[3], g[4]))
+                else:
+                    N.need(g[0] == 'scale', 'Known scalar action')
+                    q = Q(g[2], g[3]); rows[target] = {i: q*x for i, x in rows[target].items()}
+        elif kind == 'warp':
+            _, r, op, old, new = event; target = tuple(r); touched = target
+            N.need(current[target] == old, 'Warp input frame')
+            rows[target] = v.warp(rows[target], op, backward); current[target] = new
+        elif kind in ('climb', 'center'):
+            if kind == 'climb':
+                _, part, i, old, new, rank = event; target = ('L', i)
+                N.need(spaces[old] < spaces[new], 'Ascending borrowed climb')
+            else:
+                _, i, old, new, rank = event; target = ('C', i)
+                N.need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested center transport')
+            N.need(current[target] == old and rank == abs(len(c['frames'][new])-len(c['frames'][old])), 'Paid rank and source frame')
+            current[target] = new; profile[rank] += 1
+        else:
+            N.need(kind in ('phase', 'adapter', 'residual_adapter'), 'Known inert native marker')
+        if touched is not None:
+            norm = sum(map(abs, rows[touched].values()), Q(0))
+            if norm > max_l1:
+                max_l1 = norm; witness = dict(event=j, role=list(touched))
+            max_denominator = max(max_denominator, max((x.denominator for x in rows[touched].values()), default=1))
+    N.need([current['L', i] for i in range(632)] == c['final'], 'Final native frames')
+    N.need(not rows['C', 0], 'Owned C0 cleared at return')
+    return rows, dict(independent_persistent_columns=632, independent_owned_entry_columns=1,
+                      scalar_frames_checked=True, arbitrary_owned_C0_cleared=True,
+                      paid_profile=dict(sorted(profile.items())), paid_rank_mass=sum(k*x for k, x in profile.items()),
+                      real_scalar_allowance=cost, max_formal_prefix_l1=str(max_l1), max_denominator=max_denominator,
+                      l1_witness=witness)
+
+
+def check_rows(v, rows, geo, kind, backward=False, cache_roles=()):
+    mismatch = []
+    for r in range(632):
+        actual = rows['L', r]
+        if kind == 'wrapped' and r < 224:
+            port = r % 112; wanted = {}
+            for j, q in geo['H'][port].items():
+                v.add(wanted, v.identity(('L', (112 if r >= 112 else 0)+j)), q)
+                if backward and r < 112:
+                    v.add(wanted, v.identity(('L', 112+j)), -q)
+                if not backward and r >= 112:
+                    v.add(wanted, v.identity(('L', j)), q)
+        else:
+            wanted = v.identity(('L', r))
+            if 112 <= r < 224:
+                for j, q in geo['H'][r-112].items():
+                    v.add(wanted, v.identity(('L', j)), q)
+            if r in cache_roles:
+                k = list(cache_roles).index(r)
+                for j, q in {geo['selected'][k]: Q(1), **geo['L'][k]}.items():
+                    v.add(wanted, v.identity(('L', j)), q)
+        if actual != wanted:
+            mismatch.append(r)
+    N.need(not mismatch, 'Fresh exact endpoint mismatch '+repr(mismatch[:5]))
+
+
+def check_scalar_h(v, geo):
+    """Independent112-column execution without native body or Clifford data."""
+    rows = {i: {i: Q(1)} for i in range(112)}
+    program = common_frame_h(geo, 0, 0)
+    for event in program:
+        if event[0] != 'scalar':
+            continue
+        g = event[1]; target = g[1][1]
+        if g[0] == 'scale':
+            q = Q(g[2], g[3]); rows[target] = {i: q*x for i, x in rows[target].items()}
+        else:
+            v.add(rows[target], rows[g[2][1]], Q(g[3], g[4]))
+    N.need(all(rows[i] == geo['H'][i] for i in range(112)), 'Three balanced shears exactly equal H')
+    return dict(all_columns=112, real_scalar_allowance=B.scalar_sum(program),
+                additions=sum(e[0] == 'scalar' and e[1][0] == 'add' for e in program),
+                unit_add_coefficients=True, owned_fields=0, new_recursive_children=0,
+                required_physical_precondition='All112 fields occupy one actual common frame reference.')
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--out', type=Path, default=HERE/'extension-certificates')
+    args = ap.parse_args(); args.out.mkdir(parents=True, exist_ok=True)
+    N.need(N.digest(HERE/'rebuild_native.py') == B.N_SHA and N.digest(HERE/'power_two_balance.py') == B_SHA,
+           'Authenticated fresh prerequisite sources')
+    p, v, ce, receipt, inherited = N.authenticated(); geo = N.geometry(v.PACKET)
+    result = dict(schema='fresh-native-helper-log-and-common-frame-conjugation/1',
+                  source_sha256=N.digest(Path(__file__)), reconstruction_source_sha256=B.N_SHA,
+                  balance_source_sha256=B_SHA, scalar_H=check_scalar_h(v, geo), providers={}, no_new_kappa_claimed=True)
+    for tag in N.TAGS:
+        c = N.read(N.BASE/(tag+'-CANONICAL.json.gz')); word = N.read(N.BASE/(tag+'-NATIVE-WORD.json.gz'))
+        base_scalar = B.scalar_sum(word['forward'])
+        roles = embedded_cache_roles(c); embedded = make_embedded_logger(c, word, geo)
+        rows, embedded_check = literal_replay(v, c, embedded)
+        check_rows(v, rows, geo, 'embedded', cache_roles=roles)
+        N.need(embedded_check['real_scalar_allowance'] == base_scalar+3504+3440, 'Embedded complete scalar invoice')
+        wrapped = make_wrapped_h(c, word, geo); wrapped_checks = {}
+        for direction, program in wrapped.items():
+            back = direction == 'backward'
+            rows, checked = literal_replay(v, c, program, back)
+            check_rows(v, rows, geo, 'wrapped', back)
+            N.need(checked['real_scalar_allowance'] == base_scalar+3504+2*10096, 'Wrapped H complete scalar invoice')
+            wrapped_checks[direction] = checked
+        ep = args.out/(tag+'-EMBEDDED-LOGGER.json.gz'); wp = args.out/(tag+'-SCALAR-WRAPPED-H.json.gz')
+        result['providers'][tag] = dict(
+            embedded_logger=dict(artifact=ep.name, sha256=N.save(ep, embedded), check=embedded_check,
+                                 cache_roles=roles, exactly_400_other_helpers_restored=True,
+                                 cache_output='d_k + X_A[k] + L[k] X_U', extra_children=0,
+                                 extra_persistent_fields=0, extra_owned_fields=0, extra_scalar_allowance=3440,
+                                 independent_clean_output_credit_for_eight_caches=False),
+            scalar_wrapped_H=dict(artifact=wp.name, sha256=N.save(wp, wrapped), checks=wrapped_checks,
+                                  endpoint='diag(H,H) times the corresponding identity shear in local logical coordinates',
+                                  new_recursive_children_beyond_H=0, extra_scalar_allowance=20192,
+                                  all_408_helpers_restored=True,
+                                  outer_intercall_frame_identification_certified=False))
+        N.save(args.out/'RESULT.json', result)
+        print('PASS extensions', tag, 'embedded0 extra children; wrapped H20192 extra scalars', flush=True)
+    result['status'] = 'PASS_LOCAL_NATIVE_ENDPOINTS_WITH_EXPLICIT_OUTER_FRAME_OBLIGATION'
+    N.save(args.out/'RESULT.json', result)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz b/research/owned-relation-independent-validation/capsule/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz
new file mode 100644
index 0000000000..46d929df83
Binary files /dev/null and b/research/owned-relation-independent-validation/capsule/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz differ
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz b/research/owned-relation-independent-validation/capsule/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz
new file mode 100644
index 0000000000..ac77b78547
Binary files /dev/null and b/research/owned-relation-independent-validation/capsule/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz differ
diff --git a/research/owned-relation-independent-validation/capsule/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json b/research/owned-relation-independent-validation/capsule/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json
new file mode 100644
index 0000000000..0fdb65f946
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json
@@ -0,0 +1,241 @@
+{
+  "compiler": {
+    "H": 38569300000000000,
+    "N": "2^38569300000000000",
+    "eta": {
+      "lower": "0.000000204535199106284215364833",
+      "upper": "0.000000204535199106284215364834"
+    },
+    "gap": "1/700000000000",
+    "integer_test_exponent": 55099,
+    "logarithm_power": 1000,
+    "theta": "63/64",
+    "uniform_saving": "1057621533/350000000000",
+    "word_materialized": false
+  },
+  "gain_over_PR4535": "4027/2500000000",
+  "kappa": "15108879/5000000000",
+  "local_helpers": {
+    "4": 28,
+    "7": 7,
+    "8": 47,
+    "9": 326
+  },
+  "local_paid": {
+    "1": 2201,
+    "2": 412,
+    "3": 510,
+    "4": 127,
+    "5": 40,
+    "8": 8
+  },
+  "margin_at_old_root_upper": [
+    "78072058023577019965454984044224523228758899702419408235/196159429230833773869868419475239575503198607639501078528",
+    "1249152928377232319447279744707592371660142395238823308861/3138550867693340381917894711603833208051177722232017256448"
+  ],
+  "native_receipt_sha256": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428",
+  "negative_controls": {
+    "closed_epsilon": [
+      "epsilon_below_one",
+      "global_gamma_power_slack",
+      "actual_logarithmic_gamma_guard",
+      "source_axis_superpolynomial",
+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
+    ],
+    "closed_uniform": [
+      "new_complex_uniform_saving_above_b"
+    ],
+    "old_BIT": [
+      "actual_bit_above_effective"
+    ],
+    "unfunded_endpoint": [
+      "main_transform_above_kappa",
+      "global_coordinate_router_above_kappa",
+      "fused_gaussian_above_kappa",
+      "group_bit_router_above_kappa",
+      "boundary_algebraic_matrix_above_kappa"
+    ]
+  },
+  "nonrecursive": {
+    "local_routes": 4802000,
+    "local_scalar": 158168,
+    "raw_scalar_upper": 181098496
+  },
+  "ordinary_BIT": {
+    "admitted": "17/5000",
+    "after_cover": "69/20000",
+    "atom": "1/250",
+    "before_cover": "3459/1000000",
+    "ordinary_saving": "8590884599/2500000000000",
+    "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+  },
+  "outer": {
+    "functional_checks": {
+      "actual_new_BIT_stock_sublinear": "174299999999253/175000000000000",
+      "fixed_halo_explicit_metadata_branch": "13475000000001/175000000000",
+      "new_BIT_row_stock_sublinear_in_active_group": "697899999997009/700000000000000",
+      "new_semantic_group_guard": "3/700000000000"
+    },
+    "margins": {
+      "boundary_algebraic_matrix": "1480670144797884756937/490000000000000000000000",
+      "fused_gaussian": "1480670144793654270811/490000000000000000000000",
+      "global_coordinate_router": "264405383/87500000000",
+      "group_bit_router": "185083768186706783851/61250000000000000000000",
+      "group_scans": "349999999999/350000000000",
+      "main_transform": "1480670144097884756937/490000000000000000000000",
+      "microbox_face_corrections": "13475000000001/175000000000",
+      "polynomial_products": "699999999999/700000000000",
+      "sparse_union_movement": "200543170144797884756937/490000000000000000000000"
+    },
+    "parameters": {
+      "a": "264405383/87500000000",
+      "b": "423048613/140000000000",
+      "beta": "699999999997/700000000000",
+      "bit_saving": "17/5000",
+      "cap_xi": "445543170144097884756937/490000000000000000000000",
+      "complex_uniform_saving": "1057621533/350000000000",
+      "d": "1/700000000000",
+      "epsilon": "699999999999/700000000000",
+      "kappa": "15108879/5000000000",
+      "lambda_": "199395644839/200000000000",
+      "lambda_prime": "697884756937/700000000000",
+      "layout": "1/700000000000",
+      "q": "2115243063/700000000000",
+      "r0": "1/7000000000000",
+      "stop": "1/700000000000",
+      "tested_saving": "302177581/100000000000"
+    },
+    "strict_checks": {
+      "actual_bit_above_effective": "33094617/87500000000",
+      "actual_logarithmic_gamma_guard": "1/700000000000",
+      "actual_logarithmic_group_guard": "44456829856952115243063/245000000000000000000000",
+      "alpha_logarithm_absorption": "1/7000000000000",
+      "boundary_algebraic_matrix_above_kappa": "2797884756937/490000000000000000000000",
+      "cap_above_band": "200543170144097884756937/490000000000000000000000",
+      "cap_below_cell": "44456829855202115243063/490000000000000000000000",
+      "cap_below_phase_cell_power": "534456829855902115243063/490000000000000000000000",
+      "complex_above_effective": "1/700000000000",
+      "complex_below_one_over_32": "3951951387/140000000000",
+      "complex_endpoint": "1/350000000000",
+      "epsilon_below_one": "1/700000000000",
+      "epsilon_positive": "699999999999/700000000000",
+      "fine_prime_halo_umbrella": "7/2",
+      "fused_gaussian_above_kappa": "2793654270811/490000000000000000000000",
+      "gaussian_above_main": "347884756937/245000000000000000000000",
+      "global_coordinate_router_above_kappa": "1/175000000000",
+      "global_gamma_power_slack": "9/7000000000000",
+      "group_below_dimension": "1/350000000000",
+      "group_bit_router_above_kappa": "436706783851/61250000000000000000000",
+      "group_gauge_power_slack": "44456829856917115243063/245000000000000000000000",
+      "group_key_fits_record": "1/350000000000",
+      "group_positive": "699999999997/700000000000",
+      "group_scans_above_kappa": "348942378469/350000000000",
+      "halo_covers_generic_inverse_radius": "5",
+      "improvement_over_user_baseline": "645402690400418148631/500000000000000000000000",
+      "lambda_above_internal": "1/1400000000000",
+      "lambda_above_sigma": "3/1400000000000",
+      "lambda_above_tau": "1/1400000000000",
+      "lambda_prime_above_lambda": "1/1400000000000",
+      "lambda_prime_above_leaf": "279576951387/98000000000000000000000",
+      "leaf_saving_above_effective": "139576951387/98000000000000000000000",
+      "main_transform_above_kappa": "2097884756937/490000000000000000000000",
+      "membership_arithmetic_fits_record": "1/700000000000",
+      "microbox_face_corrections_above_kappa": "3368617797309/43750000000",
+      "microbox_halo_volume": "55300000000003/700000000000",
+      "new_complex_uniform_saving_above_b": "1/700000000000",
+      "new_semantic_guard_with_C1_one": "1/700000000000",
+      "polynomial_products_above_kappa": "697884756939/700000000000",
+      "positive_layout_slack": "1/700000000000",
+      "q_below_effective": "1/700000000000",
+      "q_below_internal": "1/700000000000",
+      "q_below_leaf": "279576951387/98000000000000000000000",
+      "q_positive": "2115243063/700000000000",
+      "short_record_fallback": "139576951387/140000000000",
+      "source_axis_superpolynomial": "1/700000000000",
+      "sparse_union_movement_above_kappa": "199062500002797884756937/490000000000000000000000",
+      "stop_below_one": "699999999999/700000000000",
+      "stop_positive": "1/700000000000",
+      "strassen_integer_power_gap": "1951441519231",
+      "support_router_span": "3/700000000000",
+      "theta_positive_polynomial_power": "2",
+      "union_header_fits_record": "3/700000000000",
+      "union_tag_work_per_visit_fits_record": "3/700000000000"
+    }
+  },
+  "paid": {
+    "1": 41298,
+    "16": 448,
+    "2": 7416,
+    "24": 448,
+    "3": 9180,
+    "32": 448,
+    "4": 2286,
+    "40": 448,
+    "48": 448,
+    "5": 720,
+    "56": 448,
+    "64": 448,
+    "72": 224,
+    "8": 144
+  },
+  "paid_calls": 64404,
+  "productive_fields": 10928,
+  "rank_mass_surplus": 752,
+  "raw_root_interval": [
+    "302177587077/100000000000000",
+    "151088793539/50000000000000"
+  ],
+  "scope": "Exact changed-profile arithmetic only. Requires separately admitted changed native programs, paid transports and absolute phases. Retained compiler/native/precision/tape/analytic/recovery assumptions.",
+  "source_sha256": {
+    "research/fresh-helper-boundary/native.py": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29",
+    "research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326",
+    "research/joint-helper-lattice/CONTROLLER.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f",
+    "research/joint-helper-lattice/native_joint.py": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46",
+    "research/joint-helper-lattice/verify.py": "8eb13f77a94315f811612cb557a17edeecb6b9d9a75dfa238b112dd6520c336f",
+    "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85",
+    "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a",
+    "research/kappa-rebuild/bit/complex_controller_factor.py": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497",
+    "research/kappa-rebuild/bit/mixed_productive_bit.py": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e",
+    "research/kappa-round6-compiler-tightening-20261022/arithmetic.py": "960864e5427a1ca2c319a7b2dee292b6fe50bd5964830031e611591af10dac38",
+    "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15",
+    "research/query-thinned-controllers/RESULT.json": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f",
+    "research/query-thinned-controllers/controller.py": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2"
+  },
+  "status": "PASS_CHANGED_PROFILE_ARITHMETIC_NATIVE_ADMISSION_SEPARATE",
+  "strictification": {
+    "alpha": {
+      "lower": "0.999999999936687383304469699479",
+      "upper": "0.999999999936687383304469699480"
+    },
+    "cutoff": 20,
+    "delta": {
+      "lower": "0.958285308639504859158849914083",
+      "upper": "0.958285308639504859158849914084"
+    },
+    "floor": 21,
+    "gamma": {
+      "lower": "0.956217509753795293454516855483",
+      "upper": "0.956217509753795293454516855484"
+    },
+    "normalized_paid_upper": "104857600097656251/104857601073741824",
+    "power": 1024,
+    "tail_offset": "1/5",
+    "tested": "302177581/100000000000"
+  },
+  "targets": {
+    "145": 224,
+    "17": 448,
+    "25": 448,
+    "33": 448,
+    "4": 504,
+    "41": 448,
+    "49": 448,
+    "57": 448,
+    "65": 448,
+    "7": 126,
+    "73": 224,
+    "8": 846,
+    "9": 5868
+  }
+}
diff --git a/research/owned-relation-independent-validation/capsule/research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py b/research/owned-relation-independent-validation/capsule/research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py
new file mode 100644
index 0000000000..340e1f0ffb
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py
@@ -0,0 +1,240 @@
+#!/usr/bin/env python3
+"""Exact endpoint refill conditional on the source PR4359 construction.
+
+Apache-2.0. Substantial OpenAI assistance. The mixed inventory and elementary
+function enclosure are zxv's PR4359; mixed-target flow is Jacob Alan Sussman's
+Theorem 1G. Outer formulas retain the attribution in PR4359 outer_parameters.py.
+This file checks arithmetic, not the native or all-size proof hypotheses.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import importlib.util
+import json
+import sys
+
+sys.dont_write_bytecode = True
+HERE = Path(__file__).resolve().parent
+PREFIX = Path('research/kappa-rebuild')
+OLD_BASELINE = Q('0.001730970419199163702738')
+KAPPA = Q('0.00230509')
+TESTED = Q('0.00230509019')
+ROOT_UPPER = Q('0.002306')
+
+
+def need(value, message):
+    if not value:
+        raise AssertionError(message)
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def ceil(value):
+    value = Q(value)
+    return -((-value.numerator) // value.denominator)
+
+
+def encode(value):
+    if isinstance(value, Q):
+        return str(value)
+    if isinstance(value, dict):
+        return {str(k): encode(v) for k, v in value.items()}
+    if isinstance(value, (tuple, list)):
+        return [encode(v) for v in value]
+    return value
+
+
+def family(kappa, tested):
+    """One explicit slack family approaching the same source mixed root."""
+    need(Q(0) < kappa < tested < ROOT_UPPER, 'Positive strictly ordered savings')
+    d = (tested-kappa)/7
+    return {'kappa': kappa, 'tested_saving': tested,
+            'complex_uniform_saving': kappa+6*d,
+            'b': kappa+5*d, 'a': kappa+4*d, 'q': kappa+3*d,
+            'bit_saving': Q('0.0027'), 'epsilon': 1-d, 'beta': 1-3*d,
+            'r0': d/10, 'stop': d, 'layout': d, 'd': d}
+
+
+def ledger(p):
+    """Recompute all 54 named PR4359 checks with freely supplied parameters."""
+    kappa, b, a, q = (p[key] for key in ('kappa', 'b', 'a', 'q'))
+    epsilon, beta, r0, stop, layout = (p[key] for key in
+                                      ('epsilon', 'beta', 'r0', 'stop', 'layout'))
+    sigma, tau = 1-b, 1-a
+    internal = tau+(1-stop)*max(sigma-tau, Q(0))
+    leaf = sigma+stop*(1-sigma)
+    lam, c = 1-(q+a)/2, Q(3, 32)
+    xi, key = epsilon*(1+q)-c+layout, beta+1-epsilon
+    margins = {
+        'main_transform': epsilon*q,
+        'global_coordinate_router': a,
+        'fused_gaussian': 1-epsilon+q*beta,
+        'group_bit_router': 1-epsilon+a*beta,
+        'group_scans': 1-epsilon+beta,
+        'boundary_algebraic_matrix': c+xi-epsilon,
+        'sparse_union_movement': xi+Q(1, 2)-epsilon,
+        'polynomial_products': epsilon,
+        'microbox_face_corrections': 1-(epsilon+beta+48-128+2),
+    }
+    checks = {
+        'actual_bit_above_effective': p['bit_saving']-a,
+        'complex_above_effective': b-a,
+        'q_positive': q, 'complex_endpoint': b-q, 'q_below_effective': a-q,
+        'stop_positive': stop, 'stop_below_one': 1-stop,
+        'leaf_saving_above_effective': (1-stop)*b-a,
+        'q_below_internal': 1-internal-q, 'q_below_leaf': 1-leaf-q,
+        'lambda_above_tau': lam-tau, 'lambda_above_sigma': lam-sigma,
+        'lambda_above_internal': lam-internal,
+        'lambda_prime_above_lambda': 1-q-lam,
+        'lambda_prime_above_leaf': 1-q-leaf,
+        'epsilon_positive': epsilon, 'epsilon_below_one': 1-epsilon,
+        'cap_above_band': xi-Q(1, 2), 'cap_below_cell': epsilon-xi,
+        'group_positive': beta, 'group_below_dimension': epsilon-beta,
+        'support_router_span': 1-beta,
+        'group_gauge_power_slack': 1-(2*xi-2)-r0-beta,
+        'actual_logarithmic_group_guard': 1-(2*xi-2)-beta,
+        'global_gamma_power_slack': 1-epsilon-r0,
+        'actual_logarithmic_gamma_guard': 1-epsilon,
+        'alpha_logarithm_absorption': r0,
+        'group_key_fits_record': 1-key,
+        'membership_arithmetic_fits_record': 1-beta-2*(1-epsilon),
+        'microbox_halo_volume': 128-48-beta,
+        'positive_layout_slack': layout,
+        'short_record_fallback': epsilon-a,
+        'complex_below_one_over_32': Q(1, 32)-b,
+        'strassen_integer_power_gap': Q(2**45-7**16),
+        'theta_positive_polynomial_power': Q(2),
+        'cap_below_phase_cell_power': 2-xi,
+        'halo_covers_generic_inverse_radius': Q(48-43),
+        'union_tag_work_per_visit_fits_record': 1-beta,
+        'union_header_fits_record': 1-beta,
+        'source_axis_superpolynomial': 1-epsilon,
+        'gaussian_above_main': margins['fused_gaussian']-margins['main_transform'],
+        'new_complex_uniform_saving_above_b': p['complex_uniform_saving']-b,
+        'improvement_over_user_baseline': kappa-OLD_BASELINE,
+        'new_semantic_guard_with_C1_one': 1-epsilon,
+        'fine_prime_halo_umbrella': 10-(2*2+2+Q(1, 2)),
+    }
+    checks.update({name+'_above_kappa': value-kappa for name, value in margins.items()})
+    # These are the additional functional conditions in the independent
+    # PR4359 outer_transfer_audit.py, beyond the 54-row parameter ledger.
+    functional = {
+        'new_semantic_group_guard': 1-beta,
+        'new_BIT_row_stock_sublinear_in_active_group': beta*(1-Q(3, 1000)),
+        'fixed_halo_explicit_metadata_branch': 128-48-epsilon-beta-1,
+    }
+    return {'parameters': dict(p, cap_xi=xi, lambda_=lam, lambda_prime=1-q),
+            'margins': margins, 'strict_checks': checks, 'functional_checks': functional}
+
+
+def compiler_rank(E, targets, paid, tested, uniform):
+    """The original sufficient bound, re-instantiated for the new exponent."""
+    m, kmin, rmax = max(targets), min(targets), max(paid)
+    need((m, kmin, rmax) == (57, 6, 5), 'Pinned complex separation')
+    t, z = 1-tested, 1-uniform
+    z0, h = (t+z)/2, Q(1, 10)
+    delta = z0-t
+    need(0 < t < z0 < z < 1, 'Compiler exponent order')
+    need(5**10 < 6**9 and 57 < 2**10, 'Exact source rank bounds')
+    need(z0 > Q(1, 2) and (1-z0)*E.log_interval(m)[1] < E.log_interval(2)[0],
+         'Original eta strictly exceeds 1/4')
+    H0 = ceil((3+4*delta)/(h*delta))
+    ratio = H0*(1-z0)/(z-z0)
+    H1 = ratio.numerator//ratio.denominator+1
+    need(H0 >= m.bit_length() and H0*h*delta >= 3+4*delta, 'Induction starts')
+    need(H1*(z-z0) > H0*(1-z0), 'Strict winning uniform rank')
+    need((H0-1)*h*delta < 3+4*delta, 'Reject one lower threshold exponent')
+    need((H1-1)*(z-z0) <= H0*(1-z0), 'Reject one lower final exponent')
+    return {'t': t, 'z0': z0, 'z': z, 'theta_upper': Q(9, 10),
+            'H0': H0, 'H1': H1, 'N_encoding': '2^H1',
+            'strict_final_gap': H1*(z-z0)-H0*(1-z0),
+            'winning_word_materialized': False,
+            'bound': 'Original sufficient inequality; a sharper bound is separate.'}
+
+
+def run(source_root):
+    base = source_root/PREFIX
+    interval_path = base/'architecture/mixed_target_probe.py'
+    spec = importlib.util.spec_from_file_location('pr4359_moment', interval_path)
+    E = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(E)
+    cover = read(base/'controller/P3-NATIVE-COVER.json.gz')['cover']
+    targets = {int(k): int(v) for k, v in cover['targets'].items()}
+    paid = {int(k): int(v) for k, v in cover['paid'].items()}
+    need(targets == {6: 192, 7: 56, 8: 93, 9: 1229, 25: 448, 57: 224},
+         'Exact source productive inventory')
+    need(paid == {1: 17623, 2: 5065, 3: 1738, 4: 714, 5: 254},
+         'Exact source paid inventory')
+    signed = Counter(targets)
+    signed.subtract(paid)
+    need(sum(k*v for k, v in signed.items()) == 224, 'Rank-one surplus')
+    bracket = {'lower': E.moment(signed, TESTED), 'upper': E.moment(signed, ROOT_UPPER)}
+    need(bracket['lower'][0] > 0 and bracket['upper'][1] < 0,
+         'Strict mixed test and upper root bound')
+
+    original = read(base/'controller/OUTER-PARAMETERS.json')['outer']
+    old = ledger({'kappa': Q('0.0023'), 'complex_uniform_saving': Q('0.002304'),
+                  'b': Q('0.002303'), 'a': Q('0.0023025'), 'q': Q('0.002302'),
+                  'bit_saving': Q('0.0027'), 'epsilon': Q('0.99999'),
+                  'beta': Q('0.99997'), 'r0': Q(1, 10**6),
+                  'stop': Q(1, 10**8), 'layout': Q(1, 10**6)})
+    for group in ('margins', 'strict_checks'):
+        frozen = {key: Q(value['rational']) for key, value in original[group].items()}
+        need(old[group] == frozen, 'Exact reproduction of every old '+group)
+    p = family(KAPPA, TESTED)
+    result = ledger(p)
+    need(all(v > 0 for v in result['strict_checks'].values()), 'All 54 new outer predicates')
+    need(all(v > 0 for v in result['functional_checks'].values()), 'Additional functional predicates')
+    need(min(result['margins'].values()) == result['margins']['main_transform'],
+         'Main transform remains limiting')
+    need(result['parameters']['cap_xi'] == Q(29, 32)+(1-p['d'])*p['q'],
+         'Cofinal cap simplification')
+    controls = {}
+    for label, updates in [('closed_epsilon_gap', {'epsilon': Q(1)}),
+                           ('missing_layout', {'layout': Q(0)}),
+                           ('unfunded_kappa', {'kappa': Q('0.002306')}),
+                           ('BIT_below_effective', {'bit_saving': OLD_BASELINE}),
+                           ('no_complex_slack', {'complex_uniform_saving': p['b']})]:
+        tested = ledger(dict(p, **updates))
+        failures = {k: v for k, v in tested['strict_checks'].items() if v <= 0}
+        need(failures, 'Mutation rejected: '+label)
+        controls[label] = failures
+    need(E.moment(signed, Q('0.004'))[1] < 0, 'Unsupported mixed target is rejected')
+    inputs = [interval_path, base/'controller/P3-NATIVE-COVER.json.gz',
+              base/'controller/OUTER-PARAMETERS.json']
+    return encode({'schema': 'pr4359-cofinal-outer-refill/1',
+                   'status': 'PASS_EXACT_CONDITIONAL_ENDPOINT_REFILL',
+                   'kappa': KAPPA, 'gain_over_PR4359': KAPPA-Q('0.0023'),
+                   'unchanged_paid': paid, 'unchanged_targets': targets,
+                   'mixed_test_saving': TESTED, 'mixed_test_margin': E.show(bracket['lower']),
+                   'root_upper_test': ROOT_UPPER, 'root_upper_margin': E.show(bracket['upper']),
+                   'old_ledger_crosscheck': {'matched_savings': len(old['margins']),
+                                           'matched_checks': len(old['strict_checks'])},
+                   'outer': result, 'limiting_margin': min(result['margins'].values())-KAPPA,
+                   'compiler': compiler_rank(E, targets, paid, TESTED, p['complex_uniform_saving']),
+                   'negative_controls': controls,
+                   'source_sha256': {str(p.relative_to(source_root)): sha256(p.read_bytes()).hexdigest()
+                                     for p in inputs},
+                   'scope': 'Conditional arithmetic and specified finite rank. The PR4359 native, compiler, cover, precision, fixed-tape and outer hypotheses remain premises; no full theorem or practical word is certified.'})
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--source-root', type=Path, default=HERE/'source')
+    parser.add_argument('--out', type=Path)
+    args = parser.parse_args()
+    result = run(args.source_root)
+    if args.out:
+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    print(json.dumps({key: result[key] for key in
+                      ('status', 'kappa', 'gain_over_PR4359', 'limiting_margin', 'compiler')}, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/capsule/research/query-thinned-controllers/RESULT.json b/research/owned-relation-independent-validation/capsule/research/query-thinned-controllers/RESULT.json
new file mode 100644
index 0000000000..e0695152c9
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/research/query-thinned-controllers/RESULT.json
@@ -0,0 +1,356 @@
+{
+  "bit_invoice": {
+    "main": {
+      "127": 222,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222
+    },
+    "owned_streams_reused_sequentially": 1,
+    "paid": {
+      "1": 25479,
+      "14": 444,
+      "2": 24156,
+      "21": 444,
+      "28": 444,
+      "3": 1422,
+      "35": 444,
+      "4": 792,
+      "42": 444,
+      "49": 444,
+      "5": 1836,
+      "56": 444,
+      "6": 198,
+      "63": 222,
+      "7": 342
+    },
+    "paid_calls": 57555,
+    "productive_fields": 11454,
+    "rank_surplus": 753,
+    "raw_scalar_record_bound": 1000000000,
+    "targets": {
+      "127": 222,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222,
+      "8": 7902
+    },
+    "thick_calls": 18,
+    "thick_stages": [
+      0,
+      1,
+      3,
+      5,
+      7,
+      9,
+      11,
+      13,
+      15,
+      17,
+      19,
+      21,
+      23,
+      25,
+      27,
+      29,
+      31,
+      32
+    ],
+    "thin_queries": 1665,
+    "whole_idle": {
+      "14": 444,
+      "21": 444,
+      "28": 444,
+      "35": 444,
+      "42": 444,
+      "49": 444,
+      "56": 444,
+      "63": 222
+    }
+  },
+  "bit_strictification": {
+    "alpha": {
+      "lower": "0.999995735238059506641600561767",
+      "upper": "0.999995735238059506641600561768"
+    },
+    "compiler_H0": 3755884544,
+    "cutoff_base": 17,
+    "delta": {
+      "lower": "0.949707924144871179442776557218",
+      "upper": "0.949707924144871179442776557219"
+    },
+    "gamma": {
+      "lower": "0.957429821066420278606254392110",
+      "upper": "0.957429821066420278606254392111"
+    },
+    "normalized_surplus_lower": "68719461047/16845935476736",
+    "tail_exponent": "1/5",
+    "target_floor_base": 18,
+    "tensor_power": 1024,
+    "tested_saving": "173/50000",
+    "uniform_H1": 25986965159937,
+    "uniform_N": "2^25986965159937",
+    "uniform_saving": "3459/1000000",
+    "winning_word_materialized": false
+  },
+  "complex_invoice": {
+    "main": {
+      "153": 224,
+      "17": 448,
+      "25": 448,
+      "33": 448,
+      "41": 448,
+      "49": 448,
+      "57": 448,
+      "65": 448,
+      "73": 448
+    },
+    "owned_streams_reused_sequentially": 1,
+    "paid": {
+      "1": 49045,
+      "16": 448,
+      "2": 13547,
+      "24": 448,
+      "3": 4256,
+      "32": 448,
+      "4": 1938,
+      "40": 448,
+      "48": 448,
+      "5": 380,
+      "56": 448,
+      "64": 448,
+      "72": 448,
+      "8": 152
+    },
+    "paid_calls": 72902,
+    "productive_fields": 11560,
+    "rank_surplus": 800,
+    "raw_scalar_record_bound": 1000000000,
+    "targets": {
+      "153": 224,
+      "17": 448,
+      "25": 448,
+      "33": 448,
+      "41": 448,
+      "49": 448,
+      "5": 532,
+      "57": 448,
+      "6": 342,
+      "65": 448,
+      "7": 1064,
+      "73": 448,
+      "8": 1767,
+      "9": 4047
+    },
+    "thick_calls": 19,
+    "thick_stages": [
+      0,
+      1,
+      3,
+      5,
+      7,
+      9,
+      11,
+      13,
+      15,
+      17,
+      19,
+      21,
+      23,
+      25,
+      27,
+      29,
+      31,
+      33,
+      34
+    ],
+    "thin_queries": 1792,
+    "whole_idle": {
+      "16": 448,
+      "24": 448,
+      "32": 448,
+      "40": 448,
+      "48": 448,
+      "56": 448,
+      "64": 448,
+      "72": 448
+    }
+  },
+  "complex_strictification": {
+    "alpha": {
+      "lower": "0.999999952117240859760145478345",
+      "upper": "0.999999952117240859760145478346"
+    },
+    "compiler_H0": 75415467350,
+    "cutoff_base": 20,
+    "delta": {
+      "lower": "0.941649713484853845388929204840",
+      "upper": "0.941649713484853845388929204841"
+    },
+    "gamma": {
+      "lower": "0.967466409565147920980822933859",
+      "upper": "0.967466409565147920980822933860"
+    },
+    "normalized_surplus_lower": "8589700209/251666829934592",
+    "tail_exponent": "1/5",
+    "target_floor_base": 21,
+    "tensor_power": 1024,
+    "tested_saving": "29603/10000000",
+    "uniform_H1": 10418370291022217,
+    "uniform_N": "2^10418370291022217",
+    "uniform_saving": "103609/35000000",
+    "winning_word_materialized": false
+  },
+  "kappa": "37/12500",
+  "minimum_outer_margin_minus_kappa": "629378373/4900000000000000",
+  "native": {
+    "binary_charts": 111,
+    "complex_contacts_and_inverses": 896,
+    "owned_stream_restored_zero": true,
+    "thin_paid_rank_per_port": 1,
+    "thin_productive_credit": 0
+  },
+  "negative_controls": {
+    "closed_epsilon": [
+      "epsilon_below_one",
+      "global_gamma_power_slack",
+      "actual_logarithmic_gamma_guard",
+      "source_axis_superpolynomial",
+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
+    ],
+    "closed_uniform_gap": [
+      "new_complex_uniform_saving_above_b"
+    ],
+    "missing_layout": [
+      "positive_layout_slack"
+    ],
+    "old_BIT_cap": [
+      "actual_bit_above_effective"
+    ],
+    "unfunded_kappa": [
+      "main_transform_above_kappa",
+      "global_coordinate_router_above_kappa",
+      "fused_gaussian_above_kappa",
+      "group_bit_router_above_kappa",
+      "boundary_algebraic_matrix_above_kappa"
+    ]
+  },
+  "old_atom_rejected": true,
+  "ordinary_BIT": {
+    "admitted": "17/5000",
+    "after_cover": "69/20000",
+    "atom": "1/250",
+    "before_cover": "3459/1000000",
+    "ordinary_saving": "8590884599/2500000000000",
+    "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+  },
+  "outer": {
+    "functional_checks": {
+      "actual_new_BIT_stock_sublinear": "17429997759/17500000000",
+      "fixed_halo_explicit_metadata_branch": "1347500003/17500000",
+      "new_BIT_row_stock_sublinear_in_active_group": "69789991027/70000000000",
+      "new_semantic_group_guard": "9/70000000"
+    },
+    "margins": {
+      "boundary_algebraic_matrix": "14504839378373/4900000000000000",
+      "fused_gaussian": "14504838135119/4900000000000000",
+      "global_coordinate_router": "51803/17500000",
+      "group_bit_router": "3626262033773/1225000000000000",
+      "group_scans": "34999997/35000000",
+      "main_transform": "14504629378373/4900000000000000",
+      "microbox_face_corrections": "1347500003/17500000",
+      "polynomial_products": "69999997/70000000",
+      "sparse_union_movement": "2005129839378373/4900000000000000"
+    },
+    "parameters": {
+      "a": "51803/17500000",
+      "b": "41443/14000000",
+      "beta": "69999991/70000000",
+      "bit_saving": "17/5000",
+      "cap_xi": "4455129629378373/4900000000000000",
+      "complex_uniform_saving": "103609/35000000",
+      "d": "3/70000000",
+      "epsilon": "69999997/70000000",
+      "kappa": "37/12500",
+      "lambda_": "19940797/20000000",
+      "lambda_prime": "69792791/70000000",
+      "layout": "3/70000000",
+      "q": "207209/70000000",
+      "r0": "3/700000000",
+      "stop": "3/70000000",
+      "tested_saving": "29603/10000000"
+    },
+    "strict_checks": {
+      "actual_bit_above_effective": "7697/17500000",
+      "actual_logarithmic_gamma_guard": "3/70000000",
+      "actual_logarithmic_group_guard": "444870685621627/2450000000000000",
+      "alpha_logarithm_absorption": "3/700000000",
+      "boundary_algebraic_matrix_above_kappa": "839378373/4900000000000000",
+      "cap_above_band": "2005129629378373/4900000000000000",
+      "cap_below_cell": "444870160621627/4900000000000000",
+      "cap_below_phase_cell_power": "5344870370621627/4900000000000000",
+      "complex_above_effective": "3/70000000",
+      "complex_below_one_over_32": "396057/14000000",
+      "complex_endpoint": "3/35000000",
+      "epsilon_below_one": "3/70000000",
+      "epsilon_positive": "69999997/70000000",
+      "fine_prime_halo_umbrella": "7/2",
+      "fused_gaussian_above_kappa": "838135119/4900000000000000",
+      "gaussian_above_main": "104378373/2450000000000000",
+      "global_coordinate_router_above_kappa": "3/17500000",
+      "global_gamma_power_slack": "27/700000000",
+      "group_below_dimension": "3/35000000",
+      "group_bit_router_above_kappa": "262033773/1225000000000000",
+      "group_gauge_power_slack": "444870675121627/2450000000000000",
+      "group_key_fits_record": "3/35000000",
+      "group_positive": "69999991/70000000",
+      "group_scans_above_kappa": "34896397/35000000",
+      "halo_covers_generic_inverse_radius": "5",
+      "improvement_over_user_baseline": "614514790400418148631/500000000000000000000000",
+      "lambda_above_internal": "3/140000000",
+      "lambda_above_sigma": "9/140000000",
+      "lambda_above_tau": "3/140000000",
+      "lambda_prime_above_lambda": "3/140000000",
+      "lambda_prime_above_leaf": "83875671/980000000000000",
+      "leaf_saving_above_effective": "41875671/980000000000000",
+      "main_transform_above_kappa": "629378373/4900000000000000",
+      "membership_arithmetic_fits_record": "3/70000000",
+      "microbox_face_corrections_above_kappa": "1347448203/17500000",
+      "microbox_halo_volume": "5530000009/70000000",
+      "new_complex_uniform_saving_above_b": "3/70000000",
+      "new_semantic_guard_with_C1_one": "3/70000000",
+      "polynomial_products_above_kappa": "69792797/70000000",
+      "positive_layout_slack": "3/70000000",
+      "q_below_effective": "3/70000000",
+      "q_below_internal": "3/70000000",
+      "q_below_leaf": "83875671/980000000000000",
+      "q_positive": "207209/70000000",
+      "short_record_fallback": "13958557/14000000",
+      "source_axis_superpolynomial": "3/70000000",
+      "sparse_union_movement_above_kappa": "1990625839378373/4900000000000000",
+      "stop_below_one": "69999997/70000000",
+      "stop_positive": "3/70000000",
+      "strassen_integer_power_gap": "1951441519231",
+      "support_router_span": "9/70000000",
+      "theta_positive_polynomial_power": "2",
+      "union_header_fits_record": "9/70000000",
+      "union_tag_work_per_visit_fits_record": "9/70000000"
+    }
+  },
+  "relative_gain_over_p7": "27353/268647",
+  "schema": "query-thinned-productive-controllers/1",
+  "scope": "Conditional native construction; all-column, erasure, whole-job matching, fixed-tape, precision, analytic, prime and exact-recovery premises retained. No unconditional theorem or selected promotion.",
+  "source_inputs_authenticated": 17,
+  "status": "PASS_CONDITIONAL_QUERY_THINNED_KAPPA_00296"
+}
diff --git a/research/owned-relation-independent-validation/capsule/scripts/check_research_commit.py b/research/owned-relation-independent-validation/capsule/scripts/check_research_commit.py
new file mode 100644
index 0000000000..7ab20e1487
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/scripts/check_research_commit.py
@@ -0,0 +1,149 @@
+#!/usr/bin/env python3
+"""Compare package working bytes with a commit before publishing hash receipts.
+
+This is a byte-transport preflight, not a research verifier or CI-equivalence
+claim. Prepared for ywz65 with OpenAI Codex assistance. Apache-2.0.
+"""
+import argparse
+import hashlib
+import json
+import os
+import re
+import subprocess
+from contextlib import closing
+from pathlib import Path
+
+from research_package import (
+    canonical_relative_path,
+    git,
+    git_blobs,
+    git_source_env,
+    relative_file,
+    require,
+    source_pin,
+)
+
+ROOT = Path(__file__).resolve().parents[1]
+MAX_SOURCE_METADATA_BYTES = 16 * 1024 * 1024
+MAX_SOURCE_ROWS = 100000
+MAX_SOURCE_COMMITS = 256
+
+
+def history_git(root, *args):
+    env = git_source_env()
+    env['GIT_GRAFT_FILE'] = os.devnull
+    env.pop('GIT_SHALLOW_FILE', None)
+    return subprocess.run(['git', '--no-replace-objects', *args], cwd=root, env=env,
+                          capture_output=True, check=False, timeout=30)
+
+
+def publication_sources(root, package, commit):
+    """Read bounded, immutable metadata without local replacements or grafts."""
+    spec = commit + ':' + package + '/SOURCES.json'
+    size = history_git(root, 'cat-file', '-s', spec)
+    require(size.returncode == 0 and size.stdout.strip().isdigit(), 'missing publication SOURCES.json')
+    require(int(size.stdout) <= MAX_SOURCE_METADATA_BYTES, 'source metadata byte limit exceeded')
+    payload = history_git(root, 'cat-file', 'blob', spec)
+    require(payload.returncode == 0 and len(payload.stdout) == int(size.stdout),
+            'incomplete publication SOURCES.json')
+    return json.loads(payload.stdout)
+
+
+def source_history(root, package, commit):
+    """Check committed pins against raw publication ancestry, not local refs.
+
+    This is declared history availability, not full SOURCES.json validation
+    or discovery of imports, archive references or runtime dependencies.
+    """
+    sources = publication_sources(root, package, commit)
+    require(isinstance(sources, dict), 'SOURCES.json must be an object')
+    base = sources.get('base_commit')
+    require(isinstance(base, str) and re.fullmatch(r'[0-9a-f]{40,64}', base),
+            'SOURCES.json base_commit must be an exact commit ID')
+    rows = sources.get('files')
+    require(isinstance(rows, list), 'SOURCES.json files must be a list')
+    require(len(rows) <= MAX_SOURCE_ROWS, 'source row limit exceeded')
+    commits = {base}
+    for row in rows:
+        require(isinstance(row, dict) and isinstance(row.get('path'), str),
+                'SOURCES.json files rows need a string path')
+        canonical_relative_path(row['path'])
+        commits.add(source_pin(row, base).split(':', 1)[0])
+    require(len(commits) <= MAX_SOURCE_COMMITS, 'source commit limit exceeded')
+    shallow = history_git(root, 'rev-parse', '--is-shallow-repository')
+    require(shallow.returncode == 0, 'cannot inspect Git history')
+    require(shallow.stdout.strip() == b'false', 'source-history check requires full Git history')
+    for pin in sorted(commits):
+        resolved = history_git(root, 'rev-parse', '--verify', '--end-of-options', pin + '^{commit}')
+        require(resolved.returncode == 0 and resolved.stdout.strip() == pin.encode('ascii'),
+                'unavailable source commit: ' + pin)
+        ancestor = history_git(root, 'merge-base', '--is-ancestor', pin, commit)
+        require(ancestor.returncode in (0, 1),
+                'Git ancestry check failed: ' + ancestor.stderr.decode('utf-8', errors='replace').strip())
+        require(ancestor.returncode == 0,
+                'source pin is not an ancestor of publication ' + commit + ': ' + pin
+                + '; a separate cached branch/object is not publication history')
+    return sorted(commits)
+
+
+def check(root, package, ref='HEAD', check_source_history=False):
+    require(re.fullmatch(r'research/[a-z0-9][a-z0-9-]*', package), 'package must be research/<slug>')
+    manifest = json.loads(relative_file(root, package+'/VERIFY.json').read_text(encoding='utf-8'))
+    require(isinstance(manifest, dict), 'VERIFY.json must be an object')
+    inputs = manifest.get('inputs')
+    require(isinstance(inputs, list), 'declare input paths in VERIFY.json')
+    for name in inputs:
+        canonical_relative_path(name)
+    commit = git(root, 'rev-parse', '--verify', '--end-of-options', ref+'^{commit}').decode('ascii').strip()
+    # Literal pathspecs keep wildcard filenames from selecting other files.
+    records = git(root, '--literal-pathspecs', 'ls-tree', '-r', '-z', '--full-tree',
+                  commit, '--', package, *inputs).split(b'\0')
+    entries = {}
+    for record in records:
+        if not record:
+            continue
+        header, raw_name = record.split(b'\t', 1)
+        mode, kind, obj = header.split()
+        name = raw_name.decode('utf-8')
+        require(mode in (b'100644', b'100755') and kind == b'blob',
+                'commit contains a non-regular file: '+name)
+        entries[name] = obj.decode('ascii')
+    # New nonignored local checkers must not disappear from the publication.
+    local = git(root, '--literal-pathspecs', 'ls-files', '-c', '-o', '--exclude-standard',
+                '-z', '--', package).decode('utf-8').split('\0')
+    expected = {name for name in local if name} | set(inputs)
+    require(set(entries) == expected, 'working/commit file inventory differs: '+
+            ', '.join(sorted(set(entries) ^ expected)))
+    names = sorted(entries)
+    require(names, 'empty package inventory')
+    with closing(git_blobs(root, [entries[name] for name in names])) as blobs:
+        # Advance the blob iterator once past its last yield, so its final
+        # Git exit-status check runs before reporting success.
+        for (_, committed), name in zip(blobs, names):
+            working = relative_file(root, name).read_bytes()
+            require(working == committed,
+                    'working/commit bytes differ: '+name+' (working SHA256 '+
+                    hashlib.sha256(working).hexdigest()+', commit SHA256 '+
+                    hashlib.sha256(committed).hexdigest()+')')
+    result = {'commit':commit, 'files':len(names), 'package':package}
+    if check_source_history:
+        result['source_history_commits'] = source_history(root, package, commit)
+    return result
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--package', required=True)
+    parser.add_argument('--ref', default='HEAD', help='commit to publish; default HEAD')
+    parser.add_argument('--check-source-history', action='store_true',
+                        help='also require declared SOURCES.json pin commits in publication ancestry; full history only')
+    args = parser.parse_args()
+    try:
+        result = check(ROOT, args.package, args.ref, args.check_source_history)
+    except (OSError, ValueError, TypeError, subprocess.SubprocessError) as exc:
+        parser.exit(1, str(exc)+'\n')
+    print('PASS_RESEARCH_COMMIT_BYTES '+json.dumps(result))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/capsule/scripts/research_package.py b/research/owned-relation-independent-validation/capsule/scripts/research_package.py
new file mode 100644
index 0000000000..ef9b52c392
--- /dev/null
+++ b/research/owned-relation-independent-validation/capsule/scripts/research_package.py
@@ -0,0 +1,1022 @@
+#!/usr/bin/env python3
+"""Validate and replay explicitly registered research packages, never every verify.py.
+
+Douglas Colkitt, with OpenAI Codex assistance. Apache-2.0.
+"""
+import argparse
+import errno
+from contextlib import closing, contextmanager
+from itertools import chain
+import hashlib
+import importlib.metadata
+import json
+import os
+from pathlib import Path, PurePosixPath
+import re
+import signal
+import stat
+import subprocess
+import sys
+import tempfile
+import threading
+
+ROOT = Path(__file__).resolve().parents[1]
+GIT_BLOB_RESPONSE_TIMEOUT = 90
+
+
+def require(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def canonical_relative_path(name):
+    # Git's changed paths use one repository-relative POSIX spelling. Accepting
+    # aliases here would let a declared input evade the planner's exact match.
+    require(isinstance(name, str), "canonical relative path must be a string")
+    path = PurePosixPath(name)
+    require(bool(path.parts) and not path.is_absolute() and ".." not in path.parts
+            and "\\" not in name and path.as_posix() == name,
+            "use a canonical repository-relative POSIX path: " + name)
+    return path
+
+
+def symlink_free_relative_path(root, name):
+    """Reject symlink components without requiring a deleted input to exist.
+
+    Git reports changes under the target's path, not a symlink alias declared
+    by its consumer. Inspect existing components below the repository root;
+    the checkout must remain stable during planning, validation and replay.
+    """
+    parts = canonical_relative_path(name).parts
+    current = root
+    for part in parts:
+        current = current / part
+        try:
+            mode = current.lstat().st_mode
+        except (FileNotFoundError, NotADirectoryError):
+            break
+        require(not stat.S_ISLNK(mode), "symlink in repository-relative path: " + name)
+    return root / name
+
+
+def relative_file(root, name):
+    result = symlink_free_relative_path(root, name)
+    require(result.resolve().is_relative_to(root.resolve()) and result.is_file(),
+            "missing or external file: " + name)
+    return result
+
+
+# Adapted from the package-local policy in
+# research/t74-2530-source-partner-audit/audit_common.py (Apache-2.0).
+# Keep repository configuration and linked-worktree .git discovery intact;
+# inherited shell overrides must not choose a different repository or index.
+_GIT_REDIRECT_VARS = frozenset((
+    "GIT_DIR", "GIT_WORK_TREE", "GIT_INDEX_FILE", "GIT_OBJECT_DIRECTORY",
+    "GIT_ALTERNATE_OBJECT_DIRECTORIES", "GIT_NAMESPACE", "GIT_CEILING_DIRECTORIES",
+    "GIT_COMMON_DIR", "GIT_CONFIG_PARAMETERS", "GIT_CONFIG_COUNT",
+))
+_GIT_CONFIG_PREFIXES = ("GIT_CONFIG_KEY_", "GIT_CONFIG_VALUE_")
+
+
+def git_source_env():
+    """Use cwd's repository and stored objects, without changing the parent.
+
+    Git can ignore cwd when inherited selection variables point elsewhere.
+    Config-injection variables can also redirect worktree/index operations.
+    This policy is only for Git metadata/source subprocesses, not verifiers.
+    """
+    env = {name: value for name, value in os.environ.items()
+           if name not in _GIT_REDIRECT_VARS and not name.startswith(_GIT_CONFIG_PREFIXES)}
+    # Replacement refs can report an original ID while returning other bytes.
+    env["GIT_NO_REPLACE_OBJECTS"] = "1"
+    return env
+
+
+def git(root, *args):
+    return subprocess.run(["git", *args], cwd=root, env=git_source_env(),
+                          capture_output=True, check=True).stdout
+
+
+def tracked_input_paths(root):
+    """Use HEAD spelling, never case folding, filesystem resolution or the index.
+
+    Staged/untracked files are not replay inputs until committed. NUL framing
+    preserves Git filenames containing whitespace, including CR and LF.
+    """
+    raw = subprocess.run(
+        ["git", "ls-tree", "-r", "--name-only", "-z", "HEAD"], cwd=root, env=git_source_env(),
+        capture_output=True, check=True, timeout=30).stdout
+    return frozenset(name.decode("utf-8") for name in raw.split(b"\0") if name)
+
+
+def require_tracked_input(name, paths):
+    canonical_relative_path(name)
+    require(name in paths, "use an exact Git-tracked input path from HEAD: " + name)
+
+
+def git_source_rows(root, base, names):
+    """Read one pinned object at a time through one Git process; no persistent cache.
+
+    Each request is consumed before the next is sent. This avoids pipe deadlocks
+    and retains the old one-blob memory bound, even for large source archives.
+    Newline paths and non-blob objects retain the legacy Git-show semantics.
+    The caller must close this generator if source validation fails mid-stream.
+    """
+    with subprocess.Popen(["git", "cat-file", "--batch"], cwd=root, env=git_source_env(),
+                          stdin=subprocess.PIPE, stdout=subprocess.PIPE,
+                          stderr=subprocess.PIPE) as process:
+        try:
+            for name in names:
+                expression = base + ":" + name
+                if "\n" in expression or "\r" in expression:
+                    yield git(root, "rev-parse", expression).decode().strip(), git(root, "show", expression)
+                    continue
+                process.stdin.write(expression.encode("utf-8") + b"\n")
+                process.stdin.flush()
+                header = process.stdout.readline().rstrip(b"\n").split(b" ")
+                require(len(header) == 3 and re.fullmatch(rb"[0-9a-f]{40,64}", header[0])
+                        and header[2].isdigit(), "missing or invalid Git source: " + name)
+                size = int(header[2])
+                payload = process.stdout.read(size)
+                require(len(payload) == size and process.stdout.read(1) == b"\n",
+                        "truncated Git source: " + name)
+                if header[1] != b"blob":
+                    payload = git(root, "show", expression)
+                yield header[0].decode("ascii"), payload
+            process.stdin.close()
+            code = process.wait(timeout=90)
+            require(code == 0, "Git source reader failed: " + process.stderr.read().decode("utf-8", errors="replace"))
+        finally:
+            if not process.stdin.closed:
+                process.stdin.close()
+            if process.poll() is None:
+                try:
+                    process.wait(timeout=5)
+                except subprocess.TimeoutExpired:
+                    process.kill()
+                    process.wait()
+
+
+class _UnsupportedNulBatch(Exception):
+    """Git rejected the initial NUL-mode request before yielding any source."""
+
+
+def _closed_stdin_error(error):
+    # Windows can report EINVAL instead of EPIPE when a child closes stdin.
+    # This classifies the pipe error only; the retry still requires exit 129.
+    return (isinstance(error, BrokenPipeError)
+            or (os.name == "nt" and error.errno == errno.EINVAL))
+
+
+def _stop_git_blob_process(process):
+    """Stop this reader's owned POSIX group even after its leader exits."""
+    try:
+        if os.name == "posix":
+            # Reap an exited leader first: signaling a group containing only
+            # its unreaped zombie can report EPERM on macOS. A surviving
+            # descendant keeps the group alive after the leader is reaped.
+            process.poll()
+            os.killpg(process.pid, signal.SIGKILL)
+        else:
+            process.kill()
+    except ProcessLookupError:
+        pass
+
+
+@contextmanager
+def _git_blob_response_deadline(stop):
+    """Bound one response, excluding time spent by its consumer.
+
+    On POSIX the reader owns a session: ordinary descendants retaining a pipe
+    are stopped with the leader. Escaped sessions and separate git() calls are
+    outside this contract; non-POSIX retains the direct-child deadline.
+    """
+    expired = threading.Event()
+
+    def terminate():
+        expired.set()
+        stop()
+
+    timer = threading.Timer(GIT_BLOB_RESPONSE_TIMEOUT, terminate)
+    timer.start()
+    try:
+        yield
+    finally:
+        timer.cancel()
+        timer.join()
+        if expired.is_set():
+            raise subprocess.TimeoutExpired("git cat-file blob response", GIT_BLOB_RESPONSE_TIMEOUT)
+
+
+def _git_blob_batch(root, specs, nul):
+    argv = ["git", "cat-file", "--batch"] + (["-z"] if nul else [])
+    # Usage diagnostics from the unsupported-option probe are expected. Avoid
+    # a second pipe that could block while we consume the framed stdout reply.
+    with subprocess.Popen(argv, cwd=root, env=git_source_env(), stdin=subprocess.PIPE,
+                          stdout=subprocess.PIPE, stderr=subprocess.DEVNULL,
+                          start_new_session=(os.name == "posix")) as process:
+        stopped = False
+
+        def stop():
+            nonlocal stopped
+            if not stopped:
+                _stop_git_blob_process(process)
+                stopped = True
+
+        try:
+            for index, spec in enumerate(specs):
+                require("\0" not in spec, "invalid Git object request")
+                request = spec
+                if not nul and ("\n" in spec or "\r" in spec):
+                    # Resolve one literal argument, never split a path into requests.
+                    request = git(root, "rev-parse", "--verify", "--end-of-options", spec).decode("ascii").strip()
+                    require(re.fullmatch(r"[0-9a-f]{40,64}", request), "invalid Git object ID")
+                with _git_blob_response_deadline(stop):
+                    try:
+                        process.stdin.write(request.encode("utf-8") + (b"\0" if nul else b"\n"))
+                        process.stdin.flush()
+                    except OSError as exc:
+                        if not _closed_stdin_error(exc):
+                            raise
+                        header = b""
+                    else:
+                        header = process.stdout.readline()
+                    if nul and index == 0 and not header and process.wait(timeout=90) == 129:
+                        raise _UnsupportedNulBatch(spec)
+                    fields = header.rstrip(b"\n").split(b" ")
+                    require(len(fields) == 3 and re.fullmatch(rb"[0-9a-f]{40,64}", fields[0])
+                            and fields[1] == b"blob" and fields[2].isdigit(),
+                            "missing or non-blob Git source: " + spec)
+                    size = int(fields[2])
+                    pinned = process.stdout.read(size)
+                    require(len(pinned) == size and process.stdout.read(1) == b"\n",
+                            "incomplete Git blob response: " + spec)
+                yield fields[0].decode("ascii"), pinned
+            process.stdin.close()
+            require(process.wait(timeout=90) == 0, "Git source reader failed")
+        finally:
+            # Terminate ordinary descendants before closing buffered pipes. This
+            # also covers successful leader exit and an early generator close.
+            if os.name == "posix":
+                stop()
+            # Option rejection can close stdin before our first write/flush.
+            try:
+                process.stdin.close()
+            except OSError as exc:
+                if not _closed_stdin_error(exc):
+                    raise
+            process.stdout.close()
+            if process.poll() is None:
+                try:
+                    process.wait(timeout=5)
+                except subprocess.TimeoutExpired:
+                    process.kill()
+                    process.wait()
+
+
+def git_blobs(root, specs):
+    """Stream exact blobs, retaining the one-process NUL protocol on newer Git.
+
+    Git without -z rejects it with usage status 129. Retry only before any
+    response, replaying the consumed first request through the line protocol.
+    The fallback resolves CR/LF paths to object IDs before requesting content.
+    The caller must close this iterator if validation stops before exhaustion.
+    """
+    specs = iter(specs)
+    sentinel = object()
+    first = next(specs, sentinel)
+    if first is sentinel:
+        return
+    with closing(_git_blob_batch(root, chain((first,), specs), nul=True)) as rows:
+        try:
+            yield from rows
+        except _UnsupportedNulBatch as exc:
+            with closing(_git_blob_batch(root, chain((exc.args[0],), specs), nul=False)) as legacy:
+                yield from legacy
+
+
+def meaningful(value):
+    return isinstance(value, str) and bool(value.strip()) and not re.search(r"\bTODO\b", value, re.I)
+
+
+def brief(value):
+    text = json.dumps(value, ensure_ascii=True, sort_keys=True)
+    return text if len(text) <= 120 else text[:117] + "..."
+
+
+def require_key(mapping, key, where, shape=None):
+    """Name the missing key and its expected shape instead of a bare KeyError."""
+    require(isinstance(mapping, dict),
+            where + " must be a JSON object; found " + type(mapping).__name__ + ": " + brief(mapping))
+    require(key in mapping, where + "." + key + " is missing"
+            + ("; expected " + shape if shape else ""))
+    return mapping[key]
+
+
+def require_text(mapping, key, where, shape="a non-empty string without TODO"):
+    """Name the key and distinguish missing, wrong-shaped and weak values."""
+    require(isinstance(mapping, dict),
+            where + " must be a JSON object; found " + type(mapping).__name__ + ": " + brief(mapping))
+    require(key in mapping, where + "." + key + " is missing; expected " + shape)
+    value = mapping[key]
+    require(isinstance(value, str) and meaningful(value),
+            where + "." + key + " must be " + shape + "; found " + type(value).__name__ + ": " + brief(value))
+
+
+def card_differences(own, pinned):
+    """Name every key by which a TASK.json original_card differs from its pin."""
+    if not isinstance(own, dict):
+        return "TASK.json original_card is " + type(own).__name__ + ", expected a JSON object"
+    details = []
+    missing = [key for key in pinned if key not in own]
+    extra = [key for key in own if key not in pinned]
+    if missing:
+        details.append("missing keys: " + ", ".join(missing))
+    if extra:
+        details.append("unexpected keys: " + ", ".join(extra))
+    for key in (key for key in pinned if key in own and own[key] != pinned[key]):
+        details.append(key + " differs (TASK.json: " + brief(own[key]) + "; pinned: " + brief(pinned[key]) + ")")
+    return "; ".join(details) or "cards compare unequal without a key difference"
+
+
+def source_pin(row, base):
+    """Resolve one SOURCES.json row to its exact Git object expression.
+
+    Rows without an explicit pin keep the historical base_commit:<path> form.
+    A file vendored from a pull-request head is pinned exactly with
+    head:<40-hex sha>:<path>, so its bytes resolve at that commit, not at the
+    package base. An explicit but unparseable pin fails closed.
+    """
+    name = row["path"]
+    pin = row.get("pin")
+    if pin is None:
+        return base + ":" + name
+    if pin == "base_commit:" + name:
+        return base + ":" + name
+    # Git filenames can contain LF; it is part of the exact path, not a delimiter.
+    match = re.fullmatch(r"head:([0-9a-f]{40}):(.+)", pin, re.DOTALL) if isinstance(pin, str) else None
+    if match is not None and match.group(2) == name:
+        return match.group(1) + ":" + name
+    raise ValueError("SOURCES.json pin for " + name + " is not a supported pin form: " + brief(pin)
+                     + "; accepted pin forms are base_commit:<path> and head:<40-hex sha>:<path>")
+
+
+def validate(root, package, check_pins=True):
+    parts = PurePosixPath(package).parts
+    require(len(parts) == 2 and parts[0] == "research" and re.fullmatch(r"[a-z0-9][a-z0-9-]*", parts[1]),
+            "package must be research/<slug>")
+    data = {}
+    for name in ("TASK.json", "SOURCES.json", "VERIFY.json"):
+        data[name] = json.loads(relative_file(root, package + "/" + name).read_text(encoding="utf-8"))
+        version = require_key(data[name], "schema_version", name)
+        require(version == 1, name + ".schema_version must be 1; found " + brief(version))
+    task, sources, manifest = (data[n] for n in ("TASK.json", "SOURCES.json", "VERIFY.json"))
+    scope_status = require_key(task, "scope_status", "TASK.json", "unchanged, refined or changed")
+    require(scope_status in ("unchanged", "refined", "changed"),
+            "TASK.json.scope_status must be unchanged, refined or changed; found " + brief(scope_status))
+    for field in ("actual_scope", "bottleneck_link", "stop_rule", "evidence", "author", "ai_assistance"):
+        require_text(task, field, "TASK.json")
+    if scope_status == "unchanged":
+        question = require_key(require_key(task, "original_card", "TASK.json",
+                                           "the pinned catalogue card object"),
+                               "question", "TASK.json.original_card")
+        require(task["actual_scope"] == question,
+                "different wording/scope requires refined or changed plus a reason"
+                + " (TASK.json.actual_scope " + brief(task["actual_scope"])
+                + " differs from TASK.json.original_card.question " + brief(question) + ")")
+    else:
+        require_text(task, "scope_change_reason", "TASK.json",
+                     "a non-empty string without TODO explaining the scope refinement/change")
+    outcome = require_key(task, "outcome", "TASK.json",
+                          "partial, completed, blocked or negative-result")
+    require(outcome in ("partial", "completed", "blocked", "negative-result"),
+            "TASK.json.outcome must be partial, completed, blocked or negative-result; found " + brief(outcome))
+    questions = task.get("open_questions")
+    require(isinstance(questions, list),
+            "TASK.json.open_questions must be a list; found " + type(questions).__name__ + ": " + brief(questions))
+    if not questions:
+        require_text(task, "no_open_questions_reason", "TASK.json",
+                     "a non-empty string without TODO explaining an empty next-question list")
+    for position, question in enumerate(questions):
+        for field in ("question", "why_it_matters", "first_step", "blocked_by"):
+            require_text(question, field, "TASK.json.open_questions[" + str(position) + "]")
+    readme = relative_file(root, package + "/README.md").read_text(encoding="utf-8")
+    require("## Open next questions" in readme, "README.md needs an \"## Open next questions\" section")
+    status = require_key(manifest, "status", "VERIFY.json")
+    require(status == "ready",
+            "VERIFY.json.status must be \"ready\"; complete the draft before requesting replay; found " + brief(status))
+    python = require_key(manifest, "python", "VERIFY.json")
+    require(python == "3.12",
+            "VERIFY.json.python must be \"3.12\" (generic replay currently uses Python 3.12); found " + brief(python))
+    requirements = manifest.get("requirements", [])
+    require(isinstance(requirements, list),
+            "VERIFY.json.requirements must be a list of exact \"name==version\" pins; found "
+            + type(requirements).__name__ + ": " + brief(requirements))
+    require(len(requirements) == len(set(requirements)), "VERIFY.json.requirements must not repeat a pin")
+    for item in requirements:
+        require(isinstance(item, str)
+                and re.fullmatch(r"(?:numpy|sympy|scipy)==[0-9]+(?:\.[0-9]+){1,2}", item),
+                "generic CI supports exact numpy/sympy/scipy pins; use a dedicated workflow for other environments"
+                + "; offending entry: " + brief(item))
+    names = [item.split("==")[0] for item in requirements]
+    require(len(names) == len(set(names)), "declare only one version per dependency")
+    # Validation already treats an omitted list as empty; execution must receive
+    # that same default without rewriting the contributor's manifest on disk.
+    manifest["requirements"] = requirements
+    commands = manifest.get("commands")
+    require(isinstance(commands, list) and 1 <= len(commands) <= 8,
+            "VERIFY.json.commands must be a list of 1..8 explicit verification commands; found "
+            + type(commands).__name__ + ": " + brief(commands))
+    total = 0
+    for position, command in enumerate(commands):
+        path = "VERIFY.json.commands[" + str(position) + "]"
+        require(isinstance(command, dict),
+                path + " must be a JSON object; found " + type(command).__name__ + ": " + brief(command))
+        argv = command.get("argv")
+        require(isinstance(argv, list) and len(argv) >= 2 and all(isinstance(a, str) for a in argv),
+                path + ".argv must be a list of at least 2 strings; found " + brief(argv))
+        require(argv[0] == "{python}", path + ".argv must explicitly use {python}; no implicit shell")
+        require_text(command, "checks", path, "a non-empty string without TODO describing command coverage")
+        seconds = command.get("timeout_seconds")
+        require(type(seconds) is int,
+                path + ".timeout_seconds must be an integer number of seconds; found "
+                + type(seconds).__name__ + ": " + brief(seconds))
+        require(1 <= seconds <= 600,
+                path + ".timeout_seconds " + str(seconds)
+                + (" exceeds the 600 s per-command cap" if seconds > 600
+                   else " is below the 1 s per-command minimum"))
+        total += seconds
+    require(total <= 1200, "declared replay budget " + str(total)
+            + " s (sum of timeout_seconds) exceeds the 1200 s total cap"
+            + "; use a dedicated job for larger checks")
+    inputs = manifest.get("inputs")
+    require(isinstance(inputs, list),
+            "VERIFY.json.inputs must be a list of canonical repository-relative paths; found "
+            + type(inputs).__name__ + ": " + brief(inputs))
+    tracked = tracked_input_paths(root)
+    for name in inputs:
+        symlink_free_relative_path(root, name)
+        require_tracked_input(name, tracked)
+        relative_file(root, name)
+    files = require_key(sources, "files", "SOURCES.json")
+    require(files, "SOURCES.json.files is empty; declare the source inventory")
+    base = require_key(sources, "base_commit", "SOURCES.json", "a 40-64 hex string pinning an exact base commit")
+    require(isinstance(base, str) and re.fullmatch(r"[0-9a-f]{40,64}", base),
+            "SOURCES.json.base_commit must be a 40-64 hex string pinning an exact base commit; found " + brief(base))
+    task_base = require_key(task, "base_commit", "TASK.json",
+                            "a 40-64 hex string equal to SOURCES.json.base_commit")
+    require(task_base == base, "TASK.json.base_commit " + brief(task_base)
+            + " must equal SOURCES.json.base_commit " + brief(base))
+    for row in files:
+        require(isinstance(row, dict) and isinstance(row.get("path"), str),
+                "SOURCES.json.files rows must be JSON objects with a string path; offending row: " + brief(row))
+        require(row.get("usage") in ("input", "provenance"),
+                "SOURCES.json.files row " + row["path"] + " must declare usage \"input\" or \"provenance\"; found "
+                + brief(row.get("usage")))
+    undeclared = sorted({r["path"] for r in sources["files"] if r["usage"] == "input"} - set(inputs))
+    require(not undeclared,
+            "every SOURCES.json files row with usage \"input\" must also be declared in VERIFY.json inputs"
+            + " (they drive CI invalidation); undeclared: " + ", ".join(undeclared))
+    if check_pins:
+        catalog_name = "docs/research/agent-task-catalog.json"
+        require(catalog_name in {r["path"] for r in sources["files"]},
+                "SOURCES.json.files must pin the originating task catalogue " + catalog_name
+                + " (a provenance row pinned at base_commit)")
+        names = [r["path"] for r in sources["files"]]
+        for name in names:
+            p = PurePosixPath(name)
+            require(not p.is_absolute() and ".." not in p.parts, "invalid source path")
+        specs = [source_pin(row, sources["base_commit"]) for row in sources["files"]]
+        require(all(spec == sources["base_commit"] + ":" + catalog_name
+                    for name, spec in zip(names, specs) if name == catalog_name),
+                "originating task catalogue must be pinned at base_commit")
+        with closing(git_blobs(root, specs)) as objects:
+            for index, (obj, pinned) in enumerate(objects):
+                row = sources["files"][index]
+                name = row["path"]
+                require(obj == row["git_blob"], "source blob provenance mismatch: " + name)
+                require(hashlib.sha256(pinned).hexdigest() == row["sha256"], "source SHA256 provenance mismatch: " + name)
+                if row["usage"] == "input":
+                    require(pinned == relative_file(root, name).read_bytes(), "working source drift: " + name)
+                if name == catalog_name:
+                    catalog = json.loads(pinned)
+        cards = [t for tr in catalog["tracks"] for t in tr["tasks"] if t["id"] == task["task_id"]]
+        require(len(cards) == 1,
+                "TASK.json task_id " + brief(task["task_id"]) + " matches " + str(len(cards))
+                + " cards in pinned " + catalog_name + " at base_commit " + sources["base_commit"]
+                + "; need exactly one")
+        original_card = require_key(task, "original_card", "TASK.json",
+                                    "the pinned catalogue card object (copy --print-card output verbatim)")
+        if original_card != cards[0]:
+            raise ValueError("original card in TASK.json must equal the pinned catalogue card object exactly; "
+                             "copy it verbatim from " + catalog_name + " at base_commit " + sources["base_commit"]
+                             + ": " + card_differences(original_card, cards[0]))
+    return task, manifest
+
+
+def catalogue_card(root, package, task_id):
+    """The exact original_card object a hand-authored TASK.json must copy.
+
+    Reads the catalogue blob pinned at the package base commit, never the
+    working tree, because validate() compares original_card against that pin.
+    """
+    sources = json.loads(relative_file(root, package + "/SOURCES.json").read_text(encoding="utf-8"))
+    name = "docs/research/agent-task-catalog.json"
+    rows = require_key(sources, "files", "SOURCES.json")
+    row = next((r for r in rows if isinstance(r, dict) and r.get("path") == name), None)
+    require(row is not None, "SOURCES.json.files must pin the originating task catalogue " + name)
+    base = require_key(sources, "base_commit", "SOURCES.json", "a 40-64 hex string pinning an exact base commit")
+    spec = source_pin(row, base)
+    require(spec == base + ":" + name, "originating task catalogue must be pinned at base_commit")
+    catalog = json.loads(git(root, "show", spec))
+    cards = [t for tr in catalog["tracks"] for t in tr["tasks"] if t["id"] == task_id]
+    require(len(cards) == 1,
+            "task_id " + brief(task_id) + " matches " + str(len(cards))
+            + " cards in pinned " + name + " at base_commit " + base + "; need exactly one")
+    return cards[0]
+
+
+_WINDOWS_GATE = r"""
+import ctypes
+from ctypes import wintypes
+import json
+import subprocess
+import sys
+api = ctypes.WinDLL('kernel32', use_last_error=True)
+api.OpenEventW.argtypes = [wintypes.DWORD, wintypes.BOOL, wintypes.LPCWSTR]
+api.OpenEventW.restype = wintypes.HANDLE
+api.WaitForSingleObject.argtypes = [wintypes.HANDLE, wintypes.DWORD]
+api.WaitForSingleObject.restype = wintypes.DWORD
+api.CloseHandle.argtypes = [wintypes.HANDLE]
+api.CloseHandle.restype = wintypes.BOOL
+event = api.OpenEventW(0x00100000, False, sys.argv[1])
+if not event:
+    raise ctypes.WinError(ctypes.get_last_error())
+try:
+    if api.WaitForSingleObject(event, 30000) != 0:
+        raise RuntimeError('replay ownership gate was not released')
+finally:
+    api.CloseHandle(event)
+# No verification command or descendant starts until the parent owns this job.
+sys.exit(subprocess.call(json.loads(sys.argv[2])))
+"""
+
+def run_windows_command(argv, cwd, timeout, env):
+    """Own ordinary verification descendants even after their leader exits.
+
+    The gated launcher joins a kill-on-close Job Object before it may spawn
+    the requested command. A late taskkill cannot recover an exited leader's
+    tree. Job handles are not inherited and breakaway is not enabled.
+    """
+    import ctypes
+    from ctypes import wintypes
+    import time
+    import uuid
+
+    class BasicLimits(ctypes.Structure):
+        _fields_ = [("ProcessTime", ctypes.c_int64), ("JobTime", ctypes.c_int64),
+                    ("Flags", wintypes.DWORD), ("MinWorkingSet", ctypes.c_size_t),
+                    ("MaxWorkingSet", ctypes.c_size_t), ("ActiveProcessLimit", wintypes.DWORD),
+                    ("Affinity", ctypes.c_size_t), ("Priority", wintypes.DWORD),
+                    ("Scheduling", wintypes.DWORD)]
+
+    class IOCounts(ctypes.Structure):
+        _fields_ = [(name, ctypes.c_uint64) for name in
+                    ("ReadOps", "WriteOps", "OtherOps", "ReadBytes", "WriteBytes", "OtherBytes")]
+
+    class ExtendedLimits(ctypes.Structure):
+        _fields_ = [("Basic", BasicLimits), ("IO", IOCounts),
+                    ("ProcessMemory", ctypes.c_size_t), ("JobMemory", ctypes.c_size_t),
+                    ("PeakProcessMemory", ctypes.c_size_t), ("PeakJobMemory", ctypes.c_size_t)]
+
+    class Accounting(ctypes.Structure):
+        _fields_ = [(name, ctypes.c_int64) for name in
+                    ("UserTime", "KernelTime", "PeriodUserTime", "PeriodKernelTime")] + [
+                    (name, wintypes.DWORD) for name in
+                    ("PageFaults", "TotalProcesses", "ActiveProcesses", "TerminatedProcesses")]
+
+    api = ctypes.WinDLL("kernel32", use_last_error=True)
+
+    def native(name, result, *arguments):
+        fn = getattr(api, name)
+        fn.restype, fn.argtypes = result, arguments
+        return fn
+
+    handle, dword, boolean = wintypes.HANDLE, wintypes.DWORD, wintypes.BOOL
+    create_job = native("CreateJobObjectW", handle, ctypes.c_void_p, wintypes.LPCWSTR)
+    set_info = native("SetInformationJobObject", boolean, handle, ctypes.c_int, ctypes.c_void_p, dword)
+    assign = native("AssignProcessToJobObject", boolean, handle, handle)
+    terminate = native("TerminateJobObject", boolean, handle, wintypes.UINT)
+    query = native("QueryInformationJobObject", boolean, handle, ctypes.c_int,
+                   ctypes.c_void_p, dword, ctypes.c_void_p)
+    create_event = native("CreateEventW", handle, ctypes.c_void_p, boolean, boolean, wintypes.LPCWSTR)
+    set_event = native("SetEvent", boolean, handle)
+    close = native("CloseHandle", boolean, handle)
+
+    def checked(ok):
+        if not ok:
+            raise ctypes.WinError(ctypes.get_last_error())
+        return ok
+
+    job = checked(create_job(None, None))
+    event, process, assigned = None, None, False
+    try:
+        limits = ExtendedLimits()
+        limits.Basic.Flags = 0x2000  # JOB_OBJECT_LIMIT_KILL_ON_JOB_CLOSE
+        checked(set_info(job, 9, ctypes.byref(limits), ctypes.sizeof(limits)))
+        name = "Local\\research-replay-" + uuid.uuid4().hex
+        event = checked(create_event(None, True, False, name))
+        # A name collision must not attach to an already-signaled event.
+        if ctypes.get_last_error() == 183:
+            raise ValueError("replay ownership gate name already exists")
+        process = subprocess.Popen(
+            # The gate itself must not run sitecustomize/PYTHONPATH startup
+            # code before ownership. The requested command retains env/argv.
+            # Windows accepts Unicode argv directly. ASCII JSON escaping can
+            # expand an otherwise valid command past its UTF-16 launch limit.
+            [sys.executable, "-I", "-S", "-c", _WINDOWS_GATE, name,
+             json.dumps(argv, ensure_ascii=False)],
+            cwd=cwd, env=env, start_new_session=True)
+        checked(assign(job, int(process._handle)))
+        assigned = True
+        checked(set_event(event))
+        try:
+            return process.wait(timeout=timeout)
+        except subprocess.TimeoutExpired:
+            raise ValueError("verification timed out") from None
+    finally:
+        try:
+            if process is not None:
+                if assigned:
+                    checked(terminate(job, 1))
+                    # Termination is asynchronous. Require the job to report
+                    # no active processes before releasing its ownership handle.
+                    deadline = time.monotonic() + 10
+                    while True:
+                        state = Accounting()
+                        checked(query(job, 1, ctypes.byref(state), ctypes.sizeof(state), None))
+                        if not state.ActiveProcesses:
+                            break
+                        if time.monotonic() >= deadline:
+                            raise ValueError("verification process cleanup timed out")
+                        time.sleep(0.01)
+                elif process.poll() is None:
+                    # Assignment failed before the gate opened: no command child
+                    # exists, so only this known gated launcher needs stopping.
+                    process.kill()
+                process.wait(timeout=10)
+        finally:
+            try:
+                if event:
+                    checked(close(event))
+            finally:
+                checked(close(job))
+
+def run_command(argv, cwd, timeout):
+    # Assertion checks must not disappear because of the caller's environment.
+    # Keep explicit manifest options (including deliberate -O controls) intact.
+    # PYTHONPATH precedes the standard library on a child's sys.path, so a stray
+    # same-named module could end a verifier with exit code 0 before any check.
+    env = os.environ.copy()
+    env.pop("PYTHONOPTIMIZE", None)
+    # Ambient inspection can turn a verifier exception into a successful REPL
+    # exit at terminal EOF. Keep explicit -i and the caller's stdin unchanged.
+    env.pop("PYTHONINSPECT", None)
+    env.pop("PYTHONPATH", None)
+    if os.name == "nt":
+        code = run_windows_command(argv, cwd, timeout, env)
+        require(code == 0, f"verification command exited {code}")
+        return
+    previous_handler = None
+    terminating = False
+    waiting = False
+    process = None
+
+    def terminate(signum, frame):
+        nonlocal terminating
+        if not terminating:
+            terminating = True
+            # Only interrupt the protected wait. Launch/assignment and cleanup
+            # defer delivery; repeated signals cannot interrupt group cleanup.
+            if waiting:
+                raise SystemExit(128 + signum)
+
+    # Own a group for POSIX cleanup of this command and its descendants.
+    try:
+        if (threading.current_thread() is threading.main_thread()
+                and signal.getsignal(signal.SIGTERM) == signal.SIG_DFL):
+            previous_handler = signal.SIG_DFL
+            signal.signal(signal.SIGTERM, terminate)
+        if terminating:
+            raise SystemExit(143)
+        process = subprocess.Popen(argv, cwd=cwd, env=env, start_new_session=True)
+        try:
+            try:
+                waiting = True
+                if terminating:
+                    raise SystemExit(143)
+                code = process.wait(timeout=timeout)
+            finally:
+                waiting = False
+        except subprocess.TimeoutExpired:
+            raise ValueError("verification timed out") from None
+        require(code == 0, f"verification command exited {code}")
+    finally:
+        try:
+            if process is not None:
+                if hasattr(os, "killpg"):
+                    # The leader may have exited while descendants hold its group.
+                    try:
+                        os.killpg(process.pid, signal.SIGKILL)
+                    except ProcessLookupError:
+                        pass
+                elif process.poll() is None:
+                    subprocess.run(["taskkill", "/F", "/T", "/PID", str(process.pid)], capture_output=True)
+                process.wait()
+        finally:
+            if previous_handler is not None:
+                signal.signal(signal.SIGTERM, previous_handler)
+    if terminating:
+        raise SystemExit(143)
+
+
+def isolated_python_argv(argv, cache_directory):
+    """Place our cache option after interpreter flags, before the entry point.
+
+    -B prevents writes, not reads of existing .pyc files. A fresh namespace
+    keeps preexisting source-adjacent and externally configured caches out of
+    this registered interpreter. It is not inherited by child interpreters.
+    """
+    require(argv and argv[0] == sys.executable, "cache isolation requires the registered Python interpreter")
+    index = 1
+    options = [argv[0]]
+    while index < len(argv):
+        option = argv[index]
+        if option in ("-", "--") or not option.startswith("-"):
+            break
+        if option == "--check-hash-based-pycs":
+            require(index + 1 < len(argv), "missing Python hash-cache option argument")
+            options.extend(argv[index:index + 2])
+            index += 2
+            continue
+        if option.startswith("--"):
+            options.append(option)
+            index += 1
+            continue
+        # Python permits combined short flags, attached -c/-m payloads, and
+        # attached or separate -W/-X arguments. Stop scanning an option once
+        # its argument begins: letters inside that argument are not flags.
+        entry = False
+        consumed = 1
+        replace_cache = False
+        for offset, flag in enumerate(option[1:], start=1):
+            if flag in "cm":
+                entry = True
+                break
+            if flag in "WX":
+                if offset == len(option) - 1:
+                    require(index + 1 < len(argv), "missing Python interpreter option argument")
+                    consumed = 2
+                value = argv[index + 1] if consumed == 2 else option[offset + 1:]
+                if flag == "X" and value.split("=", 1)[0] == "pycache_prefix":
+                    replace_cache = True
+                    if offset > 1:
+                        options.append(option[:offset])
+                break
+        if entry:
+            break
+        if not replace_cache:
+            options.extend(argv[index:index + consumed])
+        index += consumed
+    # CPython's effective prefix can use the first duplicate -X value even
+    # when sys._xoptions shows the last. Remove only earlier cache-prefix
+    # settings; script arguments remain untouched, even when spelled -X.
+    return [*options, "-X", "pycache_prefix=" + str(cache_directory), *argv[index:]]
+
+
+def run_python_replay(argv, cwd, timeout):
+    with tempfile.TemporaryDirectory(prefix="research-replay-pycache-") as cache:
+        run_command(isolated_python_argv(argv, cache), cwd, timeout)
+
+
+def run_package(root, package, install=False):
+    task, manifest = validate(root, package)
+    require(sys.version_info[:2] == (3, 12), "run replay with Python 3.12 (metadata check is version-independent)")
+    if install and manifest["requirements"]:
+        run_command([sys.executable, "-m", "pip", "install", "--disable-pip-version-check", *manifest["requirements"]], root, 300)
+    for requirement in manifest["requirements"]:
+        name, version = requirement.split("==")
+        require(importlib.metadata.version(name) == version, "dependency version mismatch: " + requirement)
+    # Coverage labels are UTF-8 metadata but a redirected Windows stdout may
+    # use cp1252. Escape unrepresentable display characters instead of aborting
+    # before replay. This changes only our stream, not child encoding or env.
+    if hasattr(sys.stdout, "reconfigure"):
+        sys.stdout.reconfigure(errors="backslashreplace")
+    for command in manifest["commands"]:
+        argv = [sys.executable if item == "{python}" else item.replace("{package}", package) for item in command["argv"]]
+        print("CHECK " + command["checks"], flush=True)
+        run_python_replay(argv, root, command["timeout_seconds"])
+    print("PASS_REGISTERED_RESEARCH_PACKAGE " + package + " outcome=" + task["outcome"])
+
+
+def planning_manifests(root, tracked):
+    """Include deliberate sparse omissions without disguising deletions or drift.
+
+    The fallback follows the chooser's PR3102 contract: one stage-zero regular
+    skip-worktree index entry must match the exact HEAD mode and blob. This is
+    declaration discovery only, not permission to replay absent package code.
+    """
+    committed = {name for name in tracked
+                 if name.startswith("research/") and name.count("/") == 2
+                 and name.endswith("/VERIFY.json")}
+    # Explicit scandir retains error detection; only an absent directory is OK.
+    try:
+        with os.scandir(root / "research") as entries:
+            local = {Path(entry.path) / "VERIFY.json" for entry in entries}
+    except FileNotFoundError:
+        local = set()
+    present, missing = {}, set()
+    for path in sorted(local | {root / name for name in committed}):
+        name = path.relative_to(root).as_posix()
+        symlink_free_relative_path(root, name)
+        try:
+            mode = path.lstat().st_mode
+        except (FileNotFoundError, NotADirectoryError):
+            if name in committed:
+                missing.add(name)
+            continue
+        require(stat.S_ISREG(mode), "non-regular replay manifest: " + name)
+        present[name] = path
+    fallback = {}
+    if missing:
+        indexed, objects = {}, {}
+        for record in git(root, "ls-files", "-t", "--stage", "-z", "--", "research").split(b"\0"):
+            if not record:
+                continue
+            header, raw_name = record.split(b"\t", 1)
+            name = raw_name.decode("utf-8")
+            if name in missing:
+                indexed.setdefault(name, []).append(header.split())
+        for record in git(root, "ls-tree", "-r", "-z", "HEAD", "--", "research").split(b"\0"):
+            if not record:
+                continue
+            header, raw_name = record.split(b"\t", 1)
+            name = raw_name.decode("utf-8")
+            if name in missing:
+                objects[name] = header.split()
+        for name in sorted(missing):
+            metadata = objects.get(name, [])
+            require(len(metadata) == 3 and metadata[0] in (b"100644", b"100755")
+                    and metadata[1] == b"blob"
+                    and indexed.get(name) == [[b"S", metadata[0], metadata[2], b"0"]],
+                    "missing replay manifest is not an unchanged sparse HEAD input: " + name
+                    + "; materialize it or commit its intended deletion")
+            # A regular file occupying the package directory is not an omission.
+            require(not (root / name).parent.exists() or (root / name).parent.is_dir(),
+                    "non-directory replay package: " + name)
+        names = sorted(missing)
+        with closing(git_blobs(root, [objects[n][2].decode("ascii") for n in names])) as rows:
+            for (oid, raw), name in zip(rows, names):
+                require(oid.encode("ascii") == objects[name][2], "sparse manifest blob mismatch: " + name)
+                fallback[name] = raw
+    # Preserve Path's component ordering: package "a" precedes "a-extra".
+    for name in sorted(present.keys() | fallback.keys(), key=lambda name: PurePosixPath(name).parts):
+        yield root / name, fallback[name] if name in fallback else present[name].read_bytes(), name in fallback
+
+
+def plan_details(root, changed):
+    """One selection pass with exact causes; no replay or acceptance decision."""
+    changed = set(changed)
+    # A removed input is absent from HEAD, including an old case-only rename
+    # spelling on case-insensitive filesystems. Git's exact changed paths remain
+    # eligible so its consumer is selected, rather than rejected or skipped.
+    head_tracked = tracked_input_paths(root)
+    tracked = head_tracked | changed
+    replay_changed = sorted(changed.intersection({
+        "scripts/research_package.py", ".github/workflows/research-packages.yml",
+        ".github/workflows/research-package-batch.yml"}))
+    # Group literal Git paths once. Keep removed paths and exact spellings.
+    changed_packages = {}
+    for name in sorted(changed):
+        parts = name.split("/", 2)
+        if len(parts) == 3 and parts[0] == "research":
+            changed_packages.setdefault("/".join(parts[:2]), []).append(name)
+    packages = []
+    sparse_count = 0
+    for path, raw, sparse in planning_manifests(root, head_tracked):
+        sparse_count += sparse
+        package = path.parent.relative_to(root).as_posix()
+        manifest = json.loads(raw.decode("utf-8"))
+        # Parse only for selection; validate fully in the isolated replay job.
+        inputs = manifest.get("inputs", [])
+        require(isinstance(inputs, list), "declare input paths for CI invalidation")
+        for name in inputs:
+            # Do not require existence: a deleted input must still trigger replay.
+            symlink_free_relative_path(root, name)
+            require_tracked_input(name, tracked)
+        causes = {
+            "declared_inputs": sorted(changed.intersection(inputs)),
+            "package_files": changed_packages.get(package, []),
+            "shared_controls": replay_changed,
+        }
+        if any(causes.values()):
+            packages.append({"package": package, "causes": causes,
+                             "manifest_sha256": hashlib.sha256(raw).hexdigest()})
+    if sparse_count:
+        print(f"Planning includes {sparse_count} unchanged sparse manifests from HEAD; "
+              "materialize packages and inputs before replay.", file=sys.stderr)
+    return packages
+
+
+def plan(root, changed):
+    return [row["package"] for row in plan_details(root, changed)]
+
+
+def write_plan_explanation(path, base, head, changed, details):
+    """Publish a complete sidecar before stdout/GitHub matrix publication."""
+    matched = {name for row in details for names in row["causes"].values() for name in names}
+    report = {
+        "schema_version": 1, "base": base, "head": head,
+        "mode": "all-tracked" if base is None else "commit-diff",
+        "scope": "Selection from working or authenticated sparse HEAD manifests, not replay or mathematical acceptance. "
+                 "Manifest hashes bind the declarations read; checkout must remain stable.",
+        "changed_paths": sorted(set(changed) - {""}), "selected": details,
+        "unmatched_paths": sorted(set(changed) - matched - {""}),
+    }
+    fd, temporary = tempfile.mkstemp(prefix=".replay-plan-", dir=path.parent)
+    try:
+        with os.fdopen(fd, "w", encoding="utf-8") as stream:
+            json.dump(report, stream, indent=2)
+            stream.write("\n")
+        os.replace(temporary, path)
+    finally:
+        Path(temporary).unlink(missing_ok=True)
+
+
+def replay_matrix(packages, batch_size=None):
+    """Retain the flat CLI format, or group complete coverage into bounded matrices."""
+    if batch_size is None:
+        return {"include": [{"package": p} for p in packages]}
+    require(type(batch_size) is int and 1 <= batch_size <= 256,
+            "matrix batch size must be 1..256")
+    batches = [packages[i:i + batch_size] for i in range(0, len(packages), batch_size)]
+    require(len(batches) <= 256,
+            "more than 256 matrix batches required; no packages were truncated")
+    return {"include": [{"packages": batch} for batch in batches]}
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument("--package")
+    ap.add_argument("--check-only", action="store_true")
+    ap.add_argument("--print-card", metavar="TASK_ID",
+                    help="print the exact pinned catalogue card object to copy into TASK.json original_card")
+    ap.add_argument("--install-deps", action="store_true", help="explicit opt-in to install manifest's allowed pinned dependencies")
+    ap.add_argument("--changed-since", help="plan affected opt-in packages relative to this Git commit")
+    ap.add_argument("--github-output", type=Path)
+    ap.add_argument("--explain-plan", type=Path,
+                    help="write exact replay-selection causes to JSON; matrix output stays unchanged")
+    ap.add_argument("--matrix-batch-size", type=int,
+                    help="group planned packages for bounded reusable-workflow matrices (1..256)")
+    args = ap.parse_args()
+    if args.explain_plan and (not args.changed_since or args.package or args.print_card):
+        ap.error("--explain-plan requires --changed-since without --package or --print-card")
+    if args.explain_plan and args.github_output and args.explain_plan.resolve() == args.github_output.resolve():
+        ap.error("--explain-plan and --github-output must use different files")
+    try:
+        if args.print_card:
+            require(args.package,
+                    "--print-card needs --package research/<slug> to resolve its pinned catalogue")
+            sys.stdout.write(json.dumps(catalogue_card(ROOT, args.package, args.print_card), indent=2) + "\n")
+        elif args.changed_since:
+            if set(args.changed_since) == {"0"}:
+                base = None
+                changed = git(ROOT, "ls-files", "-z").decode().split("\0")
+            else:
+                base = git(ROOT, "rev-parse", "--verify", args.changed_since + "^{commit}").decode().strip()
+                # A rename must invalidate both the removed input and its new path.
+                changed = git(ROOT, "diff", "--no-renames", "--name-only", "-z", base, "HEAD").decode().split("\0")
+            details = plan_details(ROOT, changed)
+            packages = [row["package"] for row in details]
+            matrix = json.dumps(replay_matrix(packages, args.matrix_batch_size))
+            if args.explain_plan:
+                head = git(ROOT, "rev-parse", "--verify", "HEAD^{commit}").decode().strip()
+                write_plan_explanation(args.explain_plan, base, head, changed, details)
+            print(matrix)
+            if args.github_output:
+                with args.github_output.open("a", encoding="utf-8") as out:
+                    out.write(f"matrix={matrix}\ncount={len(packages)}\n")
+        elif args.package:
+            if args.check_only:
+                validate(ROOT, args.package)
+                print("PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)")
+            else:
+                run_package(ROOT, args.package, args.install_deps)
+        else:
+            ap.error("use --package, --print-card or --changed-since")
+    except (OSError, ValueError, KeyError, TypeError, subprocess.SubprocessError, importlib.metadata.PackageNotFoundError) as exc:
+        ap.exit(1, str(exc) + "\n")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/owned-relation-independent-validation/engines/cost/check_cost.py b/research/owned-relation-independent-validation/engines/cost/check_cost.py
new file mode 100644
index 0000000000..5e89428037
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/check_cost.py
@@ -0,0 +1,127 @@
+#!/usr/bin/env python3
+"""Independent directed scalar and literal census screen of PR5377.
+
+Does not import/run either PR5377 interval engine or native verifier. Uses
+newly written atanh60/Taylor32 directed rationals; reuses the separately
+implemented PR5241 outer ledger formula only, explicitly below.
+Substantial OpenAI Codex assistance. Predecessors: Cao Yifan, Cinna Davis,
+zxv, Jacob Alan Sussman and Chris R/Clear1nsight.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from functools import lru_cache
+from pathlib import Path
+import ast,gzip,json,hashlib,time
+F=Path(__file__).resolve().parent/'frozen'
+UNIT=10**55
+def need(ok,s):
+    if not ok: raise ValueError(s)
+def dn(x):return Q(x.numerator*UNIT//x.denominator,UNIT)
+def up(x):return -dn(-x)
+def mul(a,b):
+    v=[x*y for x in a for y in b];return dn(min(v)),up(max(v))
+def div(a,b):
+    need(b[0]>0,'positive divisor');return mul(a,(1/b[1],1/b[0]))
+def logsmall(x):
+    z=(x-1)/(x+1);s=Q(0);term=z
+    need(0<=z<=Q(1,3),'log domain')
+    for j in range(60):s+=2*term/(2*j+1);term*=z*z
+    return dn(s),up(s+2*term/(121*(1-z*z)))
+@lru_cache(None)
+def logint(n):
+    k=n.bit_length()-1;a,b=logsmall(Q(n,2**k));c,d=logsmall(Q(2));return a+k*c,b+k*d
+def expone(x):
+    if x<0:
+        a,b=expone(-x);return dn(1/b),up(1/a)
+    s=term=Q(1);shift=0
+    while x>Q(1,32):x/=2;shift+=1
+    for j in range(1,33):term*=x/j;s+=term
+    tail=term*x/33/(1-x/34);a,b=dn(s),up(s+tail)
+    for _ in range(shift):a,b=dn(a*a),up(b*b)
+    return a,b
+@lru_cache(None)
+def power(r,t):
+    a,b=logint(r);a,b=sorted([a*t,b*t]);return expone(a)[0],expone(b)[1]
+def moment(p,t):return tuple(sum((n*power(r,t)[i] for r,n in p.items()),Q(0)) for i in (0,1))
+def minus(a,b):return a[0]-b[1],a[1]-b[0]
+def scalar(g):
+    if g[0] in ('copy','clear'):return 2
+    q=Q(*g[3:]) if g[0]=='add' else Q(*g[2:]);n,d=abs(q.numerator),q.denominator
+    need(n>0 and d&(d-1)==0,'dyadic scalar')
+    if g[0]=='scale':
+        need(n&(n-1)==0,'dyadic unit');return 2*(abs(n.bit_length()-d.bit_length())+int(q<0))
+    need(g[0]=='add','scalar opcode');return 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1)
+def read(n):
+    p=F/n;b=p.read_bytes();return json.loads(gzip.decompress(b) if n.endswith('.gz') else b)
+def enc(x):
+    if isinstance(x,Q):return str(x)
+    if isinstance(x,dict):return {str(k):enc(v) for k,v in x.items()}
+    if isinstance(x,(list,tuple)):return [enc(v) for v in x]
+    return x
+def main():
+    start=time.monotonic();src=read('ACTUAL-WORD.json.gz');cand=read('WORD.json.gz');ctl=read('controller-CONTROLLER.json');old=read('4610-round6-ARITHMETIC.json');author=read('RESULT.json')['arithmetic']
+    local={};cost={};T=Counter();P=Counter();orient=Counter();queries=0
+    c=cand['canonical']
+    for d,events in cand['programs'].items():
+        paid=Counter();cost[d]=0
+        for e in events:
+            if e[0] in ('climb','center'):paid[e[-1]]+=1
+            elif e[0]=='scalar':cost[d]+=scalar(e[1])
+        helpers=Counter(len(c['frames'][c['final'][i]])-len(c['frames'][c['start'][i]]) for i in range(224,632) if not (d=='backward' and i==230))
+        local[d]=(paid,helpers)
+        oldcost=sum(scalar(e[1]) for e in src['programs'][d] if e[0]=='scalar')
+        need(cost[d]-oldcost==(46 if d=='backward' else 0),'all changed scalar operations charged')
+    for e in ctl['physical_events']:
+        if e[0]=='LOCAL':
+            d='backward' if e[3] else 'forward';orient[d]+=1;P.update(local[d][0]);T.update(local[d][1])
+        elif e[0]=='QUERY_SHEAR':queries+=1;P[1]+=112
+        elif e[0]=='IDLE':P[8*len(e[2])]+=224
+    for term in ctl['diagonal']:T[1+8*sum(term[1:])]+=112
+    need(orient=={'backward':16,'forward':2} and queries==15,'literal controller orientations')
+    priorT=Counter({int(k):v for k,v in old['targets'].items()});priorP=Counter({int(k):v for k,v in old['paid'].items()});priorT[9]-=16;priorP[1]-=16;priorP[8]-=16
+    need(T==priorT and P==priorP,'old-to-new exact complete delta')
+    need(dict(T)=={int(k):v for k,v in author['targets'].items()} and dict(P)=={int(k):v for k,v in author['paid'].items()},'author invoice crosscheck')
+    need((sum(T.values()),sum(P.values()))==(10912,64372),'complete census')
+    masses=[sum(r*n for r,n in p.items()) for p in (T,P)];need(masses==[239742,238990],'rank masses')
+    k,s=Q('.00302235'),Q('.00302236');gap=(s-k)/7;t=1-s
+    lo,hi=Q('.00302238736347'),Q('.00302238736348')
+    signs=[minus(moment(T,1-x),moment(P,1-x)) for x in [lo,hi]]
+    need(signs[0][0]>0>signs[1][1] and k<s<lo,'root endpoints and strict headroom')
+    target,paid=moment(T,t),moment(P,t)
+    ratios={'alpha':div(paid,target),'gamma':div(moment(P,t+Q(1,5)),mul(power(20,Q(1,5)),target)),'delta':div((Q(sum(T.values())*21),)*2,mul(power(20,s),target))}
+    reserve=Q(1,10**9);theta=Q(63,64)
+    need(ratios['alpha'][1]<1-reserve and all(ratios[x][1]<Q(97,100) for x in ['gamma','delta']),'reserve and both charged tails')
+    for n,v in ratios.items():need(Q(author['strictification'][n]['lower'])<=v[0]<=v[1]<=Q(author['strictification'][n]['upper']),'author outward interval contains independent '+n)
+    normalized=1/(1+1024*reserve)+Q(4,2**32);eta=mul((t,t),power(145,-1024*s))
+    capacity={'normalized':normalized<1,'tail_block':Q(97,100)**128<Q(1,16),'total_tails':4*Q(97,100)**1024<Q(4,2**32),'split':20**64<21**63,'shifted_exits':2*(20**1024)**64<=(145**1024)**63,'eta':eta[0]>theta**1000,'initial_range':power(145,1024*s)[1]<2**1000}
+    H,j=31385200000000,44836;step=gap.denominator
+    capacity.update(height_encoding=H==step*j and gap==Q(1,700000000),height_domain=H>8*1024,integer_success=(H+1)**1000<2**j,preceding_grid_fails=(step*(j-1)+1)**1000>=2**(j-1))
+    need(all(capacity.values()),'finite compiler capacities')
+    # Concavity of log(step*j+1)-j*log(2)/1000 gives one positive
+    # crossing; success and preceding-grid failure establish grid minimality.
+    signed={r:T[r]-P[r] for r in T.keys()|P.keys()};derivative_lowers=[];away_uppers=[]
+    for i in range(16):
+        l,r=Q(i,320),Q(i+1,320);bound=Q(0)
+        for rank,n in signed.items():
+            term=mul(power(rank,1-r if n>0 else 1-l),logint(rank));bound+=n*term[0 if n>0 else 1]
+        derivative_lowers.append(bound)
+    for i in range(128):
+        l,r=Q(1,20)+Q(19*i,2560),Q(1,20)+Q(19*(i+1),2560)
+        away_uppers.append(sum(n*power(rank,1-l if n>0 else 1-r)[1 if n>0 else 0] for rank,n in signed.items()))
+    need(min(derivative_lowers)>0 and max(away_uppers)<0,'global fixed-profile root uniqueness')
+    # Independently transcribed selected5241 ledger, not the author ledger.
+    tree=ast.parse((F/'compiler.py').read_text());node=next(x for x in tree.body if isinstance(x,ast.FunctionDef) and x.name=='ledger');ns={'F':Q};exec(compile(ast.Module(body=[node],type_ignores=[]),str(F/'compiler.py'),'exec'),ns)
+    params=dict(kappa=k,tested_saving=s,complex_uniform_saving=k+6*gap,b=k+5*gap,a=k+4*gap,q=k+3*gap,bit_saving=Q('.0034'),epsilon=1-gap,beta=1-3*gap,r0=gap/10,stop=gap,layout=gap,d=gap)
+    m,strict,func=ns['ledger'](params)
+    for group,values in [('margins',m),('strict_checks',strict),('functional_checks',func)]:need(values=={n:Q(v) for n,v in author['outer'][group].items()},'54+4 outer values agree '+group)
+    need(len(strict)==54 and len(func)==4 and min(strict.values())>0 and min(func.values())>0,'complete outer inventory')
+    controls={}
+    for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':s}),('closed_epsilon',{'epsilon':Q(1)})]:
+        _,bad,_=ns['ledger'](dict(params,**patch));controls[name]=[n for n,v in bad.items() if v<=0];need(controls[name],'outer control '+name)
+    bit=author['ordinary_BIT'];ordinary=(1-Q(bit['atom']))*Q(bit['after_cover'])+Q(bit['atom'])*Q('.0000384599');need(Q(bit['ordinary_saving'])==ordinary and Q(bit['atom'])>ordinary>Q(bit['admitted'])>s,'unchanged ordinary BIT domain')
+    routes=(max(sum(x[0].values()) for x in local.values())+2*408+688+4)*1000
+    raw=18*10**7+15*1792+32*112*(len(ctl['physical_events'])+sum(len(ctl['boundaries'][x+'_program']) for x in ['left','right']))
+    need(routes==4806000 and max(cost.values())==158214 and routes+max(cost.values())<10**7 and raw==181098496<10**9,'fresh raw costs')
+    out=dict(status='PASS_INDEPENDENT_SCALAR_CENSUS_MOMENT_COMPILER_OUTER_SCREEN',head='c448d13c71908647f968b06cddb795ce7d288139',kappa=k,tested=s,gain=k-Q('.0030217758'),root=[lo,hi],root_signs=signs,targets=T,paid=P,rank_masses=masses,local_scalar=cost,local_routes=routes,raw=raw,ratios=ratios,normalized=normalized,capacity=capacity,eta=eta,derivative_upper=-min(derivative_lowers),away_moment_upper=max(away_uppers),outer_min=min(strict.values()),outer_strict_count=len(strict),outer_functional_count=len(func),controls=controls,gap=gap,uniform_saving=k+6*gap,H=H,j=j,seconds=time.monotonic()-start,independent_native_replay=False,expanded_word_materialized=False,scope='Finite scalar/census check. Physical replacement and all-f specialization reviewed separately; same five conditional assumptions retained. Raw bound is not an expanded precision/storage bound.',sha256={p.name:hashlib.sha256(p.read_bytes()).hexdigest() for p in F.iterdir() if p.is_file()})
+    print(json.dumps(enc(out),indent=2,sort_keys=True))
+if __name__=='__main__':main()
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/4610-round6-ARITHMETIC.json b/research/owned-relation-independent-validation/engines/cost/frozen/4610-round6-ARITHMETIC.json
new file mode 100644
index 0000000000..0fdb65f946
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/4610-round6-ARITHMETIC.json
@@ -0,0 +1,241 @@
+{
+  "compiler": {
+    "H": 38569300000000000,
+    "N": "2^38569300000000000",
+    "eta": {
+      "lower": "0.000000204535199106284215364833",
+      "upper": "0.000000204535199106284215364834"
+    },
+    "gap": "1/700000000000",
+    "integer_test_exponent": 55099,
+    "logarithm_power": 1000,
+    "theta": "63/64",
+    "uniform_saving": "1057621533/350000000000",
+    "word_materialized": false
+  },
+  "gain_over_PR4535": "4027/2500000000",
+  "kappa": "15108879/5000000000",
+  "local_helpers": {
+    "4": 28,
+    "7": 7,
+    "8": 47,
+    "9": 326
+  },
+  "local_paid": {
+    "1": 2201,
+    "2": 412,
+    "3": 510,
+    "4": 127,
+    "5": 40,
+    "8": 8
+  },
+  "margin_at_old_root_upper": [
+    "78072058023577019965454984044224523228758899702419408235/196159429230833773869868419475239575503198607639501078528",
+    "1249152928377232319447279744707592371660142395238823308861/3138550867693340381917894711603833208051177722232017256448"
+  ],
+  "native_receipt_sha256": "eec3b14241430b6c9f5de3cbf0e3d45a172d8071d2dccd2b59d56a1fbac3d428",
+  "negative_controls": {
+    "closed_epsilon": [
+      "epsilon_below_one",
+      "global_gamma_power_slack",
+      "actual_logarithmic_gamma_guard",
+      "source_axis_superpolynomial",
+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
+    ],
+    "closed_uniform": [
+      "new_complex_uniform_saving_above_b"
+    ],
+    "old_BIT": [
+      "actual_bit_above_effective"
+    ],
+    "unfunded_endpoint": [
+      "main_transform_above_kappa",
+      "global_coordinate_router_above_kappa",
+      "fused_gaussian_above_kappa",
+      "group_bit_router_above_kappa",
+      "boundary_algebraic_matrix_above_kappa"
+    ]
+  },
+  "nonrecursive": {
+    "local_routes": 4802000,
+    "local_scalar": 158168,
+    "raw_scalar_upper": 181098496
+  },
+  "ordinary_BIT": {
+    "admitted": "17/5000",
+    "after_cover": "69/20000",
+    "atom": "1/250",
+    "before_cover": "3459/1000000",
+    "ordinary_saving": "8590884599/2500000000000",
+    "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+  },
+  "outer": {
+    "functional_checks": {
+      "actual_new_BIT_stock_sublinear": "174299999999253/175000000000000",
+      "fixed_halo_explicit_metadata_branch": "13475000000001/175000000000",
+      "new_BIT_row_stock_sublinear_in_active_group": "697899999997009/700000000000000",
+      "new_semantic_group_guard": "3/700000000000"
+    },
+    "margins": {
+      "boundary_algebraic_matrix": "1480670144797884756937/490000000000000000000000",
+      "fused_gaussian": "1480670144793654270811/490000000000000000000000",
+      "global_coordinate_router": "264405383/87500000000",
+      "group_bit_router": "185083768186706783851/61250000000000000000000",
+      "group_scans": "349999999999/350000000000",
+      "main_transform": "1480670144097884756937/490000000000000000000000",
+      "microbox_face_corrections": "13475000000001/175000000000",
+      "polynomial_products": "699999999999/700000000000",
+      "sparse_union_movement": "200543170144797884756937/490000000000000000000000"
+    },
+    "parameters": {
+      "a": "264405383/87500000000",
+      "b": "423048613/140000000000",
+      "beta": "699999999997/700000000000",
+      "bit_saving": "17/5000",
+      "cap_xi": "445543170144097884756937/490000000000000000000000",
+      "complex_uniform_saving": "1057621533/350000000000",
+      "d": "1/700000000000",
+      "epsilon": "699999999999/700000000000",
+      "kappa": "15108879/5000000000",
+      "lambda_": "199395644839/200000000000",
+      "lambda_prime": "697884756937/700000000000",
+      "layout": "1/700000000000",
+      "q": "2115243063/700000000000",
+      "r0": "1/7000000000000",
+      "stop": "1/700000000000",
+      "tested_saving": "302177581/100000000000"
+    },
+    "strict_checks": {
+      "actual_bit_above_effective": "33094617/87500000000",
+      "actual_logarithmic_gamma_guard": "1/700000000000",
+      "actual_logarithmic_group_guard": "44456829856952115243063/245000000000000000000000",
+      "alpha_logarithm_absorption": "1/7000000000000",
+      "boundary_algebraic_matrix_above_kappa": "2797884756937/490000000000000000000000",
+      "cap_above_band": "200543170144097884756937/490000000000000000000000",
+      "cap_below_cell": "44456829855202115243063/490000000000000000000000",
+      "cap_below_phase_cell_power": "534456829855902115243063/490000000000000000000000",
+      "complex_above_effective": "1/700000000000",
+      "complex_below_one_over_32": "3951951387/140000000000",
+      "complex_endpoint": "1/350000000000",
+      "epsilon_below_one": "1/700000000000",
+      "epsilon_positive": "699999999999/700000000000",
+      "fine_prime_halo_umbrella": "7/2",
+      "fused_gaussian_above_kappa": "2793654270811/490000000000000000000000",
+      "gaussian_above_main": "347884756937/245000000000000000000000",
+      "global_coordinate_router_above_kappa": "1/175000000000",
+      "global_gamma_power_slack": "9/7000000000000",
+      "group_below_dimension": "1/350000000000",
+      "group_bit_router_above_kappa": "436706783851/61250000000000000000000",
+      "group_gauge_power_slack": "44456829856917115243063/245000000000000000000000",
+      "group_key_fits_record": "1/350000000000",
+      "group_positive": "699999999997/700000000000",
+      "group_scans_above_kappa": "348942378469/350000000000",
+      "halo_covers_generic_inverse_radius": "5",
+      "improvement_over_user_baseline": "645402690400418148631/500000000000000000000000",
+      "lambda_above_internal": "1/1400000000000",
+      "lambda_above_sigma": "3/1400000000000",
+      "lambda_above_tau": "1/1400000000000",
+      "lambda_prime_above_lambda": "1/1400000000000",
+      "lambda_prime_above_leaf": "279576951387/98000000000000000000000",
+      "leaf_saving_above_effective": "139576951387/98000000000000000000000",
+      "main_transform_above_kappa": "2097884756937/490000000000000000000000",
+      "membership_arithmetic_fits_record": "1/700000000000",
+      "microbox_face_corrections_above_kappa": "3368617797309/43750000000",
+      "microbox_halo_volume": "55300000000003/700000000000",
+      "new_complex_uniform_saving_above_b": "1/700000000000",
+      "new_semantic_guard_with_C1_one": "1/700000000000",
+      "polynomial_products_above_kappa": "697884756939/700000000000",
+      "positive_layout_slack": "1/700000000000",
+      "q_below_effective": "1/700000000000",
+      "q_below_internal": "1/700000000000",
+      "q_below_leaf": "279576951387/98000000000000000000000",
+      "q_positive": "2115243063/700000000000",
+      "short_record_fallback": "139576951387/140000000000",
+      "source_axis_superpolynomial": "1/700000000000",
+      "sparse_union_movement_above_kappa": "199062500002797884756937/490000000000000000000000",
+      "stop_below_one": "699999999999/700000000000",
+      "stop_positive": "1/700000000000",
+      "strassen_integer_power_gap": "1951441519231",
+      "support_router_span": "3/700000000000",
+      "theta_positive_polynomial_power": "2",
+      "union_header_fits_record": "3/700000000000",
+      "union_tag_work_per_visit_fits_record": "3/700000000000"
+    }
+  },
+  "paid": {
+    "1": 41298,
+    "16": 448,
+    "2": 7416,
+    "24": 448,
+    "3": 9180,
+    "32": 448,
+    "4": 2286,
+    "40": 448,
+    "48": 448,
+    "5": 720,
+    "56": 448,
+    "64": 448,
+    "72": 224,
+    "8": 144
+  },
+  "paid_calls": 64404,
+  "productive_fields": 10928,
+  "rank_mass_surplus": 752,
+  "raw_root_interval": [
+    "302177587077/100000000000000",
+    "151088793539/50000000000000"
+  ],
+  "scope": "Exact changed-profile arithmetic only. Requires separately admitted changed native programs, paid transports and absolute phases. Retained compiler/native/precision/tape/analytic/recovery assumptions.",
+  "source_sha256": {
+    "research/fresh-helper-boundary/native.py": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29",
+    "research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326",
+    "research/joint-helper-lattice/CONTROLLER.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f",
+    "research/joint-helper-lattice/native_joint.py": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46",
+    "research/joint-helper-lattice/verify.py": "8eb13f77a94315f811612cb557a17edeecb6b9d9a75dfa238b112dd6520c336f",
+    "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85",
+    "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a",
+    "research/kappa-rebuild/bit/complex_controller_factor.py": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497",
+    "research/kappa-rebuild/bit/mixed_productive_bit.py": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e",
+    "research/kappa-round6-compiler-tightening-20261022/arithmetic.py": "960864e5427a1ca2c319a7b2dee292b6fe50bd5964830031e611591af10dac38",
+    "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15",
+    "research/query-thinned-controllers/RESULT.json": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f",
+    "research/query-thinned-controllers/controller.py": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2"
+  },
+  "status": "PASS_CHANGED_PROFILE_ARITHMETIC_NATIVE_ADMISSION_SEPARATE",
+  "strictification": {
+    "alpha": {
+      "lower": "0.999999999936687383304469699479",
+      "upper": "0.999999999936687383304469699480"
+    },
+    "cutoff": 20,
+    "delta": {
+      "lower": "0.958285308639504859158849914083",
+      "upper": "0.958285308639504859158849914084"
+    },
+    "floor": 21,
+    "gamma": {
+      "lower": "0.956217509753795293454516855483",
+      "upper": "0.956217509753795293454516855484"
+    },
+    "normalized_paid_upper": "104857600097656251/104857601073741824",
+    "power": 1024,
+    "tail_offset": "1/5",
+    "tested": "302177581/100000000000"
+  },
+  "targets": {
+    "145": 224,
+    "17": 448,
+    "25": 448,
+    "33": 448,
+    "4": 504,
+    "41": 448,
+    "49": 448,
+    "57": 448,
+    "65": 448,
+    "7": 126,
+    "73": 224,
+    "8": 846,
+    "9": 5868
+  }
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/4610review-pinned.txt b/research/owned-relation-independent-validation/engines/cost/frozen/4610review-pinned.txt
new file mode 100644
index 0000000000..bf5ff049da
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/4610review-pinned.txt
@@ -0,0 +1,137 @@
+# PR4610: conditional admission through the PR5241 audit
+
+**Pass under the unchanged five selected framework assumptions:**
+κ = 15108879/5000000000 = **0.0030217758**.
+This is Cao Yifan / intqwq's construction at
+`20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`, independently audited in
+Chris R / Clear1nsight's PR5241 at
+`13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2`.
+Maintainer review: Douglas Colkitt's OpenAI assistant, with substantial AI
+assistance. Apache-2.0. No independent human or end-to-end formal proof is claimed.
+
+## Changed construction and exact coverage
+
+The accepted object is the frozen round3 native word and round6 compiler point,
+not every exploratory claim or intermediate result in PR4610. Relative to
+selected PR4470, 20 native binary maps and 26 helper boundary interfaces change;
+all twelve shared prelude maps and the main endpoints remain fixed. The complete
+local paid profile becomes `{1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}`.
+The productive helper profile remains `{4:28, 7:7, 8:47, 9:326}`.
+
+The fresh audit passes all eleven required stages. It checks 480 signed warp
+events, 180 signed warp classes in both orientations, all 408 helper inputs
+through 34 oriented endpoint classes, and all 5,710 oriented paid classes
+covering 6,596 local event instances. No earlier receipt's PASS flag substitutes
+for phase correctness. The frozen paid catalogue is candidate data; its
+compiler is not imported by the acceptance path.
+
+The reviewer inspected the independent Clifford evaluation and phase test:
+equality on the 18 Pauli generators identifies the operator up to a scalar;
+equality on an exactly normalized nonzero state fixes that scalar. All factors
+are validated monomial/Clifford operations, so this is a complete finite-operator
+argument, not a sample of input vectors. Phase-only mutations preserve the
+tableau and are nevertheless rejected. Positive recursive ranks are checked
+against the actual nested bases, including all eight owned rank-eight calls.
+
+The chronological symbolic interpreter tracks all 632 independent persistent
+inputs, current frames, inverse orientations and the owned C0. It verifies a
+free-group identity on arbitrary dirty inputs, with each helper restored and
+only the owned stream erased. Left multiplication on reduced free words is
+injective; its dictionary update does not silently discard colliding words.
+Main chart and scalar opcode/coefficient sequences are compared to retained
+source. No arbitrary borrowed input is treated as initialized workspace.
+
+## Uniform lift and physical specialization
+
+We reviewed PROOF.md and SPECIALIZATION.md against the pinned PR4359, PR4416
+and PR4470 reviews and the general-frame/compact-movement notes. The retained
+contract already permits arbitrary fixed nested binary frames with independent
+two-sided monomial adapters. The new recipes lie in that class: invertible
+nine-bit affine maps and Z4 quadratic phases. Elimination, translations and
+phase operations need at most 171 primitive records per monomial, hence at
+most 342 for two adapters, within the retained 1000-record raw allowance.
+This counts retained physical primitive records, not constant literal tape
+steps at arbitrary column multiplicity.
+
+Tensor power is applied to products and individual operator factors. The scalar
+ADD program instead lifts by evaluation of its proved free-group identity.
+Tensor power is never distributed over a sum. Absolute phase is repeated once
+per column. Algebraic equality holds at every positive multiplicity; the
+physical tariff retains its source hypotheses on complete slots, restored
+controls, record fibers and the f,p domain. Spectators and independent ownership
+remain explicit. Thus the changed catalogue does not add a candidate-specific
+oracle to the old assumptions.
+
+Expanded template counts, owned banks, routing and coefficient envelopes must
+be substituted into the retained precision/stock formulas. The new enormous
+compiler does not inherit an old numerical template-size cap. This remains a
+conditional application of the selected physical and analytic framework;
+finite computations do not independently prove its fixed-tape, precision or
+integer-recovery theorems.
+
+## Invoice, completion and outer transfer
+
+The unchanged p16/query-thinned controller is source-identical to the selected
+review. The audit independently reconstructs its events and boundary programs;
+the previously reviewed Laurent endpoint and stage-zero commutation argument
+are reused with unchanged main operators. Eighteen full calls, fifteen thin
+queries, fifteen idle windows, all main/helper targets and owned centers give
+**64,404 paid calls and 10,928 productive fields**. Target and paid rank masses
+remain 239,886 and 239,134, giving surplus 752. Compared with PR4470 the whole
+paid histogram changes by `{-648 H1, +432 H2, +288 H3, -360 H4, +72 H5}`:
+216 fewer calls, without removing rank mass or reusing output credit.
+
+Two independently implemented directed interval engines check the freshly
+derived invoice. The raw crossing is bracketed by
+(.00302177587077, .00302177587078). The tested saving .00302177581 exceeds the
+claim .0030217758. The old selected invoice fails at the new claim; this is a
+changed-construction gain, not decimal refinement of the old crossing.
+
+At tensor power 1024, cutoff 20, completion floor 21 and tail shift 1/5,
+alpha < 1-10^-11 and both charged tail ratios are below 97/100. The complete
+bound `1/(1+1024*10^-11)+4/2^32 < 1` is checked exactly. The old 10^-9 reserve
+would fail here and is explicitly rejected. The reviewed product/completion
+and splitting arguments apply with these new constants and actual profiles.
+The compiler's sufficient integer test gives H=38,569,300,000,000,000 and
+N=2^H. This is a finite specified construction; no expanded word is materialized.
+
+The ordinary BIT interface is exactly equal to the selected source and admits
+.0034, above the required effective saving. Its already reviewed supplier and
+conversion are reused, not established anew by the complex checks. All nine
+outer cost rows, 54 strict predicates and four functional predicates pass.
+The minimum recorded strict predicate is 1/7,000,000,000,000. Both arithmetic
+engines retain the charged targets, owned centers and compiler tails.
+
+## Execution, provenance and invalidation
+
+COLD-REPLAY.json and BOUNDED-RUN.json record the complete serial CPython 3.12
+run: 137.25 seconds and 184,928 KiB peak sampled descendant RSS, below the
+660-second / 1 GiB guard. All 82 committed-byte bindings, canonical source
+ancestry and registered metadata/pins checks passed. No Lean, Docker, hosted
+Linux run or historical all-suite replay was performed.
+
+The current selected metadata is changing, but PR5241 authenticates the exact
+old PR4470 record as its baseline. The new reproduction entrypoint therefore
+exports that historical record from `certificates/checkpoints/frontier4470.json`
+to its original path, explicitly. The research package and scientific source
+bytes remain unchanged. Canonical Git objects are used only for ancestry and
+stored-blob checks; the mathematical code reads its closed exported input set.
+The source manifest also retains the prior reviewed foundation closure.
+
+Changes to frames, native phases, scalar chronology, helper endpoints,
+controller, actual ownership, paid completion, compiler parameters, source
+bytes or physical/outer contracts invalidate the affected review. Optional
+optimizers, claimed global optima and later scalar-compression variants are
+outside this acceptance. The result remains conditional on precisely the five
+PR4470 assumption records, copied without weakening or deletion.
+
+## Credit
+
+Cao Yifan / intqwq: changed construction and compiler point (PR4610).
+Chris R / Clear1nsight: complete independent admission package (PR5241).
+Cinna Davis /1337isnot1337: joint-helper, query-thinned controller and preceding
+construction chain. zxv: productive-helper native/compiler machinery.
+Jacob Alan Sussman: mixed-target recursion. Dugongue: transported frames and
+physical interfaces. Mihir Srivastava, Ryanson Jonathan and Mark / Matarener:
+retained independent checks and adversarial questions. All BIT, geometry,
+Clifford, precision and analytic contributors retain their earlier credit.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/4610validation-pinned.txt b/research/owned-relation-independent-validation/engines/cost/frozen/4610validation-pinned.txt
new file mode 100644
index 0000000000..98fa64f279
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/4610validation-pinned.txt
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_CONDITIONAL_CHANGED_CONSTRUCTION_REVIEW",
+  "construction_pr": 4610,
+  "construction_head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296",
+  "audit_pr": 5241,
+  "audit_head": "13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2",
+  "tested_repository_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "date": "2026-10-23",
+  "kappa": "15108879/5000000000",
+  "cold_replay": "COLD-REPLAY.json",
+  "cold_replay_sha256": "a5124421d0281bcc36ac08d3c1aae6f8768c77db92977ab9f31471ed33b65511",
+  "bounded_run": {
+    "command": [
+      "/usr/local/bin/python3.12",
+      "-B",
+      "/Users/colkitt/sith/toys/math/integerMult-review4610-20261023/research/final4610-independent-admission/verify.py",
+      "--repo",
+      "/Users/colkitt/sith/toys/math/integerMult-review4610-20261023",
+      "--receipt",
+      "/tmp/final4610-maintainer-20261023/COLD-REPLAY.json"
+    ],
+    "exit": 0,
+    "resource_stop": null,
+    "timeout_seconds": 660,
+    "seconds": 137.25,
+    "peak_sampled_rss_kib": 184928,
+    "log": "cold.log",
+    "log_sha256": "67f309119bbe03a48060e1e3904e1f64e9082a69a7c7ff4ae9fe08644f2f1011"
+  },
+  "source_preflight": "82 committed-byte bindings and canonical source ancestry passed; registered package metadata/pins passed.",
+  "stages": {
+    "all_helpers": "PASS_ALL408_HELPER_RELATIVE_OPERATORS_AND_ABSOLUTE_PHASES",
+    "arithmetic": "PASS_INDEPENDENT_COMPLETE_DIRECTED_MOMENTS_AND_OUTER",
+    "compiler": "PASS_INDEPENDENT_EXACT_FINITE_COMPILER_AND_58_OUTER",
+    "frame": "PASS_ALL480_SIGNED_WARP_EVENTS",
+    "helpers": "PASS_SCOPED_HELPER_CONTRACTS_UNIFORM_PREMISES_REMAIN",
+    "invoice": "PASS_COMPLETE_LITERAL_P16_INVOICE",
+    "lift": "PASS_SCOPED_TENSOR_BOOKKEEPING_CONTROLS",
+    "lineage": "PASS_EXACT_HELPER_PHASE_LINEAGE_MAP",
+    "native": "PASS_INDEPENDENT_ALL_180_NATIVE_PHASE_CLASSES",
+    "paid": "PASS_ALL_PAID_PAIR_PHASES_BOTH_ACTUAL_ORIENTATIONS",
+    "specialization": "PASS_EXACT_CATALOGUE_SPECIALIZATION_SCHEMA_AND_RAW_FINITE_TARIFF"
+  },
+  "inherited_assumptions": [
+    {
+      "id": "native_all_columns",
+      "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity."
+    },
+    {
+      "id": "owned_erasure",
+      "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts."
+    },
+    {
+      "id": "compiler",
+      "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract."
+    },
+    {
+      "id": "precision_tape",
+      "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template."
+    },
+    {
+      "id": "analytic_recovery",
+      "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework."
+    }
+  ],
+  "independent_human_review": false,
+  "Lean_run": false,
+  "uniform_word_materialized": false,
+  "hosted_ci": "Not run in this review; no hosted pass claimed.",
+  "scope": "Fresh complete PR5241 audit replay plus maintainer code/proof review. Source-identical PR4470 controller, ordinary BIT and PR4359/4416 framework coverage reused explicitly, not rerun."
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/ACTUAL-WORD.json.gz b/research/owned-relation-independent-validation/engines/cost/frozen/ACTUAL-WORD.json.gz
new file mode 100644
index 0000000000..46d929df83
Binary files /dev/null and b/research/owned-relation-independent-validation/engines/cost/frozen/ACTUAL-WORD.json.gz differ
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/FINITE-TEMPLATE-CLOSURE.md b/research/owned-relation-independent-validation/engines/cost/frozen/FINITE-TEMPLATE-CLOSURE.md
new file mode 100644
index 0000000000..9917ac5543
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/FINITE-TEMPLATE-CLOSURE.md
@@ -0,0 +1,339 @@
+# Native closure and explicit constants for the finite uniform template
+
+Status: independently audited, conditional on the retained native movement,
+fixed-tape, and analytic interfaces stated below. This note supplies the new
+finite-template constants; it does not reuse the old supplier's scalar cap,
+row reserve, or obsolete pathwise precision exponent. It complements
+`AUDIT.md`, `P3-NATIVE-AUDIT.json.gz`, and `P3-COVER-AUDIT.json`.
+
+Apache-2.0. Substantial OpenAI assistance. The semantic completed-child
+argument is the attributed argument in
+[`references/semantic-bulk/pr23/semantic-bulk-17-note.tex`](../../../references/semantic-bulk/pr23/semantic-bulk-17-note.tex),
+section “Linear semantic precision for this actual circuit.” Its later
+explicit-constant application is also in
+[`notes/stopped-product-complex.tex`](../../../notes/stopped-product-complex.tex).
+The paths in the machine-readable receipt are relative to the repository
+root and bind the exact reviewed versions by SHA-256.
+
+## 1. What has actually been instantiated
+
+The p3 complex unit is a complete native word, not just a histogram. The
+independent audits verify its serialized scalar controller, 3,136 physical
+main-contact maps and their absolute phases, 672 complete main endpoints,
+2,856 actual local helper roles, causal idle windows, every paid completion,
+and the final order of whole-field normalizers. Its productive targets are
+
+```
+{6:192, 7:56, 8:93, 9:1229, 25:448, 57:224}.
+```
+
+There are 2,242 independent productive fields, one explicitly owned center,
+and paid children
+
+```
+{1:17623, 2:5065, 3:1738, 4:714, 5:254}.
+```
+
+All productive inputs are arbitrary. The owned center is initialized and
+cleared; it is never an additional credited output. Every helper endpoint
+is autonomous at the completed local boundary. Independent normalizers
+therefore surround an entire local call, without changing the frames of
+internal ADD instructions.
+
+The exact integer precompiler in `AUDIT.md` turns this unit into a finite
+uniform word with parameters
+
+* ambient rank `N >= 2`;
+* `W` productive arrays, each receiving the **full** rank-`N` transform;
+* `P` rank-one paid children;
+* `U` copies of the mixed unit in the completely expanded finite word;
+* at most `O=U` owned centers, conservatively one per mixed-unit instance.
+
+For every rational `z` strictly above the mixed root and below one, the
+constructive count argument provides an `N` with `P < W*N^z`.
+“Finite” here means fixed before the eventual multiplication input grows.
+It can be astronomically large. Neither this note nor the receipts claim
+to have materialized the winning near-threshold instance. The later
+`../controller/EXPLICIT-TEMPLATE-BOUNDS.md` strengthens the existence
+argument to the specified complex rank `N=2^276540184361`, with uniform
+saving `0.002304`; no search for a successful rank is left unperformed.
+The integer recursion defines its exact finite `W,P,U`, and the constants
+below are computable functions of that finite result.
+
+The fully materialized, depth-zero `N=57` example has `W=2242`, `P=127570`,
+and `U=1`. It is a useful independent check that complementary source jobs
+are really paid: `57*2242-127570=224`. This small example is not claimed to
+attain the limiting mixed exponent.
+
+## 2. Every column count and every complete spectator field
+
+The local logical identities were replayed in a free noncommuting operator
+word algebra. Apart from rational scalar arithmetic, the checker uses only
+composition and cancellation of an operator with its recorded inverse.
+For any positive integer `f`, substitute the `f`-column physical operator
+for each such generator. This extends to an algebra homomorphism on the
+free word algebra and preserves the checked identities.
+
+This is not the false assertion that tensor power is additive on arbitrary
+matrix sums. The role-level scalar word is unchanged. Each physical address
+generator is replaced by its column lift, while its formal products and
+linear combinations are evaluated on the same independent role arrays.
+
+A rank-zero native monomial has the form
+
+```
+|x> -> i^(a+q(x)) |M*x+b>,
+```
+
+with invertible binary `M` and a permitted quadratic phase `q`. Its column
+lift has blockwise address map `M`, translation `b` in every column, and
+phase `a*f + sum_j q(x_j)` modulo four. This explicitly retains the absolute
+phase. A fixed coordinate matcher in the precompiler becomes the same
+fixed permutation of `f`-axis blocks. All untouched axes remain complete
+spectator fields. A rank-one leaf becomes the standard rank-`f` child.
+
+The retained exact Clifford normal form supplies the monomial factors
+around each child. The independent p3 audit checks the whole main boundary,
+including the output translations required by negative powers of `C_q`.
+The fixed THREE/base selection is valid for every column count: THREE/base
+and THREE/extra have identical entrance and exit operators; their difference
+is an internal frame and its associated warps. No layer-dependent selector
+is required for the endpoint contract.
+
+For any integer input width `e=N*f+r`, first apply the `r<N` individual
+kernels and preserve these axes as completed spectators. Then apply the
+lifted finite word on the consecutive `N*f` active axes. Its final endpoint
+is the full selected-axis tensor, so the separately completed remainder
+commutes with it. This gives the ordinary arbitrary-width interface and
+strict child ratio at most `1/N`.
+
+## 3. An actual new coefficient charge
+
+`precision_closure.py` reads the authenticated serialized forward and
+backward native words. For every scalar macro it independently checks that
+the coefficient is dyadic and that the elementary allowance dominates its
+logarithmic row-norm and denominator-height increment. For an ADD with
+coefficient `a`, a sufficient height increment is
+
+```
+ceil(log2(1+abs(a))) + log2(denominator(a)).
+```
+
+For a dyadic SCALE replace `1+abs(a)` by `max(1,abs(a))`. COPY and CLEAR
+have zero height increment and still retain their implementation cost.
+The audit reproduces the native real primitive allowances 158,120 forward
+and 158,168 backward, and the complete p3 arithmetic charge 1,147,304.
+In particular, the six boundary swaps contribute their six additional
+negations; they have not been priced as signed swaps.
+
+Address permutations and fourth-root unit phases do not increase magnitude
+or denominator height. We nevertheless add an explicit conservative charge
+of eight for every non-scalar native record and every listed whole-field
+normalization. The respective counts are:
+
+| Kind | Count |
+| --- | ---: |
+| Non-scalar records in the seven native calls | 36,260 |
+| Complete helper normalizations | 2,856 |
+| Main contact monomials | 3,136 |
+| Complete main endpoint normalizations | 672 |
+| Paid completion normalizations | 460 |
+
+This gives the complete elementary coefficient/unit-phase envelope
+
+```
+G_unit = 1,147,304 + 8*(36,260+2,856+3,136+672+460)
+       = 1,494,376.
+```
+
+Eight bounds the two monomial factors around a native child, each of which
+needs at most a sign and an `i` phase. Some records are just annotations, so
+this deliberately overcounts. The pointwise phase descriptor may have
+larger fixed geometry, but each resulting coefficient is still a unit.
+
+Whole-job coordinate matchers in the finite compiler have zero coefficient
+height. The canonical positive tensor jobs can be placed on disjoint axes
+by binary coordinate permutations; there is no new scalar mixing at these
+boundaries. The final scalar/phase charge is therefore bounded by
+
+```
+G = 1,494,376 * U.
+```
+
+This charge is not a promise that an arbitrary binary address map costs
+eight tape steps. Every actual matrix has its separately paid native
+row-addition decomposition and compact movement implementation. The finite
+number of those operations is another fixed constant of the expanded word.
+
+## 4. Explicit linear semantic guard
+
+Put `Z=W+O` and replace the old constants by
+
+```
+E  = 64*(Z+N+P+G+1)^3,
+B  = P+E,
+C0 = 32*N*B^2,
+C1 = 1.
+```
+
+In particular
+
+```
+2*G*Z^2 + 8*P + 4*Z + 4 + 32*N < E.
+```
+
+The receipt verifies this exact inequality. It is deliberately much larger
+than necessary: it pays the full elementary word, unit phases, role and
+owned-field passes, and fewer than `N` remainder kernels. The inclusion of
+`P` in the fresh cubic bound avoids relying on any old relation between the
+paid-child count and the number of physical fields.
+
+Let `A(e)` bound both temporary magnitude exponent and binary denominator
+excess relative to the incoming common fine grid. A **completed** forward
+or inverse `u`-axis child has coefficients in `2^-u Z[i]` and absolute row
+sum at most `2^u`; the unit sign wrappers preserve those bounds. Thus its
+returned stream costs at most `u` in each semantic measure. Its larger
+internal temporary values do not become unfinished parent operands.
+
+At a node of width `e`, set `f=floor(e/N)`. At most `P` completed child calls
+have preceded any active child; their total selected width is at most
+`P*f`. Their input contents may be arbitrary, including data on the owned
+centers. All scalar growth and remainder kernels fit in `E`. Consequently
+
+```
+A(e) <= A(f) + P*f + E.
+```
+
+For an elementary leaf, `A(e)<=8e`. Since `N>=2`, `B=P+E`, and `E>=64`,
+
+```
+2*B*(N-1) >= P+E,
+2*B*f+P*f+E <= 2*B*N*f <= 2*B*e.
+```
+
+Induction gives `A(e)<=2B e`. Completed disjoint selected-axis pieces have
+total width at most `d`. The retained prefix kernels, outer phases and
+normalization add at most `18d`, giving
+
+```
+A_layer <= (2*B+18)*d < C0*d.
+```
+
+Every calculation remains on one fixed fine grid. A child is never rounded,
+compressed, or re-encoded at return. The change is to the proof's bound on a
+completed value, not to its stored representation. Other fields remain
+parked while the child executes. This is why the linear semantic bound
+survives a huge scalar word and why the older pathwise `C1>1` estimate is
+unnecessary.
+
+The stopping rule can be any fixed rational `0<beta<1`. Above the eventual
+threshold `d^beta>=2N`, every internal call has the required positive `f`;
+the completed-leaf estimate remains `8e` at the stopping leaves. No old
+numerical cutoff is carried over.
+
+### An effective threshold, including enormous constants
+
+Suppose `d<=c*p^epsilon`, with fixed `c>=1` and rational
+`epsilon=a/b` in `(0,1)`. Let `L` be the binary bit length of
+`4*C0*ceil(c)` and choose
+
+```
+t = max(4, ceil(b*L/(b-a))),       p0 = 2^t.
+```
+
+For all `p>=p0`, `p^(1-epsilon)>4*C0*c`, so the integer guard
+`Delta=C0*d` is at most `p/4`. Signed components with `p+Delta` fractional
+bits and `Delta+3` magnitude/sign bits have width
+
+```
+p+2*Delta+3 <= 2p.
+```
+
+The audit emits `p0` as a compressed power of two. It does not try to
+allocate that many bits. This construction proves the eventual `O(p)` word
+bound for the new finite template, including the current outer choice
+`epsilon=99999/100000`. Huge fixed constants change `p0`, not `C1` or the
+power in the final exponent inequalities.
+
+## 5. Productive stock, owned storage, and native tape closure
+
+For the ordinary uniform complex word, let
+
+```
+D(e)=0 if e<N;  D(e)=1+D(floor(e/N)) otherwise,
+q0=ceil(log2 W)*D(d).
+```
+
+Use the original compact front and back fields separately. The first `q0`
+reserved complete chunks provide a physically preceding row field. Their
+individual selected-axis kernels need not be completed beforehand: the
+active invocation acts as identity on these coordinates for arbitrary
+incoming contents. In the support-local outer wrapper their kernels must
+be deferred to later phases, as explained in `OUTER-TRANSFER-AUDIT.md`.
+The row field's cardinality is
+`R=2^(q0*K)>=W^D(d)` for `K>=1`. Pad complete rows once to the next multiple
+of `W^D(d)`. The padding factor is below two. Every descendant then has
+exactly `1/W` of its parent's productive volume and enough divisibility for
+its remaining depth, with complete active, control and spectator fields.
+All-row endpoint correctness restores appended zero rows to zero.
+
+Owned storage contributes no factor to productive output credit. A safe
+choice is one full center field per finite mixed-unit instance, namely
+`O=U`. At an ordinary recursion node each such field has the same shape as
+one productive role stream, of volume `V/W`. Initialize, retain and clear
+it as its actual word prescribes. If simultaneously suspended units keep
+live centers, they receive distinct banks. Reusing one bank per recursion
+depth would not suffice. Owned-space scans and parking cost fixed multiples
+of volume; paid calls on those banks are already in `P`.
+
+The integer audit checks row divisibility and one-time padding at several
+floor-depth boundaries. It also gives an explicit sufficient threshold
+for `q0<d/4`. In general `q0=O(log d)` with a possibly huge fixed
+coefficient. This does not change the compact-field reservation exponents.
+If an inherited implementation uses separate simultaneous BIT stock, its
+factor must also be retained in the row product; taking only the maximum
+of two stocks would be invalid. The delayed BIT cover has its own updated
+row-reserve argument and must not be charged to old constants.
+
+Each fixed binary matrix factors into finitely many row additions and
+coordinate swaps. `notes/compact-control-movement.tex` implements these on
+complete packed rectangles, with the actual compact cost and polynomial
+descriptor preparation. The finite compiler's matrices have fixed rank
+`N`; their `f`-column lifts are therefore fixed block recipes, not dynamic
+RAM gathers. They preserve the retained native operation alphabet.
+
+The depth-first fixed-tape execution parks unused role streams, their
+owned banks and descriptors while a child runs. The numbers of roles,
+tapes, routers and instruction types are fixed constants of this one
+template. The ordinary tree has at most `P^D(d)=d^O(1)` nodes. Polynomial
+description/setup costs still have a fixed degree and are absorbed by the
+retained superpolynomial record fiber when `epsilon<1`. That absorption
+needs a new eventual threshold if the degree grows; it does not authorize
+an unpriced RAM-to-tape conversion.
+
+## 6. Consequence for the new outer calculation
+
+After the finite precompilation and the native phase/ownership audits,
+the complex supplier fits the retained ordinary uniform interface with
+moment `(P/W)*N^-sigma<1`. All real primitive, movement, center and row
+constants are replaced as above. Its precise stopping and internal-cost
+exponents are still the retained weighted-tree bounds; only their constant
+multipliers and eventual cutoffs change. The nearly critical outer ledger
+can therefore use `C1=1` with the new complex saving.
+
+This closes the **complex finite-template** precision and stock obligation
+under the inherited native movement and outer hypotheses. A complete
+conditional multiplication claim additionally needs the independently
+bound BIT uniform interface, the strict mixed moments, and the actual outer
+parameter inequalities. Those are separate receipts rather than implicit
+consequences of the favorable complex histogram.
+
+Replay:
+
+```sh
+python3 -B research/kappa-rebuild/transfer-audit/precision_closure.py
+```
+
+The output `PRECISION-CLOSURE.json` includes exact source hashes, independently
+recounted scalar charges, the generic substitution formulas, and the fully
+numeric rank-57 example.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/README.md b/research/owned-relation-independent-validation/engines/cost/frozen/README.md
new file mode 100644
index 0000000000..777f4e1d51
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/README.md
@@ -0,0 +1,249 @@
+# Conditional kappa 0.00302235 from one owned helper relation
+
+This construction gives **conditional kappa = 60447/20000000 = 0.00302235**.
+The gain over Cao Yifan's final
+[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)
+value, 0.0030217758, is **2871/5000000000 = 0.0000005742**.
+The construction changes the complete paid profile. It does not obtain the
+gain by taking more digits of the old root.
+
+One helper becomes owned storage in each backward call. A prepared relation
+then makes one paid rank-eight center equal to an earlier saved value. The same
+relation makes one later rank-one job act on zero. Both jobs can be removed,
+with the rank-nine helper credit also removed. All other independent outputs
+and all main interfaces keep their source operators.
+
+[WORD.json.gz](WORD.json.gz) is the complete emitted word.
+[RESULT.json](RESULT.json) records the exact native checks, the two source
+identities, both full profiles, completion, compiler and outer calculations.
+[SOURCES.json](SOURCES.json) pins every external input by Git blob and SHA256.
+The proof below explains why the changed word has the stated contract.
+
+## Source and scope
+
+The base is canonical main
+[7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56).
+The native source is the final PR #4610 word at
+[20bb93cd990d2ff683e4d0fc56b87a42cd5d3296](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz).
+Its decompressed SHA256 is
+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.
+The comparison value and old crossing come from its
+[final compiler arithmetic](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json).
+All consumed bytes are already in the recorded main base.
+
+This is one instance of the current `complex-new-helper-inventory` priority.
+The [scoped claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737)
+reserves only the relation and two replacements below.
+[Discussion #5355](https://github.com/CrocSwap/integer-mult-bounds/discussions/5355)
+retains all 632 independent inputs and all eight centers.
+[Discussion #4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930)
+retains every original helper endpoint. This construction removes the
+independent L230 job in backward calls. It does not claim those broader scopes.
+The selected certificate is unchanged. A fresh check at 20:20 UTC found that
+Discussion #5355 had released its original-input scope without a saving.
+Canonical main still had the recorded base commit.
+
+## Exact replacement proof
+
+All indices below are zero-based indices in the frozen backward program.
+Let `h_r` be the source logical input of helper `Lr`. The five helpers in
+
+```math
+\Delta=h_{230}-h_{324}+h_{326}+h_{328}-h_{333}
+```
+
+all start in frame 0 and finish in frame 1, of rank nine. The new backward
+contract has 224 independent main fields and 407 independent helper fields.
+L230 is private. Clear it, then use four same-frame ADDs to prepare
+
+```math
+h_{230}=h_{324}-h_{326}-h_{328}+h_{333}.
+```
+
+The other helper inputs remain arbitrary and independent. This preparation
+sets Delta to zero for every input. It uses no recursive job. It removes one
+rank-nine productive target; the dependent field receives no output credit.
+
+Run the original source program on unrestricted inputs. Let `q` be the
+logical row of L92 just after event 11205, a paid climb into frame 254.
+The separate predecessor row engine gives these exact identities:
+
+| Source position | Exact logical row |
+| --- | --- |
+| C0 at the rank-eight center, event 11332 | `q + Delta/4` |
+| L92 at the rank-one climb, event 15584 | `-Delta/4` |
+
+These identities are over rational coefficients and free native operator
+words. They hold for every value of every source input and for every invertible
+interpretation of the native symbols. They do not use numerical samples or an
+assumed relation between distinct native maps.
+
+For every positive tensor width f, substitute each native generator by its
+source operator tensor power and each inverse by the inverse tensor power.
+This defines a representation of the free group. Keep the rational scalar
+coefficients outside the substitution. The two row identities therefore hold
+at every such width. In particular, Delta/4 remains a scalar linear form; it
+is not a tensor power of that sum. This uses the termwise argument recorded in
+the [free-word tensor audit](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/free-word-tensor-lift-audit/PROOF.md),
+which credits Cinna Davis's proposal and ToikY's scoped audit. Physical frame
+realization and the complete all-size compiler retain their source contracts.
+
+Immediately after event 11205, clear a new private field C1 in frame 254 and
+COPY L92 into it. C1 is not written until the replacement of event 11332. At
+that event, clear owned C0, set its frame to 254, COPY C1 into C0, then clear C1.
+The copy coefficient is exactly one. Under Delta = 0, the copied field is the
+same physical value as the old center output: the logical rows and the exact
+frame gauge are equal. The old C0 input can be erased because C0 is owned.
+This removes one rank-eight recursive job.
+
+At event 15584, L92 is exactly zero in every input column. The physical
+identity therefore has the same result as the old rank-one frame change.
+`zero_retag` records this fact. It performs no physical write and is accepted
+only when the full exact row is empty and the current frame is 254. It then
+records frame 1. This removes one rank-one recursive job. It does not erase a
+main input or replace a nonzero transform with a free frame change.
+
+Every other event stays in source order. Clear private L230 at return. The
+source clears C0, and the new program has already cleared C1. The original
+linear endpoint identity, restricted by the prepared relation, gives all 224
+main outputs and all 407 retained helper outputs. The literal new-word replay
+checks these outputs separately, with all 631 retained inputs and all three
+owned entry fields initially arbitrary. It also checks every scalar frame,
+paid rank, native frame transition and final frame.
+
+The 4,429 source frames, 72 native maps, all remaining paid operators, and main
+adapters are unchanged. The source
+[absolute-phase certificate](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz)
+is authenticated and reused. Same-frame COPY and identity on zero introduce no
+phase recipe. The source's amplitude and Clifford-lowering checks are not
+rerun by this package. The new free-word identities prove equivalence for the
+source operators with their full phases, not just their projective classes.
+
+## Complete cost and conditional compiler
+
+The forward word is unchanged. Each backward call has these counts:
+
+```text
+paid:    {1:2200, 2:412, 3:510, 4:127, 5:40, 8:7}
+helpers: {4:28, 7:7, 8:47, 9:325}
+```
+
+The full p16/a7 controller contains 16 backward calls, two forward calls and
+15 query shears. Thus the complete difference is **minus 16 H1 and 16 H8 paid
+jobs, and minus 16 H9 productive targets**. It includes every idle and main
+target. There are 64,372 paid jobs and 10,912 productive fields. Their rank
+masses are 238,990 and 239,742; the surplus remains 752.
+
+For every real `0 < t < 1`, the complete target-minus-paid moment increases by
+
+```math
+16(1+8^t-9^t)>0.
+```
+
+For a direct proof, both `(1/9)^t > 1/9` and `(8/9)^t > 8/9`; multiply their
+sum by `9^t`. The improvement is strict throughout the required range.
+
+The backward word has 158,214 real scalar operations under the source macro
+allowance, exactly 46 more than its source. Its maximum formal prefix L1 norm
+is 169, with maximum denominator 64; both equal the source bounds. The forward
+bounds remain 457 and 32. One extra physical private slot holds C1. L230 uses
+an existing slot. The route bound also charges two routes for each of the two
+new owned lifetimes. The local scalar-plus-route bound stays below 10^7, and
+the complete raw nonrecursive bound stays **181,098,496 < 10^9**. Preparation,
+COPY, CLEAR and storage therefore do not introduce an unpaid recursive cost.
+
+Two rational interval engines check the complete moment. Its unique crossing
+in `0 < kappa < 1` lies in
+**(0.00302238736347, 0.00302238736348)**. The verifier proves the moment decreases
+on `[0,0.05]` and remains negative on `[0.05,1]`. This is a ceiling for this
+fixed complete profile, not an optimum over circuits or helper relations.
+The claimed kappa leaves more than **0.00000003736347** raw headroom.
+
+The separately tested saving is 0.00302236. The paid/target ratio is below
+`0.999999971483293515393313955730`, with reserve `1e-9`. Both charged tails are
+below `0.97`. The source power 1024, cutoff 20, floor 21, tail offset 1/5,
+complement factor 63/64 and logarithm power 1000 still pass. The compiler gap
+is `1/700000000`, with `j=44836`, `H=31385200000000` and `N=2^31385200000000`.
+The exact integer test `(H+1)^1000 < 2^44836` passes; the preceding grid integer
+fails. The uniform complex saving is `2115651/700000000`. All 54 strict outer
+predicates and four functional predicates pass, using the retained ordinary
+BIT saving 0.0034.
+
+## Verification and reproduction
+
+Use Python 3.12 or 3.14, with the standard library only. From the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023 --check-only
+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023
+```
+
+The registered commands run normal and optimized Python. The direct command,
+also used for a Git-free export, is:
+
+```sh
+python3 -B research/kappa-owned-relation-20261023/verify.py
+python3 -O -B research/kappa-owned-relation-20261023/verify.py
+```
+
+Each prints status
+`PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION`.
+The verifier reconstructs the word and compares its bytes and exact result with
+the published artifacts. `--write` is a separate authoring command. It changes
+only this package's word and result after all checks pass.
+
+Fresh checks cover both source words, both candidate words, every independent
+entry column and owned return, the two unrestricted source identities, retained
+phase bindings, the p16 rational Laurent factorization, both scalar boundary
+programs, two complete invoice counts, two rational interval engines, the fixed
+profile ceiling, completion, compiler, BIT conversion and all outer predicates.
+The emitted word replaces the old single `canonical.local_profile` metadata
+field with explicit `paid_profiles` for the two directions.
+
+Seven native controls reject a wrong relation sign, omitted input clear, wrong
+snapshot, wrong zero frame, wrong paid rank, wrong copy gauge, and omitted
+output clear. Five cost/outer controls reject the lost helper's output credit,
+old BIT stock, closed uniform gap, unfunded endpoint and closed epsilon.
+
+Normal and optimized registered replays passed on CPython 3.12.14. The direct
+author check also passed on CPython 3.14. Source metadata and pins passed.
+The optional full-history preflight is not claimed in the shallow checkout.
+The publication handoff records export and committed-byte checks.
+
+The full source phase lowering, BIT native replay, Lean, Docker, physical tape
+execution, numerical precision execution, analytic decomposition and integer
+recovery are not rerun here. The complete bound retains those predecessor
+contracts, including permitted owned erasure, whole-job normalizers, mixed
+productive-target recursion and all-size closure. The expanded compiled word
+is specified by a finite algorithm, not materialized. This is a conditional
+construction with exact finite evidence, not an unconditional multiplication
+theorem, a practical timing result or independent human acceptance.
+
+## Credit
+
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+Cao Yifan's [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)
+supplies the exact source word, phase evidence and previous compiler value.
+Cinna Davis's [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470)
+supplies the p16 controller and helper-interface lineage. The source code keeps
+credit for Dugongue's transported frames, zxv's native and finite-compiler
+work, Jacob Alan Sussman's mixed-target recursion and their predecessors.
+The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py)
+and [literal native source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-rebuild/complex/native_extensions.py)
+are pinned as provenance for the adapted checks.
+
+zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283)
+supplies the related cache contract and the explicit handoff to find actual
+matching rows and their lifetimes. Its standalone cache example is not part of
+this word. The new contribution is the five-helper relation, its actual cache
+and zero identities, the full owned-field replacement and the complete positive
+bill. No priority is claimed for the general cache or paid-history ideas.
+
+## Open next questions
+
+Independent review should first check the three source rows and the physical
+COPY/zero argument above, then the retained all-size and phase premises.
+A later construction could test a different helper relation, but it must claim
+a disjoint scope and pay every lost target and owned field. This package does
+not classify such relations. [TASK.json](TASK.json) records the first steps,
+relevance and blockers for both questions.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/RESULT.json b/research/owned-relation-independent-validation/engines/cost/frozen/RESULT.json
new file mode 100644
index 0000000000..27b4e54708
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/RESULT.json
@@ -0,0 +1,373 @@
+{
+  "arithmetic": {
+    "compiler": {
+      "H": 31385200000000,
+      "N": "2^31385200000000",
+      "eta": {
+        "lower": "0.000000203927056311365991628189",
+        "upper": "0.000000203927056311365991628190"
+      },
+      "gap": "1/700000000",
+      "integer_test_exponent": 44836,
+      "logarithm_power": 1000,
+      "theta": "63/64",
+      "uniform_saving": "2115651/700000000",
+      "word_materialized": false
+    },
+    "fixed_profile_ceiling": {
+      "decreasing_through": "1/20",
+      "derivative_upper": {
+        "lower": "-195778.630038840116414999953237565269",
+        "upper": "-195778.630038840116414999953237565268"
+      },
+      "remaining_interval_moment_upper": {
+        "lower": "-6836.549542075249598033582799619360",
+        "upper": "-6836.549542075249598033582799619359"
+      }
+    },
+    "full_backward": 16,
+    "full_forward": 2,
+    "gain_over_PR4610": "2871/5000000000",
+    "kappa": "60447/20000000",
+    "kappa_decimal": ".00302235",
+    "margin_at_previous_kappa": {
+      "lower": "0.151161494385402651700356241377",
+      "upper": "0.151161494385402651700356241378"
+    },
+    "margin_at_previous_root_upper": {
+      "lower": "0.151143999513185007311808491175",
+      "upper": "0.151143999513185007311808491176"
+    },
+    "negative_controls": {
+      "closed_epsilon": [
+        "epsilon_below_one",
+        "global_gamma_power_slack",
+        "actual_logarithmic_gamma_guard",
+        "source_axis_superpolynomial",
+        "gaussian_above_main",
+        "new_semantic_guard_with_C1_one"
+      ],
+      "closed_uniform": [
+        "new_complex_uniform_saving_above_b"
+      ],
+      "old_BIT": [
+        "actual_bit_above_effective"
+      ],
+      "unearned_helper_credit": "Rejected by the independent complete census",
+      "unfunded_endpoint": [
+        "main_transform_above_kappa",
+        "global_coordinate_router_above_kappa",
+        "fused_gaussian_above_kappa",
+        "group_bit_router_above_kappa",
+        "boundary_algebraic_matrix_above_kappa"
+      ]
+    },
+    "nonrecursive": {
+      "additional_private_slots": 1,
+      "local_routes": 4806000,
+      "local_scalar": 158214,
+      "owned_slots_backward": 3,
+      "raw_budget": 1000000000,
+      "raw_scalar_upper": 181098496
+    },
+    "ordinary_BIT": {
+      "admitted": "17/5000",
+      "after_cover": "69/20000",
+      "atom": "1/250",
+      "before_cover": "3459/1000000",
+      "ordinary_saving": "8590884599/2500000000000",
+      "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+    },
+    "outer": {
+      "functional_checks": {
+        "actual_new_BIT_stock_sublinear": "174299999253/175000000000",
+        "fixed_halo_explicit_metadata_branch": "13475000001/175000000",
+        "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000",
+        "new_semantic_group_guard": "3/700000000"
+      },
+      "margins": {
+        "boundary_algebraic_matrix": "23139910904443/7656250000000000",
+        "fused_gaussian": "23139910838329/7656250000000000",
+        "global_coordinate_router": "2115649/700000000",
+        "group_bit_router": "1480954993653053/490000000000000000",
+        "group_scans": "349999999/350000000",
+        "main_transform": "23139899966943/7656250000000000",
+        "microbox_face_corrections": "13475000001/175000000",
+        "polynomial_products": "699999999/700000000",
+        "sparse_union_movement": "3133491473404443/7656250000000000"
+      },
+      "parameters": {
+        "a": "2115649/700000000",
+        "b": "42313/14000000",
+        "beta": "699999997/700000000",
+        "bit_saving": "17/5000",
+        "cap_xi": "6961616462466943/7656250000000000",
+        "complex_uniform_saving": "2115651/700000000",
+        "d": "1/700000000",
+        "epsilon": "699999999/700000000",
+        "kappa": "60447/20000000",
+        "lambda_": "199395529/200000000",
+        "lambda_prime": "10904443/10937500",
+        "layout": "1/700000000",
+        "q": "33057/10937500",
+        "r0": "1/7000000000",
+        "stop": "1/700000000",
+        "tested_saving": "75559/25000000"
+      },
+      "strict_checks": {
+        "actual_bit_above_effective": "264351/700000000",
+        "actual_logarithmic_gamma_guard": "1/700000000",
+        "actual_logarithmic_group_guard": "694633553939307/3828125000000000",
+        "alpha_logarithm_absorption": "1/7000000000",
+        "boundary_algebraic_matrix_above_kappa": "43716943/7656250000000000",
+        "cap_above_band": "3133491462466943/7656250000000000",
+        "cap_below_cell": "694633526595557/7656250000000000",
+        "cap_below_phase_cell_power": "8350883537533057/7656250000000000",
+        "complex_above_effective": "1/700000000",
+        "complex_below_one_over_32": "395187/14000000",
+        "complex_endpoint": "1/350000000",
+        "epsilon_below_one": "1/700000000",
+        "epsilon_positive": "699999999/700000000",
+        "fine_prime_halo_umbrella": "7/2",
+        "fused_gaussian_above_kappa": "43650829/7656250000000000",
+        "gaussian_above_main": "5435693/3828125000000000",
+        "global_coordinate_router_above_kappa": "1/175000000",
+        "global_gamma_power_slack": "9/7000000000",
+        "group_below_dimension": "1/350000000",
+        "group_bit_router_above_kappa": "3493653053/490000000000000000",
+        "group_gauge_power_slack": "43414597087027/239257812500000",
+        "group_key_fits_record": "1/350000000",
+        "group_positive": "699999997/700000000",
+        "group_scans_above_kappa": "697884353/700000000",
+        "halo_covers_generic_inverse_radius": "5",
+        "improvement_over_user_baseline": "645689790400418148631/500000000000000000000000",
+        "lambda_above_internal": "1/1400000000",
+        "lambda_above_sigma": "3/1400000000",
+        "lambda_above_tau": "1/1400000000",
+        "lambda_prime_above_lambda": "1/1400000000",
+        "lambda_prime_above_leaf": "27957687/9800000000000000",
+        "leaf_saving_above_effective": "13957687/9800000000000000",
+        "main_transform_above_kappa": "32779443/7656250000000000",
+        "membership_arithmetic_fits_record": "1/700000000",
+        "microbox_face_corrections_above_kappa": "53897884359/700000000",
+        "microbox_halo_volume": "55300000003/700000000",
+        "new_complex_uniform_saving_above_b": "1/700000000",
+        "new_semantic_guard_with_C1_one": "1/700000000",
+        "polynomial_products_above_kappa": "348942177/350000000",
+        "positive_layout_slack": "1/700000000",
+        "q_below_effective": "1/700000000",
+        "q_below_internal": "1/700000000",
+        "q_below_leaf": "27957687/9800000000000000",
+        "q_positive": "33057/10937500",
+        "short_record_fallback": "13957687/14000000",
+        "source_axis_superpolynomial": "1/700000000",
+        "sparse_union_movement_above_kappa": "3110351606216943/7656250000000000",
+        "stop_below_one": "699999999/700000000",
+        "stop_positive": "1/700000000",
+        "strassen_integer_power_gap": "1951441519231",
+        "support_router_span": "3/700000000",
+        "theta_positive_polynomial_power": "2",
+        "union_header_fits_record": "3/700000000",
+        "union_tag_work_per_visit_fits_record": "3/700000000"
+      }
+    },
+    "paid": {
+      "1": 41282,
+      "16": 448,
+      "2": 7416,
+      "24": 448,
+      "3": 9180,
+      "32": 448,
+      "4": 2286,
+      "40": 448,
+      "48": 448,
+      "5": 720,
+      "56": 448,
+      "64": 448,
+      "72": 224,
+      "8": 128
+    },
+    "paid_calls": 64372,
+    "productive_fields": 10912,
+    "query_shears": 15,
+    "rank_mass_surplus": 752,
+    "raw_headroom": [
+      "3736347/100000000000000",
+      "934087/25000000000000"
+    ],
+    "raw_root_interval": [
+      "302238736347/100000000000000",
+      "75559684087/25000000000000"
+    ],
+    "strictification": {
+      "alpha": {
+        "lower": "0.999999971483293515393313955729",
+        "upper": "0.999999971483293515393313955730"
+      },
+      "cutoff": 20,
+      "delta": {
+        "lower": "0.957459689758527661921334851512",
+        "upper": "0.957459689758527661921334851513"
+      },
+      "floor": 21,
+      "gamma": {
+        "lower": "0.956310980726438847618396606911",
+        "upper": "0.956310980726438847618396606912"
+      },
+      "normalized_paid_upper": "2097152001953127/2097154147483648",
+      "power": 1024,
+      "reserve": "1/1000000000",
+      "tail_offset": "1/5",
+      "tested": "75559/25000000"
+    },
+    "targets": {
+      "145": 224,
+      "17": 448,
+      "25": 448,
+      "33": 448,
+      "4": 504,
+      "41": 448,
+      "49": 448,
+      "57": 448,
+      "65": 448,
+      "7": 126,
+      "73": 224,
+      "8": 846,
+      "9": 5852
+    }
+  },
+  "candidate_native": {
+    "backward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 325
+      },
+      "independent_owned_entry_columns": 3,
+      "independent_persistent_columns": 631,
+      "max_denominator": 64,
+      "max_formal_prefix_l1": "169",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2200,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 7
+      },
+      "real_scalar_allowance": 158214,
+      "zero_identities": 1
+    },
+    "forward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "max_denominator": 32,
+      "max_formal_prefix_l1": "457",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158120,
+      "zero_identities": 0
+    }
+  },
+  "independent_source_identities": {
+    "center_minus_snapshot": "Delta/4",
+    "center_replaced": 11332,
+    "copy_coefficient": "1",
+    "relation": {
+      "230": 1,
+      "324": -1,
+      "326": 1,
+      "328": 1,
+      "333": -1
+    },
+    "snapshot_after": 11205,
+    "snapshot_terms_before_substitution": 61,
+    "source_event_indices_are_zero_based": true,
+    "zero_identity_at": 15584,
+    "zero_site_row": "-Delta/4"
+  },
+  "native_negative_controls": {
+    "missing_owned_input_clear": "Every independent main/helper endpoint: 0",
+    "uncleared_owned_output": "Every owned entry column is erased at return",
+    "under_or_overstated_paid_rank": "Exact paid rank and frame",
+    "wrong_copy_gauge": "Exact scalar destination frame",
+    "wrong_relation_sign": "Every independent main/helper endpoint: 0",
+    "wrong_snapshot_source": "Zero identity requires an identically zero full row",
+    "wrong_zero_input_frame": "Zero identity requires an identically zero full row"
+  },
+  "phase_inheritance": {
+    "absolute_phase_receipt_reused": "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+    "all_retained_paid_events_and_warps_from_source": true,
+    "new_gaussian_operators": 0,
+    "new_native_maps": 0,
+    "new_operations": "Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.",
+    "source_amplitudes_and_phase_lowering_freshly_replayed": false
+  },
+  "scope": "Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.",
+  "source_native": {
+    "backward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "max_denominator": 64,
+      "max_formal_prefix_l1": "169",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158168,
+      "zero_identities": 0
+    },
+    "forward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "max_denominator": 32,
+      "max_formal_prefix_l1": "457",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158120,
+      "zero_identities": 0
+    }
+  },
+  "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION",
+  "word_payload_sha256": "645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35"
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/SOURCES.json b/research/owned-relation-independent-validation/engines/cost/frozen/SOURCES.json
new file mode 100644
index 0000000000..9854abbb4f
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/SOURCES.json
@@ -0,0 +1,90 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/free-word-tensor-lift-audit/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "69c337a7704ce589798269ab4b8606189c070c4e",
+      "sha256": "cc8ad3698a673fb225419a3636a39aa99a66c7a0676f12e329b1e76564fa1459"
+    },
+    {
+      "path": "research/higher-moment-strictification/verify.py",
+      "usage": "input",
+      "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699",
+      "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326"
+    },
+    {
+      "path": "research/joint-helper-lattice/CONTROLLER.json",
+      "usage": "input",
+      "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5",
+      "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f"
+    },
+    {
+      "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+      "usage": "input",
+      "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb",
+      "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7"
+    },
+    {
+      "path": "research/kappa-interface-round2-20261022/price_profile.py",
+      "usage": "provenance",
+      "git_blob": "1d93e43d1cb888d128c2faa2be83a96d85b84295",
+      "sha256": "adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb"
+    },
+    {
+      "path": "research/kappa-rebuild/architecture/mixed_target_probe.py",
+      "usage": "input",
+      "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e",
+      "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a"
+    },
+    {
+      "path": "research/kappa-rebuild/complex/native_extensions.py",
+      "usage": "provenance",
+      "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8",
+      "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+      "usage": "input",
+      "git_blob": "ac77b78547d6dbf2e6bd102e1047c5b16c1bca88",
+      "sha256": "6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b"
+    },
+    {
+      "path": "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json",
+      "usage": "input",
+      "git_blob": "0fdb65f946d557c13d8e2781b9151e2a8ddee5c3",
+      "sha256": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de"
+    },
+    {
+      "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py",
+      "usage": "input",
+      "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59",
+      "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15"
+    },
+    {
+      "path": "research/query-thinned-controllers/RESULT.json",
+      "usage": "input",
+      "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c",
+      "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f"
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/SPECIALIZATION.md b/research/owned-relation-independent-validation/engines/cost/frozen/SPECIALIZATION.md
new file mode 100644
index 0000000000..7ee84b3089
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/SPECIALIZATION.md
@@ -0,0 +1,130 @@
+# P1: specialize the selected physical grammar to final #4610
+
+This note proves a conditional **specialization**, not a new physical primitive theorem. Let H_selected denote precisely the native normal-form, compact movement/repair, scalar/owned-storage, completed-call, fixed-tape and outer hypotheses retained by selected #4470 through its reviewed #4359/#4416 lineage. Under H_selected, the actual final #4610 catalogue is an instance of that same physical grammar, with newly counted fixed constants. The proof does not introduce a separate assumption that the new recipes work.
+
+Candidate #4610 is Cao Yifan/intqwq's existing construction, head `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`, final local-word payload `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. Pinned canonical source is `ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c`. Selected #4470 remains .00302015; this note does not modify selection or claim construction/gain priority. Exact source bytes, including the following premise texts, are bound in `SOURCES.json`.
+
+## 1. The selected premise already quantifies over the required class
+
+The premises used here are the following statements in the selected source closure, with their original physical qualifications retained:
+
+1. `notes/general-clifford-frames.tex`, “Exact representatives and nested children”: for an arbitrary binary subspace U and deterministic invertible basis extension G, the exact Gaussian-dyadic K_G and its conjugate by F have rank zero and are fixed binary address permutations with unit quadratic phases. For **every** nested U subset V, the exact transition is two rank-zero adapters around a positive coordinate C child. Exact phases and finite movement/scalars are charged. The statement is not restricted to the selected word's list of old frame labels.
+2. `notes/compact-control-movement.tex`, “Compact-control selected-bit addition” and “Application to a fixed binary change of basis”: either ordering of two complete slots admits exact selected-bit row addition with restored arbitrary temporary fields; a fixed binary basis change is a fixed number of such additions. The fixed-tape bound is `O(V*((e*log p)^tau+1))`, including repair and descriptor work, under the stated complete-field reservations and record-size hypotheses. Constants and cutoffs are uniform within each fixed parameter family.
+3. Selected #4359 `PROOF-REVIEW.md` section2: free-word evaluation allows arbitrary positive column multiplicity by substituting lifted generators, separately tensor-lifting exact paid/helper factorizations. Absolute monomial phase is `a*f+sum q(x_j)`. Helpers are normalized only after their autonomous completed endpoint. Section3 explicitly permits fixed template matrices/matchers to change dimensions/counts/constants while retaining the same movement exponent and tape uniformity. Section4 separately pays address permutations and unit phases and replaces semantic precision constants.
+4. Selected #4416 `PROOF-REVIEW.md` section2: exact whole-job normal forms use independent **two-sided** recorded factors. They need not be an inverse pair. Canonicalize the complete job, place its axes by a charged coordinate matcher, execute the child, and restore the prescribed adapters before resuming its parent. Distinct physical owners and separate live centers are preserved.
+5. Selected #4470 `PROOF-REVIEW.md` sections1–3 applies these rules to new actual helper normalizers, paid transports, p16/query/idle events and their new finite scalar/route/owner/precision constants. The retained conditions include all-column implementation, whole-job adapters, owned erasure, fixed-tape movement, precision and outer hypotheses.
+
+Consequently the permitted class is generic fixed finite Gaussian-dyadic monomial/positive-child programs with the stated arbitrary-owner and spectator ABI. It is not the stronger assertion that an arbitrary RAM gather or arbitrary address function is cheap. The reduction below uses only the selected binary row-addition/ordered-movement operations, finite unit phases and the same scalar/child/owned alphabet.
+
+## 2. A constructive grammar for every actual monomial
+
+Use the source's exact composition convention. A record m has invertible binary matrix A of size9, affine offset b, constant a modulo4, linear coefficients alpha_i modulo4 and symmetric binary quadratic matrix Q, with `alpha_i mod2=Q_ii`. On a basis address x it acts as
+
+```
+|x> -> i^(a+q(x)) |A*x xor b>,
+q(x) = sum_i alpha_i*x_i + 2*sum_(i<j,Q_ij=1) x_i*x_j  (mod4).
+```
+
+This is exactly `prune_native.monomial`: diagonal phase first, then binary permutation, translation and absolute phase. The Q diagonal is encoded in alpha, not added again as a quadratic term. No phase convention is inferred from the binary matrix alone.
+
+Gaussian row elimination reduces any such A to identity with at most72 row additions and8 row swaps. Reversing that list implements A. Replace a row swap by three XOR row additions. This gives at most96 selected-bit row-addition records. The affine offset takes at most9 selected-bit translations. The phase takes at most27 unit-S records for the nine alpha values,36 controlled-sign records for the off-diagonal pairs, and3 global i records. Thus **any** admitted nine-axis monomial, including its inverse, has a recipe of at most
+
+```
+96+9+27+36+3 = 171
+```
+
+retained elementary movement/phase records; two independent adapters need at most342. These bounds are conservative and independent of f and the eventual multiplication input. The checker constructively reconstructs A, checks symmetry/parity and phase coefficients, and verifies the decomposition on zero, basis, pair and additional addresses. The algebraic row-reduction and degree-two polynomial argument establish the universal nine-bit statement; the probes corroborate it.
+
+The physical interpretation introduces no new instruction species. A row addition is precisely the selected compact-control addition with its full dirty-control restoration and repair. XOR translations are fixed selected-bit affine operations. For a phase, compute its fixed degree-two residue modulo4 once per complete record from address/descriptors, then apply one of `{1,i,-1,-i}` to its Gaussian-dyadic value. This is a sign change and/or exchange of real and imaginary components on the retained fine grid, with zero coefficient height. For f columns, computing the residue scans at most O(f) selected address bits and therefore costs a fixed polynomial in the existing descriptor length A. The record-paid offset/phase setup is absorbed by the **same** retained superpolynomial record fiber, not charged as a new per-payload-bit scan. Complete address ranges and control reservations are the selected source hypotheses throughout.
+
+In particular, neither a new field extension nor scalar rounding nor a free arbitrary permutation is used. The full address transformation is factored into the selected row-addition primitive and inverse routes; its workspace is the source's restored complete control fields and fixed work tapes, with newly substituted template constants.
+
+## 3. Quantifiers and the all-f lift, including the absolute phase
+
+First fix the complete finite word, every matrix/phase recipe, its ordered owner list and all fixed matchers. Only after those choices let f be any positive integer column multiplicity. For x=(x_1,...,x_f), the lifted monomial is
+
+```
+x_j -> A*x_j xor b  for every j,
+phase = a*f + sum_(j=1..f) q(x_j)  (mod4).
+```
+
+Apply the finite row-addition list to the corresponding pair of complete f-axis slots, and use the pointwise residue above. Each selected slot is a full range; arbitrary intervening, preceding and following spectator fields remain present. The temporary complete compact fields are returned by each addition. Thus the lift is exactly m tensor-powered f, acting as identity on the other address fields. It uses one fixed list of primitive **types/operations**, rather than f separately allocated tapes. Its per-record descriptor arithmetic is polynomial in the same selected address bound, and the number of work tapes stays fixed for the template.
+
+For a recorded positive-rank recipe, source equality is the ordered product `right.then(C_r).then(left)`. Tensoring this product gives `right_f.then(C_(r*f)).then(left_f)` after the fixed coordinate reordering. This is one ordinary positive rank-r*f child on the actual owner's full stream, with its input and output monomials independently retained. Inverse orientation and Pauli corrections are included by the actual signed recipes. No identity distributes a tensor power over a matrix sum.
+
+For the scalar word itself, use selected #4359's free-word substitution theorem: replace each warp generator by its f-column lift while leaving ADD/SCALE coefficients and chronology unchanged. This is an algebra homomorphism from the noncommuting free-word algebra; hence the already checked arbitrary-input word identity survives. The scalar program is not itself tensor-powered. Keeping a single constant phase a instead of a*f would violate the lift; a negative control explicitly distinguishes that mutation at f=2.
+
+The ideal algebraic lift holds for every positive f. Its physical tariff applies only in the selected source domain: f<=p, A=O(p), K/log p tending to infinity, and a superpolynomial record fiber. In the actual layer f<=e<=floor(b_in^epsilon) and p=6*b_in eventually. No tariff is extrapolated to arbitrary independent f,p/geometry. The compact-control parameter hypotheses are unchanged: f slots, complete dirty reservations, `A=O(p)`, record fiber beyond fixed powers, and the same selected movement exponent. The final uniform template may have much larger fixed dimensions and operation counts. That changes constants and thresholds through section6 below, rather than changing these quantifiers or creating a new tape per coordinate.
+
+## 4. Exhaustive family/owner specialization
+
+The executable source census is over the actual final payload, not its proposed histogram. It classifies every event in both21449-record orientations, and checks exact scalar coefficients/opcodes/chronology against the selected THREE-base word. Main charts on all224 persistent main owners are exact retained records. Every scalar target/source belongs to the632 declared persistent owners or the one declared owned C0. Clear and overwrite COPY target only C0; ADD arguments are distinct owners; no new borrowed owner, alias or productive C0 is introduced.
+
+| Actual family | Membership/coverage | Selected physical interpretation |
+| --- | --- | --- |
+| 180 signed warp classes,240 occurrences | Each actual G is invertible; both signed recipes have rank0;800new monomial records cover this and the changed families below | Fixed affine binary permutation and unit quadratic phase from section2; same all-f native generator |
+| 3290 borrowed climbs per orientation | Actual source/target bases strictly nested, correct current owner/frame and rank | The selected arbitrary-U-subset-V factorization: two rank-zero adapters and one positive rank-r*f child |
+| Eight center calls per orientation | Actual nested comparable bases, owned C0 only, all eight rank8 jobs billed | Same positive child plus signed adapters; no productive credit, no allocation of a new arbitrary input |
+| 408 helper endpoints | Actual strict nested entrance/exit, profile `{4:28,7:7,8:47,9:326}` | Complete two-sided normal form on each distinct arbitrary input field; no internal scalar reframing shortcut |
+| 448 main entrance/exit charts | Exact event equality with retained base main charts | Source-identical selected chart/axis interface, with its retained charge |
+| 17453 scalar records per orientation | Exact old opcode/coefficient sequence, dyadic grammar and current-frame checks | Retained ADD, dyadic unit SCALE, owned COPY/CLEAR; identical scalar tariff |
+| Ten phase labels | Fixed annotations, no new physical instruction | Existing scalar-word scope boundaries; not extra outputs or uncharged operators |
+
+Exact factorization equality and arbitrary-input endpoints are independently established by the admission dossier's native/phase replays, not by a syntactic schema. This module supplies the missing **physical class implication** for those exact factors. The new phase receipt covers180signedwarp classes,105newpaid pairs and5changedhelper pairs. The382 unchanged helpers are bound to the selected #4470 phase receipt through gain_acceptance's exact ordered-basis/owner lineage;26changed helpers use the new five-pair receipt. The independently replayed all2855paid-pair factorization module supplies the full actual paid-pair coverage. These coverage claims remain separate from this module's fresh class/census checks.
+
+For owned return, the local word retains one physical C0 and ends its C0 updates with a permitted erase. The existing arbitrary-input native proof establishes completed main/helper endpoints and C0 clearance. During product/compiler substitution, each suspended local occurrence receives its own center bank; all child inputs are distinct actual fields, even when values are correlated or one input is a parent's center. The child finishes and its adapters/role ordering return **before** the parent resumes. The parent clears only its own bank after its last use. Every such bank is excluded from productive W and included in full O. This is exactly the selected compiler ownership rule; no one-bank-per-depth reuse or undeclared initialized input is used.
+
+## 5. Finite raw tariffs in the selected unit
+
+The tariff unit here is a retained elementary scalar/movement/phase **record**, each realized with the selected physical primitive's asymptotic bound. It is not one literal tape instruction and does not suppress the f-dependent movement bound. Choose the same common upper unit for the fixed primitive alphabet as in the selected finite-word accounting. Each new two-sided nine-axis recipe has at most342 elementary records, below the retained conservative1000-per-group allowance. Unchanged main charts retain their selected count/unit. The selected primitive implementation constants, record-paid setup, scans and repair remain paid in that common physical unit. Changing the finite catalogue does not require a new asymptotic movement assumption.
+
+The actual local route groups are
+
+```
+3298 paid jobs + 2*408 helper wrappers + 240 warps + 448 main charts
+  = 4802 groups,
+4802*1000 = 4,802,000.
+```
+
+The source scalar allowance formula, reimplemented directly without importing its evaluator, gives158120 forward and158168 backward. Therefore
+
+```
+158168 + 4802000 = 4960168 < 10^7.
+```
+
+This is an instantiation of the selected raw-unit bound with a smaller changed paid count, not reuse of an old expanded compiler cap. The controller remains18full calls and15thin queries, with the exact retained physical-event and boundary programs. The complete source raw bound is
+
+```
+18*10^7 + 15*1792
+  + 32*112*(#physical_events + #left_boundary_program + #right_boundary_program)
+  = 181098496 < 10^9.
+```
+
+Each thin query's paid rank-one request, owned copy/add/erase and inverse orientation remain in the source invoice. Idle jobs, main normalizations, inherited controller geometry and actual exact phase bills remain charged. No local or controller charge is credited as a new productive output. These numerical bounds concern **raw** supplier records only; they are not the expanded uniform word's operation count, storage or literal physical runtime.
+
+## 6. Expanded compiler, precision and tape constants
+
+Apply the selected chronological product, same-owner paid completion, disjoint splitting and integer finite compiler to this now-specialized raw program. The algorithms are finite and only instantiate the same grammar. Their matching uses complete job endpoints and restores adapters, and their owner allocation is the rule just proved applicable. No new movement species occurs when a fixed matcher has a larger fixed rank: binary basis/coordinate permutations have the same finite elimination construction, now with a larger fixed list.
+
+Let W,P,O be the actual final productive width, paid rank-one count and full owned-bank allocation; let R count the full native/movement/normalizer records, including product, completion, split and compiler routes. Let G be their fresh dyadic coefficient/phase allowance, computed by summing the actual scalar allowances (plus the source's conservative non-scalar charge). These are finite computable integers of the new expanded template. They are fixed before multiplication input size varies. A record-count overestimate and one owned bank per relevant occurrence suffice; no practical materialization or old p3 numerical count is needed.
+
+Use the **new** values in the selected semantic prescription:
+
+```
+Z=W+O,
+E=64*(Z+N+P+G+1)^3,
+B=P+E,
+C0=32*N*B^2.
+```
+
+The selected completed-child argument gives `A(e)<=A(floor(e/N))+P*floor(e/N)+E`, hence `A(e)<=2B*e`. Monomial permutations/unit phases add no coefficient height but do retain their execution/descriptor costs. The new C0 determines a new eventual fine-grid threshold. The compact row reserve, full simultaneous stock products, depth-first parking, fixed tape inventory and polynomial setup degrees also use the new W,P,O,R,N and selected formulas. Fixed enlarged degrees/counts are absorbed by the same retained superpolynomial record fiber and strict outer epsilon<1 after increasing the threshold. In particular, neither raw10^9 nor selected p3/p16 reserve constants stand in for these expanded values.
+
+Thus P2–P4 can consume a genuine new finite instance of H_selected's grammar and precision/stock/tape prescriptions. This note does not independently prove the historical native movement/repair or outer analytic/recovery stack. Those are exactly the assumptions already retained by selected #4470, with no additional candidate-specific implementation assumption.
+
+## 7. Conclusion and exact limits
+
+Given H_selected and the source-bound exact semantic/phase endpoints supplied by the independent native dossier, the final catalogue has permitted explicit all-f realizations, legal actual-owner return, finite raw tariffs and the selected expanded-constant substitution. No extra primitive or changed movement exponent is required. P1 is therefore a **consequence** of H_selected for this instance. It need not be restated as a new hypothesis “the new recipes implement.”
+
+`checks/specialization.py` runs through the master verifier and its source-authenticated `--repo` working-byte loader; it never substitutes clean Git blobs for dirty inputs. Its new actual catalogue has800monomials with at most83 elementary records each, compared with the uniform171 bound. It also checks1692selected monomial records by the identical schema, exhaustive event/role/rank/scalar census in both orientations, helper geometry, retained main charts, the4802route grouping and raw bounds. Controls reject singular maps, non-Z4 absolute phases, borrowed clear, unpaid rank changes, non-dyadic scalars and an unlifted f=2 global phase. Exact phase/operator equality is intentionally supplied by the separate phase/native verification rather than inferred from membership.
+
+Credits remain with Cao Yifan/intqwq (#4610), Cinna Davis (#4470/#4416/controller/helper lineage), zxv (#4359/native/compiler/semantic precision), icekylinx and Dugongue (general Clifford/transported frames), Jacob Alan Sussman (mixed integer compiler), and all retained physical/BIT/geometry/analytic contributors. This new specialization/proof/check uses substantial OpenAI assistance. It is a scoped conditional AI verification contribution, not an unconditional multiplication theorem or independent human/kernel acceptance.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/TASK.json b/research/owned-relation-independent-validation/engines/cost/frozen/TASK.json
new file mode 100644
index 0000000000..f5df24ffe3
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/TASK.json
@@ -0,0 +1,80 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 7,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json",
+      "research/selected-k8-unrestricted-ends/README.md"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+    "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts.",
+      "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": [
+      "Mixing only providers already inside the pinned catalogue.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Make helper L230 owned in each backward call, prepare one five-helper relation, retain one exact frame-254 snapshot, remove one rank-eight center and one rank-one zero job, and debit one rank-nine target.",
+  "scope_change_reason": "This uses the current helper-inventory priority. It changes the independent input inventory and scalar word; all physical native maps and the p16 controller remain fixed.",
+  "bottleneck_link": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737",
+  "budget_minutes": 240,
+  "stop_rule": "Publish one exact complete-profile kappa improvement after native, ownership, phase-inheritance, compiler and cold-export checks.",
+  "outcome": "completed",
+  "evidence": "README.md, WORD.json.gz, RESULT.json and verify.py. The complete conditional kappa is 60447/20000000.",
+  "author": "Ali Romman",
+  "ai_assistance": "Substantial OpenAI Codex assistance in discovery, code, proof, verification and publication.",
+  "open_questions": [
+    {
+      "question": "Can a separate reviewer validate this one-relation restriction and the inherited physical transfer premises?",
+      "why_it_matters": "The new finite construction is exact, but the complete bound still uses the source phase and all-size contracts.",
+      "first_step": "Replay the three unrestricted source rows in native.py and check the COPY and zero-identity argument in README.md.",
+      "blocked_by": "Independent review has not yet occurred."
+    },
+    {
+      "question": "Can a different helper relation give another complete positive bill?",
+      "why_it_matters": "This construction gives one positive instance, not an optimum for changed helper inventories.",
+      "first_step": "Claim a disjoint relation in Discussions, derive its exact rows, and include every lost target and owned-storage cost.",
+      "blocked_by": "Current active cache and paid-history scopes must be checked first."
+    }
+  ],
+  "coordination": {
+    "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737",
+    "distinct_scopes": [
+      "https://github.com/CrocSwap/integer-mult-bounds/discussions/5355",
+      "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930"
+    ],
+    "boundary": "The first scope retains 632 arbitrary inputs and eight centers. The second retains every original helper endpoint. This package removes the independent L230 job only in backward calls and claims only the stated relation and two event replacements."
+  }
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/VERIFY.json b/research/owned-relation-independent-validation/engines/cost/frozen/VERIFY.json
new file mode 100644
index 0000000000..8098df4c80
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/VERIFY.json
@@ -0,0 +1,38 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/higher-moment-strictification/verify.py",
+    "research/joint-helper-lattice/CONTROLLER.json",
+    "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+    "research/kappa-rebuild/architecture/mixed_target_probe.py",
+    "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+    "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+    "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json",
+    "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py",
+    "research/query-thinned-controllers/RESULT.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "The same checks remain active with Python assertions disabled."
+    }
+  ]
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/WORD.json.gz b/research/owned-relation-independent-validation/engines/cost/frozen/WORD.json.gz
new file mode 100644
index 0000000000..5e79bd826c
Binary files /dev/null and b/research/owned-relation-independent-validation/engines/cost/frozen/WORD.json.gz differ
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/agents-initial.txt b/research/owned-relation-independent-validation/engines/cost/frozen/agents-initial.txt
new file mode 100644
index 0000000000..aea5573d1b
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/agents-initial.txt
@@ -0,0 +1,86 @@
+# Agent entry point
+
+For open-ended requests such as “contribute,” “use spare inference,” or
+“improve the bound,” start with [autoresearch.md](autoresearch.md). It links
+the current priorities and standing procedure. Check open handoffs
+before using the task picker; its coverage fields identify prior checks and
+remaining obligations. Explicit user tasks take precedence over that default
+assignment; do not reroll an already assigned task.
+
+For repeated/overnight loops, follow the
+[upstream refresh checkpoint](autoresearch.md#looping-agents-refresh-upstream-at-each-research-checkpoint)
+at every new round, before a major pivot and before submission. Fetch canonical
+main (not an unmaintained fork), compare priority revisions, and read changed
+guidance. The local task picker does not fetch updates. Preserve work in progress
+and frozen evidence; start new tasks from the refreshed base.
+
+Default to one session of about 60 minutes unless the donor sets another budget.
+For a concrete introduction, read [the bottleneck brief](docs/research/bottleneck-brief.md)
+and [glossary](docs/research/research-glossary.md). Use the card's first working
+example before choosing a detour. A useful finding or handoff can finish a
+session; a PR is not mandatory. Read the [family status and expansion gate](docs/research/research-family-status.md)
+before extending a mechanism: newer pending work may change the missing task,
+and a local improvement does not by itself justify another construction round.
+Partial contributions remain welcome; the director owns the complete budget.
+
+Before substantial research, read the
+[discussion-board start here](https://github.com/CrocSwap/integer-mult-bounds/discussions/1163)
+and check [active discussions](https://github.com/CrocSwap/integer-mult-bounds/discussions)
+alongside open PRs for overlap. Use the
+[handoff thread](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166)
+for concrete requests and the
+[mechanism-proposals thread](https://github.com/CrocSwap/integer-mult-bounds/discussions/1167)
+for early ideas. Follow the claim/update conventions in `autoresearch.md`;
+claims are advisory and discussion posts are provisional evidence. Keep one
+canonical investigation thread with a current status and public artifact link;
+use hub threads for short pointers. Local-only evidence must be labelled, and
+useful partial/negative results do not need a new κ to merit a focused PR.
+
+Use `python3 scripts/find_overlap.py --task TASK_ID` for a cached search of PR
+bodies, discussions and local package notes. The report states its coverage and
+freshness; no matches is not proof of novelty. If changing a card's premise,
+record the scope change and why the new question matters.
+
+When acting as an authorized maintainer/director and reassessing research
+direction, follow the [priority-review procedure](autoresearch.md#6-maintainerdirector-priority-review).
+Update the task catalogue and evidence log together; do not infer a new frontier
+or a universal barrier from assignment weights or unreviewed discussion claims.
+
+Read [CONTRIBUTING.md](CONTRIBUTING.md) before making changes. Resolve the current
+result, review, source manifest and reproduction command through
+`certificates/selected-result.json`. Historical research notes may use “current”
+for an obsolete checkpoint.
+
+For authorized maintainer PR work, **first follow [delta-only queue intake](docs/research/pr-intake.md)**.
+Run `python3 scripts/pr_intake.py plan --refresh --output /tmp/pr-intake-plan.json`.
+Read selected actionable entries; do not rereview unchanged holds, recreate
+100-entry audit packages, or rerun historical suites after compaction. Persist
+changed scheduling decisions in `docs/research/pr-intake-state.json` and actual
+review evidence in the central ledger. This scheduling procedure takes precedence
+over older batch recipes. No automatic Lean, Docker, or concurrent heavy replays.
+See [research archive status](docs/research/research-archive-intake.md) for acceptance
+rules: a merged archive can remain **partially reviewed**; merging is not scientific
+approval or a selected-frontier update.
+
+Keep `upstream/`, frozen source archives and pinned evidence unchanged. Put new
+research in its own scoped directory and retain predecessor attribution.
+Distinguish a finite certificate, a scoped proof, a search failure and a complete
+multiplication theorem. They are different claims.
+
+Use an isolated branch/worktree when sharing a checkout. Run checks relevant to
+the change; do not run concurrent artifact-regenerating suites in one worktree.
+Record exact sources, commands, environments and any unrun proof obligations.
+
+The standard donation prompt authorizes routine Discussion participation and
+opening focused PRs. When that prompt is the user's assignment, post claims,
+questions, findings, handoffs and feedback without asking again for each post;
+the same applies to opening the contribution PR. Respect any narrower donor or
+account restrictions. Merely reading this file does not override those restrictions.
+Do not change the selected frontier or merge/close others' PRs without maintainer
+authorization; existing explicit authorization remains valid.
+
+New research packages should include **Open next questions** and can use the
+[minimal package generator and explicit replay hook](docs/research/research-package-guide.md).
+Optional workflow feedback goes in the PR or the
+[feedback discussion](https://github.com/CrocSwap/integer-mult-bounds/discussions/1200).
+Link it once; no separate session report is required.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/autoresearch-initial.txt b/research/owned-relation-independent-validation/engines/cost/frozen/autoresearch-initial.txt
new file mode 100644
index 0000000000..2fe84a7b30
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/autoresearch-initial.txt
@@ -0,0 +1,104 @@
+# Contributing donated research effort
+
+**Start here if you were told to “contribute.”** Aim for one useful, independently
+reviewable result in about **60 minutes**, unless your donor specifies a budget.
+A precise partial result, counterexample, missing-lemma audit or handoff can be
+valuable; producing a PR or increasing κ is not required.
+
+1. Read [current priorities](docs/research/current-priorities.md) and the
+   [selected record](certificates/selected-result.json). Use the
+   [bottleneck brief](docs/research/bottleneck-brief.md) and
+   [glossary](docs/research/research-glossary.md) as needed.
+2. **Check [handoffs #1166](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166)
+   before drawing a card.** Prefer a suitable open request on your track; check
+   its artifacts, claims and live PR overlap. Do not reroll an assigned task.
+3. If no suitable request fits, run `python3 scripts/choose_research_task.py`.
+   Inspect the card's `existing_checks` and remaining obligations. Unknown
+   coverage is not evidence of novelty; old source contexts need reassessment.
+4. Follow the [standing procedure](docs/research/agent-procedure.md),
+   [CONTRIBUTING.md](CONTRIBUTING.md), and the relevant
+   [family expansion gate](docs/research/research-family-status.md).
+   Name one concrete question, success/stop test, and bounded verification.
+5. Preserve source attribution and report exactly what was established.
+   [Post updates from a file](docs/research/coordination.md); structured metadata
+   is optional and advisory. Under the standard donation prompt below, routine
+   Discussion participation and focused PRs are authorized. Merging, closing
+   others' PRs and changing the selected frontier require maintainer authorization.
+
+For short sessions finishing within an hour, an advance CLAIM is optional after
+overlap checking. Claim a handoff you take, likely overlapping work and work
+continuing across sessions. FINDING/DONE does not imply scientific approval.
+
+## Looping agents: refresh upstream at each research checkpoint
+
+At each new round, before a major pivot and before submission, fetch canonical
+main and pin its commit. During a longer round, check at a safe point roughly
+once per hour. Read changed priorities, catalogue, selected record and relevant
+evidence. The picker does not fetch or reserve work. Preserve in-progress work
+and frozen inputs; fetching does not update your checkout. See the
+[exact refresh procedure](docs/research/agent-procedure.md#looping-agents-refresh-upstream-at-each-research-checkpoint).
+
+## 1. Orient briefly, then choose a distinct task
+
+[Handoff-first selection and overlap checks](docs/research/agent-procedure.md#1-orient-briefly-then-choose-a-distinct-task).
+An existing overlap cache can surface structured claims and handoffs with
+`python3 scripts/choose_research_task.py --coordination-cache /tmp/overlap.json`.
+Check the reported freshness and prose-only discussions too.
+
+## 2. Where effort is most useful
+
+[Current diagnosis and allocation](docs/research/current-priorities.md),
+[machine-readable cards](docs/research/agent-task-catalog.json), and
+[priority decisions](docs/research/research-priority-log.md).
+
+## 3. Make parallel effort meaningfully different
+
+[Task cards, claims, handoffs and stopping rules](docs/research/agent-procedure.md).
+
+## 4. Bound the experiment and kill unpromising routes early
+
+[Session budgets and stopping rules](docs/research/agent-procedure.md#4-bound-the-experiment-and-kill-unpromising-routes-early).
+
+## 5. Verify and submit one useful result
+
+[Verification, scope and attribution](docs/research/agent-procedure.md#5-verify-and-submit-one-useful-result).
+
+## 6. Maintainer/director priority review
+
+Use the [director review procedure](docs/research/agent-procedure.md#6-maintainerdirector-priority-review).
+Update current priorities, affected cards and their coverage, and the evidence
+log together. For PR work, use [delta-only intake](docs/research/pr-intake.md)
+and its construction-grouped view. Do not rerun unchanged historical reviews.
+
+## Hill-climbing track
+
+For κ-oriented work, beat the best open conditional κ by a small, exact step.
+A step must change the complete paid profile (more digits of the same root do
+not count), pass an exact operator replay, and state its ceiling and headroom.
+Title the PR with the new κ and its gain over the PR it improves, for example
+`Conditional κ = … (+1.140e-9 over #4088)`. When a climb reaches a proved
+fixed-model ceiling, or two rounds pass without a step, say so in a short PR
+or handoff and climb by changing the model (words, interfaces, providers or
+stock) instead of repacking the same invoice. This is not admission; the
+selected record still decides the frontier.
+
+## Short prompt for donating a session
+
+> Contribute one useful, independently reviewable result to
+> https://github.com/CrocSwap/integer-mult-bounds. Read AGENTS.md, autoresearch.md
+> and CONTRIBUTING.md from the current main branch first. Use the repository's
+> task-selection and overlap process unless I assigned a specific task. In a loop,
+> fetch canonical main and recheck priorities at every round using the guide's
+> checkpoint procedure; preserve in-progress work and frozen inputs. Work for
+> one session of about 60 minutes unless I specify another budget, keeping the
+> final quarter for verification and a concise handoff,
+> and report the exact scope, evidence, remaining obligations and predecessor
+> credit. You may post routine claims, questions, findings, handoffs and feedback
+> in Discussions and open a focused PR without asking me again for each action.
+> Do not merge, close others' PRs or change the selected frontier.
+
+Maintainers should update the catalogue when new evidence changes priorities.
+External donation prompts should point here rather than freeze a second set of
+weights, frontier values or supposedly open problems.
+
+Prepared by Douglas Colkitt with OpenAI Codex assistance. Apache-2.0.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/compiler.py b/research/owned-relation-independent-validation/engines/cost/frozen/compiler.py
new file mode 100644
index 0000000000..6a6f9373fe
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/compiler.py
@@ -0,0 +1,138 @@
+"""Independent stdlib finite compiler audit. No project code is imported.
+
+Exact atanh logarithm and Taylor exponential with rational remainder bounds;
+all acceptance comparisons are rational/integer. Authored for the swarm audit,
+retaining Cao Yifan/zxv/Cinna Davis/Jacob Alan Sussman predecessor credit.
+"""
+from fractions import Fraction as F
+from collections import Counter
+from functools import lru_cache
+from pathlib import Path
+from hashlib import sha256
+import argparse, json, time, platform, re
+from . import source
+
+UNIT=2**240
+def down(x): return F(x.numerator*UNIT//x.denominator,UNIT)
+def up(x): return -down(-x)
+def add(x,y): return x[0]+y[0],x[1]+y[1]
+def mul(x,y):
+    v=[a*b for a in x for b in y];return down(min(v)),up(max(v))
+def divide(x,y):
+    assert y[0]>0
+    return mul(x,(1/y[1],1/y[0]))
+def logbase(x):
+    z=(x-1)/(x+1);term=z;s=F(0)
+    for j in range(100):s+=term/F(2*j+1);term*=z*z
+    rem=2*abs(term)/(201*(1-z*z))
+    return down(2*s-rem),up(2*s+rem)
+@lru_cache(None)
+def logint(n):
+    b=n.bit_length()-1
+    a=logbase(F(n,2**b));l2=logbase(F(2))
+    return a[0]+b*l2[0],a[1]+b*l2[1]
+def exp_point(x):
+    if x<0:
+        l,u=exp_point(-x);return down(1/u),up(1/l)
+    shifts=0
+    while x>F(1,16):x/=2;shifts+=1
+    term=s=F(1)
+    for j in range(1,51):term=term*x/j;s+=term
+    nxt=term*x/51
+    # Ratios in the remaining positive Taylor series are <= x/52.
+    l,u=down(s),up(s+nxt/(1-x/52))
+    for _ in range(shifts):l,u=down(l*l),up(u*u)
+    return l,u
+def power(n,e):
+    l,u=logint(n);l,u=(e*l,e*u) if e>=0 else (e*u,e*l)
+    return exp_point(l)[0],exp_point(u)[1]
+def moment(p,e):
+    l=u=F(0)
+    for n,c in p.items():a,b=power(n,e);l+=c*a;u+=c*b
+    return l,u
+def ledger(p):
+    # Manually transcribed from the exact source; no AST/source execution.
+    k,b,a,q,ep,be,r,st,la=(p[x] for x in ['kappa','b','a','q','epsilon','beta','r0','stop','layout'])
+    si,ta=1-b,1-a;it=ta+(1-st)*max(si-ta,F(0));lf=si+st*(1-si)
+    lm=1-(q+a)/2;xi=ep*(1+q)-F(3,32)+la;key=be+1-ep
+    m=dict(main_transform=ep*q,global_coordinate_router=a,fused_gaussian=1-ep+q*be,group_bit_router=1-ep+a*be,group_scans=1-ep+be,boundary_algebraic_matrix=F(3,32)+xi-ep,sparse_union_movement=xi+F(1,2)-ep,polynomial_products=ep,microbox_face_corrections=1-(ep+be+48-128+2))
+    c=dict(actual_bit_above_effective=p['bit_saving']-a,complex_above_effective=b-a,q_positive=q,complex_endpoint=b-q,q_below_effective=a-q,stop_positive=st,stop_below_one=1-st,leaf_saving_above_effective=(1-st)*b-a,q_below_internal=1-it-q,q_below_leaf=1-lf-q,lambda_above_tau=lm-ta,lambda_above_sigma=lm-si,lambda_above_internal=lm-it,lambda_prime_above_lambda=1-q-lm,lambda_prime_above_leaf=1-q-lf,epsilon_positive=ep,epsilon_below_one=1-ep,cap_above_band=xi-F(1,2),cap_below_cell=ep-xi,group_positive=be,group_below_dimension=ep-be,support_router_span=1-be,group_gauge_power_slack=1-(2*xi-2)-r-be,actual_logarithmic_group_guard=1-(2*xi-2)-be,global_gamma_power_slack=1-ep-r,actual_logarithmic_gamma_guard=1-ep,alpha_logarithm_absorption=r,group_key_fits_record=1-key,membership_arithmetic_fits_record=1-be-2*(1-ep),microbox_halo_volume=128-48-be,positive_layout_slack=la,short_record_fallback=ep-a,complex_below_one_over_32=F(1,32)-b,strassen_integer_power_gap=F(2**45-7**16),theta_positive_polynomial_power=F(2),cap_below_phase_cell_power=2-xi,halo_covers_generic_inverse_radius=F(5),union_tag_work_per_visit_fits_record=1-be,union_header_fits_record=1-be,source_axis_superpolynomial=1-ep,gaussian_above_main=m['fused_gaussian']-m['main_transform'],new_complex_uniform_saving_above_b=p['complex_uniform_saving']-b,improvement_over_user_baseline=k-F('.001730970419199163702738'),new_semantic_guard_with_C1_one=1-ep,fine_prime_halo_umbrella=F(7,2))
+    c.update({n+'_above_kappa':v-k for n,v in m.items()})
+    f=dict(new_semantic_group_guard=1-be,new_BIT_row_stock_sublinear_in_active_group=be*F(997,1000),fixed_halo_explicit_metadata_branch=128-48-ep-be-1,actual_new_BIT_stock_sublinear=be*F(996,1000))
+    return m,c,f
+def enc(x):
+    if isinstance(x,F):return str(x)
+    if isinstance(x,dict):return {str(k):enc(v) for k,v in x.items()}
+    if isinstance(x,(tuple,list)):return [enc(y) for y in x]
+    return x
+def run(root,invoice):
+    start=time.monotonic();pkg='research/kappa-round6-compiler-tightening-20261022/'
+    a=source.js(pkg+'ARITHMETIC.json');controller=source.js('research/joint-helper-lattice/CONTROLLER.json')
+    assert source.digest(source.raw('research/joint-helper-lattice/CONTROLLER.json'))==a['source_sha256']['research/joint-helper-lattice/CONTROLLER.json']
+    assert source.digest(source.raw('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py'))==a['source_sha256']['research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py']
+    H={4:28,7:7,8:47,9:326};P0={1:2201,2:412,3:510,4:127,5:40,8:8};T,P=Counter(),Counter()
+    for e in controller['physical_events']:
+        if e[0]=='LOCAL':T.update(H);P.update(P0)
+        elif e[0]=='QUERY_SHEAR':P[1]+=112
+        elif e[0]=='IDLE':P[8*len(e[2])]+=224
+        elif e[0] in {'ADD','SIGNED_SWAP'}:pass # Scalar operations, priced below.
+        else:raise AssertionError(e[0])
+    for e in controller['diagonal']:T[1+8*sum(e[1:])]+=112
+    assert dict(T)=={int(k):v for k,v in invoice['targets'].items()} and dict(P)=={int(k):v for k,v in invoice['paid'].items()}
+    assert dict(T)=={int(k):v for k,v in a['targets'].items()} and dict(P)=={int(k):v for k,v in a['paid'].items()}
+    assert H=={int(k):v for k,v in a['local_helpers'].items()} and P0=={int(k):v for k,v in a['local_paid'].items()}
+    assert sum(T.values())==10928 and sum(P.values())==64404
+    assert sum(n*c for n,c in T.items())-sum(n*c for n,c in P.items())==752
+    k=F('.0030217758');s=F('.00302177581');g=(s-k)/7;t=1-s;reserve=F(1,10**11)
+    assert F(a['kappa'])==k and F(a['strictification']['tested'])==s
+    tt,pp=moment(T,t),moment(P,t)
+    rootlow,roothigh=map(F,a['raw_root_interval'])
+    ml=moment(T,1-rootlow)[0]-moment(P,1-rootlow)[1]
+    mh=moment(T,1-roothigh)[1]-moment(P,1-roothigh)[0]
+    assert ml>0>mh and s<rootlow
+    ratios=dict(alpha=divide(pp,tt),gamma=divide(moment(P,t+F(1,5)),mul(power(20,F(1,5)),tt)),delta=divide((F(sum(T.values())*21),)*2,mul(power(20,s),tt)))
+    for n,x in ratios.items():assert F(a['strictification'][n]['lower'])<=x[0]<=x[1]<=F(a['strictification'][n]['upper'])
+    assert ratios['alpha'][1]<1-reserve and ratios['alpha'][0]>1-F(1,10**9)
+    assert ratios['gamma'][1]<F(97,100) and ratios['delta'][1]<F(97,100)
+    assert F(97,100)**128<F(1,16)
+    normalized=1/(1+1024*reserve)+F(4,2**32)
+    assert normalized==F(a['strictification']['normalized_paid_upper'])<1
+    # 1024=8*128; both tails contribute <=2/2^32, total <=4/2^32.
+    assert 2*F(97,100)**1024+2*F(97,100)**1024<F(4,2**32)
+    assert t+F(1,5)>=1 and 20**64<21**63
+    theta=F(63,64);assert 2*(20**1024)**64<=(145**1024)**63
+    # Ambient m=145^1024; compiler eta=t*m^(t-1).
+    assert 1024*s<F(25,8) and 145<2**8
+    assert 2*145**3==6097250 and theta**1000<t/F(6097250)
+    assert 6097250<2**1000
+    eta=mul((t,t),power(145,-1024*s));assert eta[0]>theta**1000
+    j=55099;step=g.denominator;h=step*j
+    assert g==F(1,700000000000) and h==a['compiler']['H']==38569300000000000 and j==a['compiler']['integer_test_exponent']
+    assert (h+1)**1000<2**j and (step*(j-1)+1)**1000>=2**(j-1)
+    assert h>8*1024
+    # Strict convex log ratio has one positive crossing; previous-grid failure
+    # plus success establishes minimality on this grid (not among programs).
+    uniform=k+6*g;assert s-uniform==g and uniform==F(a['compiler']['uniform_saving'])
+    p=dict(kappa=k,tested_saving=s,complex_uniform_saving=uniform,b=k+5*g,a=k+4*g,q=k+3*g,bit_saving=F(17,5000),epsilon=1-g,beta=1-3*g,r0=g/10,stop=g,layout=g,d=g)
+    for n,v in p.items():assert F(a['outer']['parameters'][n])==v
+    m,c,f=ledger(p)
+    for n,tab in [('margins',m),('strict_checks',c),('functional_checks',f)]:assert tab=={x:F(y) for x,y in a['outer'][n].items()}
+    assert len(c)==54 and len(f)==4 and min(c.values())>0 and min(f.values())>0
+    assert 0<f['actual_new_BIT_stock_sublinear']<1 and 0<f['new_BIT_row_stock_sublinear_in_active_group']<1
+    controls={}
+    for n,patch in [('old_BIT',dict(bit_saving=F('.0027'))),('closed_uniform',dict(complex_uniform_saving=p['b'])),('unfunded_endpoint',dict(kappa=s)),('closed_epsilon',dict(epsilon=F(1))),('missing_layout',dict(layout=F(0))),('group_full_dimension',dict(beta=p['epsilon']))]:
+        _,bad,_=ledger(dict(p,**patch));failed=[x for x,v in bad.items() if v<=0];assert failed;controls[n]=failed
+    # Explicit parameter mutations fail charged compiler inequalities.
+    controls['old_reserve_rejected']=ratios['alpha'][0]>1-F(1,10**9)
+    controls['power128_does_not_fit_rounded_tail_envelope']=1/(1+128*reserve)+4*F(97,100)**128>1
+    controls['preceding_grid_rejected']=(step*(j-1)+1)**1000>=2**(j-1)
+    assert all(controls[x] for x in controls)
+    scalar=158168;routes=(sum(P0.values())+2*408+688)*1000
+    raw=18*10**7+15*1792+32*112*(len(controller['physical_events'])+sum(len(controller['boundaries'][x+'_program']) for x in ['left','right']))
+    assert routes==4802000 and scalar+routes<10**7 and raw==181098496<10**9
+    assert a['nonrecursive']=={'local_scalar':scalar,'local_routes':routes,'raw_scalar_upper':raw}
+    bit=a['ordinary_BIT'];ordinary=(1-F(bit['atom']))*F(bit['after_cover'])+F(bit['atom'])*F('.0000384599')
+    assert ordinary==F(bit['ordinary_saving']) and F(bit['atom'])>ordinary>F(bit['admitted'])>s
+    assert F(bit['atom'])<1-ordinary
+    result=dict(status='PASS_INDEPENDENT_EXACT_FINITE_COMPILER_AND_58_OUTER',command='final4610-independent-admission compiler stage',python=platform.python_version(),seconds=time.monotonic()-start,repository_pin='ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c',arithmetic_sha256=source.digest(source.raw(pkg+'ARITHMETIC.json')),source_sha256=sha256(Path(__file__).read_bytes()).hexdigest(),targets=dict(T),paid=dict(P),kappa=k,tested=s,ratios=ratios,eta=eta,normalized_paid_upper=normalized,completion_slack=1-normalized,uniform_saving=uniform,gap=g,H=h,j=j,root_signs=[ml,mh],nonrecursive=dict(scalar=scalar,routes=routes,raw_controller_scalar=raw),outer_strict_count=len(c),functional_count=len(f),minimum_outer_strict_slack=min(c.values()),outer_strict_slacks=c,functional_slacks=f,controls=controls,fresh_author_recorded_modules=[],reused_author_recorded_modules=[],objects_checked=False,Lean_run=False,scope='Fresh independent exact arithmetic from the independently derived invoice; no Lean/log acceptance inherited and no end-to-end multiplication theorem.')
+    return enc(result)
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/contributing-initial.txt b/research/owned-relation-independent-validation/engines/cost/frozen/contributing-initial.txt
new file mode 100644
index 0000000000..fe54f23f19
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/contributing-initial.txt
@@ -0,0 +1,101 @@
+# Contributing and independent review
+
+**For donated inference or an open-ended “contribute” task, start with
+[autoresearch.md](autoresearch.md).** It provides weighted task suggestions,
+semantic overlap checks and bounded stopping criteria. Follow explicit user
+assignments instead of drawing a new task. The root [AGENTS.md](AGENTS.md) also
+points agents there. Existing external donation prompts should use this
+repository-owned guidance for current priorities.
+
+Before substantial research, check the
+[discussion board](https://github.com/CrocSwap/integer-mult-bounds/discussions)
+alongside open PRs. The [start-here post](https://github.com/CrocSwap/integer-mult-bounds/discussions/1163)
+explains claims and updates; use [handoffs](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166)
+for concrete requests and [mechanism proposals](https://github.com/CrocSwap/integer-mult-bounds/discussions/1167)
+for early ideas. Existing discussion claims are advisory, and findings remain
+provisional until their evidence is checked.
+
+New research packages should include **Open next questions**, with relevance,
+a feasible first step and blockers. Use the optional
+[package generator and replay manifest](docs/research/research-package-guide.md)
+to reduce packaging work. Keep frozen predecessor packages unchanged. A focused
+finding or handoff is also a valid session outcome; a PR is not mandatory.
+
+The standard donation prompt in autoresearch.md authorizes routine Discussion
+posts and opening focused PRs without repeated permission checks. Respect narrower
+donor instructions. Optional workflow feedback belongs in the PR or the
+[feedback discussion](https://github.com/CrocSwap/integer-mult-bounds/discussions/1200).
+
+
+For maintainer queue work, start with the [delta-only intake procedure](docs/research/pr-intake.md)
+and persistent scheduling cache. Do not repeat unchanged blocked reviews.
+
+Before reviewing an existing PR, consult the [central review ledger](docs/research/pr-ledger.md).
+Record the reviewed commit and its evidence separately from publication and GitHub closure.
+Recheck the current head before closing incorporated work, link its retained source and attribution,
+and leave partial or changed submissions open with the remaining question recorded. Research notes
+and verification tools can merit integration even when they do not improve the selected bound.
+
+Maintainers distinguish **archival intake** from **validated incorporation**.
+New isolated research packages may be merged after source/integrity intake while
+remaining `partially_reviewed` in the ledger, with the unverified obligations
+preserved. Such a merge retains the contribution; it does not verify a theorem,
+certify a new κ, or change the selected result. Shared-code changes and known
+correctness objections remain in substantive review. See the
+[archive policy and exact-head index](docs/research/research-archive-intake.md).
+
+This is a research draft. Corrections to the mathematics, implementation,
+source attribution, and stated scope are welcome through issues or pull requests.
+
+For a mathematical issue, identify the exact proposition, source label, or
+inequality; give a counterexample or the missing implication when possible;
+and distinguish numerical validation from an algorithmic proof obligation.
+For the current result, start with the
+[current status](docs/research/current-status.md),
+[selected record](certificates/selected-result.json), and the maintainer review
+at that record's `review` path.
+The selected record and review identify the actual supplier sources,
+reproduction command, evidence and remaining assumptions. Earlier construction
+notes are historical checkpoints, even when their text calls a result current.
+The [original audit](docs/audit.md) describes the retained upstream assumptions.
+
+For a parameter improvement, supply exact rational choices, the full dependency
+argument, and an updated patch against the pinned source. Explain whether the
+change stays within the parameter ceiling or changes one of its hypotheses.
+
+Keep `upstream/`, frozen source archives and pinned evidence unchanged. When
+changing generated artifacts, edit their generators and include the regenerated
+certificates and patches in the same change. Run the checks affected by your
+changes; do not launch every historical replay for an unrelated contribution.
+Changes to the selected construction also need its applicable complete cold
+replay: use the `reproduce` command in the selected record rather than copying a
+target from a historical note. Source-bound reuse must preserve explicit coverage
+and invalidation. Run artifact-regenerating suites in isolated worktrees.
+The historical `make gen4-bank-verify` target checks the earlier generation,
+not the selected frontier. The proof and bank scheduling supplements are supplied as Markdown;
+historical PDF targets belong to their respective checkpoints. Review changes to
+claims in the README and note together. Finite tests should address a mathematical
+identity or a failure mode, rather than simply restating implementation details.
+
+**Regenerated artifacts and hashes.** When verification regenerates a compressed artifact, compare its decompressed payload (or a documented canonical representation of every proof-relevant field). Compression headers and streams can differ across Python, zlib and tar versions. Keep exact hashes for committed source archives and other immutable inputs; a regenerated container hash may be recorded with environment details but should not determine mathematical equality across environments. See the [community reproducibility audit](research/gzip-container-reproducibility/README.md) by Maxime Fleury, following Antoine Olivier’s independent replay findings.
+
+New contributions are under the repository's Apache-2.0 license. Retain source
+attribution and disclose substantial AI assistance. Do not describe certificate
+success as a formal verification of the full multiplication theorem.
+
+Before building on pending work, consult the [contribution-review index](docs/research/contribution-review.md), pin its sources, and preserve contributor attribution.
+
+Parallel approaches, small improvements, independent reproductions, review and
+well-scoped negative results are welcome. Please identify predecessor work and
+explain what your submission adds, even if a concurrent result has a stronger
+headline. We preserve credit for useful contributions that are superseded or not
+imported; see [CONTRIBUTORS.md](CONTRIBUTORS.md). Attribution corrections are
+welcome too. State which proof obligations remain open rather than presenting
+finite certificate checks as a complete theorem audit.
+
+The historical `integration/community` workflow used `make verify` for its
+imported candidate chain; it is not the current selected cold replay. See
+[the integration ledger](docs/research/community-integration.md) for that history
+and [the batching guide](docs/research/batched-review.md) for the changed recursive
+interface. Preserve the historical checkpoint tests.
+Imported CC0 proof sources retain their source-specific license and notice.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/controller-CONTROLLER.json b/research/owned-relation-independent-validation/engines/cost/frozen/controller-CONTROLLER.json
new file mode 100644
index 0000000000..49a2f06758
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/controller-CONTROLLER.json
@@ -0,0 +1,5224 @@
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+      5,
+      [
+        0,
+        1,
+        3,
+        5,
+        7,
+        9
+      ]
+    ],
+    [
+      "ADD",
+      8,
+      10,
+      1
+    ],
+    [
+      "ADD",
+      11,
+      9,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      10,
+      4,
+      false
+    ],
+    [
+      "ADD",
+      8,
+      10,
+      -1
+    ],
+    [
+      "ADD",
+      11,
+      9,
+      1
+    ],
+    [
+      "LOCAL",
+      11,
+      5,
+      true
+    ],
+    [
+      "IDLE",
+      6,
+      [
+        0,
+        1,
+        3,
+        5,
+        7,
+        9,
+        11
+      ]
+    ],
+    [
+      "ADD",
+      10,
+      12,
+      1
+    ],
+    [
+      "ADD",
+      13,
+      11,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      12,
+      5,
+      false
+    ],
+    [
+      "ADD",
+      10,
+      12,
+      -1
+    ],
+    [
+      "ADD",
+      13,
+      11,
+      1
+    ],
+    [
+      "LOCAL",
+      13,
+      6,
+      true
+    ],
+    [
+      "IDLE",
+      7,
+      [
+        0,
+        1,
+        3,
+        5,
+        7,
+        9,
+        11,
+        13
+      ]
+    ],
+    [
+      "ADD",
+      12,
+      14,
+      1
+    ],
+    [
+      "ADD",
+      15,
+      13,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      14,
+      6,
+      false
+    ],
+    [
+      "ADD",
+      12,
+      14,
+      -1
+    ],
+    [
+      "ADD",
+      15,
+      13,
+      1
+    ],
+    [
+      "LOCAL",
+      15,
+      7,
+      true
+    ],
+    [
+      "ADD",
+      14,
+      16,
+      1
+    ],
+    [
+      "ADD",
+      17,
+      15,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      16,
+      7,
+      false
+    ],
+    [
+      "ADD",
+      14,
+      16,
+      -1
+    ],
+    [
+      "ADD",
+      17,
+      15,
+      1
+    ],
+    [
+      "LOCAL",
+      17,
+      8,
+      true
+    ],
+    [
+      "ADD",
+      16,
+      18,
+      1
+    ],
+    [
+      "ADD",
+      19,
+      17,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      18,
+      8,
+      false
+    ],
+    [
+      "ADD",
+      16,
+      18,
+      -1
+    ],
+    [
+      "ADD",
+      19,
+      17,
+      1
+    ],
+    [
+      "LOCAL",
+      19,
+      9,
+      true
+    ],
+    [
+      "ADD",
+      18,
+      20,
+      1
+    ],
+    [
+      "ADD",
+      21,
+      19,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      20,
+      9,
+      false
+    ],
+    [
+      "ADD",
+      18,
+      20,
+      -1
+    ],
+    [
+      "ADD",
+      21,
+      19,
+      1
+    ],
+    [
+      "LOCAL",
+      21,
+      10,
+      true
+    ],
+    [
+      "ADD",
+      20,
+      22,
+      1
+    ],
+    [
+      "ADD",
+      23,
+      21,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      22,
+      10,
+      false
+    ],
+    [
+      "ADD",
+      20,
+      22,
+      -1
+    ],
+    [
+      "ADD",
+      23,
+      21,
+      1
+    ],
+    [
+      "LOCAL",
+      23,
+      11,
+      true
+    ],
+    [
+      "ADD",
+      22,
+      24,
+      1
+    ],
+    [
+      "ADD",
+      25,
+      23,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      24,
+      11,
+      false
+    ],
+    [
+      "ADD",
+      22,
+      24,
+      -1
+    ],
+    [
+      "ADD",
+      25,
+      23,
+      1
+    ],
+    [
+      "LOCAL",
+      25,
+      12,
+      true
+    ],
+    [
+      "ADD",
+      24,
+      26,
+      1
+    ],
+    [
+      "ADD",
+      27,
+      25,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      26,
+      12,
+      false
+    ],
+    [
+      "ADD",
+      24,
+      26,
+      -1
+    ],
+    [
+      "ADD",
+      27,
+      25,
+      1
+    ],
+    [
+      "LOCAL",
+      27,
+      13,
+      true
+    ],
+    [
+      "ADD",
+      26,
+      28,
+      1
+    ],
+    [
+      "ADD",
+      29,
+      27,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      28,
+      13,
+      false
+    ],
+    [
+      "ADD",
+      26,
+      28,
+      -1
+    ],
+    [
+      "ADD",
+      29,
+      27,
+      1
+    ],
+    [
+      "LOCAL",
+      29,
+      14,
+      true
+    ],
+    [
+      "ADD",
+      28,
+      30,
+      1
+    ],
+    [
+      "ADD",
+      31,
+      29,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      30,
+      14,
+      false
+    ],
+    [
+      "ADD",
+      28,
+      30,
+      -1
+    ],
+    [
+      "ADD",
+      31,
+      29,
+      1
+    ],
+    [
+      "LOCAL",
+      31,
+      15,
+      true
+    ],
+    [
+      "LOCAL",
+      32,
+      15,
+      false
+    ],
+    [
+      "IDLE",
+      7,
+      [
+        17,
+        19,
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      8,
+      [
+        19,
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      9,
+      [
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      10,
+      [
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      11,
+      [
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      12,
+      [
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      13,
+      [
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      14,
+      [
+        31,
+        32
+      ]
+    ],
+    [
+      "ADD",
+      30,
+      28,
+      1
+    ],
+    [
+      "ADD",
+      29,
+      31,
+      -1
+    ],
+    [
+      "ADD",
+      28,
+      26,
+      1
+    ],
+    [
+      "ADD",
+      27,
+      29,
+      -1
+    ],
+    [
+      "ADD",
+      26,
+      24,
+      1
+    ],
+    [
+      "ADD",
+      25,
+      27,
+      -1
+    ],
+    [
+      "ADD",
+      24,
+      22,
+      1
+    ],
+    [
+      "ADD",
+      23,
+      25,
+      -1
+    ],
+    [
+      "ADD",
+      22,
+      20,
+      1
+    ],
+    [
+      "ADD",
+      21,
+      23,
+      -1
+    ],
+    [
+      "ADD",
+      20,
+      18,
+      1
+    ],
+    [
+      "ADD",
+      19,
+      21,
+      -1
+    ],
+    [
+      "ADD",
+      18,
+      16,
+      1
+    ],
+    [
+      "ADD",
+      17,
+      19,
+      -1
+    ],
+    [
+      "ADD",
+      16,
+      14,
+      1
+    ],
+    [
+      "ADD",
+      15,
+      17,
+      -1
+    ],
+    [
+      "ADD",
+      14,
+      12,
+      1
+    ],
+    [
+      "ADD",
+      13,
+      15,
+      -1
+    ],
+    [
+      "ADD",
+      12,
+      10,
+      1
+    ],
+    [
+      "ADD",
+      11,
+      13,
+      -1
+    ],
+    [
+      "ADD",
+      10,
+      8,
+      1
+    ],
+    [
+      "ADD",
+      9,
+      11,
+      -1
+    ],
+    [
+      "ADD",
+      8,
+      6,
+      1
+    ],
+    [
+      "ADD",
+      7,
+      9,
+      -1
+    ],
+    [
+      "ADD",
+      6,
+      4,
+      1
+    ],
+    [
+      "ADD",
+      5,
+      7,
+      -1
+    ],
+    [
+      "ADD",
+      4,
+      2,
+      1
+    ],
+    [
+      "ADD",
+      3,
+      5,
+      -1
+    ],
+    [
+      "ADD",
+      2,
+      0,
+      1
+    ],
+    [
+      "ADD",
+      1,
+      3,
+      -1
+    ],
+    [
+      "SIGNED_SWAP",
+      0,
+      1
+    ],
+    [
+      "SIGNED_SWAP",
+      2,
+      3
+    ],
+    [
+      "SIGNED_SWAP",
+      4,
+      5
+    ],
+    [
+      "SIGNED_SWAP",
+      6,
+      7
+    ],
+    [
+      "SIGNED_SWAP",
+      8,
+      9
+    ],
+    [
+      "SIGNED_SWAP",
+      10,
+      11
+    ],
+    [
+      "SIGNED_SWAP",
+      12,
+      13
+    ],
+    [
+      "SIGNED_SWAP",
+      14,
+      15
+    ],
+    [
+      "SIGNED_SWAP",
+      16,
+      17
+    ],
+    [
+      "SIGNED_SWAP",
+      18,
+      19
+    ],
+    [
+      "SIGNED_SWAP",
+      20,
+      21
+    ],
+    [
+      "SIGNED_SWAP",
+      22,
+      23
+    ],
+    [
+      "SIGNED_SWAP",
+      24,
+      25
+    ],
+    [
+      "SIGNED_SWAP",
+      26,
+      27
+    ],
+    [
+      "SIGNED_SWAP",
+      28,
+      29
+    ],
+    [
+      "SIGNED_SWAP",
+      30,
+      31
+    ]
+  ],
+  "prefix_pairs": 7
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/mixed_target_probe.py b/research/owned-relation-independent-validation/engines/cost/frozen/mixed_target_probe.py
new file mode 100644
index 0000000000..4fc05ab081
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/mixed_target_probe.py
@@ -0,0 +1,291 @@
+#!/usr/bin/env python3
+"""Exact tariffs for productive helpers with heterogeneous target sizes.
+
+This is a conditional recursion-contract probe, not a new kappa claim.  The
+native helper adapters, main controller closure, scalar/precision charges,
+and the mixed-target outer theorem remain separate obligations.
+
+Apache-2.0. Substantial OpenAI assistance. The original pruned native profile
+and helper inventory come from the preserved kappa-function-composition work.
+Mixed-target balance follows Jacob Alan Sussman's PR4268 proposal; this file
+does not reprove or admit its all-size or integer-multiplication transfer.
+The rational elementary-function enclosure follows the independently retained
+productive_helper_forest.py recovery certificate, with fresh source identity.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from functools import lru_cache
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import json
+import math
+import sys
+
+sys.dont_write_bytecode = True
+HERE = Path(__file__).resolve().parent
+NATIVE = Counter({1:2453, 2:716, 3:224, 4:74, 5:48})
+HELPERS = Counter({5:28, 6:18, 7:56, 8:93, 9:213})
+OLD_PAIRS = [(56,9,7),(56,7,9),(18,9,6),(18,6,9),
+             (16,9,5),(16,5,9),(44,8,8)]
+OLD_MIDDLE = [(93,8),(56,7),(18,6),(28,5),(29,0)]
+
+def need(ok, message):
+    if not ok:
+        raise AssertionError(message)
+
+@lru_cache(None)
+def log_interval(r):
+    def odd_series(x):
+        z = (x-1)/(x+1)
+        n = 80
+        low = 2*sum((z**(2*j+1)/(2*j+1) for j in range(n)), Q(0))
+        high = low+2*z**(2*n+1)/((2*n+1)*(1-z*z))
+        return low, high
+    exponent = r.bit_length()-1
+    a,b = odd_series(Q(2))
+    c,d = odd_series(Q(r,2**exponent))
+    return exponent*a+c, exponent*b+d
+
+def exp_interval(x):
+    need(0 <= x < 1, 'Enclosure range')
+    term = total = Q(1)
+    n = 48
+    for j in range(1,n+1):
+        term *= x/j
+        total += term
+    following = term*x/(n+1)
+    return total, total+following/(1-x/(n+2))
+
+@lru_cache(None)
+def h_interval(r,c):
+    if r in (0,1):
+        return Q(r),Q(r)
+    a,b = log_interval(r)
+    low,_ = exp_interval(c*a)
+    _,high = exp_interval(c*b)
+    return Q(r)/high,Q(r)/low
+
+def moment(profile,c):
+    low=high=Q(0)
+    for r,n in profile.items():
+        a,b=h_interval(r,c)
+        low += n*(a if n >= 0 else b)
+        high += n*(b if n >= 0 else a)
+    return low,high
+
+def show(bounds):
+    scale=10**35
+    low,high=bounds
+    a=low.numerator*scale//low.denominator
+    b=-((-high.numerator*scale)//high.denominator)
+    def fixed(n):
+        sign='-' if n<0 else ''
+        s=str(abs(n)).rjust(36,'0')
+        return sign+s[:-35]+'.'+s[-35:]
+    return {'lower':fixed(a),'upper':fixed(b)}
+
+def split_rank(r,maximum):
+    """Least concave tariff partition with positive integers <= maximum."""
+    need(maximum>=1 and r>=0, 'Legal split')
+    q,remainder=divmod(r,maximum)
+    result=Counter()
+    if q:
+        result[maximum]+=q
+    if remainder:
+        result[remainder]+=1
+    return result
+
+def split_profile(profile,maximum):
+    result=Counter()
+    for r,n in profile.items():
+        for child,count in split_rank(r,maximum).items():
+            result[child]+=n*count
+    return result
+
+def add_scaled(target,source,multiple=1):
+    for key,value in source.items():
+        target[key]+=multiple*value
+
+def base_case(p,minimum,pairs=None,middle=None):
+    """Expand all role inventories; one fresh global field per unhosted role."""
+    need(p in (1,2), 'Only reconstructed p1 and p2 schedules are in scope')
+    need(2<=minimum<=41, 'Finite minimum-target menu')
+    calls=2*p+1
+    main_fields=224*p
+    main_rank=16*p+9
+    inventories=[Counter(HELPERS) for _ in range(calls)]
+    paid=split_profile(NATIVE,minimum-1)
+    paid=Counter({r:calls*n for r,n in paid.items()})
+    paid[1]+=8*calls  # same-width H completion, never waived
+    targets=Counter({main_rank:main_fields})
+    if p==1:
+        need(pairs is None and middle is None, 'p1 has no original idle bins')
+    else:
+        pairs=pairs if pairs is not None else [(224,0,0)]
+        middle=middle if middle is not None else [(224,0)]
+        need(sum(n for n,a,b in pairs)==224, 'Each pair window has 224 bins')
+        need(sum(n for n,a in middle)==224, 'Middle window has 224 bins')
+        for stages in [(0,1),(3,4)]:
+            for n,a,b in pairs:
+                need(a+b<=16 and a in (0,5,6,7,8,9) and b in (0,5,6,7,8,9), 'Pair capacities')
+                for stage,r in zip(stages,(a,b)):
+                    if r:
+                        inventories[stage][r]-=n
+                add_scaled(paid,split_rank(16-a-b,minimum-1),n)
+        for n,r in middle:
+            need(r in (0,5,6,7,8), 'Middle capacity')
+            if r:
+                inventories[2][r]-=n
+            add_scaled(paid,split_rank(8-r,minimum-1),n)
+    global_roles=Counter()
+    for inventory in inventories:
+        need(all(n>=0 for n in inventory.values()), 'No helper role used twice')
+        global_roles.update(inventory)
+    for r,n in global_roles.items():
+        if not n:
+            continue
+        target=max(r,minimum)
+        targets[target]+=n
+        add_scaled(paid,split_rank(target-r,minimum-1),n)
+    paid=+paid
+    targets=+targets
+    need(max(paid)<min(targets), 'Strict child/target separation')
+    signed=Counter(targets)
+    signed.subtract(paid)
+    rank_credit=sum(r*n for r,n in targets.items())
+    rank_bill=sum(r*n for r,n in paid.items())
+    need(rank_credit-rank_bill==224*p-8*calls, 'Complete displayed rank balance')
+    return {'p':p,'minimum_target_parameter':minimum,'targets':dict(sorted(targets.items())),
+            'paid':dict(sorted(paid.items())), 'signed':signed,
+            'global_helper_roles':dict(sorted(global_roles.items())),
+            'global_productive_fields':sum(global_roles.values()),
+            'pair_patterns':pairs,'middle_patterns':middle,
+            'rank_credit':rank_credit,'rank_bill':rank_bill,'rank_margin':rank_credit-rank_bill,
+            'strict_separation':{'maximum_child':max(paid),'minimum_target':min(targets)}}
+
+def serialize_case(case):
+    result={k:v for k,v in case.items() if k!='signed'}
+    result['targets_at_C']={}
+    for text in ('0.001745','0.004'):
+        c=Q(text)
+        allowance=moment(case['signed'],c)
+        row={'after_native_completion_before_main_closure':show(allowance)}
+        for debt in (112,224):
+            row[f'after_{debt}_H1_head_debt']=show((allowance[0]-debt,allowance[1]-debt))
+        # A head may be cut only when it is a literal private first transform.
+        # Target shrink is charged; this is the strongest favorable eligibility grant.
+        rank=16*case['p']+9
+        for count in (112,224):
+            delta=Counter({1:count,rank-1:count,rank:-count})
+            gain=moment(delta,c)
+            row[f'literal_{count}_H1_cut_gain_over_paying_heads']=show(gain)
+            loss=Counter({rank:count,rank-1:-count})
+            a,b=moment(loss,c)
+            row[f'after_cutting_{count}_literal_H1_heads_and_shrinking_targets']=show((allowance[0]-b,allowance[1]-a))
+        result['targets_at_C'][text]=row
+    return result
+
+def numerical_value(profile,c):
+    return sum(n*r**(1-c) for r,n in profile.items())
+
+def discover_pair_patterns(minimum,c):
+    """Optional small MILP; exact replay never relies on solver's optimal flag."""
+    import numpy as np
+    from scipy.optimize import milp, Bounds, LinearConstraint
+    widths=(0,5,6,7,8,9)
+    patterns=[(a,b) for a in widths for b in widths if a+b<=16]
+    h=lambda r:r**(1-c) if r else 0.0
+    sp=lambda r:sum(n*h(k) for k,n in split_rank(r,minimum-1).items())
+    value=lambda r:0.0 if not r else h(max(r,minimum))-sp(max(0,minimum-r))
+    gain=np.array([sp(16)-sp(16-a-b)-value(a)-value(b) for a,b in patterns])
+    rows=[np.ones(len(patterns))]
+    lower=[224.0]
+    upper=[224.0]
+    for side in (0,1):
+        for r in widths[1:]:
+            rows.append(np.array([float(pair[side]==r) for pair in patterns]))
+            lower.append(0.0)
+            upper.append(float(HELPERS[r]))
+    out=milp(c=-gain,integrality=np.ones(len(patterns)),bounds=Bounds(0,np.inf),
+             constraints=LinearConstraint(np.array(rows),lower,upper),
+             options={'time_limit':10,'mip_rel_gap':0})
+    need(out.x is not None, 'Discovery produced a candidate')
+    pairs=[(int(round(n)),a,b) for n,(a,b) in zip(out.x,patterns) if round(n)>0]
+    # Middle bins are independent single slots; choose positive-gain roles first.
+    candidates=sorted(((sp(8)-sp(8-r)-value(r),r) for r in (5,6,7,8)),reverse=True)
+    middle=[]
+    left=224
+    for gain,r in candidates:
+        if gain>1e-12:
+            n=min(HELPERS[r],left)
+            if n:
+                middle.append((n,r))
+                left-=n
+    if left:
+        middle.append((left,0))
+    return pairs,middle,{'status':int(out.status),'message':out.message,'not_an_exact_optimality_claim':True}
+
+def run(discover=False):
+    candidates=[]
+    for p in (1,2):
+        for minimum in range(2,26):
+            candidates.append(base_case(p,minimum))
+    candidates.append(base_case(2,9,OLD_PAIRS,OLD_MIDDLE))
+    discovery=[]
+    if discover:
+        for c in (.001745,.004):
+            for minimum in range(5,18):
+                pairs,middle,meta=discover_pair_patterns(minimum,c)
+                case=base_case(2,minimum,pairs,middle)
+                case['discovery_target']=str(c)
+                case['solver']=meta
+                discovery.append(case)
+        candidates.extend(discovery)
+    best={}
+    for p in (1,2):
+        for text in ('0.001745','0.004'):
+            c=Q(text)
+            rows=[case for case in candidates if case['p']==p]
+            ranked=sorted(rows,key=lambda case:-numerical_value(case['signed'],float(c)))
+            winner=ranked[0]
+            # Certify that this displayed winner beats all numerically distinct
+            # profiles in the finite scanned menu, not all possible schedules.
+            win=moment(winner['signed'],c)
+            for case in ranked[1:]:
+                if dict(case['signed'])!=dict(winner['signed']):
+                    need(win[0]>moment(case['signed'],c)[1], 'Exact finite-menu ordering')
+            best[f'p{p}_{text}']=serialize_case(winner)
+    controls={}
+    wrong=base_case(1,6)
+    wrong['targets'][6]+=1
+    controls['unearned_output_credit_rejected']=(sum(r*n for r,n in wrong['targets'].items())-wrong['rank_bill']!=wrong['rank_margin'])
+    controls['rank5_child_with_job5_rejected']=not(5<5)
+    need(all(controls.values()), 'Corruption controls')
+    return {'schema':'productive-helper-mixed-target-tariff/1',
+            'status':'PASS_CONDITIONAL_EXACT_ACCOUNTING',
+            'source_sha256':sha256(Path(__file__).read_bytes()).hexdigest(),
+            'native_profile':dict(NATIVE),'helper_inventory':dict(HELPERS),
+            'assumed_recursive_rule':'sum_paid n_r r^(1-C) < sum_targets W_k k^(1-C); max_paid_rank < min_target_rank',
+            'best_in_finite_menu':best,
+            'fixed_p2_minimum9':serialize_case(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)),
+            'discovery_candidates':[serialize_case(c) for c in discovery],
+            'controls':controls,
+            'not_proved':['native whole-helper adapters and arbitrary-input block diagonal contract',
+                          'correct main controller and all its heads/caches/cleanup',
+                          'literal eligibility of any displayed head-cut grant',
+                          'mixed-target all-size recursion in this native model',
+                          'finite-precision integer-multiplication transfer and scalar/stock costs'],
+            'new_kappa':False}
+
+def main():
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--discover',action='store_true')
+    parser.add_argument('--output',type=Path,default=HERE/'MIXED-TARGET-PROBE.json')
+    args=parser.parse_args()
+    result=run(args.discover)
+    args.output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+    print(json.dumps({'status':result['status'],'best':{k:v['targets_at_C'][k.split('_',1)[1]]['after_native_completion_before_main_closure'] for k,v in result['best_in_finite_menu'].items()}},sort_keys=True))
+
+if __name__=='__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/native.py b/research/owned-relation-independent-validation/engines/cost/frozen/native.py
new file mode 100644
index 0000000000..b8249ed7ba
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/native.py
@@ -0,0 +1,299 @@
+"""One prepared helper removes two paid jobs in the PR4610 backward word.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+The source word is by Cao Yifan. The row convention and scalar allowance
+follow the credited native work of Cinna Davis and zxv.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha1, sha256
+from pathlib import Path
+import gzip
+import importlib.util
+import json
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'
+PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz'
+PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'
+RELATION = {230: 1, 324: -1, 326: 1, 328: 1, 333: -1}
+OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}
+NEW_PAID = dict(OLD_PAID)
+NEW_PAID[1] -= 1
+NEW_PAID[8] -= 1
+OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326}
+
+
+def need(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def encode(x):
+    if isinstance(x, Q):
+        return str(x)
+    if isinstance(x, dict):
+        return {str(k): encode(v) for k, v in x.items()}
+    if isinstance(x, (list, tuple)):
+        return [encode(v) for v in x]
+    return x
+
+
+def load(relative, name):
+    spec = importlib.util.spec_from_file_location(name, ROOT / relative)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+
+def authenticate():
+    pins = read(HERE / 'SOURCES.json')
+    for row in pins['files']:
+        if row['usage'] != 'input':
+            continue
+        p = ROOT
+        for part in Path(row['path']).parts:
+            p /= part
+            need(not p.is_symlink(), 'No source aliases')
+        raw = p.read_bytes()
+        need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path'])
+        need(sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob')
+    need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload')
+    return pins
+
+
+def span(basis):
+    out = {0}
+    for vector in basis:
+        need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate')
+        out |= {v ^ vector for v in tuple(out)}
+    need(len(out) == 2 ** len(basis), 'Independent frame basis')
+    return out
+
+
+def add(dst, src, q):
+    for k, v in tuple(src.items()):
+        value = dst.get(k, Q(0)) + q * v
+        if value:
+            dst[k] = value
+        else:
+            dst.pop(k, None)
+
+
+def allowance(g):
+    if g[0] in ('clear', 'copy'):
+        return 2
+    q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:])
+    n, d = abs(q.numerator), q.denominator
+    need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar')
+    if g[0] == 'scale':
+        need(n & (n - 1) == 0, 'Dyadic unit SCALE')
+        return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0))
+    need(g[0] == 'add', 'Known scalar operation')
+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)
+
+
+def construct(source):
+    c = source['canonical']
+    old = source['programs']['backward']
+    need(old[11205] == ['climb', 'warp_retimed', 92, 310, 254, 4], 'Snapshot source event')
+    need(old[11332] == ['center', 0, 0, 254, 8], 'Center source event')
+    need(old[15584] == ['climb', 'warp_retimed', 92, 254, 1, 1], 'Zero source event')
+    need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in RELATION), 'Five cold full-ended helpers')
+    word = [['scalar', ['clear', ['L', 230]], 0]]
+    word += [['scalar', ['add', ['L', 230], ['L', h], -q, 1], 0]
+             for h, q in RELATION.items() if h != 230]
+    for i, event in enumerate(old):
+        if i == 11332:
+            word += [['scalar', ['clear', ['C', 0]], 254],
+                     ['scalar', ['copy', ['C', 0], ['C', 1]], 254],
+                     ['scalar', ['clear', ['C', 1]], 254]]
+        elif i == 15584:
+            word.append(['zero_retag', ['L', 92], 254, 1])
+        else:
+            word.append(deepcopy(event))
+        if i == 11205:
+            word += [['scalar', ['clear', ['C', 1]], 254],
+                     ['scalar', ['copy', ['C', 1], ['L', 92]], 254]]
+    word.append(['scalar', ['clear', ['L', 230]], 1])
+    physical = deepcopy(c)
+    physical.pop('local_profile')
+    return {'schema': 'owned-helper-relation-word/1', 'canonical': physical,
+            'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID},
+            'owned': {'forward': [['C', 0]], 'backward': [['C', 0], ['C', 1], ['L', 230]]},
+            'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}}
+
+
+def replay(c, program, backward, specialized):
+    """Run every event on all independent entry columns and exact frames."""
+    owned = {('C', 0)} | ({('C', 1), ('L', 230)} if specialized else set())
+    roles = {('L', i) for i in range(632)} | owned
+    rows = {r: {(r, ()): Q(1)} for r in roles}
+    frames = {('L', i): f for i, f in enumerate(c['start'])}
+    frames.update({r: None for r in owned if r[0] == 'C'})
+    spaces = [span(b) for b in c['frames']]
+    paid = Counter()
+    cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0
+    for e in program:
+        kind, touched = e[0], None
+        if kind == 'scalar':
+            g, frame = e[1:]
+            dst = tuple(g[1]); touched = dst
+            need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame')
+            cost += allowance(g)
+            if g[0] == 'clear':
+                need(dst in owned, 'Only owned fields can be erased')
+                rows[dst] = {}; frames[dst] = frame
+            else:
+                need(frames[dst] == frame, 'Exact scalar destination frame')
+                if g[0] in ('add', 'copy'):
+                    src = tuple(g[2])
+                    need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame')
+                    if g[0] == 'copy':
+                        need(dst in owned and not rows[dst], 'COPY into cleared owned storage')
+                        rows[dst] = dict(rows[src])
+                    else:
+                        add(rows[dst], rows[src], Q(g[3], g[4]))
+                else:
+                    need(g[0] == 'scale', 'Known scalar operation')
+                    rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()}
+        elif kind == 'warp':
+            _, role, op, old, new = e
+            dst = tuple(role); touched = dst
+            need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input')
+            symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0))
+            rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q
+                         for (r, w), q in rows[dst].items()}
+            frames[dst] = new
+        elif kind in ('climb', 'center'):
+            if kind == 'climb':
+                _, _, i, old, new, rank = e
+                dst = ('L', i)
+                need(spaces[old] < spaces[new], 'Ascending paid climb')
+            else:
+                _, i, old, new, rank = e
+                dst = ('C', i)
+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center')
+            need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame')
+            frames[dst] = new; paid[rank] += 1
+        elif kind == 'zero_retag':
+            _, role, old, new = e
+            dst = tuple(role)
+            need(specialized and backward and dst == ('L', 92), 'Declared zero identity')
+            need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row')
+            need((old, new) == (254, 1), 'Declared zero frame change')
+            frames[dst] = new; zero_count += 1
+        else:
+            need(kind in ('phase', 'adapter'), 'Known inert source marker')
+        if touched is not None:
+            max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0)))
+            denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1))
+    need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame')
+    for i in range(632):
+        r = ('L', i)
+        if r in owned:
+            continue
+        expected = {(r, ()): Q(1)}
+        if i < 112 if backward else 112 <= i < 224:
+            expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1)
+        need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i))
+    need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return')
+    need(zero_count == int(specialized), 'Exactly one checked zero identity')
+    helpers = Counter()
+    for i in range(224, 632):
+        if ('L', i) in owned:
+            continue
+        a, b = c['start'][i], c['final'][i]
+        need(spaces[a] < spaces[b], 'Strict independent productive helper')
+        helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1
+    return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())),
+            'independent_persistent_columns': 631 if specialized else 632,
+            'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True,
+            'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1),
+            'max_denominator': denominator, 'zero_identities': zero_count}
+
+
+def independent_source_identities(source):
+    """Use the predecessor row engine on the unrestricted original word."""
+    v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'owned_relation_source_rows')
+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}
+    rows['C', 0] = v.identity(('C', 0))
+    delta = {(('L', i), ()): Q(q) for i, q in RELATION.items()}
+    saved = None
+    for index, e in enumerate(source['programs']['backward']):
+        if e[0] == 'scalar':
+            g = e[1]; dst = tuple(g[1])
+            if g[0] == 'clear': rows[dst] = {}
+            elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])])
+            elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()}
+            else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4]))
+        elif e[0] == 'warp':
+            dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True)
+        if index == 11205: saved = dict(rows['L', 92])
+        if index == 11332:
+            diff = dict(rows['C', 0]); v.add(diff, saved, -1)
+            need(diff == {k: q / 4 for k, q in delta.items()}, 'Independent exact center minus snapshot = Delta/4')
+        if index == 15584:
+            need(rows['L', 92] == {k: -q / 4 for k, q in delta.items()}, 'Independent exact zero-site row = -Delta/4')
+    need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints')
+    return {'source_event_indices_are_zero_based': True, 'snapshot_after': 11205,
+            'center_replaced': 11332, 'zero_identity_at': 15584,
+            'snapshot_terms_before_substitution': len(saved), 'copy_coefficient': '1',
+            'center_minus_snapshot': 'Delta/4', 'zero_site_row': '-Delta/4', 'relation': RELATION}
+
+
+def phase_inheritance(source, candidate):
+    receipt = read(ROOT / PHASE)
+    need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and
+         receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt')
+    physical = deepcopy(source['canonical']); physical.pop('local_profile')
+    need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged')
+    for direction, program in candidate['programs'].items():
+        old = source['programs'][direction]
+        for kind in ('warp', 'adapter', 'phase'):
+            need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence')
+        old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center'))
+        new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center'))
+        expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for i in (11332, 15584))
+        need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the two proved jobs are removed')
+    return {'new_gaussian_operators': 0, 'new_native_maps': 0,
+            'all_retained_paid_events_and_warps_from_source': True,
+            'absolute_phase_receipt_reused': PHASE,
+            'source_amplitudes_and_phase_lowering_freshly_replayed': False,
+            'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'}
+
+
+def controls(c, candidate):
+    controls = {}
+    base = candidate['programs']['backward']
+    variants = {}
+    bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad
+    variants['missing_owned_input_clear'] = deepcopy(base[1:])
+    bad = deepcopy(base)
+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63]
+    variants['wrong_snapshot_source'] = bad
+    bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0
+    variants['wrong_zero_input_frame'] = bad
+    bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1
+    variants['under_or_overstated_paid_rank'] = bad
+    bad = deepcopy(base)
+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0
+    variants['wrong_copy_gauge'] = bad
+    variants['uncleared_owned_output'] = deepcopy(base[:-1])
+    for name, program in variants.items():
+        try:
+            replay(c, program, True, True)
+        except ValueError as err:
+            controls[name] = str(err)
+        else:
+            raise ValueError('Control accepted: ' + name)
+    return controls
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/price.py b/research/owned-relation-independent-validation/engines/cost/frozen/price.py
new file mode 100644
index 0000000000..6077adf74c
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/price.py
@@ -0,0 +1,196 @@
+"""Complete p16 bill and finite compiler for one owned helper relation.
+
+The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna
+Davis's PR4470 controller, zxv's completion and logarithmic majorant, and
+Jacob Alan Sussman's mixed-target recursion. Apache-2.0.
+Ali Romman, with substantial OpenAI Codex assistance.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from native import ROOT, read, load, need, encode, OLD_PAID, OLD_HELPERS
+
+KAPPA = Q('.00302235')
+TESTED = Q('.00302236')
+PREVIOUS = Q('.0030217758')
+OLD_ROOT_UPPER = Q('.00302177587078')
+
+
+def controller():
+    """Check the literal p16 word and both rational boundary programs."""
+    word = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json')
+    need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller')
+    zero = (0,) * 34
+    def plus(dst, src, q):
+        for k, v in src.items():
+            value = dst.get(k, Q(0)) + q * v
+            if value: dst[k] = value
+            else: dst.pop(k, None)
+    def shifted(row, term, sign=1):
+        return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row]
+    for side in ('left', 'right'):
+        matrix = [[Q(i == j) for j in range(32)] for i in range(32)]
+        for e in word['boundaries'][side + '_program']:
+            if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]]
+            elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]]
+            else:
+                need(e[0] == 'ADD', 'Boundary scalar opcode')
+                matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])]
+        need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program')
+    rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']]
+    for e in word['physical_events']:
+        if e[0] in ('LOCAL', 'QUERY_SHEAR'):
+            _, stage, pair, back = e
+            x, y = 2 * pair, 2 * pair + 1
+            if back: x, y = y, x
+            term = (1 if back else -1,) + (0,) * 33
+            for dst, src in zip(rows[y], shifted(rows[x], term)):
+                plus(dst, src, Q(-1 if back else 1))
+            if e[0] == 'LOCAL':
+                term = (0,) + tuple(int(s == stage) for s in range(33))
+                for r in (x, y): rows[r] = shifted(rows[r], term)
+        elif e[0] == 'IDLE':
+            term = (0,) + tuple(int(s in e[2]) for s in range(33))
+            for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term)
+        elif e[0] == 'ADD':
+            for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3]))
+        else:
+            need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode')
+            rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1)
+    out = [[{} for _ in range(32)] for _ in range(32)]
+    for i, row in enumerate(word['boundaries']['left']):
+        for k, q in enumerate(row):
+            if Q(q):
+                for j in range(32): plus(out[i][j], rows[k][j], Q(q))
+    expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)]
+    need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors')
+    return word
+
+
+def assemble(native, word):
+    T, P = Counter(), Counter()
+    orientations = Counter(); thin = 0
+    for e in word['physical_events']:
+        if e[0] == 'LOCAL':
+            direction = 'backward' if e[3] else 'forward'
+            orientations[direction] += 1
+            T.update(native[direction]['helpers']); P.update(native[direction]['paid'])
+        elif e[0] == 'QUERY_SHEAR': thin += 1; P[1] += 112
+        elif e[0] == 'IDLE': P[8 * len(e[2])] += 224
+    main = Counter()
+    for term in word['diagonal']:
+        need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole Gaussian main target')
+        main[1 + 8 * sum(term[1:])] += 112
+    T.update(main)
+    need(orientations == {'backward': 16, 'forward': 2} and thin == 15, 'Every actual call orientation')
+    # This second census uses the source invoice and the two local deltas.
+    check_T = Counter({int(r): n for r, n in word['invoice']['main'].items()})
+    check_T.update({r: 18 * n for r, n in OLD_HELPERS.items()}); check_T[9] -= 16
+    check_P = Counter({int(r): n for r, n in word['invoice']['whole_idle'].items()})
+    check_P.update({r: 18 * n for r, n in OLD_PAID.items()}); check_P[1] += 1680 - 16; check_P[8] -= 16
+    need(T == check_T and P == check_P, 'Independent full invoice substitution')
+    need(sum(T.values()) == 10912 and sum(P.values()) == 64372, 'Complete productive and paid counts')
+    need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Unchanged complete rank surplus')
+    return T, P
+
+
+def run(native):
+    word = controller(); T, P = assemble(native, word)
+    prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json')
+    need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing')
+    prior_T = Counter({int(r): n for r, n in prior['targets'].items()})
+    prior_P = Counter({int(r): n for r, n in prior['paid'].items()})
+    prior_T[9] -= 16; prior_P[1] -= 16; prior_P[8] -= 16
+    need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill')
+    E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals')
+    other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals')
+    def margin(c):
+        t, p = E.moment(T, 1 - c), E.moment(P, 1 - c)
+        return t[0] - p[1], t[1] - p[0]
+    need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint')
+    lo, hi, grid = 0, 10**12, 10**14
+    while hi - lo > 1:
+        mid = (lo + hi) // 2
+        if margin(Q(mid, grid))[0] > 0: lo = mid
+        else: hi = mid
+    root_low, root_high = Q(lo, grid), Q(hi, grid)
+    need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure')
+    need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom')
+    # The complete signed profile decreases on [0, .05], and stays negative
+    # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling.
+    signed = {r: T[r] - P[r] for r in T.keys() | P.keys()}
+    derivative, upper = None, None
+    for i in range(16):
+        l, r = Q(i, 320), Q(i + 1, 320); low = Q(0)
+        for rank, n in signed.items():
+            term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank))
+            low += n * term[0 if n > 0 else 1]
+        derivative = low if derivative is None else min(derivative, low)
+    for i in range(128):
+        l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560)
+        value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items())
+        upper = value if upper is None else max(upper, value)
+    need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1')
+    t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21
+    target, paid = E.moment(T, t), E.moment(P, t)
+    tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED)
+    need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree')
+    alpha = E.divide(paid, target)
+    gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target))
+    delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target))
+    reserve = Q(1, 10**9); g = d = Q(97, 100)
+    need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged')
+    need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks')
+    normalized = 1 / (1 + v * reserve) + Q(4, 2**32)
+    need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding')
+    theta, power = Q(63, 64), 1000
+    eta = E.scale(E.power(145, -v * TESTED), t)
+    need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')
+    need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range')
+    gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid')
+    step = gap.denominator
+    def wins(j): return (step * j + 1)**power < 2**j
+    left, right = 1, 2
+    while not wins(right): left, right = right, 2 * right
+    while right - left > 1:
+        mid = (left + right) // 2
+        if wins(mid): right = mid
+        else: left = mid
+    height = step * right
+    need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold')
+    local_scalar = max(x['real_scalar_allowance'] for x in native.values())
+    # The old route allowance is retained. Charge two additional owned field
+    # lifetimes at two routes each, even though L230 uses an existing slot.
+    routes = (max(sum(x['paid'].values()) for x in native.values()) + 2 * 408 + 688 + 4) * 1000
+    need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit')
+    scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right')))
+    need(scalar_upper < 10**9, 'Complete raw nonrecursive bound')
+    bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']
+    atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted'])
+    need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock')
+    L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer')
+    params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap,
+              'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted,
+              'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap}
+    outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom)
+    need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')
+    need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict')
+    controls = {}
+    for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]:
+        bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0]
+        need(failed, 'Reject outer patch ' + name); controls[name] = failed
+    bad_native = {d: dict(x) for d, x in native.items()}
+    bad_native['backward']['helpers'] = OLD_HELPERS
+    try: assemble(bad_native, word)
+    except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census'
+    else: raise ValueError('Unowned helper credit was accepted')
+    return encode({'kappa': KAPPA, 'kappa_decimal': '.00302235', 'gain_over_PR4610': KAPPA - PREVIOUS,
+                   'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA],
+                   'margin_at_previous_kappa': E.display(margin(PREVIOUS)),
+                   'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)),
+                   'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)},
+                   'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752,
+                   'full_backward': 16, 'full_forward': 2, 'query_shears': 15,
+                   'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized},
+                   'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False},
+                   'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': 1, 'owned_slots_backward': 3},
+                   'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls})
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/priorities-pinned.txt b/research/owned-relation-independent-validation/engines/cost/frozen/priorities-pinned.txt
new file mode 100644
index 0000000000..b4ece97a60
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/priorities-pinned.txt
@@ -0,0 +1,164 @@
+# Current research priorities
+
+This is the changing diagnosis and allocation; [autoresearch.md](../../autoresearch.md)
+links the standing session procedure. Refresh this file and the task catalogue
+at each research checkpoint.
+
+**Priority revision 7 — October 20, 2026**, assessed against main
+`9200177938843d92957bbfe6f1fdbe88768d8cc5`.
+**Selection refresh — October 23, 2026:** the
+[selected conditional result](../../certificates/selected-result.json) is now
+**κ = 0.0030217758 (#4610, independently audited in #5241)**. Read the
+[changed-construction review](pr-intake-evidence/pr4610/PROOF-REVIEW.md) and
+[contributor map](community-native4610-contributors.md). Cao Yifan's native/helper
+changes retain the PR4470 controller and productive profile; Chris R / Clear1nsight
+supplies the complete independent admission package. The same five framework
+assumptions remain. This small improvement does not change the mechanism-search
+allocation. Admission of this exact #4610 witness is complete; source-sensitive
+follow-ups must use its final word and compiler parameters.
+Use `python3 -B scripts/research_selected_baseline.py` for source-bound orientation;
+the older `research_baseline.py` uses a historical balanced-transfer schema.
+The revision-7 allocation below is retained pending a separate strategic review.
+Its old-inventory ceilings, stale admission tasks and a/(1+a) conversion are
+not constraints on this mixed-target selection. Check the selected assumptions
+and latest handoffs before adopting an old card.
+
+**Keep broad mechanism exploration; update the exact missing work.** Roughly
+60% of the portfolio remains on bit mechanisms, complex mechanisms and recursive
+interfaces. The latest packages justify fresher assignments, not a measured
+claim that any track has a higher success rate. Use the
+[family record](research-family-status.md#revision-7-evidence-and-assignments)
+for source pins, attribution, remaining obligations and stop rules. Check live
+[handoffs](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166)
+before selecting a card.
+
+| Card | Current evidence, author-checked unless stated otherwise | Next bounded decision |
+|---|---|---|
+| `uniform-transfer-audit` | #4100 proposed all-size construction | Audit **one** quantified implication at its actual caller: CRT total repair, native/free-algebra lift, precision/conditioning, or fixed-tape cost. Independent acceptance is absent. |
+| `supplier-boundary-audit` | #4088 mixed four-provider local construction | Rebind the ordinary/outer admission engine to all four providers and dispatch, preserving every predicate and rejection control. The full mixed engine has not been rerun. |
+| `joint-query-controller` | #4166 actual QQ16 caller installation | Compare the complete matched parent park/restore and external-call protocols, retaining all later calls; or change the actual demand to remove paid work. The native-component profile loses. |
+| `r437-carrier-integration` | #4067 paid two-window carrier; #4147 reverse coefficient | Close one pooled compiler/request, physical caller, or precision/stock obligation. Do not rederive the covered coefficient. |
+| `p104-side-correction` | #4133/#4136/#4140/#4153/#4154 scoped slot, commutation, encoding, chart and fiber-seam objections | Name a changed producer/consumer premise, then test literal action, dirty restoration and the fully charged boundary. Static flags alone do not supply it. |
+| `independent-moment` | #4088 changed ledger; #4091 proposed fixed-inventory ceiling; #4067 paid exchange | Independently bind a changed mechanism to its bill or check the scoped pooled dual. More digits of the same root are not additional mechanism coverage. |
+| `formal-interface-lemma` | #3807 gate-operand and #3857 endpoint formalizations | Target an uncovered interface statement. Audit the proposed compact-switch contract before a formalization campaign. |
+
+**Separate admission from proof audit.** #4088 needs finite/compiler integration;
+#4100 claims to discharge all-size premises. Those are different tasks, and neither
+is closed by checking the other's numerical root. Partition work by proposition,
+caller and domain, with one canonical thread and exact source pins. A short session
+can produce an acceptance coverage map, a counterexample or a single proved lemma.
+A complete ordinary/outer replay or Lean build needs a separate resource budget;
+no heavy run is part of default orientation.
+
+**Pause repetitive searches within a fixed invoice.** #4091 proposes a sharp
+pooled ceiling for the fixed THREE/FOUR words and inventory. It is pinned to an
+earlier #4088 revision: verify local-word, capacity and stock equivalence before
+applying it to the later 1090-call fill. Its pooled witness is not a chronological
+implementation. The `selected-packing` card now starts with this scope/headroom
+check; any tiny residual search is explicitly bounded and optional. Changed words
+or interfaces require a fresh model, not the old ceiling.
+
+Likewise, #3998/#4019 and #4112/#4152 cover scalar A2 contractions and related
+audits. The `scalar-to-moment` card requires an actual removed paid transition,
+a legal replacement itinerary and the complete cost delta. Stop if only scalar
+ADD counts change; that may have a separate benefit, but does not justify a larger
+κ-oriented scan of the same domain.
+
+**Local contributions remain welcome.** A checked partial identity, interface
+lemma or scoped obstruction can be valuable without a complete supplier. Before
+expanding a family, update its full producer/consumer ledger: proved costs,
+constructive upper bounds, unknowns, and why the consumer does not repay the gain.
+Unknown costs are not zero. Use the [five-point expansion gate](research-family-status.md#contribution-acceptance-and-family-expansion-are-different-gates).
+This is an evidence checkpoint, not an approval queue or an extra reporting task.
+
+The selected stock coefficients remain a targeted audit obligation; cutoff
+arithmetic does not provide them. For census and exporter work, check successor
+corrections and their exact scope before repeating a tiny example. Independent
+verification must name missing coverage. The reviewed #1995/#2013 fixed-word
+frame bounds, #2017 fixed-model C=40 result and #1974 bounded census remain scoped
+predecessors, not universal barriers. The maintainer's older product checkpoint
+also remains local-only evidence as labelled in the family record.
+
+**Retained selected-profile diagnosis (revision 3; scoped arithmetic independently replayed for #1240 and #1264).** This paragraph and its lever table concern the frozen selected profile, not the changed #4088 words or every possible supplier. On the binding complex side, a ≈ D/E:
+
+- **D is small.** Each call has about 99.6 live families. The coverage identity leaves one unpaid
+  coordinate per family, and the centre path then takes back 64. Only about 35.6 of 7,232 paid
+  coordinates per call remain unpaid.
+- **E comes from small children.** The effective child rank is about 3.9, and rank-1 children are
+  about half of the recursive cost.
+
+[The packing ceiling](../../research/complex-local-word-ceiling/README.md) caps every hosting, owner or
+idle repacking of the selected word at **+0.87%** (κ < 0.001687203). The open-claim census in #1264
+finds no covered claim able to pass κ ≈ 0.0016873 by packing. Its leading claims use paid local profiles with
+*lower* relaxation caps than the selected profile; this does not compare attainable packing optima.
+
+A target-scale gain must change the structure. Ideal one-at-a-time budgets (`levers.py`):
+
+| Lever | Ideal primitive-saving ceiling multiplier |
+|---|---:|
+| Centre path free | 2.80× |
+| Centre path shared by two calls | 1.90× |
+| Rank-16 local children | 2.31× |
+| Two unpaid coordinates per family | 3.77× |
+| Centre free and rank-16 combined | 6.5× (κ cap ≈ 0.0109) |
+
+These are favorable relaxations, not expected gains. Screen any changed local profile with
+`ceiling.ceiling()` before building a network when its coverage law and halving guard apply.
+For a changed interface outside those hypotheses, state the replacement model and derive its own
+fully charged optimistic moment bound; do not force it into the incumbent calculator.
+
+For a supplier with width `m`, role count `W`, and `n_r` children of rank `r`,
+price the **whole completed construction**, including its additional charges:
+
+\[
+\frac1W\sum_r n_r(r/m)^{1-a}<1.
+\]
+
+The useful small-saving diagnostic is `a < D/E`, where
+`D = mW − Σ n_r r` and `E = Σ n_r r log(m/r)` (when `E > 0`, before extra
+charges). The exact moment is the acceptance test. Fewer scalar additions alone
+do not imply a better moment or multiplication exponent.
+
+Under the retained limiting balanced transfer `κ = a/(1+a)`, the ambitious
+`κ > .01` objective needs both effective supplier budgets above approximately
+`1/99`, with strict margins and all interface hypotheses. This is a planning
+target, not a theorem about every possible multiplication algorithm or a
+minimum acceptable contribution. Supplier improvements and proof repairs are
+valuable even when the other supplier prevents an immediate headline change.
+
+The helper allocates effort as follows. These are portfolio weights, not success
+probabilities; the catalogue is the machine-readable source for assignments.
+Revision 7 keeps the track weights: current evidence supports fresher tasks and
+stronger expansion decisions, not a measured reason to reallocate the portfolio.
+Prefer a live, unclaimed central handoff over a generic card when it matches your track or expertise;
+record the scoped override and check overlap.
+
+| Track | Share | Useful outcome |
+|---|---:|---|
+| Bit mechanisms (`bit-mechanisms`) | 20% | A changed decoder/frame contract with a full paid budget |
+| Complex mechanisms (`complex-mechanisms`) | 20% | A completed P104 correction or changed decoder with a favorable full bill |
+| Recursive interfaces (`recursive-interfaces`) | 20% | A changed joint-query controller, centre path or coverage law with real eliminated work |
+| Adversarial audit (`adversarial-audit`) | 15% | A selected stock envelope or another specific missing implication/counterexample |
+| Independent verification/formalization (`independent-verification`) | 10% | A separately implemented check or scoped formal lemma |
+| Verifier engineering (`verifier-engineering`) | 8% | Faster, reproducible checks with unchanged coverage |
+| Consolidation (`consolidation`) | 5% | Evidence-backed overlap, attribution or navigation repair |
+| Incumbent optimization (`incumbent-optimization`) | 2% | A genuinely new, fully priced improvement, reported against its packing cap |
+
+Before reopening a negative result, name the hypothesis you change. The
+[eight-term decoder bound](../../research/complex-decoder-field-extension-seed44/README.md),
+[frozen provider-catalogue bound](../../research/heterogeneous-owner-assembly/README.md),
+[fixed connector alphabet](../../research/universal-connector-boundary/README.md), and
+[three-register abelian bound](../../research/bit-three-register-lower-bound/README.md)
+have restricted scopes. Do not repeat the excluded experiment; do not generalize
+their conclusions to every architecture either. Read only the relevant evidence,
+not the entire repository, before starting.
+
+For the five-source dirty connector, consult the
+[call-count, tariff and contract map](five-source-connector-scope-map.md)
+before repricing the original alphabet. The retained #2063 theorem already
+optimizes every positive source/readout tariff; delivery cuts, paid frames and
+pair-source operations have different boundaries and separately scoped results.
+
+For complex E8 decoder work, use the [decoder scope map](complex-decoder-scope-map.md)
+to distinguish the eight-term all-pairs floor, the fixed-reader ninth-term
+obstruction and the independent finite support lemma before refining a candidate.
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/query-thinned-RESULT.json b/research/owned-relation-independent-validation/engines/cost/frozen/query-thinned-RESULT.json
new file mode 100644
index 0000000000..e0695152c9
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/query-thinned-RESULT.json
@@ -0,0 +1,356 @@
+{
+  "bit_invoice": {
+    "main": {
+      "127": 222,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222
+    },
+    "owned_streams_reused_sequentially": 1,
+    "paid": {
+      "1": 25479,
+      "14": 444,
+      "2": 24156,
+      "21": 444,
+      "28": 444,
+      "3": 1422,
+      "35": 444,
+      "4": 792,
+      "42": 444,
+      "49": 444,
+      "5": 1836,
+      "56": 444,
+      "6": 198,
+      "63": 222,
+      "7": 342
+    },
+    "paid_calls": 57555,
+    "productive_fields": 11454,
+    "rank_surplus": 753,
+    "raw_scalar_record_bound": 1000000000,
+    "targets": {
+      "127": 222,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222,
+      "8": 7902
+    },
+    "thick_calls": 18,
+    "thick_stages": [
+      0,
+      1,
+      3,
+      5,
+      7,
+      9,
+      11,
+      13,
+      15,
+      17,
+      19,
+      21,
+      23,
+      25,
+      27,
+      29,
+      31,
+      32
+    ],
+    "thin_queries": 1665,
+    "whole_idle": {
+      "14": 444,
+      "21": 444,
+      "28": 444,
+      "35": 444,
+      "42": 444,
+      "49": 444,
+      "56": 444,
+      "63": 222
+    }
+  },
+  "bit_strictification": {
+    "alpha": {
+      "lower": "0.999995735238059506641600561767",
+      "upper": "0.999995735238059506641600561768"
+    },
+    "compiler_H0": 3755884544,
+    "cutoff_base": 17,
+    "delta": {
+      "lower": "0.949707924144871179442776557218",
+      "upper": "0.949707924144871179442776557219"
+    },
+    "gamma": {
+      "lower": "0.957429821066420278606254392110",
+      "upper": "0.957429821066420278606254392111"
+    },
+    "normalized_surplus_lower": "68719461047/16845935476736",
+    "tail_exponent": "1/5",
+    "target_floor_base": 18,
+    "tensor_power": 1024,
+    "tested_saving": "173/50000",
+    "uniform_H1": 25986965159937,
+    "uniform_N": "2^25986965159937",
+    "uniform_saving": "3459/1000000",
+    "winning_word_materialized": false
+  },
+  "complex_invoice": {
+    "main": {
+      "153": 224,
+      "17": 448,
+      "25": 448,
+      "33": 448,
+      "41": 448,
+      "49": 448,
+      "57": 448,
+      "65": 448,
+      "73": 448
+    },
+    "owned_streams_reused_sequentially": 1,
+    "paid": {
+      "1": 49045,
+      "16": 448,
+      "2": 13547,
+      "24": 448,
+      "3": 4256,
+      "32": 448,
+      "4": 1938,
+      "40": 448,
+      "48": 448,
+      "5": 380,
+      "56": 448,
+      "64": 448,
+      "72": 448,
+      "8": 152
+    },
+    "paid_calls": 72902,
+    "productive_fields": 11560,
+    "rank_surplus": 800,
+    "raw_scalar_record_bound": 1000000000,
+    "targets": {
+      "153": 224,
+      "17": 448,
+      "25": 448,
+      "33": 448,
+      "41": 448,
+      "49": 448,
+      "5": 532,
+      "57": 448,
+      "6": 342,
+      "65": 448,
+      "7": 1064,
+      "73": 448,
+      "8": 1767,
+      "9": 4047
+    },
+    "thick_calls": 19,
+    "thick_stages": [
+      0,
+      1,
+      3,
+      5,
+      7,
+      9,
+      11,
+      13,
+      15,
+      17,
+      19,
+      21,
+      23,
+      25,
+      27,
+      29,
+      31,
+      33,
+      34
+    ],
+    "thin_queries": 1792,
+    "whole_idle": {
+      "16": 448,
+      "24": 448,
+      "32": 448,
+      "40": 448,
+      "48": 448,
+      "56": 448,
+      "64": 448,
+      "72": 448
+    }
+  },
+  "complex_strictification": {
+    "alpha": {
+      "lower": "0.999999952117240859760145478345",
+      "upper": "0.999999952117240859760145478346"
+    },
+    "compiler_H0": 75415467350,
+    "cutoff_base": 20,
+    "delta": {
+      "lower": "0.941649713484853845388929204840",
+      "upper": "0.941649713484853845388929204841"
+    },
+    "gamma": {
+      "lower": "0.967466409565147920980822933859",
+      "upper": "0.967466409565147920980822933860"
+    },
+    "normalized_surplus_lower": "8589700209/251666829934592",
+    "tail_exponent": "1/5",
+    "target_floor_base": 21,
+    "tensor_power": 1024,
+    "tested_saving": "29603/10000000",
+    "uniform_H1": 10418370291022217,
+    "uniform_N": "2^10418370291022217",
+    "uniform_saving": "103609/35000000",
+    "winning_word_materialized": false
+  },
+  "kappa": "37/12500",
+  "minimum_outer_margin_minus_kappa": "629378373/4900000000000000",
+  "native": {
+    "binary_charts": 111,
+    "complex_contacts_and_inverses": 896,
+    "owned_stream_restored_zero": true,
+    "thin_paid_rank_per_port": 1,
+    "thin_productive_credit": 0
+  },
+  "negative_controls": {
+    "closed_epsilon": [
+      "epsilon_below_one",
+      "global_gamma_power_slack",
+      "actual_logarithmic_gamma_guard",
+      "source_axis_superpolynomial",
+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
+    ],
+    "closed_uniform_gap": [
+      "new_complex_uniform_saving_above_b"
+    ],
+    "missing_layout": [
+      "positive_layout_slack"
+    ],
+    "old_BIT_cap": [
+      "actual_bit_above_effective"
+    ],
+    "unfunded_kappa": [
+      "main_transform_above_kappa",
+      "global_coordinate_router_above_kappa",
+      "fused_gaussian_above_kappa",
+      "group_bit_router_above_kappa",
+      "boundary_algebraic_matrix_above_kappa"
+    ]
+  },
+  "old_atom_rejected": true,
+  "ordinary_BIT": {
+    "admitted": "17/5000",
+    "after_cover": "69/20000",
+    "atom": "1/250",
+    "before_cover": "3459/1000000",
+    "ordinary_saving": "8590884599/2500000000000",
+    "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+  },
+  "outer": {
+    "functional_checks": {
+      "actual_new_BIT_stock_sublinear": "17429997759/17500000000",
+      "fixed_halo_explicit_metadata_branch": "1347500003/17500000",
+      "new_BIT_row_stock_sublinear_in_active_group": "69789991027/70000000000",
+      "new_semantic_group_guard": "9/70000000"
+    },
+    "margins": {
+      "boundary_algebraic_matrix": "14504839378373/4900000000000000",
+      "fused_gaussian": "14504838135119/4900000000000000",
+      "global_coordinate_router": "51803/17500000",
+      "group_bit_router": "3626262033773/1225000000000000",
+      "group_scans": "34999997/35000000",
+      "main_transform": "14504629378373/4900000000000000",
+      "microbox_face_corrections": "1347500003/17500000",
+      "polynomial_products": "69999997/70000000",
+      "sparse_union_movement": "2005129839378373/4900000000000000"
+    },
+    "parameters": {
+      "a": "51803/17500000",
+      "b": "41443/14000000",
+      "beta": "69999991/70000000",
+      "bit_saving": "17/5000",
+      "cap_xi": "4455129629378373/4900000000000000",
+      "complex_uniform_saving": "103609/35000000",
+      "d": "3/70000000",
+      "epsilon": "69999997/70000000",
+      "kappa": "37/12500",
+      "lambda_": "19940797/20000000",
+      "lambda_prime": "69792791/70000000",
+      "layout": "3/70000000",
+      "q": "207209/70000000",
+      "r0": "3/700000000",
+      "stop": "3/70000000",
+      "tested_saving": "29603/10000000"
+    },
+    "strict_checks": {
+      "actual_bit_above_effective": "7697/17500000",
+      "actual_logarithmic_gamma_guard": "3/70000000",
+      "actual_logarithmic_group_guard": "444870685621627/2450000000000000",
+      "alpha_logarithm_absorption": "3/700000000",
+      "boundary_algebraic_matrix_above_kappa": "839378373/4900000000000000",
+      "cap_above_band": "2005129629378373/4900000000000000",
+      "cap_below_cell": "444870160621627/4900000000000000",
+      "cap_below_phase_cell_power": "5344870370621627/4900000000000000",
+      "complex_above_effective": "3/70000000",
+      "complex_below_one_over_32": "396057/14000000",
+      "complex_endpoint": "3/35000000",
+      "epsilon_below_one": "3/70000000",
+      "epsilon_positive": "69999997/70000000",
+      "fine_prime_halo_umbrella": "7/2",
+      "fused_gaussian_above_kappa": "838135119/4900000000000000",
+      "gaussian_above_main": "104378373/2450000000000000",
+      "global_coordinate_router_above_kappa": "3/17500000",
+      "global_gamma_power_slack": "27/700000000",
+      "group_below_dimension": "3/35000000",
+      "group_bit_router_above_kappa": "262033773/1225000000000000",
+      "group_gauge_power_slack": "444870675121627/2450000000000000",
+      "group_key_fits_record": "3/35000000",
+      "group_positive": "69999991/70000000",
+      "group_scans_above_kappa": "34896397/35000000",
+      "halo_covers_generic_inverse_radius": "5",
+      "improvement_over_user_baseline": "614514790400418148631/500000000000000000000000",
+      "lambda_above_internal": "3/140000000",
+      "lambda_above_sigma": "9/140000000",
+      "lambda_above_tau": "3/140000000",
+      "lambda_prime_above_lambda": "3/140000000",
+      "lambda_prime_above_leaf": "83875671/980000000000000",
+      "leaf_saving_above_effective": "41875671/980000000000000",
+      "main_transform_above_kappa": "629378373/4900000000000000",
+      "membership_arithmetic_fits_record": "3/70000000",
+      "microbox_face_corrections_above_kappa": "1347448203/17500000",
+      "microbox_halo_volume": "5530000009/70000000",
+      "new_complex_uniform_saving_above_b": "3/70000000",
+      "new_semantic_guard_with_C1_one": "3/70000000",
+      "polynomial_products_above_kappa": "69792797/70000000",
+      "positive_layout_slack": "3/70000000",
+      "q_below_effective": "3/70000000",
+      "q_below_internal": "3/70000000",
+      "q_below_leaf": "83875671/980000000000000",
+      "q_positive": "207209/70000000",
+      "short_record_fallback": "13958557/14000000",
+      "source_axis_superpolynomial": "3/70000000",
+      "sparse_union_movement_above_kappa": "1990625839378373/4900000000000000",
+      "stop_below_one": "69999997/70000000",
+      "stop_positive": "3/70000000",
+      "strassen_integer_power_gap": "1951441519231",
+      "support_router_span": "9/70000000",
+      "theta_positive_polynomial_power": "2",
+      "union_header_fits_record": "9/70000000",
+      "union_tag_work_per_visit_fits_record": "9/70000000"
+    }
+  },
+  "relative_gain_over_p7": "27353/268647",
+  "schema": "query-thinned-productive-controllers/1",
+  "scope": "Conditional native construction; all-column, erasure, whole-job matching, fixed-tape, precision, analytic, prime and exact-recovery premises retained. No unconditional theorem or selected promotion.",
+  "source_inputs_authenticated": 17,
+  "status": "PASS_CONDITIONAL_QUERY_THINNED_KAPPA_00296"
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/selected-initial.txt b/research/owned-relation-independent-validation/engines/cost/frozen/selected-initial.txt
new file mode 100644
index 0000000000..b288ae4403
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/selected-initial.txt
@@ -0,0 +1,92 @@
+{
+  "status": "Selected maintainer-reviewed conditional PR4610 construction, with independent PR5241 admission evidence and explicit inherited foundation reuse",
+  "kappa": "15108879/5000000000",
+  "decimal": "0.0030217758",
+  "source_prs": [
+    4610,
+    5241,
+    4470,
+    4447,
+    4441,
+    4440,
+    4416,
+    4433,
+    4359,
+    4268,
+    3945,
+    4085,
+    2979,
+    4076,
+    4088,
+    1673,
+    1758,
+    1786,
+    23,
+    555,
+    589
+  ],
+  "source_manifest": "certificates/frontier4610-source.json",
+  "certificate": "certificates/frontier4610/CLAIM.json",
+  "certificate_sha256": "c48376a8365a4c7b67adb368bafa128bede4cd5589a41fa276f96a350d45606c",
+  "proof": "docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md",
+  "proof_supplements": {
+    "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c",
+    "notes/batched-complex-rows.tex": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c",
+    "notes/compact-control-movement.tex": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6",
+    "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+    "notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a",
+    "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "references/semantic-bulk/pr23/semantic-bulk-17-note.tex": "652242b05174bb776ffc6165af170df9c8cf220dbd0fc26c24d778f320dbabc8",
+    "research/e8-bit-carrier-skeleton/code/bit/export_records.py": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3",
+    "research/e8-bit-carrier-skeleton/code/nine/geometry.py": "36eeda3184bd009e89462b65c8725d10860c444f8da8f1f87e5f6e50120011ca",
+    "research/e8-bit-p111-tuned/code/gen_p3.py": "438b83f10d70ceca7cf78049420204b7de2dc61682f913c50a62596106ad84cd",
+    "research/e8-bit-p111-tuned/code/xcheck_p.py": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e",
+    "research/e8-bit-p111-tuned/tune/EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "research/e8-bit-p111-tuned/tune/apply.py": "806ae4cb2648e4f05dcf56bd089891fd3ba33a6ee5fe76d3329e322c6770c1a1",
+    "research/e8-bit-p111-tuned/tune/wlib.py": "a37fdf3cdf5f62945c2a90193401c0e9edc9dd3cda8d8cb36a3b9c329ebe4dbc",
+    "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "docs/research/pr-intake-evidence/pr4359/PROOF-REVIEW.md": "7d67bb814285f7634029fbd378c6457156545f0b38858cc1c6ec34b68cd9d162",
+    "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md": "5c111dd56beb53dc44ab727d96e1af03aaf50f3023d4342e2b0a89ede6cf585b",
+    "docs/research/pr-intake-evidence/pr4416/PROOF-REVIEW.md": "2c2bbe6fe1bab44778192118f27e59a0d23dbe02c47aa8a42845093f1ce46f49",
+    "docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md": "b84f833e3072cbab372fbda2ece98fbc031c15e590cf73003ddea35a5222e148",
+    "research/final4610-independent-admission/PROOF.md": "e573cbbe6fa5481c0533e773de404e10f4dc7907b5ebfe404bdcd02dcf9844d8",
+    "research/final4610-independent-admission/SPECIALIZATION.md": "70430114f744108223bc1d44b98bc25b696c4b408b7b044c2a8bbdfdb434ac5c"
+  },
+  "review": "docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md",
+  "validation": "docs/research/pr-intake-evidence/pr4610/VALIDATION.json",
+  "integration": "docs/research/pr-intake-evidence/pr4610/INTEGRATION.json",
+  "reproduce": "make frontier4610-verify",
+  "scope": "Maintainer-reviewed conditional PR4610 construction using the PR5241 independent audit. The five PR4470 framework assumptions are unchanged. Uniform words are not materialized.",
+  "previous_kappa": "60403/20000000",
+  "previous_record": "certificates/checkpoints/frontier4470.json",
+  "audited_source_head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296",
+  "source_certificate": "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json",
+  "source_certificate_sha256": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de",
+  "replay_mode": "Fresh complete independent admission replay; source-bound preceding controller, ordinary BIT and physical/compiler foundation reuse",
+  "contributors": "docs/research/community-native4610-contributors.md",
+  "assumptions": [
+    {
+      "id": "native_all_columns",
+      "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity."
+    },
+    {
+      "id": "owned_erasure",
+      "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts."
+    },
+    {
+      "id": "compiler",
+      "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract."
+    },
+    {
+      "id": "precision_tape",
+      "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template."
+    },
+    {
+      "id": "analytic_recovery",
+      "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework."
+    }
+  ],
+  "audit_pr": 5241,
+  "audit_head": "13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2"
+}
diff --git a/research/owned-relation-independent-validation/engines/cost/frozen/verify.py b/research/owned-relation-independent-validation/engines/cost/frozen/verify.py
new file mode 100644
index 0000000000..b19f7d0ca4
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/cost/frozen/verify.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python3
+"""Replay the one-relation native word and its complete conditional kappa.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+Read README.md for the source credit and inherited proof obligations.
+"""
+from hashlib import sha256
+import argparse
+import gzip
+import json
+from pathlib import Path
+import sys
+sys.dont_write_bytecode = True
+import native as N
+import price
+
+
+def run():
+    N.authenticate()
+    source = N.read(N.ROOT / N.SOURCE)
+    candidate = N.construct(source)
+    c = candidate['canonical']
+    before, after = {}, {}
+    for direction in ('forward', 'backward'):
+        back = direction == 'backward'
+        before[direction] = N.replay(c, source['programs'][direction], back, False)
+        after[direction] = N.replay(c, candidate['programs'][direction], back, back)
+        N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Pinned source census')
+        N.need(after[direction]['paid'] == candidate['paid_profiles'][direction], 'Emitted direction-specific paid profile')
+        helpers = dict(N.OLD_HELPERS)
+        if back: helpers[9] -= 1
+        N.need(after[direction]['paid'] == (N.NEW_PAID if back else N.OLD_PAID) and after[direction]['helpers'] == helpers, 'Actual complete changed native census')
+    identities = N.independent_source_identities(source)
+    phase = N.phase_inheritance(source, candidate)
+    controls = N.controls(c, candidate)
+    arithmetic = price.run(after)
+    data = (json.dumps(candidate, sort_keys=True, separators=(',', ':')) + '\n').encode()
+    result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION',
+                       'source_payload_sha256': N.PAYLOAD, 'word_payload_sha256': sha256(data).hexdigest(),
+                       'source_native': before, 'candidate_native': after, 'independent_source_identities': identities,
+                       'phase_inheritance': phase, 'native_negative_controls': controls, 'arithmetic': arithmetic,
+                       'scope': 'Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.'})
+    return data, result
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--write', action='store_true', help='Write only this package word and result after all checks pass.')
+    ap.add_argument('--out', type=Path, help='Write a replay result to a separate path.')
+    args = ap.parse_args()
+    data, result = run()
+    if args.write:
+        (N.HERE / 'WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+        (N.HERE / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n', encoding='utf-8')
+    else:
+        N.need(gzip.decompress((N.HERE / 'WORD.json.gz').read_bytes()) == data, 'Exact literal published word')
+        N.need(N.read(N.HERE / 'RESULT.json') == result, 'Exact published replay result')
+    if args.out:
+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n', encoding='utf-8')
+    print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR4610', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/engines/physical/independent_physical_check.py b/research/owned-relation-independent-validation/engines/physical/independent_physical_check.py
new file mode 100644
index 0000000000..26a51ca920
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/independent_physical_check.py
@@ -0,0 +1,192 @@
+#!/usr/bin/env python3
+"""Bounded PR5377 physical-delta check; imports no submitted evaluator.
+
+Reverse functional propagation proves the three frozen source rows. A separate
+forward propagation checks all independent columns and native frame labels.
+This does not lower Gaussian phases or run the completion/compiler pipeline.
+"""
+from collections import Counter
+from fractions import Fraction as F
+from pathlib import Path
+import gzip, hashlib, json, time
+
+HERE = Path(__file__).resolve().parent
+P = HERE / 'pinned'
+
+def read(name):
+    raw = (P / name).read_bytes()
+    return json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw)
+
+def check(test, message):
+    if not test:
+        raise ValueError(message)
+
+def merge(dst, key, value):
+    q = dst.get(key, F(0)) + value
+    if q:
+        dst[key] = q
+    else:
+        dst.pop(key, None)
+
+def right_letter(word, op):
+    return word[:-1] if word and word[-1] == -op else word + (op,)
+
+def pullback(program, role, stop):
+    """Right-append words while pulling one output functional to source inputs."""
+    functional = {role: {(): F(1)}}
+    for event in reversed(program[:stop+1]):
+        if event[0] == 'warp':
+            dst, op = tuple(event[1]), event[2]
+            if dst in functional:
+                functional[dst] = {right_letter(w, op): q for w, q in functional[dst].items()}
+        elif event[0] == 'scalar':
+            g = event[1]; dst = tuple(g[1])
+            row = functional.get(dst, {})
+            if g[0] == 'clear':
+                functional.pop(dst, None)
+            elif g[0] == 'scale':
+                functional[dst] = {w: q*F(*g[2:]) for w,q in row.items()}
+            else:
+                src = tuple(g[2]); copy = g[0] == 'copy'
+                check(copy or g[0] == 'add', 'known scalar pullback')
+                q = F(1) if copy else F(*g[3:])
+                if copy:
+                    functional.pop(dst, None)
+                for w, a in tuple(row.items()):
+                    merge(functional.setdefault(src, {}), w, q*a)
+        else:
+            check(event[0] in ('climb','center','phase','adapter'), 'source opcode')
+    return {(r,w): q for r,row in functional.items() for w,q in row.items() if q}
+
+def difference(a,b):
+    out=dict(a)
+    for k,q in b.items(): merge(out,k,-q)
+    return out
+
+def span(basis):
+    s={0}
+    for b in basis: s |= {x^b for x in tuple(s)}
+    check(len(s)==2**len(basis), 'independent frame basis')
+    return s
+
+def advance_all(word, direction, specialized):
+    c=word['canonical']; owned={('C',0)}
+    if specialized: owned|={('C',1),('L',230)}
+    state={('L',i): {(('L',i),()): F(1)} for i in range(632)}
+    state.update({r:{(r,()):F(1)} for r in owned})
+    frames={('L',i):f for i,f in enumerate(c['start'])}
+    frames.update({r:None for r in owned if r[0]=='C'})
+    spaces=list(map(span,c['frames'])); paid=Counter(); zeros=[]
+    for index,event in enumerate(word['programs'][direction]):
+        kind=event[0]
+        if kind=='scalar':
+            g,frame=event[1:]; dst=tuple(g[1])
+            if g[0]=='clear':
+                check(dst in owned,'erase only owned storage')
+                state[dst]={}; frames[dst]=frame
+            else:
+                check(frames[dst]==frame,'scalar output gauge')
+                if g[0]=='scale': state[dst]={k:q*F(*g[2:]) for k,q in state[dst].items()}
+                else:
+                    src=tuple(g[2]); check(frames[src]==frame and src!=dst,'scalar source gauge')
+                    if g[0]=='copy':
+                        check(dst in owned and not state[dst], 'copy clears owned destination')
+                        state[dst]=dict(state[src])
+                    else:
+                        check(g[0]=='add','known scalar')
+                        for k,q in tuple(state[src].items()): merge(state[dst],k,q*F(*g[3:]))
+        elif kind=='warp':
+            _,role,op,old,new=event; dst=tuple(role)
+            check(frames[dst]==old,'native warp input gauge')
+            transformed={}
+            for (r,w),q in state[dst].items():
+                nw=w[1:] if w and w[0]==-op else (op,)+w
+                merge(transformed,(r,nw),q)
+            state[dst]=transformed; frames[dst]=new
+        elif kind in ('climb','center'):
+            if kind=='climb': _,_,i,old,new,rank=event; dst=('L',i)
+            else: _,i,old,new,rank=event; dst=('C',i)
+            check(frames[dst]==old,'paid input gauge')
+            check(spaces[old]<spaces[new] or (kind=='center' and spaces[new]<spaces[old]),'nested paid transition')
+            check(rank==abs(len(c['frames'][new])-len(c['frames'][old])),'whole paid rank')
+            frames[dst]=new; paid[rank]+=1
+        elif kind=='zero_retag':
+            _,role,old,new=event; dst=tuple(role)
+            check(direction=='backward' and specialized and (dst,old,new)==(('L',92),254,1),'authorized zero replacement')
+            check(frames[dst]==old and state[dst]=={},'all independent columns zero')
+            frames[dst]=new; zeros.append(index)
+        else:
+            check(kind in ('phase','adapter'),'known inherited marker')
+    check([frames['L',i] for i in range(632)]==c['final'],'every final gauge')
+    for i in range(632):
+        r=('L',i)
+        if r in owned: continue
+        want={(r,()):F(1)}
+        if direction=='backward' and i<112: want[(('L',i+112),())]=F(-1)
+        if direction=='forward' and 112<=i<224: want[(('L',i-112),())]=F(1)
+        check(state[r]==want,'independent endpoint '+str(i))
+    check(all(not state[r] for r in owned),'all owned outputs erased')
+    return {'persistent_inputs':632-int(specialized),'owned_arbitrary_inputs':len(owned),
+            'paid':dict(sorted(paid.items())),'checked_zero_event_indices':zeros,
+            'endpoint_pass':True,'frame_pass':True}
+
+def main():
+    start=time.monotonic(); source=read('ACTUAL-WORD.json.gz'); candidate=read('WORD.json.gz')
+    c=source['canonical']; old=source['programs']['backward']; new=candidate['programs']['backward']
+    # Pin consumed binary payloads separately from the PR's reported result.
+    pins=read('SOURCES.json')
+    for row in pins['files']:
+        basename=Path(row['path']).name
+        if basename not in ('ACTUAL-WORD.json.gz','PHASE-VALIDATION.json.gz'): continue
+        raw=(P/basename).read_bytes()
+        check(hashlib.sha256(raw).hexdigest()==row['sha256'],'source SHA256')
+        check(hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()==row['git_blob'],'source blob')
+    check(hashlib.sha1(b'blob '+str(len((P/'WORD.json.gz').read_bytes())).encode()+b'\0'+(P/'WORD.json.gz').read_bytes()).hexdigest()=='5e79bd826c6ca1e782766ea0ae28a61d136303d1','connector pinned candidate blob')
+    physical=dict(c); physical.pop('local_profile')
+    check(candidate['canonical']==physical,'all canonical physical maps unchanged')
+    check(candidate['programs']['forward']==source['programs']['forward'],'literal forward program unchanged')
+    expected=[['scalar',['clear',['L',230]],0]]
+    for helper,sign in [(324,1),(326,-1),(328,-1),(333,1)]:
+        expected.append(['scalar',['add',['L',230],['L',helper],sign,1],0])
+    for i,e in enumerate(old):
+        if i==11332:
+            expected += [['scalar',['clear',['C',0]],254],['scalar',['copy',['C',0],['C',1]],254],['scalar',['clear',['C',1]],254]]
+        elif i==15584: expected.append(['zero_retag',['L',92],254,1])
+        else: expected.append(e)
+        if i==11205: expected += [['scalar',['clear',['C',1]],254],['scalar',['copy',['C',1],['L',92]],254]]
+    expected.append(['scalar',['clear',['L',230]],1])
+    check(new==expected,'exact only declared event delta')
+    delta={(('L',i),()):F(q) for i,q in {230:1,324:-1,326:1,328:1,333:-1}.items()}
+    q=pullback(old,('L',92),11205)
+    center=pullback(old,('C',0),11332)
+    zero=pullback(old,('L',92),15584)
+    check(difference(center,q)=={k:v/4 for k,v in delta.items()},'independent reverse center-minus-snapshot')
+    check(zero=={k:-v/4 for k,v in delta.items()},'independent reverse zero-site')
+    # Negative controls change actual premises, not just reported receipts.
+    wrong=dict(delta); wrong[(('L',324),())]*=-1
+    check(difference(center,q)!={k:v/4 for k,v in wrong.items()},'wrong relation must fail')
+    wrong_q=pullback(old,('L',63),11205)
+    check(difference(center,wrong_q)!={k:v/4 for k,v in delta.items()},'wrong snapshot must fail')
+    allcolumns={}
+    for name,w,specialized in [('source',source,False),('candidate',candidate,True)]:
+        for direction in ['forward','backward']:
+            allcolumns[name+'_'+direction]=advance_all(w,direction,specialized and direction=='backward')
+    controller=read('controller-CONTROLLER.json')
+    calls=[e for e in controller['physical_events'] if e[0]=='LOCAL']
+    check([e[1] for e in calls if e[3]]==list(range(1,32,2)),'16 backward stage incidence')
+    check([e[1] for e in calls if not e[3]]==[0,32],'two retained forward calls')
+    check(sum(e[0]=='QUERY_SHEAR' for e in controller['physical_events'])==15,'all query shears')
+    phase=read('PHASE-VALIDATION.json.gz')
+    check(phase['actual_word_canonical_sha256']==hashlib.sha256(gzip.decompress((P/'ACTUAL-WORD.json.gz').read_bytes())).hexdigest(),'phase exact source payload binding')
+    check(phase['status']=='PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES','source absolute phase receipt')
+    result={'status':'PASS_BOUNDED_INDEPENDENT_PHYSICAL_DELTA','head':'c448d13c71908647f968b06cddb795ce7d288139',
+            'source_row_pullbacks':{'snapshot_terms':len(q),'center_minus_snapshot':'Delta/4','zero_site':'-Delta/4'},
+            'all_columns':allcolumns,'full_local_calls':calls,'query_shears':15,
+            'source_phase_receipt_authenticated':True,'source_phase_lowering_rerun':False,
+            'negative_controls':['wrong helper relation','wrong snapshot source'],
+            'seconds':round(time.monotonic()-start,3),
+            'scope':'Exact free-word identities, all-column boundaries, physical gauge compatibility, owned storage and controller orientation incidence. Inherits source physical native recipes, permitted erasure, all-size mixed-target compiler, precision, tape and integer recovery; no full compiler or theorem replay.'}
+    (HERE/'independent-result.json').write_text(json.dumps(result,indent=2)+'\n')
+    print(json.dumps(result,indent=2))
+
+if __name__=='__main__': main()
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/ACTUAL-WORD.json.gz b/research/owned-relation-independent-validation/engines/physical/pinned/ACTUAL-WORD.json.gz
new file mode 100644
index 0000000000..46d929df83
Binary files /dev/null and b/research/owned-relation-independent-validation/engines/physical/pinned/ACTUAL-WORD.json.gz differ
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/PHASE-VALIDATION.json.gz b/research/owned-relation-independent-validation/engines/physical/pinned/PHASE-VALIDATION.json.gz
new file mode 100644
index 0000000000..ac77b78547
Binary files /dev/null and b/research/owned-relation-independent-validation/engines/physical/pinned/PHASE-VALIDATION.json.gz differ
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/PROOF.md b/research/owned-relation-independent-validation/engines/physical/pinned/PROOF.md
new file mode 100644
index 0000000000..69c337a770
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/PROOF.md
@@ -0,0 +1,174 @@
+# Source-bound free-operator tensor lift
+
+This audit affirms one specific premise in PR4100's `COMPLEX.md`, lines 62–89:
+the retained four PR4088 words cancel in a free group algebra before any
+particular native operator is substituted. The premise is true for the exact
+source exports checked here. This is a local algebra and source-binding result;
+it supplies no new paid profile, numerical allowance, encoded implementation,
+physical hosting theorem, outer release or selected-frontier improvement.
+
+## Exact source and contract
+
+The audited text is `research/unconditional-batched-crt/COMPLEX.md`, Git blob
+`c3be56fbfdb4fb29c1ace88cbcdfa7475fb6e343`, SHA256
+`853e1295850862752e4f854aa9e8b28f9ca6eaa9306e2af110b7b77526d1b5e1`.
+It is identical at retained PR4100 head
+`337d04939571a637aeab54a0f58f54fde811663a` and canonical main
+`12fa8c5c844be21bfefb38a19503fbd867a11244`.
+
+Its stated source is PR4088 head
+`72d7efc181edb21806a878f174847c96dd410ab0`, package
+`research/staged544-mixed-fourth-entry`. This audit exports the exact four
+`inputs/{THREE,FOUR}-{base,extra}.json.gz` files, retained `vendor/audit_core.py`,
+`vendor/audit_verify.py`, source `verify.py`, `PROOF.md` and `NOTICE.md`.
+`SOURCE-PINS.json` records every original commit, path, length, Git blob and
+SHA256. Every file is authenticated before the retained checker is executed.
+No native runner, owner fill, solver, NumPy or historical outer engine is run.
+
+Each word has 632 live registers, 91 arbitrary dirty private registers,
+72 abstract unary generators and 36 listed initial correction terms. The
+forward common-label contract on the 723-register direct sum is
+
+`(x,y,h,b) -> (x,y+x,h,b)`.
+
+The dual contract is `(x,y,h,b) -> (x-y,y,h,b)`. In particular every private
+buffer is an independent input, returns identically, and has no leakage into
+live outputs. Neither contract assumes zero private inputs or a product state.
+
+## What the retained checker actually computes
+
+In `audit_core.py`, lines 297–391, a register value is a sparse dictionary
+
+`(initial_input, reduced_signed_operator_word) -> Fraction`.
+
+`program` includes every declared initial correction, precondition,
+compensation, A and cut gate, chronologically inserted B warp, B gate,
+restoration and cleanup gate. `_left` and `_right` cancel only adjacent inverse
+letters; `_axpy` adds exact rational coefficients and removes exact zeros.
+There is no commutation, finite-order relation, numerical operator matrix,
+Fourier-character evaluation or univariate minimal-polynomial reduction.
+
+`audit_verify.semantics` runs all 723 independent symbols forward and dual,
+compares an independent direction of pullback, and checks both cleanup-boundary
+contracts. Every emitted provider passes. Each endpoint consists of exactly
+835 nonzero terms: the 723 diagonal terms and 112 intended shear terms. Every
+surviving operator word is empty.
+
+That is a universal algebraic identity, rather than an identity inferred from
+one operator realization. The source's use of the word “symbolic” is justified
+by these actual data structures, reductions and endpoint predicates.
+
+## All positive tensor multiplicities
+
+Let `F` be the free group on symbols `g_1,...,g_72`, and let `A=Q[F]` be its
+rational group algebra. The finite word program is a product of elementary
+723-by-723 matrices over `A`. A correction `c*g_word*x_source` is an off-diagonal
+entry of one such elementary matrix. Scalar ADD and SCALE entries belong to
+`Q*1_A`.
+
+Let `K` be any characteristic-zero field (in particular `Q[i]`) and let `V`
+be any finite-dimensional vector space over `K`. Choose arbitrary invertible `K`-linear operators
+`G_k` on `V`. All tensor products below are over `K`. For every positive integer `f`, define
+
+`rho_f(g_k) = G_k tensor ... tensor G_k` (f factors).
+
+The assignment of free generators extends uniquely to a group homomorphism
+`F -> GL(V tensor f)`: inverses map to tensor products of inverses, and
+
+`(G H) tensor f = (G tensor f)(H tensor f)`.
+
+Extend this map rationally from `A` into the `K`-linear endomorphisms of
+`V tensor f`. This extension is a unital rational algebra
+homomorphism because multiplication of finite formal sums distributes and
+because the group map preserves products. In particular
+
+`rho_f(sum_w c_w*w) = sum_w c_w*rho_f(w)`.
+
+Apply this homomorphism entrywise to the certified elementary-matrix product.
+It preserves each elementary action, the order of events and the product.
+Since the certified endpoint has only rational multiples of empty words, its
+image is exactly the same register-level shear with each scalar multiplied
+by the identity of `V tensor f`. This proves the endpoint for every positive
+`f` and every input in the 723-register direct sum of `V tensor f`, including
+arbitrarily correlated live/private data.
+
+The number of register roles remains 723. We are changing the internal space
+of each role; we are not taking a tensor power of the 723-by-723 register matrix.
+The latter operation would create a different program with 723^f roles.
+
+The dual pass treats `d_k=G_k^(-T)` as separate free generators. The same
+argument applies, and `(G_k^(-T)) tensor f = (G_k tensor f)^(-T)` in the product
+basis. Native frame labels can be replaced by their tensor powers if the
+separately supplied directed native recipe identities are exact. This audit
+does not reprove or rerun those native recipe identities.
+
+## The distinction that must be retained
+
+This algebra homomorphism is linear on formal sums. Therefore
+
+`rho_f(g-I) = G tensor f - I`,
+
+not `(G-I) tensor f`. Likewise `rho_f(c*g)=c*(G tensor f)`, not
+`(c*G) tensor f = c^f*(G tensor f)`. A role SCALE or bridge coefficient must
+remain scalar, while a constant phase already inside a unary generator is
+part of that generator and therefore occurs in every tensor factor.
+
+For an exact small counterexample, take `G=[[1,1],[0,1]]` and `f=2`.
+Then `(G tensor G-I)` sends `e_2 tensor e_2` to
+`e_1 tensor e_1 + e_1 tensor e_2 + e_2 tensor e_1`; whereas
+`(G-I) tensor (G-I)` sends it only to `e_1 tensor e_1`. Their difference is
+nonzero over `Q` (and over the supplemental field F101).
+The code checks a distinct noncommuting 72-generator family as well, and rejects
+both the whole-difference and whole-scalar tensorization rules.
+
+## Independent evidence and its scope
+
+`independent.py` imports or executes no retained implementation. It reconstructs
+the literal sequence from the four exported words and, for each of the 723
+outputs separately, pulls the output functional backward through that sequence
+over exact `Q[F_72]`. The reverse traversal appends words on the right; a stack
+reduces only adjacent inverse letters. All four forward and all four dual
+contracts match exactly: 5784 output-functional checks, 6680 endpoint terms and
+zero surviving nonempty words. Its controls preserve a nontrivial commutator,
+a fourth power and the two distinct terms of `g-I`.
+
+This implementation is independent of the source engine; the format and
+endpoint contract were read from the same credited source. Agreement is
+supplemental to inspection of the finite exact computations, not a substitute
+for proving what the reductions mean.
+
+`verify.py` also reconstructs and executes the literal events directly on dense
+vectors over F101, with 72 distinct invertible 2-by-2 matrices. The first two do
+not commute. It substitutes their tensor powers at `f=1,2,3` in both orientations
+of all four providers, yielding 24 direct fixtures; all 723 registers are given
+deterministic dirty values. These finite-field experiments are controls, not
+the proof for every rational input or unbounded f. Erasing the actual listed
+correction generators fails at 20 registers; tensorizing the actual role SCALE
+coefficients fails at the reported registers. Exact inverse and product
+compatibility controls also pass.
+
+## Remaining obligations and credit
+
+This positive result discharges only the source's formal free-operator premise
+and its algebraic implication to per-role tensor multiplicity. The physical
+lowering of native monomials, directed native recipes, placement, common cover,
+hosted slices, analytic bounds, coefficient precision, fixed-tape inventory,
+recovery and complete ordinary/outer release are outside this audit. The source
+construction makes additional written claims about these interfaces; this audit
+neither verifies nor refutes those claims.
+No paid-rank saving, all-size multiplication theorem, independent human
+acceptance or new kappa is claimed.
+
+The tensor-lift proposal and current construction are credited to Cinna Davis,
+the PR4100 author; this audit does not claim to invent the representation argument.
+Cinna Davis's PR4088 supplies the four literal providers and source integration.
+Sagar Thakrar's PR3687 exact free-operator engine and roger-sato's PR3693
+all-dirty/reverse audit are reused explicitly. Retained lineage includes Rohan
+Arun/PR4076, Dugongue/David Ganz/PR4085 and PR3945, Nick Petalas, Ross
+Richardson/PR3605, dataisfire/PR3734, ChaloupeMusic/Erwan Secousses, Marius-Paul
+Dumitrean, zxv and the earlier geometry/native/compiler/owner contributors.
+The byte-identical source notice and source-file notices remain in `source/`.
+
+The formal and F101 implementations were separately written by one Codex agent. A second Codex agent independently reviewed them and supplied the exact rational signed-permutation oracle in `independent_real.py`; see `INDEPENDENT-REVIEW.md`. None is a human or formal-kernel acceptance.
+
+`mutation_controls.py` also produces exact actual-program counterexamples in `MUTATIONS.json`: erasing the first correction generator yields `(I-G59)x273` in output115; dropping the first nonidentity scale yields `-3*x119` in output119. Both baseline output functionals pass first. Every actual correction word has length one, so a multi-letter correction reorder is inapplicable rather than counted as an executed control.
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/README.md b/research/owned-relation-independent-validation/engines/physical/pinned/README.md
new file mode 100644
index 0000000000..777f4e1d51
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/README.md
@@ -0,0 +1,249 @@
+# Conditional kappa 0.00302235 from one owned helper relation
+
+This construction gives **conditional kappa = 60447/20000000 = 0.00302235**.
+The gain over Cao Yifan's final
+[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)
+value, 0.0030217758, is **2871/5000000000 = 0.0000005742**.
+The construction changes the complete paid profile. It does not obtain the
+gain by taking more digits of the old root.
+
+One helper becomes owned storage in each backward call. A prepared relation
+then makes one paid rank-eight center equal to an earlier saved value. The same
+relation makes one later rank-one job act on zero. Both jobs can be removed,
+with the rank-nine helper credit also removed. All other independent outputs
+and all main interfaces keep their source operators.
+
+[WORD.json.gz](WORD.json.gz) is the complete emitted word.
+[RESULT.json](RESULT.json) records the exact native checks, the two source
+identities, both full profiles, completion, compiler and outer calculations.
+[SOURCES.json](SOURCES.json) pins every external input by Git blob and SHA256.
+The proof below explains why the changed word has the stated contract.
+
+## Source and scope
+
+The base is canonical main
+[7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56).
+The native source is the final PR #4610 word at
+[20bb93cd990d2ff683e4d0fc56b87a42cd5d3296](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz).
+Its decompressed SHA256 is
+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.
+The comparison value and old crossing come from its
+[final compiler arithmetic](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json).
+All consumed bytes are already in the recorded main base.
+
+This is one instance of the current `complex-new-helper-inventory` priority.
+The [scoped claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737)
+reserves only the relation and two replacements below.
+[Discussion #5355](https://github.com/CrocSwap/integer-mult-bounds/discussions/5355)
+retains all 632 independent inputs and all eight centers.
+[Discussion #4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930)
+retains every original helper endpoint. This construction removes the
+independent L230 job in backward calls. It does not claim those broader scopes.
+The selected certificate is unchanged. A fresh check at 20:20 UTC found that
+Discussion #5355 had released its original-input scope without a saving.
+Canonical main still had the recorded base commit.
+
+## Exact replacement proof
+
+All indices below are zero-based indices in the frozen backward program.
+Let `h_r` be the source logical input of helper `Lr`. The five helpers in
+
+```math
+\Delta=h_{230}-h_{324}+h_{326}+h_{328}-h_{333}
+```
+
+all start in frame 0 and finish in frame 1, of rank nine. The new backward
+contract has 224 independent main fields and 407 independent helper fields.
+L230 is private. Clear it, then use four same-frame ADDs to prepare
+
+```math
+h_{230}=h_{324}-h_{326}-h_{328}+h_{333}.
+```
+
+The other helper inputs remain arbitrary and independent. This preparation
+sets Delta to zero for every input. It uses no recursive job. It removes one
+rank-nine productive target; the dependent field receives no output credit.
+
+Run the original source program on unrestricted inputs. Let `q` be the
+logical row of L92 just after event 11205, a paid climb into frame 254.
+The separate predecessor row engine gives these exact identities:
+
+| Source position | Exact logical row |
+| --- | --- |
+| C0 at the rank-eight center, event 11332 | `q + Delta/4` |
+| L92 at the rank-one climb, event 15584 | `-Delta/4` |
+
+These identities are over rational coefficients and free native operator
+words. They hold for every value of every source input and for every invertible
+interpretation of the native symbols. They do not use numerical samples or an
+assumed relation between distinct native maps.
+
+For every positive tensor width f, substitute each native generator by its
+source operator tensor power and each inverse by the inverse tensor power.
+This defines a representation of the free group. Keep the rational scalar
+coefficients outside the substitution. The two row identities therefore hold
+at every such width. In particular, Delta/4 remains a scalar linear form; it
+is not a tensor power of that sum. This uses the termwise argument recorded in
+the [free-word tensor audit](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/free-word-tensor-lift-audit/PROOF.md),
+which credits Cinna Davis's proposal and ToikY's scoped audit. Physical frame
+realization and the complete all-size compiler retain their source contracts.
+
+Immediately after event 11205, clear a new private field C1 in frame 254 and
+COPY L92 into it. C1 is not written until the replacement of event 11332. At
+that event, clear owned C0, set its frame to 254, COPY C1 into C0, then clear C1.
+The copy coefficient is exactly one. Under Delta = 0, the copied field is the
+same physical value as the old center output: the logical rows and the exact
+frame gauge are equal. The old C0 input can be erased because C0 is owned.
+This removes one rank-eight recursive job.
+
+At event 15584, L92 is exactly zero in every input column. The physical
+identity therefore has the same result as the old rank-one frame change.
+`zero_retag` records this fact. It performs no physical write and is accepted
+only when the full exact row is empty and the current frame is 254. It then
+records frame 1. This removes one rank-one recursive job. It does not erase a
+main input or replace a nonzero transform with a free frame change.
+
+Every other event stays in source order. Clear private L230 at return. The
+source clears C0, and the new program has already cleared C1. The original
+linear endpoint identity, restricted by the prepared relation, gives all 224
+main outputs and all 407 retained helper outputs. The literal new-word replay
+checks these outputs separately, with all 631 retained inputs and all three
+owned entry fields initially arbitrary. It also checks every scalar frame,
+paid rank, native frame transition and final frame.
+
+The 4,429 source frames, 72 native maps, all remaining paid operators, and main
+adapters are unchanged. The source
+[absolute-phase certificate](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz)
+is authenticated and reused. Same-frame COPY and identity on zero introduce no
+phase recipe. The source's amplitude and Clifford-lowering checks are not
+rerun by this package. The new free-word identities prove equivalence for the
+source operators with their full phases, not just their projective classes.
+
+## Complete cost and conditional compiler
+
+The forward word is unchanged. Each backward call has these counts:
+
+```text
+paid:    {1:2200, 2:412, 3:510, 4:127, 5:40, 8:7}
+helpers: {4:28, 7:7, 8:47, 9:325}
+```
+
+The full p16/a7 controller contains 16 backward calls, two forward calls and
+15 query shears. Thus the complete difference is **minus 16 H1 and 16 H8 paid
+jobs, and minus 16 H9 productive targets**. It includes every idle and main
+target. There are 64,372 paid jobs and 10,912 productive fields. Their rank
+masses are 238,990 and 239,742; the surplus remains 752.
+
+For every real `0 < t < 1`, the complete target-minus-paid moment increases by
+
+```math
+16(1+8^t-9^t)>0.
+```
+
+For a direct proof, both `(1/9)^t > 1/9` and `(8/9)^t > 8/9`; multiply their
+sum by `9^t`. The improvement is strict throughout the required range.
+
+The backward word has 158,214 real scalar operations under the source macro
+allowance, exactly 46 more than its source. Its maximum formal prefix L1 norm
+is 169, with maximum denominator 64; both equal the source bounds. The forward
+bounds remain 457 and 32. One extra physical private slot holds C1. L230 uses
+an existing slot. The route bound also charges two routes for each of the two
+new owned lifetimes. The local scalar-plus-route bound stays below 10^7, and
+the complete raw nonrecursive bound stays **181,098,496 < 10^9**. Preparation,
+COPY, CLEAR and storage therefore do not introduce an unpaid recursive cost.
+
+Two rational interval engines check the complete moment. Its unique crossing
+in `0 < kappa < 1` lies in
+**(0.00302238736347, 0.00302238736348)**. The verifier proves the moment decreases
+on `[0,0.05]` and remains negative on `[0.05,1]`. This is a ceiling for this
+fixed complete profile, not an optimum over circuits or helper relations.
+The claimed kappa leaves more than **0.00000003736347** raw headroom.
+
+The separately tested saving is 0.00302236. The paid/target ratio is below
+`0.999999971483293515393313955730`, with reserve `1e-9`. Both charged tails are
+below `0.97`. The source power 1024, cutoff 20, floor 21, tail offset 1/5,
+complement factor 63/64 and logarithm power 1000 still pass. The compiler gap
+is `1/700000000`, with `j=44836`, `H=31385200000000` and `N=2^31385200000000`.
+The exact integer test `(H+1)^1000 < 2^44836` passes; the preceding grid integer
+fails. The uniform complex saving is `2115651/700000000`. All 54 strict outer
+predicates and four functional predicates pass, using the retained ordinary
+BIT saving 0.0034.
+
+## Verification and reproduction
+
+Use Python 3.12 or 3.14, with the standard library only. From the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023 --check-only
+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023
+```
+
+The registered commands run normal and optimized Python. The direct command,
+also used for a Git-free export, is:
+
+```sh
+python3 -B research/kappa-owned-relation-20261023/verify.py
+python3 -O -B research/kappa-owned-relation-20261023/verify.py
+```
+
+Each prints status
+`PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION`.
+The verifier reconstructs the word and compares its bytes and exact result with
+the published artifacts. `--write` is a separate authoring command. It changes
+only this package's word and result after all checks pass.
+
+Fresh checks cover both source words, both candidate words, every independent
+entry column and owned return, the two unrestricted source identities, retained
+phase bindings, the p16 rational Laurent factorization, both scalar boundary
+programs, two complete invoice counts, two rational interval engines, the fixed
+profile ceiling, completion, compiler, BIT conversion and all outer predicates.
+The emitted word replaces the old single `canonical.local_profile` metadata
+field with explicit `paid_profiles` for the two directions.
+
+Seven native controls reject a wrong relation sign, omitted input clear, wrong
+snapshot, wrong zero frame, wrong paid rank, wrong copy gauge, and omitted
+output clear. Five cost/outer controls reject the lost helper's output credit,
+old BIT stock, closed uniform gap, unfunded endpoint and closed epsilon.
+
+Normal and optimized registered replays passed on CPython 3.12.14. The direct
+author check also passed on CPython 3.14. Source metadata and pins passed.
+The optional full-history preflight is not claimed in the shallow checkout.
+The publication handoff records export and committed-byte checks.
+
+The full source phase lowering, BIT native replay, Lean, Docker, physical tape
+execution, numerical precision execution, analytic decomposition and integer
+recovery are not rerun here. The complete bound retains those predecessor
+contracts, including permitted owned erasure, whole-job normalizers, mixed
+productive-target recursion and all-size closure. The expanded compiled word
+is specified by a finite algorithm, not materialized. This is a conditional
+construction with exact finite evidence, not an unconditional multiplication
+theorem, a practical timing result or independent human acceptance.
+
+## Credit
+
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+Cao Yifan's [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)
+supplies the exact source word, phase evidence and previous compiler value.
+Cinna Davis's [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470)
+supplies the p16 controller and helper-interface lineage. The source code keeps
+credit for Dugongue's transported frames, zxv's native and finite-compiler
+work, Jacob Alan Sussman's mixed-target recursion and their predecessors.
+The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py)
+and [literal native source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-rebuild/complex/native_extensions.py)
+are pinned as provenance for the adapted checks.
+
+zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283)
+supplies the related cache contract and the explicit handoff to find actual
+matching rows and their lifetimes. Its standalone cache example is not part of
+this word. The new contribution is the five-helper relation, its actual cache
+and zero identities, the full owned-field replacement and the complete positive
+bill. No priority is claimed for the general cache or paid-history ideas.
+
+## Open next questions
+
+Independent review should first check the three source rows and the physical
+COPY/zero argument above, then the retained all-size and phase premises.
+A later construction could test a different helper relation, but it must claim
+a disjoint scope and pay every lost target and owned field. This package does
+not classify such relations. [TASK.json](TASK.json) records the first steps,
+relevance and blockers for both questions.
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/RESULT.json b/research/owned-relation-independent-validation/engines/physical/pinned/RESULT.json
new file mode 100644
index 0000000000..27b4e54708
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/RESULT.json
@@ -0,0 +1,373 @@
+{
+  "arithmetic": {
+    "compiler": {
+      "H": 31385200000000,
+      "N": "2^31385200000000",
+      "eta": {
+        "lower": "0.000000203927056311365991628189",
+        "upper": "0.000000203927056311365991628190"
+      },
+      "gap": "1/700000000",
+      "integer_test_exponent": 44836,
+      "logarithm_power": 1000,
+      "theta": "63/64",
+      "uniform_saving": "2115651/700000000",
+      "word_materialized": false
+    },
+    "fixed_profile_ceiling": {
+      "decreasing_through": "1/20",
+      "derivative_upper": {
+        "lower": "-195778.630038840116414999953237565269",
+        "upper": "-195778.630038840116414999953237565268"
+      },
+      "remaining_interval_moment_upper": {
+        "lower": "-6836.549542075249598033582799619360",
+        "upper": "-6836.549542075249598033582799619359"
+      }
+    },
+    "full_backward": 16,
+    "full_forward": 2,
+    "gain_over_PR4610": "2871/5000000000",
+    "kappa": "60447/20000000",
+    "kappa_decimal": ".00302235",
+    "margin_at_previous_kappa": {
+      "lower": "0.151161494385402651700356241377",
+      "upper": "0.151161494385402651700356241378"
+    },
+    "margin_at_previous_root_upper": {
+      "lower": "0.151143999513185007311808491175",
+      "upper": "0.151143999513185007311808491176"
+    },
+    "negative_controls": {
+      "closed_epsilon": [
+        "epsilon_below_one",
+        "global_gamma_power_slack",
+        "actual_logarithmic_gamma_guard",
+        "source_axis_superpolynomial",
+        "gaussian_above_main",
+        "new_semantic_guard_with_C1_one"
+      ],
+      "closed_uniform": [
+        "new_complex_uniform_saving_above_b"
+      ],
+      "old_BIT": [
+        "actual_bit_above_effective"
+      ],
+      "unearned_helper_credit": "Rejected by the independent complete census",
+      "unfunded_endpoint": [
+        "main_transform_above_kappa",
+        "global_coordinate_router_above_kappa",
+        "fused_gaussian_above_kappa",
+        "group_bit_router_above_kappa",
+        "boundary_algebraic_matrix_above_kappa"
+      ]
+    },
+    "nonrecursive": {
+      "additional_private_slots": 1,
+      "local_routes": 4806000,
+      "local_scalar": 158214,
+      "owned_slots_backward": 3,
+      "raw_budget": 1000000000,
+      "raw_scalar_upper": 181098496
+    },
+    "ordinary_BIT": {
+      "admitted": "17/5000",
+      "after_cover": "69/20000",
+      "atom": "1/250",
+      "before_cover": "3459/1000000",
+      "ordinary_saving": "8590884599/2500000000000",
+      "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses"
+    },
+    "outer": {
+      "functional_checks": {
+        "actual_new_BIT_stock_sublinear": "174299999253/175000000000",
+        "fixed_halo_explicit_metadata_branch": "13475000001/175000000",
+        "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000",
+        "new_semantic_group_guard": "3/700000000"
+      },
+      "margins": {
+        "boundary_algebraic_matrix": "23139910904443/7656250000000000",
+        "fused_gaussian": "23139910838329/7656250000000000",
+        "global_coordinate_router": "2115649/700000000",
+        "group_bit_router": "1480954993653053/490000000000000000",
+        "group_scans": "349999999/350000000",
+        "main_transform": "23139899966943/7656250000000000",
+        "microbox_face_corrections": "13475000001/175000000",
+        "polynomial_products": "699999999/700000000",
+        "sparse_union_movement": "3133491473404443/7656250000000000"
+      },
+      "parameters": {
+        "a": "2115649/700000000",
+        "b": "42313/14000000",
+        "beta": "699999997/700000000",
+        "bit_saving": "17/5000",
+        "cap_xi": "6961616462466943/7656250000000000",
+        "complex_uniform_saving": "2115651/700000000",
+        "d": "1/700000000",
+        "epsilon": "699999999/700000000",
+        "kappa": "60447/20000000",
+        "lambda_": "199395529/200000000",
+        "lambda_prime": "10904443/10937500",
+        "layout": "1/700000000",
+        "q": "33057/10937500",
+        "r0": "1/7000000000",
+        "stop": "1/700000000",
+        "tested_saving": "75559/25000000"
+      },
+      "strict_checks": {
+        "actual_bit_above_effective": "264351/700000000",
+        "actual_logarithmic_gamma_guard": "1/700000000",
+        "actual_logarithmic_group_guard": "694633553939307/3828125000000000",
+        "alpha_logarithm_absorption": "1/7000000000",
+        "boundary_algebraic_matrix_above_kappa": "43716943/7656250000000000",
+        "cap_above_band": "3133491462466943/7656250000000000",
+        "cap_below_cell": "694633526595557/7656250000000000",
+        "cap_below_phase_cell_power": "8350883537533057/7656250000000000",
+        "complex_above_effective": "1/700000000",
+        "complex_below_one_over_32": "395187/14000000",
+        "complex_endpoint": "1/350000000",
+        "epsilon_below_one": "1/700000000",
+        "epsilon_positive": "699999999/700000000",
+        "fine_prime_halo_umbrella": "7/2",
+        "fused_gaussian_above_kappa": "43650829/7656250000000000",
+        "gaussian_above_main": "5435693/3828125000000000",
+        "global_coordinate_router_above_kappa": "1/175000000",
+        "global_gamma_power_slack": "9/7000000000",
+        "group_below_dimension": "1/350000000",
+        "group_bit_router_above_kappa": "3493653053/490000000000000000",
+        "group_gauge_power_slack": "43414597087027/239257812500000",
+        "group_key_fits_record": "1/350000000",
+        "group_positive": "699999997/700000000",
+        "group_scans_above_kappa": "697884353/700000000",
+        "halo_covers_generic_inverse_radius": "5",
+        "improvement_over_user_baseline": "645689790400418148631/500000000000000000000000",
+        "lambda_above_internal": "1/1400000000",
+        "lambda_above_sigma": "3/1400000000",
+        "lambda_above_tau": "1/1400000000",
+        "lambda_prime_above_lambda": "1/1400000000",
+        "lambda_prime_above_leaf": "27957687/9800000000000000",
+        "leaf_saving_above_effective": "13957687/9800000000000000",
+        "main_transform_above_kappa": "32779443/7656250000000000",
+        "membership_arithmetic_fits_record": "1/700000000",
+        "microbox_face_corrections_above_kappa": "53897884359/700000000",
+        "microbox_halo_volume": "55300000003/700000000",
+        "new_complex_uniform_saving_above_b": "1/700000000",
+        "new_semantic_guard_with_C1_one": "1/700000000",
+        "polynomial_products_above_kappa": "348942177/350000000",
+        "positive_layout_slack": "1/700000000",
+        "q_below_effective": "1/700000000",
+        "q_below_internal": "1/700000000",
+        "q_below_leaf": "27957687/9800000000000000",
+        "q_positive": "33057/10937500",
+        "short_record_fallback": "13957687/14000000",
+        "source_axis_superpolynomial": "1/700000000",
+        "sparse_union_movement_above_kappa": "3110351606216943/7656250000000000",
+        "stop_below_one": "699999999/700000000",
+        "stop_positive": "1/700000000",
+        "strassen_integer_power_gap": "1951441519231",
+        "support_router_span": "3/700000000",
+        "theta_positive_polynomial_power": "2",
+        "union_header_fits_record": "3/700000000",
+        "union_tag_work_per_visit_fits_record": "3/700000000"
+      }
+    },
+    "paid": {
+      "1": 41282,
+      "16": 448,
+      "2": 7416,
+      "24": 448,
+      "3": 9180,
+      "32": 448,
+      "4": 2286,
+      "40": 448,
+      "48": 448,
+      "5": 720,
+      "56": 448,
+      "64": 448,
+      "72": 224,
+      "8": 128
+    },
+    "paid_calls": 64372,
+    "productive_fields": 10912,
+    "query_shears": 15,
+    "rank_mass_surplus": 752,
+    "raw_headroom": [
+      "3736347/100000000000000",
+      "934087/25000000000000"
+    ],
+    "raw_root_interval": [
+      "302238736347/100000000000000",
+      "75559684087/25000000000000"
+    ],
+    "strictification": {
+      "alpha": {
+        "lower": "0.999999971483293515393313955729",
+        "upper": "0.999999971483293515393313955730"
+      },
+      "cutoff": 20,
+      "delta": {
+        "lower": "0.957459689758527661921334851512",
+        "upper": "0.957459689758527661921334851513"
+      },
+      "floor": 21,
+      "gamma": {
+        "lower": "0.956310980726438847618396606911",
+        "upper": "0.956310980726438847618396606912"
+      },
+      "normalized_paid_upper": "2097152001953127/2097154147483648",
+      "power": 1024,
+      "reserve": "1/1000000000",
+      "tail_offset": "1/5",
+      "tested": "75559/25000000"
+    },
+    "targets": {
+      "145": 224,
+      "17": 448,
+      "25": 448,
+      "33": 448,
+      "4": 504,
+      "41": 448,
+      "49": 448,
+      "57": 448,
+      "65": 448,
+      "7": 126,
+      "73": 224,
+      "8": 846,
+      "9": 5852
+    }
+  },
+  "candidate_native": {
+    "backward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 325
+      },
+      "independent_owned_entry_columns": 3,
+      "independent_persistent_columns": 631,
+      "max_denominator": 64,
+      "max_formal_prefix_l1": "169",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2200,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 7
+      },
+      "real_scalar_allowance": 158214,
+      "zero_identities": 1
+    },
+    "forward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "max_denominator": 32,
+      "max_formal_prefix_l1": "457",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158120,
+      "zero_identities": 0
+    }
+  },
+  "independent_source_identities": {
+    "center_minus_snapshot": "Delta/4",
+    "center_replaced": 11332,
+    "copy_coefficient": "1",
+    "relation": {
+      "230": 1,
+      "324": -1,
+      "326": 1,
+      "328": 1,
+      "333": -1
+    },
+    "snapshot_after": 11205,
+    "snapshot_terms_before_substitution": 61,
+    "source_event_indices_are_zero_based": true,
+    "zero_identity_at": 15584,
+    "zero_site_row": "-Delta/4"
+  },
+  "native_negative_controls": {
+    "missing_owned_input_clear": "Every independent main/helper endpoint: 0",
+    "uncleared_owned_output": "Every owned entry column is erased at return",
+    "under_or_overstated_paid_rank": "Exact paid rank and frame",
+    "wrong_copy_gauge": "Exact scalar destination frame",
+    "wrong_relation_sign": "Every independent main/helper endpoint: 0",
+    "wrong_snapshot_source": "Zero identity requires an identically zero full row",
+    "wrong_zero_input_frame": "Zero identity requires an identically zero full row"
+  },
+  "phase_inheritance": {
+    "absolute_phase_receipt_reused": "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz",
+    "all_retained_paid_events_and_warps_from_source": true,
+    "new_gaussian_operators": 0,
+    "new_native_maps": 0,
+    "new_operations": "Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.",
+    "source_amplitudes_and_phase_lowering_freshly_replayed": false
+  },
+  "scope": "Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.",
+  "source_native": {
+    "backward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "max_denominator": 64,
+      "max_formal_prefix_l1": "169",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158168,
+      "zero_identities": 0
+    },
+    "forward": {
+      "helpers": {
+        "4": 28,
+        "7": 7,
+        "8": 47,
+        "9": 326
+      },
+      "independent_owned_entry_columns": 1,
+      "independent_persistent_columns": 632,
+      "max_denominator": 32,
+      "max_formal_prefix_l1": "457",
+      "owned_outputs_zero": true,
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40,
+        "8": 8
+      },
+      "real_scalar_allowance": 158120,
+      "zero_identities": 0
+    }
+  },
+  "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION",
+  "word_payload_sha256": "645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35"
+}
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/SOURCES.json b/research/owned-relation-independent-validation/engines/physical/pinned/SOURCES.json
new file mode 100644
index 0000000000..9854abbb4f
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/SOURCES.json
@@ -0,0 +1,90 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c472563474e60185e6ca101a17622133d047e56",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
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diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/controller-CONTROLLER.json b/research/owned-relation-independent-validation/engines/physical/pinned/controller-CONTROLLER.json
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+      "QUERY_SHEAR",
+      28,
+      13,
+      false
+    ],
+    [
+      "ADD",
+      26,
+      28,
+      -1
+    ],
+    [
+      "ADD",
+      29,
+      27,
+      1
+    ],
+    [
+      "LOCAL",
+      29,
+      14,
+      true
+    ],
+    [
+      "ADD",
+      28,
+      30,
+      1
+    ],
+    [
+      "ADD",
+      31,
+      29,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      30,
+      14,
+      false
+    ],
+    [
+      "ADD",
+      28,
+      30,
+      -1
+    ],
+    [
+      "ADD",
+      31,
+      29,
+      1
+    ],
+    [
+      "LOCAL",
+      31,
+      15,
+      true
+    ],
+    [
+      "LOCAL",
+      32,
+      15,
+      false
+    ],
+    [
+      "IDLE",
+      7,
+      [
+        17,
+        19,
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      8,
+      [
+        19,
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      9,
+      [
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      10,
+      [
+        23,
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      11,
+      [
+        25,
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      12,
+      [
+        27,
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      13,
+      [
+        29,
+        31,
+        32
+      ]
+    ],
+    [
+      "IDLE",
+      14,
+      [
+        31,
+        32
+      ]
+    ],
+    [
+      "ADD",
+      30,
+      28,
+      1
+    ],
+    [
+      "ADD",
+      29,
+      31,
+      -1
+    ],
+    [
+      "ADD",
+      28,
+      26,
+      1
+    ],
+    [
+      "ADD",
+      27,
+      29,
+      -1
+    ],
+    [
+      "ADD",
+      26,
+      24,
+      1
+    ],
+    [
+      "ADD",
+      25,
+      27,
+      -1
+    ],
+    [
+      "ADD",
+      24,
+      22,
+      1
+    ],
+    [
+      "ADD",
+      23,
+      25,
+      -1
+    ],
+    [
+      "ADD",
+      22,
+      20,
+      1
+    ],
+    [
+      "ADD",
+      21,
+      23,
+      -1
+    ],
+    [
+      "ADD",
+      20,
+      18,
+      1
+    ],
+    [
+      "ADD",
+      19,
+      21,
+      -1
+    ],
+    [
+      "ADD",
+      18,
+      16,
+      1
+    ],
+    [
+      "ADD",
+      17,
+      19,
+      -1
+    ],
+    [
+      "ADD",
+      16,
+      14,
+      1
+    ],
+    [
+      "ADD",
+      15,
+      17,
+      -1
+    ],
+    [
+      "ADD",
+      14,
+      12,
+      1
+    ],
+    [
+      "ADD",
+      13,
+      15,
+      -1
+    ],
+    [
+      "ADD",
+      12,
+      10,
+      1
+    ],
+    [
+      "ADD",
+      11,
+      13,
+      -1
+    ],
+    [
+      "ADD",
+      10,
+      8,
+      1
+    ],
+    [
+      "ADD",
+      9,
+      11,
+      -1
+    ],
+    [
+      "ADD",
+      8,
+      6,
+      1
+    ],
+    [
+      "ADD",
+      7,
+      9,
+      -1
+    ],
+    [
+      "ADD",
+      6,
+      4,
+      1
+    ],
+    [
+      "ADD",
+      5,
+      7,
+      -1
+    ],
+    [
+      "ADD",
+      4,
+      2,
+      1
+    ],
+    [
+      "ADD",
+      3,
+      5,
+      -1
+    ],
+    [
+      "ADD",
+      2,
+      0,
+      1
+    ],
+    [
+      "ADD",
+      1,
+      3,
+      -1
+    ],
+    [
+      "SIGNED_SWAP",
+      0,
+      1
+    ],
+    [
+      "SIGNED_SWAP",
+      2,
+      3
+    ],
+    [
+      "SIGNED_SWAP",
+      4,
+      5
+    ],
+    [
+      "SIGNED_SWAP",
+      6,
+      7
+    ],
+    [
+      "SIGNED_SWAP",
+      8,
+      9
+    ],
+    [
+      "SIGNED_SWAP",
+      10,
+      11
+    ],
+    [
+      "SIGNED_SWAP",
+      12,
+      13
+    ],
+    [
+      "SIGNED_SWAP",
+      14,
+      15
+    ],
+    [
+      "SIGNED_SWAP",
+      16,
+      17
+    ],
+    [
+      "SIGNED_SWAP",
+      18,
+      19
+    ],
+    [
+      "SIGNED_SWAP",
+      20,
+      21
+    ],
+    [
+      "SIGNED_SWAP",
+      22,
+      23
+    ],
+    [
+      "SIGNED_SWAP",
+      24,
+      25
+    ],
+    [
+      "SIGNED_SWAP",
+      26,
+      27
+    ],
+    [
+      "SIGNED_SWAP",
+      28,
+      29
+    ],
+    [
+      "SIGNED_SWAP",
+      30,
+      31
+    ]
+  ],
+  "prefix_pairs": 7
+}
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/controller-PROOF.md b/research/owned-relation-independent-validation/engines/physical/pinned/controller-PROOF.md
new file mode 100644
index 0000000000..e41106031d
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/controller-PROOF.md
@@ -0,0 +1,102 @@
+# Construction and proof obligations
+
+## 1. Exact predecessor and changed object
+
+The input is PR4447 at commit `322e0ec764aa7ef7801383feb1f656e460dd8bed`, with its credited THREE-base native word, PR4441 helper-boundary retiming, and the added three-dimensional frame at B/480. `SOURCES.json` binds all external proof inputs by Git blob and SHA-256.
+
+There are 632 persistent local fields: 224 main fields and 408 helpers. Each helper is an arbitrary independent input, not initialized scratch. The separate owned center is initialized and erased under the inherited native contract. None of its eight uses receives productive-input credit.
+
+The patch retains the scalar order and coefficients in each orientation. It retains all native warp events and every main-field boundary. It changes 38 helper entrance frames, 47 helper terminal frames, and 414 scalar contact frames. A source pin accompanies every changed boundary or contact. The two orientations retain their exact inverse-transpose scalar correspondence.
+
+The optional search jointly optimized both helper boundaries and every mutable scalar contact over the finite intervals of subspaces of F2^9. Fixed main and warp events bound those intervals. The largest quotient dimension was five, so its interval has 374 subspaces. The discovery model used one-hot frame choices and edge marginals, with negative whole-helper credit. Its floating-point solution is a proposal, not a certificate. The following construction and exact tests do not use its claimed optimum.
+
+## 2. Frame-coordinate invariant
+
+Let C_F be the source's exact canonical frame operator for subspace F. Interpret a field at frame F as C_F applied to its logical arbitrary value. For nested frames E contained in F, the paid transport is C_F C_E^{-1}. Its Fourier rank is dim(F)-dim(E). The implementation follows the source's `adjoint().then(...)` composition convention and lowers the operator itself, not only that rank formula.
+
+At each scalar operation, all participating persistent fields are first moved into its declared common frame. A scalar linear combination commutes with the common frame operator. Therefore the operation implements the unchanged logical scalar step. A native warp is run only at its original pinned input frame, and leaves the original pinned output frame. This proves the invariant by induction through the complete chronological word.
+
+At the end of the word, main fields have their unchanged original endpoints. Helper r has the whole residual C_{T_r} C_{S_r}^{-1}, where S_r and T_r are its new entrance and exit. Every checked S_r is a proper subspace of T_r. Its positive productive rank is dim(T_r)-dim(S_r). There is no duplicate field, discarded helper, clean-input assumption, or free temporary productive input.
+
+The helper normalizers are recomputed on these whole-job boundaries. Every new transport and each distinct helper boundary is lowered in both orientations with exact Clifford tableaux and absolute phases. The receipt contains 423 distinct transport/boundary pairs, including 406 newly occurring transport pairs relative to PR4447. Two retained literal interpreters check the complete 632-column endpoint. The argument is the frame-coordinate invariant; the finite replay independently checks its application to the submitted circuit.
+
+## 3. Complete local bill and uniform moment gain
+
+Write H_r for productive helpers of rank r and P_r for paid jobs of rank r. The predecessor has
+
+    H_old = {4:26, 5:2, 7:29, 8:42, 9:309}
+    P_old = {1:2254, 2:514, 3:444, 4:103, 5:40, 8:8}.
+
+The new word has
+
+    H_new = {4:28, 7:7, 8:47, 9:326}
+    P_new = {1:2237, 2:388, 3:494, 4:147, 5:36, 8:8}.
+
+There are 408 helpers in both words. The new paid list has 3,310 entries, 53 fewer than the predecessor. Helper rank mass increases from 3,434 to 3,471, and paid rank mass from 5,290 to 5,327. Their difference remains 1,856. In particular, the improvement is not obtained by keeping old productive credit after removing paid work.
+
+For 0<t<1, define the local surplus as sum H_r r^t minus sum P_r r^t. The new-minus-old surplus is exactly
+
+    D(t) = 17 + 126*2^t - 50*3^t - 42*4^t + 2*5^t
+           - 22*7^t + 5*8^t + 17*9^t.
+
+The verifier first checks D(1)=0. It then encloses D'(t) on 128 rational subintervals covering [0,1]. On [l,r], positive terms use the upper bound for rank^r log(rank), and negative terms use the lower bound for rank^l log(rank). Every resulting upper bound is strictly negative. Thus D is strictly decreasing on [0,1], and D(t)>D(1)=0 for every 0<t<1. This proves a uniform local improvement, not just a favorable rounded score at the chosen saving.
+
+The whole rank-eight center jobs are included in both profiles. Scalar work, helper normalizers, fixed monomial routes and owned allocation/erasure are included under the explicit finite nonrecursive allowances in RESULT.json. These allowances do not claim those operations are free.
+
+## 4. The new p16 controller
+
+Use the PR4440 constructor with p=16 and prefix length a=7, hence suffix length 8. Keep the thick stages {0,32,1,3,...,31}. There are 18 full native calls and 15 query-only shears. Each full call receives a fresh, disjoint set of 408 helper fields. Each query-only shear costs one rank-one job per port and contributes no helper or scratch productive credit.
+
+CONTROLLER.json contains the complete emitted native/query/idle word and its rational scalar boundary programs. A separate literal Laurent replay checks every coefficient. The left and right boundary matrices transform it to the declared diagonal, with central exponents exactly +1 or -1. Changed query orientation and replacing a paid thin query by an unpaid full stage both change the operator and are rejected.
+
+There are 112 port copies. Main productive ranks are 145 with multiplicity 224; ranks 17,25,33,41,49,57,65 each with multiplicity 448; and rank 73 with multiplicity 224. The matching whole-idle paid ranks are 16,24,32,40,48,56,64 with multiplicity 448, and rank 72 with multiplicity 224.
+
+Add 18 copies of H_new to the targets, 18 copies of P_new to the paid list, and 112*15 additional rank-one paid queries. This gives the complete profiles recorded in RESULT.json. They have 10,928 independent productive fields, 64,620 paid jobs, target rank mass 239,886, and paid rank mass 239,134. Their surplus is 752 = 48*18-112. Literal event counting and independent whole-call substitution give exactly the same invoice.
+
+The source contact and phase proof is local to one old nine-axis block and one fresh eight-axis block. It therefore applies at every thick p16 stage after embedding, with all other axes as spectators. The new helper boundaries do not change those main contacts. Their actual residual operators are supplied by Section 2. The BIT controller and its native rational charts remain unchanged.
+
+## 5. Exact root, paid completion and splitting
+
+Let T_t and P_t be the complete target and paid moments. The new root is enclosed strictly between 0.0030201659770 and 0.0030201659771, using t=1-C. An exact interval argument verifies that the surplus is decreasing for 0<=C<=1/20 and negative on the remainder 1/20<=C<=1. This is a fixed-invoice ceiling, not a global bound for other words.
+
+Take TESTED = 0.003020155, tensor power v=1024, tail offset u=1/5, paid cutoff 20^v and productive floor 21^v. Define
+
+    alpha = P_t/T_t,
+    gamma = P_(t+u)/(20^u T_t),
+    delta = 21 * (# productive fields)/(20^TESTED T_t).
+
+Two independent rational interval implementations verify the positive raw margin. The first also certifies
+
+    alpha < 1 - 10^-9,   gamma < 97/100,   delta < 97/100.
+
+The p16 completion tail is larger than the predecessor's 19/20 limit; this package explicitly replaces that limit with 97/100. No old tail allowance is silently reused. The same exact block inequality (97/100)^128 < 1/16 handles both tails. The inherited paid-completion and higher-moment splitting theorem consequently bounds the normalized final paid moment by
+
+    1/(1 + 1024*10^-9) + 4/2^32 < 1.
+
+Every short productive job is completed on additional disjoint axes of its same arbitrary field. Every original or added large paid job is split with its full rounding surcharge. The strict inequality 20^64 < 21^63 gives paid/target separation. These are paid operations; no padded target appears without its completion charge.
+
+## 6. Effective finite compiler and outer transfer
+
+The raw ambient rank is 145, so the tensor ambient rank is 145^1024. Use theta=63/64 and logarithm power 1000 in the credited logarithmic compiler majorant. The verifier checks
+
+    2*(20^1024)^64 <= (145^1024)^63,
+    (1-TESTED)*145^(-1024*TESTED) > theta^1000,
+    145^(1024*TESTED) < 2^1000.
+
+Set kappa=0.00302015 and d=(TESTED-kappa)/7=1/1,400,000,000. The integer test
+
+    (1,400,000,000*j + 1)^1000 < 2^j
+
+passes at j=45,868 and fails at j-1. Thus the retained theorem supplies the sufficient uniform rank N=2^64,215,200,000,000. This is an existence construction with explicit finite constants. The resulting word is not materialized and no practical implementation claim follows.
+
+The new local scalar and fixed-route bound remains below 10^7 per full call. Eighteen such calls, all 15 thin-query charges, every scalar controller and boundary operation fit the complete raw bound 10^9. The number of roles, private storage, coefficient matrices and tapes is finite for the compiled template. Their sizes affect the eventual threshold and are not claimed uniform while changing that template.
+
+Retain the source BIT ordinary saving 0.0034, with atom exponent 0.004. Its delayed-cover, weighted-child, row-stock and conversion conditions are rechecked through the source package. Use complex uniform saving kappa+6d, followed by b=kappa+5d, a=kappa+4d, q=kappa+3d, epsilon=1-d, beta=1-3d, r0=d/10, stop=d and layout=d. All nine outer cost rows, 54 strict predicates and four functional guards pass exactly. The old BIT cap and closed exponent gaps are explicit rejected controls.
+
+## 7. Status of the conclusion
+
+Subject to the retained all-column/native and physical-operation contracts, owned erasure, whole-job matching, finite-template compiler closure, precision and fixed-tape bounds, analytic decomposition, prime avoidance and exact recovery, this construction gives the source framework's conditional multiplication saving kappa=0.00302015.
+
+The submitted change establishes an exact finite native word and a fully charged conditional parameter transfer. It does not remove the inherited analytic or physical premises. It does not promote the selected frontier, certify global optimality, claim a runtime speedup, or claim independent human or proof-assistant acceptance.
+
+Credits: zxv's native and higher-moment/logarithmic work; Jacob Alan Sussman's finite mixed-flow theorem; Cinna Davis's prior p7 padding, query-thinned and retimed constructions; and the unchanged credited scalar, Clifford, geometry and outer-ledger sources. New material was prepared for Cinna Davis with substantial OpenAI assistance, Apache-2.0.
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/controller-README.md b/research/owned-relation-independent-validation/engines/physical/pinned/controller-README.md
new file mode 100644
index 0000000000..8c9bd69cd4
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/controller-README.md
@@ -0,0 +1,46 @@
+# Joint helper boundaries: conditional kappa = 0.00302015
+
+This is an author-checked conditional construction, not an unconditional integer-multiplication theorem or a selected-frontier update.
+
+The new contribution is a joint finite optimization of helper entrances, exits and scalar contact frames. It builds on the exact native supplier of zxv, the retiming in PR4441, the missing span in PR4447, and the query-thinned controller in PR4440. The arithmetic scaffolding and logarithmic compiler test are adapted from PR4447 and the credited PR4433 lineage.
+
+The proposed saving is `0.00302015`, compared with `0.00300123` in PR4447: an absolute increase of `0.00001892`, or approximately **0.630408%**. This is a moderate incremental improvement. It is not a claim of a large asymptotic breakthrough.
+
+## What changed
+
+Relative to PR4447, `PATCH.json` changes 38 helper entrances, 47 helper exits and 414 scalar contact frames. Both scalar orders, every scalar coefficient, main endpoints, native warps, and the owned-center operations remain unchanged. All 408 helpers remain independent, strictly productive arbitrary inputs.
+
+The local helper profile becomes `{4:28, 7:7, 8:47, 9:326}`. The complete paid profile becomes `{1:2237, 2:388, 3:494, 4:147, 5:36, 8:8}`. This reduces local paid calls from 3,363 to 3,310. Both rank masses increase by 37, leaving the local rank-mass deficit unchanged. The eight whole rank-eight center jobs are included.
+
+The nonlinear helper credit couples the two boundaries. Separate entrance-only and exit-only updates do not represent that joint objective. The optional finite-lattice mixed-integer search found the patch; the proof does not trust that solver, its objective value, or its optimality status.
+
+The changed supplier is installed in an explicitly replayed 16-pair controller with 18 full native calls and 15 copied-query shears. Its complete invoice has 10,928 productive fields and 64,620 paid jobs. Target and paid rank masses are 239,886 and 239,134, respectively. The rank-one surplus is 752. The predecessor p17 invoice has a different number of inputs, so total call counts are not a like-for-like runtime comparison.
+
+`RESULT.json` encloses the new raw moment root in `(0.0030201659770, 0.0030201659771)`. It certifies paid tensor completion, splitting, a finite uniform compiler and every outer inequality at the smaller stated kappa. The unchanged source BIT supplier supports ordinary saving 0.0034.
+
+## Verification
+
+Run from the repository root:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/joint-helper-lattice --check-only
+python3.12 -B scripts/research_package.py --package research/joint-helper-lattice
+```
+
+The registered replay has three required gates (dependencies, native, arithmetic) and uses only the Python standard library. It authenticates the declared sources, reconstructs the changed native word, replays all 632 arbitrary-input columns in both orientations using two retained interpreters, and lowers the new transports and helper boundaries including absolute phase. It regenerates the p16 Laurent and literal controller, checks its boundary factorization, cross-checks the moments with a second rational engine, and verifies the full compiler and outer ledger. Mutation controls reject false ranks, unsupported query orientation, unpaid full stages, the old invoice at the new saving, and invalid outer parameters.
+
+`--write` is an authoring path using saved native and predecessor receipts. It is not the registered full replay. `VALIDATION.md` records the commands actually completed.
+
+`PROOF.md` states the construction, complete cost argument and inherited assumptions. `DISCOVERY.json` contains floating-point search evidence only; no solver optimality claim is part of the theorem. `PATCH.json`, `NATIVE.json.gz`, `CONTROLLER.json` and `RESULT.json` are the mathematical replay artifacts.
+
+## Scope and credit
+
+The source all-column native contract, allowed erasure of owned storage, whole-job normalizers, finite-template closure, precision and monomial tape bounds, analytic decomposition, prime avoidance, and exact recovery remain explicit premises. The enormous uniform word is algorithmically specified, not materialized. No practical speedup, global optimum, formal-kernel acceptance, or independent human review is claimed.
+
+The branch is stacked on exact PR4447 head `322e0ec764aa7ef7801383feb1f656e460dd8bed`. Its ancestors retain PR4440/PR4441 and the pending PR4447 contribution. Those inherited changes are not new work in this package. Canonical main at the final research checkpoint was `2a13eb1827784206202db90e5dc8327cf8a250db`.
+
+Credit zxv's native and compiler work, Jacob Alan Sussman's mixed-target integer flow, Cinna Davis's PR4416 padding and PR4440/PR4441/PR4447 contributions, and the retained scalar, Clifford, geometry, precision and outer-ledger authors. Source notices remain unchanged. New work prepared for Cinna Davis with substantial OpenAI assistance. Apache-2.0.
+
+## Open next questions
+
+Can a costed scalar reordering or changed warp word beat this fixed chronological graph? Start with a small commuting contact block, derive its dependency graph, then reconstruct every physical endpoint before repricing it. The finite solver's optimum report is not an exact general barrier and does not cover changed scalar orders or warps. The structured question and blocker are in `TASK.json`.
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/native.py b/research/owned-relation-independent-validation/engines/physical/pinned/native.py
new file mode 100644
index 0000000000..b8249ed7ba
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/native.py
@@ -0,0 +1,299 @@
+"""One prepared helper removes two paid jobs in the PR4610 backward word.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+The source word is by Cao Yifan. The row convention and scalar allowance
+follow the credited native work of Cinna Davis and zxv.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from hashlib import sha1, sha256
+from pathlib import Path
+import gzip
+import importlib.util
+import json
+import sys
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'
+PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz'
+PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'
+RELATION = {230: 1, 324: -1, 326: 1, 328: 1, 333: -1}
+OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}
+NEW_PAID = dict(OLD_PAID)
+NEW_PAID[1] -= 1
+NEW_PAID[8] -= 1
+OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326}
+
+
+def need(ok, why):
+    if not ok:
+        raise ValueError(why)
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def encode(x):
+    if isinstance(x, Q):
+        return str(x)
+    if isinstance(x, dict):
+        return {str(k): encode(v) for k, v in x.items()}
+    if isinstance(x, (list, tuple)):
+        return [encode(v) for v in x]
+    return x
+
+
+def load(relative, name):
+    spec = importlib.util.spec_from_file_location(name, ROOT / relative)
+    module = importlib.util.module_from_spec(spec)
+    sys.modules[name] = module
+    spec.loader.exec_module(module)
+    return module
+
+
+def authenticate():
+    pins = read(HERE / 'SOURCES.json')
+    for row in pins['files']:
+        if row['usage'] != 'input':
+            continue
+        p = ROOT
+        for part in Path(row['path']).parts:
+            p /= part
+            need(not p.is_symlink(), 'No source aliases')
+        raw = p.read_bytes()
+        need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path'])
+        need(sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob')
+    need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload')
+    return pins
+
+
+def span(basis):
+    out = {0}
+    for vector in basis:
+        need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate')
+        out |= {v ^ vector for v in tuple(out)}
+    need(len(out) == 2 ** len(basis), 'Independent frame basis')
+    return out
+
+
+def add(dst, src, q):
+    for k, v in tuple(src.items()):
+        value = dst.get(k, Q(0)) + q * v
+        if value:
+            dst[k] = value
+        else:
+            dst.pop(k, None)
+
+
+def allowance(g):
+    if g[0] in ('clear', 'copy'):
+        return 2
+    q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:])
+    n, d = abs(q.numerator), q.denominator
+    need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar')
+    if g[0] == 'scale':
+        need(n & (n - 1) == 0, 'Dyadic unit SCALE')
+        return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0))
+    need(g[0] == 'add', 'Known scalar operation')
+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)
+
+
+def construct(source):
+    c = source['canonical']
+    old = source['programs']['backward']
+    need(old[11205] == ['climb', 'warp_retimed', 92, 310, 254, 4], 'Snapshot source event')
+    need(old[11332] == ['center', 0, 0, 254, 8], 'Center source event')
+    need(old[15584] == ['climb', 'warp_retimed', 92, 254, 1, 1], 'Zero source event')
+    need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in RELATION), 'Five cold full-ended helpers')
+    word = [['scalar', ['clear', ['L', 230]], 0]]
+    word += [['scalar', ['add', ['L', 230], ['L', h], -q, 1], 0]
+             for h, q in RELATION.items() if h != 230]
+    for i, event in enumerate(old):
+        if i == 11332:
+            word += [['scalar', ['clear', ['C', 0]], 254],
+                     ['scalar', ['copy', ['C', 0], ['C', 1]], 254],
+                     ['scalar', ['clear', ['C', 1]], 254]]
+        elif i == 15584:
+            word.append(['zero_retag', ['L', 92], 254, 1])
+        else:
+            word.append(deepcopy(event))
+        if i == 11205:
+            word += [['scalar', ['clear', ['C', 1]], 254],
+                     ['scalar', ['copy', ['C', 1], ['L', 92]], 254]]
+    word.append(['scalar', ['clear', ['L', 230]], 1])
+    physical = deepcopy(c)
+    physical.pop('local_profile')
+    return {'schema': 'owned-helper-relation-word/1', 'canonical': physical,
+            'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID},
+            'owned': {'forward': [['C', 0]], 'backward': [['C', 0], ['C', 1], ['L', 230]]},
+            'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}}
+
+
+def replay(c, program, backward, specialized):
+    """Run every event on all independent entry columns and exact frames."""
+    owned = {('C', 0)} | ({('C', 1), ('L', 230)} if specialized else set())
+    roles = {('L', i) for i in range(632)} | owned
+    rows = {r: {(r, ()): Q(1)} for r in roles}
+    frames = {('L', i): f for i, f in enumerate(c['start'])}
+    frames.update({r: None for r in owned if r[0] == 'C'})
+    spaces = [span(b) for b in c['frames']]
+    paid = Counter()
+    cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0
+    for e in program:
+        kind, touched = e[0], None
+        if kind == 'scalar':
+            g, frame = e[1:]
+            dst = tuple(g[1]); touched = dst
+            need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame')
+            cost += allowance(g)
+            if g[0] == 'clear':
+                need(dst in owned, 'Only owned fields can be erased')
+                rows[dst] = {}; frames[dst] = frame
+            else:
+                need(frames[dst] == frame, 'Exact scalar destination frame')
+                if g[0] in ('add', 'copy'):
+                    src = tuple(g[2])
+                    need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame')
+                    if g[0] == 'copy':
+                        need(dst in owned and not rows[dst], 'COPY into cleared owned storage')
+                        rows[dst] = dict(rows[src])
+                    else:
+                        add(rows[dst], rows[src], Q(g[3], g[4]))
+                else:
+                    need(g[0] == 'scale', 'Known scalar operation')
+                    rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()}
+        elif kind == 'warp':
+            _, role, op, old, new = e
+            dst = tuple(role); touched = dst
+            need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input')
+            symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0))
+            rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q
+                         for (r, w), q in rows[dst].items()}
+            frames[dst] = new
+        elif kind in ('climb', 'center'):
+            if kind == 'climb':
+                _, _, i, old, new, rank = e
+                dst = ('L', i)
+                need(spaces[old] < spaces[new], 'Ascending paid climb')
+            else:
+                _, i, old, new, rank = e
+                dst = ('C', i)
+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center')
+            need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame')
+            frames[dst] = new; paid[rank] += 1
+        elif kind == 'zero_retag':
+            _, role, old, new = e
+            dst = tuple(role)
+            need(specialized and backward and dst == ('L', 92), 'Declared zero identity')
+            need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row')
+            need((old, new) == (254, 1), 'Declared zero frame change')
+            frames[dst] = new; zero_count += 1
+        else:
+            need(kind in ('phase', 'adapter'), 'Known inert source marker')
+        if touched is not None:
+            max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0)))
+            denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1))
+    need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame')
+    for i in range(632):
+        r = ('L', i)
+        if r in owned:
+            continue
+        expected = {(r, ()): Q(1)}
+        if i < 112 if backward else 112 <= i < 224:
+            expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1)
+        need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i))
+    need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return')
+    need(zero_count == int(specialized), 'Exactly one checked zero identity')
+    helpers = Counter()
+    for i in range(224, 632):
+        if ('L', i) in owned:
+            continue
+        a, b = c['start'][i], c['final'][i]
+        need(spaces[a] < spaces[b], 'Strict independent productive helper')
+        helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1
+    return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())),
+            'independent_persistent_columns': 631 if specialized else 632,
+            'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True,
+            'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1),
+            'max_denominator': denominator, 'zero_identities': zero_count}
+
+
+def independent_source_identities(source):
+    """Use the predecessor row engine on the unrestricted original word."""
+    v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'owned_relation_source_rows')
+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}
+    rows['C', 0] = v.identity(('C', 0))
+    delta = {(('L', i), ()): Q(q) for i, q in RELATION.items()}
+    saved = None
+    for index, e in enumerate(source['programs']['backward']):
+        if e[0] == 'scalar':
+            g = e[1]; dst = tuple(g[1])
+            if g[0] == 'clear': rows[dst] = {}
+            elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])])
+            elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()}
+            else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4]))
+        elif e[0] == 'warp':
+            dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True)
+        if index == 11205: saved = dict(rows['L', 92])
+        if index == 11332:
+            diff = dict(rows['C', 0]); v.add(diff, saved, -1)
+            need(diff == {k: q / 4 for k, q in delta.items()}, 'Independent exact center minus snapshot = Delta/4')
+        if index == 15584:
+            need(rows['L', 92] == {k: -q / 4 for k, q in delta.items()}, 'Independent exact zero-site row = -Delta/4')
+    need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints')
+    return {'source_event_indices_are_zero_based': True, 'snapshot_after': 11205,
+            'center_replaced': 11332, 'zero_identity_at': 15584,
+            'snapshot_terms_before_substitution': len(saved), 'copy_coefficient': '1',
+            'center_minus_snapshot': 'Delta/4', 'zero_site_row': '-Delta/4', 'relation': RELATION}
+
+
+def phase_inheritance(source, candidate):
+    receipt = read(ROOT / PHASE)
+    need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and
+         receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt')
+    physical = deepcopy(source['canonical']); physical.pop('local_profile')
+    need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged')
+    for direction, program in candidate['programs'].items():
+        old = source['programs'][direction]
+        for kind in ('warp', 'adapter', 'phase'):
+            need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence')
+        old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center'))
+        new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center'))
+        expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for i in (11332, 15584))
+        need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the two proved jobs are removed')
+    return {'new_gaussian_operators': 0, 'new_native_maps': 0,
+            'all_retained_paid_events_and_warps_from_source': True,
+            'absolute_phase_receipt_reused': PHASE,
+            'source_amplitudes_and_phase_lowering_freshly_replayed': False,
+            'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'}
+
+
+def controls(c, candidate):
+    controls = {}
+    base = candidate['programs']['backward']
+    variants = {}
+    bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad
+    variants['missing_owned_input_clear'] = deepcopy(base[1:])
+    bad = deepcopy(base)
+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63]
+    variants['wrong_snapshot_source'] = bad
+    bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0
+    variants['wrong_zero_input_frame'] = bad
+    bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1
+    variants['under_or_overstated_paid_rank'] = bad
+    bad = deepcopy(base)
+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0
+    variants['wrong_copy_gauge'] = bad
+    variants['uncleared_owned_output'] = deepcopy(base[:-1])
+    for name, program in variants.items():
+        try:
+            replay(c, program, True, True)
+        except ValueError as err:
+            controls[name] = str(err)
+        else:
+            raise ValueError('Control accepted: ' + name)
+    return controls
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/price.py b/research/owned-relation-independent-validation/engines/physical/pinned/price.py
new file mode 100644
index 0000000000..6077adf74c
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/price.py
@@ -0,0 +1,196 @@
+"""Complete p16 bill and finite compiler for one owned helper relation.
+
+The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna
+Davis's PR4470 controller, zxv's completion and logarithmic majorant, and
+Jacob Alan Sussman's mixed-target recursion. Apache-2.0.
+Ali Romman, with substantial OpenAI Codex assistance.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from native import ROOT, read, load, need, encode, OLD_PAID, OLD_HELPERS
+
+KAPPA = Q('.00302235')
+TESTED = Q('.00302236')
+PREVIOUS = Q('.0030217758')
+OLD_ROOT_UPPER = Q('.00302177587078')
+
+
+def controller():
+    """Check the literal p16 word and both rational boundary programs."""
+    word = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json')
+    need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller')
+    zero = (0,) * 34
+    def plus(dst, src, q):
+        for k, v in src.items():
+            value = dst.get(k, Q(0)) + q * v
+            if value: dst[k] = value
+            else: dst.pop(k, None)
+    def shifted(row, term, sign=1):
+        return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row]
+    for side in ('left', 'right'):
+        matrix = [[Q(i == j) for j in range(32)] for i in range(32)]
+        for e in word['boundaries'][side + '_program']:
+            if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]]
+            elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]]
+            else:
+                need(e[0] == 'ADD', 'Boundary scalar opcode')
+                matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])]
+        need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program')
+    rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']]
+    for e in word['physical_events']:
+        if e[0] in ('LOCAL', 'QUERY_SHEAR'):
+            _, stage, pair, back = e
+            x, y = 2 * pair, 2 * pair + 1
+            if back: x, y = y, x
+            term = (1 if back else -1,) + (0,) * 33
+            for dst, src in zip(rows[y], shifted(rows[x], term)):
+                plus(dst, src, Q(-1 if back else 1))
+            if e[0] == 'LOCAL':
+                term = (0,) + tuple(int(s == stage) for s in range(33))
+                for r in (x, y): rows[r] = shifted(rows[r], term)
+        elif e[0] == 'IDLE':
+            term = (0,) + tuple(int(s in e[2]) for s in range(33))
+            for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term)
+        elif e[0] == 'ADD':
+            for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3]))
+        else:
+            need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode')
+            rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1)
+    out = [[{} for _ in range(32)] for _ in range(32)]
+    for i, row in enumerate(word['boundaries']['left']):
+        for k, q in enumerate(row):
+            if Q(q):
+                for j in range(32): plus(out[i][j], rows[k][j], Q(q))
+    expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)]
+    need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors')
+    return word
+
+
+def assemble(native, word):
+    T, P = Counter(), Counter()
+    orientations = Counter(); thin = 0
+    for e in word['physical_events']:
+        if e[0] == 'LOCAL':
+            direction = 'backward' if e[3] else 'forward'
+            orientations[direction] += 1
+            T.update(native[direction]['helpers']); P.update(native[direction]['paid'])
+        elif e[0] == 'QUERY_SHEAR': thin += 1; P[1] += 112
+        elif e[0] == 'IDLE': P[8 * len(e[2])] += 224
+    main = Counter()
+    for term in word['diagonal']:
+        need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole Gaussian main target')
+        main[1 + 8 * sum(term[1:])] += 112
+    T.update(main)
+    need(orientations == {'backward': 16, 'forward': 2} and thin == 15, 'Every actual call orientation')
+    # This second census uses the source invoice and the two local deltas.
+    check_T = Counter({int(r): n for r, n in word['invoice']['main'].items()})
+    check_T.update({r: 18 * n for r, n in OLD_HELPERS.items()}); check_T[9] -= 16
+    check_P = Counter({int(r): n for r, n in word['invoice']['whole_idle'].items()})
+    check_P.update({r: 18 * n for r, n in OLD_PAID.items()}); check_P[1] += 1680 - 16; check_P[8] -= 16
+    need(T == check_T and P == check_P, 'Independent full invoice substitution')
+    need(sum(T.values()) == 10912 and sum(P.values()) == 64372, 'Complete productive and paid counts')
+    need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Unchanged complete rank surplus')
+    return T, P
+
+
+def run(native):
+    word = controller(); T, P = assemble(native, word)
+    prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json')
+    need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing')
+    prior_T = Counter({int(r): n for r, n in prior['targets'].items()})
+    prior_P = Counter({int(r): n for r, n in prior['paid'].items()})
+    prior_T[9] -= 16; prior_P[1] -= 16; prior_P[8] -= 16
+    need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill')
+    E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals')
+    other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals')
+    def margin(c):
+        t, p = E.moment(T, 1 - c), E.moment(P, 1 - c)
+        return t[0] - p[1], t[1] - p[0]
+    need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint')
+    lo, hi, grid = 0, 10**12, 10**14
+    while hi - lo > 1:
+        mid = (lo + hi) // 2
+        if margin(Q(mid, grid))[0] > 0: lo = mid
+        else: hi = mid
+    root_low, root_high = Q(lo, grid), Q(hi, grid)
+    need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure')
+    need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom')
+    # The complete signed profile decreases on [0, .05], and stays negative
+    # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling.
+    signed = {r: T[r] - P[r] for r in T.keys() | P.keys()}
+    derivative, upper = None, None
+    for i in range(16):
+        l, r = Q(i, 320), Q(i + 1, 320); low = Q(0)
+        for rank, n in signed.items():
+            term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank))
+            low += n * term[0 if n > 0 else 1]
+        derivative = low if derivative is None else min(derivative, low)
+    for i in range(128):
+        l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560)
+        value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items())
+        upper = value if upper is None else max(upper, value)
+    need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1')
+    t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21
+    target, paid = E.moment(T, t), E.moment(P, t)
+    tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED)
+    need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree')
+    alpha = E.divide(paid, target)
+    gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target))
+    delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target))
+    reserve = Q(1, 10**9); g = d = Q(97, 100)
+    need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged')
+    need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks')
+    normalized = 1 / (1 + v * reserve) + Q(4, 2**32)
+    need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding')
+    theta, power = Q(63, 64), 1000
+    eta = E.scale(E.power(145, -v * TESTED), t)
+    need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')
+    need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range')
+    gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid')
+    step = gap.denominator
+    def wins(j): return (step * j + 1)**power < 2**j
+    left, right = 1, 2
+    while not wins(right): left, right = right, 2 * right
+    while right - left > 1:
+        mid = (left + right) // 2
+        if wins(mid): right = mid
+        else: left = mid
+    height = step * right
+    need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold')
+    local_scalar = max(x['real_scalar_allowance'] for x in native.values())
+    # The old route allowance is retained. Charge two additional owned field
+    # lifetimes at two routes each, even though L230 uses an existing slot.
+    routes = (max(sum(x['paid'].values()) for x in native.values()) + 2 * 408 + 688 + 4) * 1000
+    need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit')
+    scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right')))
+    need(scalar_upper < 10**9, 'Complete raw nonrecursive bound')
+    bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']
+    atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted'])
+    need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock')
+    L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer')
+    params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap,
+              'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted,
+              'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap}
+    outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom)
+    need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')
+    need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict')
+    controls = {}
+    for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]:
+        bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0]
+        need(failed, 'Reject outer patch ' + name); controls[name] = failed
+    bad_native = {d: dict(x) for d, x in native.items()}
+    bad_native['backward']['helpers'] = OLD_HELPERS
+    try: assemble(bad_native, word)
+    except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census'
+    else: raise ValueError('Unowned helper credit was accepted')
+    return encode({'kappa': KAPPA, 'kappa_decimal': '.00302235', 'gain_over_PR4610': KAPPA - PREVIOUS,
+                   'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA],
+                   'margin_at_previous_kappa': E.display(margin(PREVIOUS)),
+                   'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)),
+                   'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)},
+                   'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752,
+                   'full_backward': 16, 'full_forward': 2, 'query_shears': 15,
+                   'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized},
+                   'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False},
+                   'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': 1, 'owned_slots_backward': 3},
+                   'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls})
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/selected-current.json b/research/owned-relation-independent-validation/engines/physical/pinned/selected-current.json
new file mode 100644
index 0000000000..b288ae4403
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/selected-current.json
@@ -0,0 +1,92 @@
+{
+  "status": "Selected maintainer-reviewed conditional PR4610 construction, with independent PR5241 admission evidence and explicit inherited foundation reuse",
+  "kappa": "15108879/5000000000",
+  "decimal": "0.0030217758",
+  "source_prs": [
+    4610,
+    5241,
+    4470,
+    4447,
+    4441,
+    4440,
+    4416,
+    4433,
+    4359,
+    4268,
+    3945,
+    4085,
+    2979,
+    4076,
+    4088,
+    1673,
+    1758,
+    1786,
+    23,
+    555,
+    589
+  ],
+  "source_manifest": "certificates/frontier4610-source.json",
+  "certificate": "certificates/frontier4610/CLAIM.json",
+  "certificate_sha256": "c48376a8365a4c7b67adb368bafa128bede4cd5589a41fa276f96a350d45606c",
+  "proof": "docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md",
+  "proof_supplements": {
+    "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c",
+    "notes/batched-complex-rows.tex": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c",
+    "notes/compact-control-movement.tex": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6",
+    "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+    "notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a",
+    "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "references/semantic-bulk/pr23/semantic-bulk-17-note.tex": "652242b05174bb776ffc6165af170df9c8cf220dbd0fc26c24d778f320dbabc8",
+    "research/e8-bit-carrier-skeleton/code/bit/export_records.py": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3",
+    "research/e8-bit-carrier-skeleton/code/nine/geometry.py": "36eeda3184bd009e89462b65c8725d10860c444f8da8f1f87e5f6e50120011ca",
+    "research/e8-bit-p111-tuned/code/gen_p3.py": "438b83f10d70ceca7cf78049420204b7de2dc61682f913c50a62596106ad84cd",
+    "research/e8-bit-p111-tuned/code/xcheck_p.py": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e",
+    "research/e8-bit-p111-tuned/tune/EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "research/e8-bit-p111-tuned/tune/apply.py": "806ae4cb2648e4f05dcf56bd089891fd3ba33a6ee5fe76d3329e322c6770c1a1",
+    "research/e8-bit-p111-tuned/tune/wlib.py": "a37fdf3cdf5f62945c2a90193401c0e9edc9dd3cda8d8cb36a3b9c329ebe4dbc",
+    "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "docs/research/pr-intake-evidence/pr4359/PROOF-REVIEW.md": "7d67bb814285f7634029fbd378c6457156545f0b38858cc1c6ec34b68cd9d162",
+    "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md": "5c111dd56beb53dc44ab727d96e1af03aaf50f3023d4342e2b0a89ede6cf585b",
+    "docs/research/pr-intake-evidence/pr4416/PROOF-REVIEW.md": "2c2bbe6fe1bab44778192118f27e59a0d23dbe02c47aa8a42845093f1ce46f49",
+    "docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md": "b84f833e3072cbab372fbda2ece98fbc031c15e590cf73003ddea35a5222e148",
+    "research/final4610-independent-admission/PROOF.md": "e573cbbe6fa5481c0533e773de404e10f4dc7907b5ebfe404bdcd02dcf9844d8",
+    "research/final4610-independent-admission/SPECIALIZATION.md": "70430114f744108223bc1d44b98bc25b696c4b408b7b044c2a8bbdfdb434ac5c"
+  },
+  "review": "docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md",
+  "validation": "docs/research/pr-intake-evidence/pr4610/VALIDATION.json",
+  "integration": "docs/research/pr-intake-evidence/pr4610/INTEGRATION.json",
+  "reproduce": "make frontier4610-verify",
+  "scope": "Maintainer-reviewed conditional PR4610 construction using the PR5241 independent audit. The five PR4470 framework assumptions are unchanged. Uniform words are not materialized.",
+  "previous_kappa": "60403/20000000",
+  "previous_record": "certificates/checkpoints/frontier4470.json",
+  "audited_source_head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296",
+  "source_certificate": "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json",
+  "source_certificate_sha256": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de",
+  "replay_mode": "Fresh complete independent admission replay; source-bound preceding controller, ordinary BIT and physical/compiler foundation reuse",
+  "contributors": "docs/research/community-native4610-contributors.md",
+  "assumptions": [
+    {
+      "id": "native_all_columns",
+      "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity."
+    },
+    {
+      "id": "owned_erasure",
+      "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts."
+    },
+    {
+      "id": "compiler",
+      "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract."
+    },
+    {
+      "id": "precision_tape",
+      "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template."
+    },
+    {
+      "id": "analytic_recovery",
+      "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework."
+    }
+  ],
+  "audit_pr": 5241,
+  "audit_head": "13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2"
+}
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/source4610-SPECIALIZATION.md b/research/owned-relation-independent-validation/engines/physical/pinned/source4610-SPECIALIZATION.md
new file mode 100644
index 0000000000..7ee84b3089
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/source4610-SPECIALIZATION.md
@@ -0,0 +1,130 @@
+# P1: specialize the selected physical grammar to final #4610
+
+This note proves a conditional **specialization**, not a new physical primitive theorem. Let H_selected denote precisely the native normal-form, compact movement/repair, scalar/owned-storage, completed-call, fixed-tape and outer hypotheses retained by selected #4470 through its reviewed #4359/#4416 lineage. Under H_selected, the actual final #4610 catalogue is an instance of that same physical grammar, with newly counted fixed constants. The proof does not introduce a separate assumption that the new recipes work.
+
+Candidate #4610 is Cao Yifan/intqwq's existing construction, head `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`, final local-word payload `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. Pinned canonical source is `ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c`. Selected #4470 remains .00302015; this note does not modify selection or claim construction/gain priority. Exact source bytes, including the following premise texts, are bound in `SOURCES.json`.
+
+## 1. The selected premise already quantifies over the required class
+
+The premises used here are the following statements in the selected source closure, with their original physical qualifications retained:
+
+1. `notes/general-clifford-frames.tex`, “Exact representatives and nested children”: for an arbitrary binary subspace U and deterministic invertible basis extension G, the exact Gaussian-dyadic K_G and its conjugate by F have rank zero and are fixed binary address permutations with unit quadratic phases. For **every** nested U subset V, the exact transition is two rank-zero adapters around a positive coordinate C child. Exact phases and finite movement/scalars are charged. The statement is not restricted to the selected word's list of old frame labels.
+2. `notes/compact-control-movement.tex`, “Compact-control selected-bit addition” and “Application to a fixed binary change of basis”: either ordering of two complete slots admits exact selected-bit row addition with restored arbitrary temporary fields; a fixed binary basis change is a fixed number of such additions. The fixed-tape bound is `O(V*((e*log p)^tau+1))`, including repair and descriptor work, under the stated complete-field reservations and record-size hypotheses. Constants and cutoffs are uniform within each fixed parameter family.
+3. Selected #4359 `PROOF-REVIEW.md` section2: free-word evaluation allows arbitrary positive column multiplicity by substituting lifted generators, separately tensor-lifting exact paid/helper factorizations. Absolute monomial phase is `a*f+sum q(x_j)`. Helpers are normalized only after their autonomous completed endpoint. Section3 explicitly permits fixed template matrices/matchers to change dimensions/counts/constants while retaining the same movement exponent and tape uniformity. Section4 separately pays address permutations and unit phases and replaces semantic precision constants.
+4. Selected #4416 `PROOF-REVIEW.md` section2: exact whole-job normal forms use independent **two-sided** recorded factors. They need not be an inverse pair. Canonicalize the complete job, place its axes by a charged coordinate matcher, execute the child, and restore the prescribed adapters before resuming its parent. Distinct physical owners and separate live centers are preserved.
+5. Selected #4470 `PROOF-REVIEW.md` sections1–3 applies these rules to new actual helper normalizers, paid transports, p16/query/idle events and their new finite scalar/route/owner/precision constants. The retained conditions include all-column implementation, whole-job adapters, owned erasure, fixed-tape movement, precision and outer hypotheses.
+
+Consequently the permitted class is generic fixed finite Gaussian-dyadic monomial/positive-child programs with the stated arbitrary-owner and spectator ABI. It is not the stronger assertion that an arbitrary RAM gather or arbitrary address function is cheap. The reduction below uses only the selected binary row-addition/ordered-movement operations, finite unit phases and the same scalar/child/owned alphabet.
+
+## 2. A constructive grammar for every actual monomial
+
+Use the source's exact composition convention. A record m has invertible binary matrix A of size9, affine offset b, constant a modulo4, linear coefficients alpha_i modulo4 and symmetric binary quadratic matrix Q, with `alpha_i mod2=Q_ii`. On a basis address x it acts as
+
+```
+|x> -> i^(a+q(x)) |A*x xor b>,
+q(x) = sum_i alpha_i*x_i + 2*sum_(i<j,Q_ij=1) x_i*x_j  (mod4).
+```
+
+This is exactly `prune_native.monomial`: diagonal phase first, then binary permutation, translation and absolute phase. The Q diagonal is encoded in alpha, not added again as a quadratic term. No phase convention is inferred from the binary matrix alone.
+
+Gaussian row elimination reduces any such A to identity with at most72 row additions and8 row swaps. Reversing that list implements A. Replace a row swap by three XOR row additions. This gives at most96 selected-bit row-addition records. The affine offset takes at most9 selected-bit translations. The phase takes at most27 unit-S records for the nine alpha values,36 controlled-sign records for the off-diagonal pairs, and3 global i records. Thus **any** admitted nine-axis monomial, including its inverse, has a recipe of at most
+
+```
+96+9+27+36+3 = 171
+```
+
+retained elementary movement/phase records; two independent adapters need at most342. These bounds are conservative and independent of f and the eventual multiplication input. The checker constructively reconstructs A, checks symmetry/parity and phase coefficients, and verifies the decomposition on zero, basis, pair and additional addresses. The algebraic row-reduction and degree-two polynomial argument establish the universal nine-bit statement; the probes corroborate it.
+
+The physical interpretation introduces no new instruction species. A row addition is precisely the selected compact-control addition with its full dirty-control restoration and repair. XOR translations are fixed selected-bit affine operations. For a phase, compute its fixed degree-two residue modulo4 once per complete record from address/descriptors, then apply one of `{1,i,-1,-i}` to its Gaussian-dyadic value. This is a sign change and/or exchange of real and imaginary components on the retained fine grid, with zero coefficient height. For f columns, computing the residue scans at most O(f) selected address bits and therefore costs a fixed polynomial in the existing descriptor length A. The record-paid offset/phase setup is absorbed by the **same** retained superpolynomial record fiber, not charged as a new per-payload-bit scan. Complete address ranges and control reservations are the selected source hypotheses throughout.
+
+In particular, neither a new field extension nor scalar rounding nor a free arbitrary permutation is used. The full address transformation is factored into the selected row-addition primitive and inverse routes; its workspace is the source's restored complete control fields and fixed work tapes, with newly substituted template constants.
+
+## 3. Quantifiers and the all-f lift, including the absolute phase
+
+First fix the complete finite word, every matrix/phase recipe, its ordered owner list and all fixed matchers. Only after those choices let f be any positive integer column multiplicity. For x=(x_1,...,x_f), the lifted monomial is
+
+```
+x_j -> A*x_j xor b  for every j,
+phase = a*f + sum_(j=1..f) q(x_j)  (mod4).
+```
+
+Apply the finite row-addition list to the corresponding pair of complete f-axis slots, and use the pointwise residue above. Each selected slot is a full range; arbitrary intervening, preceding and following spectator fields remain present. The temporary complete compact fields are returned by each addition. Thus the lift is exactly m tensor-powered f, acting as identity on the other address fields. It uses one fixed list of primitive **types/operations**, rather than f separately allocated tapes. Its per-record descriptor arithmetic is polynomial in the same selected address bound, and the number of work tapes stays fixed for the template.
+
+For a recorded positive-rank recipe, source equality is the ordered product `right.then(C_r).then(left)`. Tensoring this product gives `right_f.then(C_(r*f)).then(left_f)` after the fixed coordinate reordering. This is one ordinary positive rank-r*f child on the actual owner's full stream, with its input and output monomials independently retained. Inverse orientation and Pauli corrections are included by the actual signed recipes. No identity distributes a tensor power over a matrix sum.
+
+For the scalar word itself, use selected #4359's free-word substitution theorem: replace each warp generator by its f-column lift while leaving ADD/SCALE coefficients and chronology unchanged. This is an algebra homomorphism from the noncommuting free-word algebra; hence the already checked arbitrary-input word identity survives. The scalar program is not itself tensor-powered. Keeping a single constant phase a instead of a*f would violate the lift; a negative control explicitly distinguishes that mutation at f=2.
+
+The ideal algebraic lift holds for every positive f. Its physical tariff applies only in the selected source domain: f<=p, A=O(p), K/log p tending to infinity, and a superpolynomial record fiber. In the actual layer f<=e<=floor(b_in^epsilon) and p=6*b_in eventually. No tariff is extrapolated to arbitrary independent f,p/geometry. The compact-control parameter hypotheses are unchanged: f slots, complete dirty reservations, `A=O(p)`, record fiber beyond fixed powers, and the same selected movement exponent. The final uniform template may have much larger fixed dimensions and operation counts. That changes constants and thresholds through section6 below, rather than changing these quantifiers or creating a new tape per coordinate.
+
+## 4. Exhaustive family/owner specialization
+
+The executable source census is over the actual final payload, not its proposed histogram. It classifies every event in both21449-record orientations, and checks exact scalar coefficients/opcodes/chronology against the selected THREE-base word. Main charts on all224 persistent main owners are exact retained records. Every scalar target/source belongs to the632 declared persistent owners or the one declared owned C0. Clear and overwrite COPY target only C0; ADD arguments are distinct owners; no new borrowed owner, alias or productive C0 is introduced.
+
+| Actual family | Membership/coverage | Selected physical interpretation |
+| --- | --- | --- |
+| 180 signed warp classes,240 occurrences | Each actual G is invertible; both signed recipes have rank0;800new monomial records cover this and the changed families below | Fixed affine binary permutation and unit quadratic phase from section2; same all-f native generator |
+| 3290 borrowed climbs per orientation | Actual source/target bases strictly nested, correct current owner/frame and rank | The selected arbitrary-U-subset-V factorization: two rank-zero adapters and one positive rank-r*f child |
+| Eight center calls per orientation | Actual nested comparable bases, owned C0 only, all eight rank8 jobs billed | Same positive child plus signed adapters; no productive credit, no allocation of a new arbitrary input |
+| 408 helper endpoints | Actual strict nested entrance/exit, profile `{4:28,7:7,8:47,9:326}` | Complete two-sided normal form on each distinct arbitrary input field; no internal scalar reframing shortcut |
+| 448 main entrance/exit charts | Exact event equality with retained base main charts | Source-identical selected chart/axis interface, with its retained charge |
+| 17453 scalar records per orientation | Exact old opcode/coefficient sequence, dyadic grammar and current-frame checks | Retained ADD, dyadic unit SCALE, owned COPY/CLEAR; identical scalar tariff |
+| Ten phase labels | Fixed annotations, no new physical instruction | Existing scalar-word scope boundaries; not extra outputs or uncharged operators |
+
+Exact factorization equality and arbitrary-input endpoints are independently established by the admission dossier's native/phase replays, not by a syntactic schema. This module supplies the missing **physical class implication** for those exact factors. The new phase receipt covers180signedwarp classes,105newpaid pairs and5changedhelper pairs. The382 unchanged helpers are bound to the selected #4470 phase receipt through gain_acceptance's exact ordered-basis/owner lineage;26changed helpers use the new five-pair receipt. The independently replayed all2855paid-pair factorization module supplies the full actual paid-pair coverage. These coverage claims remain separate from this module's fresh class/census checks.
+
+For owned return, the local word retains one physical C0 and ends its C0 updates with a permitted erase. The existing arbitrary-input native proof establishes completed main/helper endpoints and C0 clearance. During product/compiler substitution, each suspended local occurrence receives its own center bank; all child inputs are distinct actual fields, even when values are correlated or one input is a parent's center. The child finishes and its adapters/role ordering return **before** the parent resumes. The parent clears only its own bank after its last use. Every such bank is excluded from productive W and included in full O. This is exactly the selected compiler ownership rule; no one-bank-per-depth reuse or undeclared initialized input is used.
+
+## 5. Finite raw tariffs in the selected unit
+
+The tariff unit here is a retained elementary scalar/movement/phase **record**, each realized with the selected physical primitive's asymptotic bound. It is not one literal tape instruction and does not suppress the f-dependent movement bound. Choose the same common upper unit for the fixed primitive alphabet as in the selected finite-word accounting. Each new two-sided nine-axis recipe has at most342 elementary records, below the retained conservative1000-per-group allowance. Unchanged main charts retain their selected count/unit. The selected primitive implementation constants, record-paid setup, scans and repair remain paid in that common physical unit. Changing the finite catalogue does not require a new asymptotic movement assumption.
+
+The actual local route groups are
+
+```
+3298 paid jobs + 2*408 helper wrappers + 240 warps + 448 main charts
+  = 4802 groups,
+4802*1000 = 4,802,000.
+```
+
+The source scalar allowance formula, reimplemented directly without importing its evaluator, gives158120 forward and158168 backward. Therefore
+
+```
+158168 + 4802000 = 4960168 < 10^7.
+```
+
+This is an instantiation of the selected raw-unit bound with a smaller changed paid count, not reuse of an old expanded compiler cap. The controller remains18full calls and15thin queries, with the exact retained physical-event and boundary programs. The complete source raw bound is
+
+```
+18*10^7 + 15*1792
+  + 32*112*(#physical_events + #left_boundary_program + #right_boundary_program)
+  = 181098496 < 10^9.
+```
+
+Each thin query's paid rank-one request, owned copy/add/erase and inverse orientation remain in the source invoice. Idle jobs, main normalizations, inherited controller geometry and actual exact phase bills remain charged. No local or controller charge is credited as a new productive output. These numerical bounds concern **raw** supplier records only; they are not the expanded uniform word's operation count, storage or literal physical runtime.
+
+## 6. Expanded compiler, precision and tape constants
+
+Apply the selected chronological product, same-owner paid completion, disjoint splitting and integer finite compiler to this now-specialized raw program. The algorithms are finite and only instantiate the same grammar. Their matching uses complete job endpoints and restores adapters, and their owner allocation is the rule just proved applicable. No new movement species occurs when a fixed matcher has a larger fixed rank: binary basis/coordinate permutations have the same finite elimination construction, now with a larger fixed list.
+
+Let W,P,O be the actual final productive width, paid rank-one count and full owned-bank allocation; let R count the full native/movement/normalizer records, including product, completion, split and compiler routes. Let G be their fresh dyadic coefficient/phase allowance, computed by summing the actual scalar allowances (plus the source's conservative non-scalar charge). These are finite computable integers of the new expanded template. They are fixed before multiplication input size varies. A record-count overestimate and one owned bank per relevant occurrence suffice; no practical materialization or old p3 numerical count is needed.
+
+Use the **new** values in the selected semantic prescription:
+
+```
+Z=W+O,
+E=64*(Z+N+P+G+1)^3,
+B=P+E,
+C0=32*N*B^2.
+```
+
+The selected completed-child argument gives `A(e)<=A(floor(e/N))+P*floor(e/N)+E`, hence `A(e)<=2B*e`. Monomial permutations/unit phases add no coefficient height but do retain their execution/descriptor costs. The new C0 determines a new eventual fine-grid threshold. The compact row reserve, full simultaneous stock products, depth-first parking, fixed tape inventory and polynomial setup degrees also use the new W,P,O,R,N and selected formulas. Fixed enlarged degrees/counts are absorbed by the same retained superpolynomial record fiber and strict outer epsilon<1 after increasing the threshold. In particular, neither raw10^9 nor selected p3/p16 reserve constants stand in for these expanded values.
+
+Thus P2–P4 can consume a genuine new finite instance of H_selected's grammar and precision/stock/tape prescriptions. This note does not independently prove the historical native movement/repair or outer analytic/recovery stack. Those are exactly the assumptions already retained by selected #4470, with no additional candidate-specific implementation assumption.
+
+## 7. Conclusion and exact limits
+
+Given H_selected and the source-bound exact semantic/phase endpoints supplied by the independent native dossier, the final catalogue has permitted explicit all-f realizations, legal actual-owner return, finite raw tariffs and the selected expanded-constant substitution. No extra primitive or changed movement exponent is required. P1 is therefore a **consequence** of H_selected for this instance. It need not be restated as a new hypothesis “the new recipes implement.”
+
+`checks/specialization.py` runs through the master verifier and its source-authenticated `--repo` working-byte loader; it never substitutes clean Git blobs for dirty inputs. Its new actual catalogue has800monomials with at most83 elementary records each, compared with the uniform171 bound. It also checks1692selected monomial records by the identical schema, exhaustive event/role/rank/scalar census in both orientations, helper geometry, retained main charts, the4802route grouping and raw bounds. Controls reject singular maps, non-Z4 absolute phases, borrowed clear, unpaid rank changes, non-dyadic scalars and an unlifted f=2 global phase. Exact phase/operator equality is intentionally supplied by the separate phase/native verification rather than inferred from membership.
+
+Credits remain with Cao Yifan/intqwq (#4610), Cinna Davis (#4470/#4416/controller/helper lineage), zxv (#4359/native/compiler/semantic precision), icekylinx and Dugongue (general Clifford/transported frames), Jacob Alan Sussman (mixed integer compiler), and all retained physical/BIT/geometry/analytic contributors. This new specialization/proof/check uses substantial OpenAI assistance. It is a scoped conditional AI verification contribution, not an unconditional multiplication theorem or independent human/kernel acceptance.
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/verify.py b/research/owned-relation-independent-validation/engines/physical/pinned/verify.py
new file mode 100644
index 0000000000..b19f7d0ca4
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/verify.py
@@ -0,0 +1,64 @@
+#!/usr/bin/env python3
+"""Replay the one-relation native word and its complete conditional kappa.
+
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+Read README.md for the source credit and inherited proof obligations.
+"""
+from hashlib import sha256
+import argparse
+import gzip
+import json
+from pathlib import Path
+import sys
+sys.dont_write_bytecode = True
+import native as N
+import price
+
+
+def run():
+    N.authenticate()
+    source = N.read(N.ROOT / N.SOURCE)
+    candidate = N.construct(source)
+    c = candidate['canonical']
+    before, after = {}, {}
+    for direction in ('forward', 'backward'):
+        back = direction == 'backward'
+        before[direction] = N.replay(c, source['programs'][direction], back, False)
+        after[direction] = N.replay(c, candidate['programs'][direction], back, back)
+        N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Pinned source census')
+        N.need(after[direction]['paid'] == candidate['paid_profiles'][direction], 'Emitted direction-specific paid profile')
+        helpers = dict(N.OLD_HELPERS)
+        if back: helpers[9] -= 1
+        N.need(after[direction]['paid'] == (N.NEW_PAID if back else N.OLD_PAID) and after[direction]['helpers'] == helpers, 'Actual complete changed native census')
+    identities = N.independent_source_identities(source)
+    phase = N.phase_inheritance(source, candidate)
+    controls = N.controls(c, candidate)
+    arithmetic = price.run(after)
+    data = (json.dumps(candidate, sort_keys=True, separators=(',', ':')) + '\n').encode()
+    result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION',
+                       'source_payload_sha256': N.PAYLOAD, 'word_payload_sha256': sha256(data).hexdigest(),
+                       'source_native': before, 'candidate_native': after, 'independent_source_identities': identities,
+                       'phase_inheritance': phase, 'native_negative_controls': controls, 'arithmetic': arithmetic,
+                       'scope': 'Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.'})
+    return data, result
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--write', action='store_true', help='Write only this package word and result after all checks pass.')
+    ap.add_argument('--out', type=Path, help='Write a replay result to a separate path.')
+    args = ap.parse_args()
+    data, result = run()
+    if args.write:
+        (N.HERE / 'WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))
+        (N.HERE / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n', encoding='utf-8')
+    else:
+        N.need(gzip.decompress((N.HERE / 'WORD.json.gz').read_bytes()) == data, 'Exact literal published word')
+        N.need(N.read(N.HERE / 'RESULT.json') == result, 'Exact published replay result')
+    if args.out:
+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n', encoding='utf-8')
+    print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR4610', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/owned-relation-independent-validation/engines/physical/pinned/verify_buffers.py b/research/owned-relation-independent-validation/engines/physical/pinned/verify_buffers.py
new file mode 100644
index 0000000000..5a55034ec9
--- /dev/null
+++ b/research/owned-relation-independent-validation/engines/physical/pinned/verify_buffers.py
@@ -0,0 +1,351 @@
+#!/usr/bin/env python3
+"""Independent literal native replay with arbitrary dirty cleanup buffers.
+
+The retained emitter supplies words; this module imports no retained evaluator.
+Free warp symbols distinguish primal and inverse-transpose operators. Physical
+phase receipts are authenticated inherited evidence, not regenerated here.
+Apache-2.0. Substantial OpenAI assistance.
+"""
+from collections import Counter, defaultdict
+from fractions import Fraction
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import ast
+import gzip
+import json
+
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[2]
+CORE = ROOT / "research/kappa-native-resume/native-source/rebased-core"
+PACKET = ROOT / "research/kappa-native-resume/causal-controller/sources/research/joint-query/certificate.json.gz"
+TAGS = ("THREE-base", "THREE-extra", "FOUR-base", "FOUR-extra")
+Q = Fraction
+
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == ".gz" else raw)
+
+
+def digest(path):
+    return sha256(path.read_bytes()).hexdigest()
+
+
+def authenticate():
+    pins = read(HERE / "SOURCES.json")
+    for relative, expected in pins.items():
+        need(digest(ROOT / relative) == expected, "Changed retained source: " + relative)
+    return pins
+
+
+def emit_original(canonical):
+    """Reuse only the pinned source's pure writer; no source verifier executes."""
+    source = CORE / "sources/bw_emit.py"
+    names = {"basis", "reg", "dual", "scalar", "lregs", "expand", "emit", "primitive_bound"}
+    tree = ast.parse(source.read_text())
+    functions = [n for n in tree.body if isinstance(n, ast.FunctionDef) and n.name in names]
+    need({n.name for n in functions} == names, "Exact writer function inventory")
+    context = dict(c=canonical, frames=canonical["frames"], v=112, R=408, h=9, n=632, Q=Q)
+    exec(compile(ast.Module(body=functions, type_ignores=[]), str(source), "exec"), context)
+    return {"forward": context["emit"](False), "backward": context["emit"](True)}
+
+
+def span(basis):
+    points = {0}
+    for vector in basis:
+        need(isinstance(vector, int) and 0 <= vector < 512, "Nine-dimensional frame")
+        points |= {v ^ vector for v in tuple(points)}
+    return frozenset(points)
+
+
+def identity(role):
+    return {(role, ()): Q(1)}
+
+
+def add(destination, source, coefficient):
+    for key, value in tuple(source.items()):
+        value = destination.get(key, Q(0)) + coefficient * value
+        if value:
+            destination[key] = value
+        else:
+            destination.pop(key, None)
+
+
+def warp(row, operator, backward):
+    symbol = (1 if operator > 0 else -1) * (abs(operator) + (10**6 if backward else 0))
+    out = {}
+    for (variable, word), coefficient in row.items():
+        moved = word[1:] if word and word[0] == -symbol else (symbol,) + word
+        key = variable, moved
+        out[key] = out.get(key, Q(0)) + coefficient
+    return {k: v for k, v in out.items() if v}
+
+
+def expected(role, R, backward, clean):
+    out = identity(role)
+    name, i = role
+    if name != "L":
+        return out
+    target = i < 112 if backward else 112 <= i < 224
+    if not target:
+        return out
+    port = i if backward else i - 112
+    source_offset = 112 if backward else 0
+    sign = -1 if backward else 1
+    add(out, identity(("L", source_offset + port)), Q(sign))
+    if clean:
+        for query in R:
+            if port in query:
+                for j, value in query.items():
+                    add(out, identity(("L", source_offset + j)), -sign * query[port] * value / 4)
+    return out
+
+
+def replay(program, canonical, R, backward, clean, omit_cleanup_last=False):
+    """All L inputs and all Z inputs are independent, including dirty outputs."""
+    n = 2 * canonical["v"] + canonical["R"]
+    need(n == 632, "Retained compact width")
+    rows = {("L", i): identity(("L", i)) for i in range(n)}
+    current = {("L", i): frame for i, frame in enumerate(canonical["start"])}
+    center_indices = set()
+    for event in program:
+        if event[0] == "scalar":
+            op = event[1]
+            for register in op[1:3] if op[0] in ("add", "copy") else op[1:2]:
+                if register[0] == "C":
+                    center_indices.add(register[1])
+        elif event[0] == "center":
+            center_indices.add(event[1])
+    need(center_indices <= set(range(8)), "Known center workspace indices")
+    for i in center_indices:
+        rows["C", i] = identity(("C", i))
+        current["C", i] = None
+    spaces = [span(vectors) for vectors in canonical["frames"]]
+    dimensions = [len(s).bit_length() - 1 for s in spaces]
+    need(dimensions[1] == 9, "Cleanup uses the full native frame")
+    live = set()
+    profile = Counter()
+    counts = Counter()
+    scalar_primitives = 0
+    cleanup_start = next(i for i, event in enumerate(program) if event == ["phase", "full_frame_cleanup"])
+    last_scalar = max(i for i, event in enumerate(program) if event[0] == "scalar" and i > cleanup_start)
+    for position, event in enumerate(program):
+        kind = event[0]
+        counts[kind] += 1
+        if kind in ("climb", "center"):
+            if kind == "climb":
+                _, part, index, old, new, rank = event
+                role = "L", index
+                need(spaces[old] < spaces[new], "Non-nested or empty paid climb")
+            else:
+                _, index, old, new, rank = event
+                role = "C", index
+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], "Center residual is not nested")
+            need(current[role] == old and rank == abs(dimensions[new] - dimensions[old]), "Paid edge source/rank")
+            current[role] = new
+            profile[rank] += 1
+        elif kind == "zero_buffer":
+            _, action, index = event
+            role = "Z", index
+            if action == "alloc":
+                need(role not in rows and role not in live, "Cleanup buffer duplicate")
+                rows[role] = identity(role)
+                current[role] = 1
+                live.add(role)
+            else:
+                need(action == "free" and role in live and current[role] == 1, "Cleanup buffer retirement")
+                live.remove(role)
+        elif kind == "warp":
+            _, role, operator, old, new = event
+            role = tuple(role)
+            need(current[role] == old, "Warp entrance frame")
+            rows[role] = warp(rows[role], operator, backward)
+            current[role] = new
+        elif kind == "scalar":
+            op, frame = event[1:]
+            target = tuple(op[1])
+            if op[0] == "clear":
+                need(target[0] == "C", "A borrowed input was cleared")
+                rows[target] = {}
+                current[target] = frame
+                scalar_primitives += 1
+                continue
+            need(current[target] == frame, "Scalar target frame")
+            if op[0] in ("add", "copy"):
+                source = tuple(op[2])
+                need(current[source] == frame, "Scalar source frame")
+                if op[0] == "copy":
+                    need(target[0] == "C", "Copy overwrites borrowed state")
+                    rows[target] = dict(rows[source])
+                    scalar_primitives += 1
+                    continue
+                coefficient = Q(op[3], op[4])
+                need(target != source, "Self-ADD is not a reversible shear")
+                numerator, denominator = abs(coefficient.numerator), coefficient.denominator
+                need(numerator and denominator & (denominator - 1) == 0, "Non-dyadic ADD")
+                scalar_primitives += 3 + numerator.bit_length() - 1 + numerator.bit_count() + denominator.bit_length() - 1
+                if not (omit_cleanup_last and position == last_scalar):
+                    add(rows[target], rows[source], coefficient)
+            else:
+                need(op[0] == "scale", "Unknown scalar event")
+                coefficient = Q(op[2], op[3])
+                numerator, denominator = abs(coefficient.numerator), coefficient.denominator
+                need(numerator and numerator & (numerator - 1) == 0 and denominator & (denominator - 1) == 0,
+                     "Nonunit dyadic SCALE")
+                scalar_primitives += abs(numerator.bit_length() - denominator.bit_length()) + int(coefficient < 0)
+                if not (omit_cleanup_last and position == last_scalar):
+                    rows[target] = {k: coefficient * v for k, v in rows[target].items()}
+        else:
+            need(kind in ("phase", "adapter", "residual_adapter"), "Unknown native event")
+    need(not live and [current["L", i] for i in range(n)] == canonical["final"], "Retired fields/final frames")
+    need(dict(profile) == {int(k): v for k, v in canonical["local_profile"].items()}, "Complete paid profile")
+    mismatches = []
+    for role, actual in rows.items():
+        wanted = {} if role[0] == "C" else expected(role, R, backward, clean)
+        if actual != wanted:
+            mismatches.append({"role": list(role), "unequal_coefficients": sum(actual.get(k, 0) != wanted.get(k, 0) for k in set(actual) | set(wanted))})
+    if not omit_cleanup_last:
+        need(not mismatches, "Native dirty-buffer operator mismatch: " + repr(mismatches[:3]))
+    else:
+        need(mismatches, "Missing-cleanup negative control unexpectedly accepted")
+    buffer_count = sum(role[0] == "Z" for role in rows)
+    return dict(direction="backward" if backward else "forward", clean_J=clean,
+                independent_borrowed_input_fields=632+buffer_count, original_data_fields=224,
+                expected_restored_helpers=408, expected_restored_arbitrary_cleanup_buffers=buffer_count,
+                explicitly_owned_C_fields_cleared=len(center_indices), event_counts=dict(counts),
+                paid_profile=dict(sorted(profile.items())), paid_rank_mass=sum(k*v for k,v in profile.items()),
+                conservative_real_scalar_primitive_allowance=2*scalar_primitives,
+                all_scalar_frames_checked=True, dyadic_coefficients_and_unit_scales_checked=True,
+                free_warp_operator_endpoint_matches=not mismatches,
+                negative_control_omitted_last_cleanup_scalar=omit_cleanup_last,
+                mismatch_examples=mismatches[:3])
+
+
+def liveness(canonical):
+    times = defaultdict(list)
+    for i, event in enumerate(canonical["cleanup"]):
+        for role in event[1:3] if event[0] == "add" else event[1:2]:
+            role = tuple(role) if isinstance(role, list) else ("L", role)
+            times[role].append(i)
+    full = [i for i, f in enumerate(canonical["final"]) if f == 1]
+    candidates = []
+    for z in canonical["zero_buffers"]:
+        begin, end = min(times["Z", z]), max(times["Z", z])
+        possible = [i for i in range(112) if all(t < begin or t > end for t in times["L", i])]
+        candidates.append(dict(buffer=z, first_use=begin, last_use=end,
+                               noninterfering_same_call_X_candidates=possible,
+                               noninterfering_full_frame_L_candidates=[i for i in full if all(t < begin or t > end for t in times["L", i])]))
+    return dict(full_frame_live_roles=len(full), full_frame_roles_unused_in_cleanup=[i for i in full if not times["L", i]],
+                same_call_X_outputs_touched=sum(bool(times["L", i]) for i in range(112)),
+                buffers_with_no_noninterfering_same_call_X=sum(not row["noninterfering_same_call_X_candidates"] for row in candidates),
+                buffers_with_no_noninterfering_full_frame_L=sum(not row["noninterfering_full_frame_L_candidates"] for row in candidates),
+                intervals=candidates,
+                conclusion="Arbitrary-buffer restoration does not establish a legal same-call completed-output alias.",
+                external_same_frame_bank_requirement=91,
+                external_bank_hosting_constructed=False)
+
+
+def find_aliases(canonical):
+    """Injective lifetime-safe matching; no native L access during its Z span."""
+    options = {row["buffer"]: row["noninterfering_full_frame_L_candidates"]
+               for row in liveness(canonical)["intervals"]}
+    owner = {}
+
+    def augment(z, seen):
+        for role in options[z]:
+            if role in seen:
+                continue
+            seen.add(role)
+            if role not in owner or augment(owner[role], seen):
+                owner[role] = z
+                return True
+        return False
+
+    for z in sorted(options, key=lambda z: (len(options[z]), z)):
+        augment(z, set())
+    bindings = {z: role for role, z in owner.items()}
+    need(len(set(bindings.values())) == len(bindings), "Alias must be injective")
+    need(all(role in options[z] for z, role in bindings.items()), "Interfering alias")
+    return bindings
+
+
+def alias_program(program, bindings):
+    """Replace only Z register operands, retaining every native/scalar event."""
+    out = []
+
+    def mapped(role):
+        return ["L", bindings[role[1]]] if role[0] == "Z" and role[1] in bindings else list(role)
+
+    for event in program:
+        if event[0] == "zero_buffer" and event[2] in bindings:
+            continue
+        if event[0] == "scalar":
+            op = event[1].copy()
+            op[1] = mapped(op[1])
+            if op[0] in ("add", "copy"):
+                op[2] = mapped(op[2])
+            out.append(["scalar", op, event[2]])
+        elif event[0] == "warp":
+            out.append([event[0], mapped(event[1]), *event[2:]])
+        else:
+            out.append(event)
+    return out
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--output", type=Path, default=HERE / "RESULT.json")
+    args = parser.parse_args()
+    pins = authenticate()
+    R = [{int(k): Q(v) for k, v in row.items()} for row in read(PACKET)["R_rows"]]
+    providers = {}
+    for tag in TAGS:
+        providers[tag] = {}
+        for clean in (False, True):
+            folder = "converted" if clean else "sources"
+            canonical = read(CORE / folder / (tag + "-CANONICAL.json.gz"))
+            programs = read(CORE / folder / (tag + "-NATIVE-WORD.json.gz")) if clean else emit_original(canonical)
+            checks = [replay(programs[direction], canonical, R, direction == "backward", clean)
+                      for direction in ("forward", "backward")]
+            bindings = find_aliases(canonical)
+            aliases = {direction: alias_program(program, bindings) for direction, program in programs.items()}
+            aliased_checks = [replay(aliases[direction], canonical, R, direction == "backward", clean)
+                              for direction in ("forward", "backward")]
+            need(len(bindings) == 53, "Expected source-bound 53-field lifetime match")
+            for original, aliased in zip(checks, aliased_checks):
+                need(original["paid_profile"] == aliased["paid_profile"] and
+                     original["conservative_real_scalar_primitive_allowance"] == aliased["conservative_real_scalar_primitive_allowance"],
+                     "Aliasing changes the charged operation list")
+            providers[tag]["clean_J" if clean else "ordinary"] = dict(checks=checks, liveness=liveness(canonical),
+                lifetime_alias_bindings={str(z): role for z, role in sorted(bindings.items())},
+                aliased_checks=aliased_checks,
+                eliminated_cleanup_fields=len(bindings), remaining_cleanup_fields=91-len(bindings),
+                aliased_word_sha256={direction: sha256(json.dumps(program, sort_keys=True, separators=(",", ":")).encode()).hexdigest()
+                                     for direction, program in aliases.items()})
+        print("PASS all arbitrary cleanup inputs", tag, flush=True)
+    canonical = read(CORE / "converted/THREE-base-CANONICAL.json.gz")
+    programs = read(CORE / "converted/THREE-base-NATIVE-WORD.json.gz")
+    controls = [replay(programs[direction], canonical, R, direction == "backward", True, True)
+                for direction in ("forward", "backward")]
+    result = dict(schema="literal-native-dirty-buffers/1", status="PASS_NATIVE_ARBITRARY_DIRTY_BUFFER_REPLAY",
+                  new_multiplication_kappa=False, physical_phase_generation_rerun=False,
+                  phase_evidence="Pinned inherited exact native phase receipts; unchanged native edges.",
+                  source_hashes=pins, verifier_sha256=digest(Path(__file__)), providers=providers,
+                  negative_controls=controls,
+                  lifetime_safe_local_full_frame_aliases_per_word=53,
+                  remaining_external_bank_fields_per_word=38,
+                  all_91_local_output_alias_claim=False, external_bank_placement_and_cost_closed=False)
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    args.output.write_text(json.dumps(result, indent=2) + "\n")
+    print(result["status"], flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/owned-relation-independent-validation/evidence/cold/BOUNDED-REGISTERED-RUN.json b/research/owned-relation-independent-validation/evidence/cold/BOUNDED-REGISTERED-RUN.json
new file mode 100644
index 0000000000..769e26fd3a
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/BOUNDED-REGISTERED-RUN.json
@@ -0,0 +1,7533 @@
+{
+  "status": "PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED",
+  "argv": [
+    "/usr/bin/python3",
+    "-B",
+    "scripts/research_package.py",
+    "--package",
+    "research/kappa-owned-relation-20261023"
+  ],
+  "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/owned-relation-5377-cold-validation-20261024/snapshot",
+  "exit": 0,
+  "resource_stop": null,
+  "seconds": 94.34425078798085,
+  "peak_sampled_descendant_rss_kib": 153572,
+  "total_timeout_seconds": 1260,
+  "rss_limit_kib": 1048576,
+  "per_registered_command_timeout_seconds": 600,
+  "scientific_bytes_changed": [],
+  "hash_inventory_files": 24,
+  "samples": [
+    {
+      "seconds": 0.0012410939671099186,
+      "rss_kib": 868,
+      "pids": [
+        3
+      ]
+    },
+    {
+      "seconds": 0.10153685900149867,
+      "rss_kib": 28324,
+      "pids": [
+        3,
+        4
+      ]
+    },
+    {
+      "seconds": 0.2021228409721516,
+      "rss_kib": 41044,
+      "pids": [
+        3
+      ]
+    },
+    {
+      "seconds": 0.3024592690053396,
+      "rss_kib": 57492,
+      "pids": [
+        3,
+        5
+      ]
+    },
+    {
+      "seconds": 0.4029838349670172,
+      "rss_kib": 47796,
+      "pids": [
+        3,
+        20
+      ]
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diff --git a/research/owned-relation-independent-validation/evidence/cold/CAPSULE-PREFLIGHT-INITIAL.json b/research/owned-relation-independent-validation/evidence/cold/CAPSULE-PREFLIGHT-INITIAL.json
new file mode 100644
index 0000000000..83031cecf5
--- /dev/null
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+}
diff --git a/research/owned-relation-independent-validation/evidence/cold/EXACT-COMMIT.raw b/research/owned-relation-independent-validation/evidence/cold/EXACT-COMMIT.raw
new file mode 100644
index 0000000000..4d1d1ea199
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/EXACT-COMMIT.raw
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+tree e4370e0bff125a6575ed3c073d24aa1a984323d1
+parent 7c472563474e60185e6ca101a17622133d047e56
+author Ali Romman <226877337+aliromman@users.noreply.github.com> 1792786992 -0500
+committer Ali Romman <226877337+aliromman@users.noreply.github.com> 1792786992 -0500
+
+Improve conditional kappa to 0.00302235 with one owned helper relation
diff --git a/research/owned-relation-independent-validation/evidence/cold/HEAD-WORKING-BLOB-BINDINGS.json b/research/owned-relation-independent-validation/evidence/cold/HEAD-WORKING-BLOB-BINDINGS.json
new file mode 100644
index 0000000000..3c182ef9d1
--- /dev/null
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+    "git_blob": "0fdb65f946d557c13d8e2781b9151e2a8ddee5c3",
+    "sha256": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de"
+  },
+  {
+    "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py",
+    "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59",
+    "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15"
+  },
+  {
+    "path": "research/query-thinned-controllers/RESULT.json",
+    "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c",
+    "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f"
+  }
+]
diff --git a/research/owned-relation-independent-validation/evidence/cold/PHYSICAL-EXTENSION-REVIEW.md b/research/owned-relation-independent-validation/evidence/cold/PHYSICAL-EXTENSION-REVIEW.md
new file mode 100644
index 0000000000..cdb05cf9ef
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/PHYSICAL-EXTENSION-REVIEW.md
@@ -0,0 +1,51 @@
+# Same-premise physical extension for PR5377
+
+Reviewed exact candidate head `c448d13c71908647f968b06cddb795ce7d288139`, package `research/kappa-owned-relation-20261023`, against selected PR4610 / exact PR5241 audit. This is this worker's static applicability review; the separate physical and cost reviewers' actual executions retain their own provenance. Full registered replay status is recorded separately in `BOUNDED-REGISTERED-RUN.json` when the live process completes.
+
+The source-specific change belongs to the selected generic scalar/owned-storage grammar. It introduces no native Gaussian operator, monomial adapter, binary map, child factorization or movement exponent. It restricts one previously arbitrary helper to an owned prepared value, retains an additional owned snapshot in its exact frame, and replaces two source jobs by same-frame COPY and identity on a proved zero row. That is a change of independent input inventory and chronological scalar word, so it needs the following new argument; the old all-632-input endpoint alone is insufficient.
+
+## Relation, all columns and phases
+
+At the cold backward entrance all five relation helpers have source frame 0. Making L230 owned permits clearing its arbitrary owned entry and preparing
+
+`h230 = h324 - h326 - h328 + h333`.
+
+Every other backward persistent input remains arbitrary and independent; L230's rank-nine productive endpoint is debited. The unrestricted source identities are `C0 - saved_L92 = Delta/4` and `L92 = -Delta/4`, with `Delta=h230-h324+h326+h328-h333`. They are equalities of rational rows over free invertible operator words, rather than identities in a chosen numerical tensor sample. Evaluating the free-group algebra at the inherited lifted physical operators therefore preserves them at every allowed column multiplicity and with arbitrary spectators. Scalar coefficients and preparation chronology stay unchanged in that evaluation; tensor power is never distributed over the relation's sum.
+
+The backward free-word symbols are deliberately disjoint from forward symbols. Their physical representation is the exact inherited oriented source gauge, not a newly assumed equality between forward and backward operators. The physical reviewer separately checks the oriented rows and frames. Both the saved L92 stream and the replaced center output are in actual frame254, so COPY requires no new transport. At the zero site the complete vector is identically zero; physical identity preserves it in the entire ambient space. The `zero_retag` record changes only the chart label attached to that same zero. It does not claim that identity transports arbitrary nonzero vectors between those frames.
+
+The exact retained warp/main-adapter sequence and all retained paid events are source-identical. Their absolute phases and whole-job factors are already covered by the complete PR5241 phase foundation, including the paid and helper classes. PR5377's phase-inheritance routine by itself checks receipt status and event equality; it is not a new replay of that foundation. Admission must retain the authenticated PR5241 scientific proof/receipt, rather than infer phases from binary frames or the author's PASS label.
+
+## Physical owner and scratch boundary
+
+Backward local owned fields are C0, C1 and L230. C1 is one newly allocated complete physical slot; L230 uses its former slot under owned status. C1 is cleared before a same-frame snapshot COPY, C0 is cleared before the saved-value COPY and C1 is erased after the final copy. L230 is cleared after its final use. No borrowed persistent slot is erased or overwritten. Every copy has distinct source/destination slots and preserves the source.
+
+The 16 backward FULL calls and two forward FULL calls each receive their own owner list; there is no aliasing between calls or between a local caller's live banks and a suspended child's banks. A conservative raw allocation has `16*3+2*1=50` LOCAL owned banks before the separately required query/completion/compiler banks. This is an allocation witness at the raw-controller level, not an expanded compiler bank count. A compiled child must finish with adapters and ordering restored before its parent resumes. Distinct chronological positions may not be batched as simultaneous owner inputs.
+
+COPY/CLEAR are already permitted primitives on owned complete fields. Four extra unit ADDs use the same frame0. Their descriptor work, dirty-control repair and movement retain the selected physical cost hypotheses. No zero predicate is tested at runtime: the compiled program uses a source-proved invariant. The ideal exact changed program simply executes physical identity at that site. Its approximation/semantic-growth bound must be derived for this changed program, including its new scalar and owned-storage counts.
+
+## Fresh tariffs, precision and storage constants
+
+The changed raw scalar allowance increases by46 per backward call:32 for four unit ADDs,14 for seven COPY/CLEAR macros. The candidate conservatively retains old helper wrappers and the maximum old paid count for routing and adds four route groups for the two newly owned lifetimes. Local scalar allowance158214 plus route4806000 is4964214, below10^7. The complete raw-controller allowance remains181098496 below10^9. These inequalities establish that the retained conservative raw unit is sufficient; they do not establish the expanded uniform word's storage or scalar envelope.
+
+Fix the entire new finite word, its1024-fold product, charged completion/splitting and finite compiler at `N=2^31385200000000` before multiplication input growth. Apply the selected finite emitter/allocation rule to the actual changed owner inventory and chronology. Let W be productive arrays, P rank-one child calls, O all owned banks including every suspended occurrence, R every movement/native/normalizer/route record, and G the new full scalar/phase coefficient allowance. Three banks per backward occurrence and one per forward occurrence, plus every query/completion/splitting/compiler bank, is a conservative finite prescription for O. None contributes productive credit.
+
+Use these new effective integers in the selected formulas:
+
+```
+Z=W+O
+E=64*(Z+N+P+G+1)^3
+B=P+E
+C0=32*N*B^2
+C1=1
+```
+
+The new E dominates `2GZ^2+8P+4Z+4+32N`. With parents waiting for completed children, the inherited recurrence is `A(e)<=A(floor(e/N))+P*floor(e/N)+E`, giving `A(e)<=2Be`. The unit preparation coefficients and complete same-frame COPY add no new scalar species. CLEAR reduces magnitude; COPY duplicates a value into a counted bank. Increased O/R/G change thresholds, parking, stock and setup constants, with the same source movement exponent and fixed number of tapes. Full simultaneous stock products remain required. No old numerical expanded size cap, old fine-grid threshold, raw10^9 cap or one-bank-per-depth shortcut is substituted for these new constants.
+
+The supplied cost review gives a constructive new-constant prescription and independently checks the complete invoice, compiler and outer arithmetic. This worker inspected that prescription against the selected PR5241 contract map. It uses the existing generic fixed finite template assumptions; it does not introduce a separate premise that the new relation/COPY program is a cheap oracle.
+
+## Conditional conclusion and limits
+
+Provided the independently checked source identities, same-frame copy/zero arguments, complete asymmetric invoice, registered artifact checks and source-bound PR5241 phase foundation pass, the candidate is an instance of the same five selected assumptions: `native_all_columns`, `owned_erasure`, `compiler`, `precision_tape`, `analytic_recovery`. The changed inventory is charged by losing16 H9 targets and saving16 H1 plus16 H8 jobs over the controller; helper restoration and private erasure are separate obligations.
+
+The original uniform physical realization, precision/tape and analytic/integer-recovery theorems remain conditional premises. This review does not materialize the compiler word, prove an unconditional multiplication theorem, run Lean, supply an independent human acceptance claim or change selected metadata. Construction credit is Ali Romman's PR5377; PR4610, controller/native/compiler, PR5241 and all physical/BIT/analytic predecessor credits remain intact. Substantial OpenAI Codex assistance was used in this review.
diff --git a/research/owned-relation-independent-validation/evidence/cold/POST-RUN-HASHES.json b/research/owned-relation-independent-validation/evidence/cold/POST-RUN-HASHES.json
new file mode 100644
index 0000000000..8f98db63cf
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/POST-RUN-HASHES.json
@@ -0,0 +1,26 @@
+{
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+  "research/joint-helper-lattice/CONTROLLER.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f",
+  "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7",
+  "research/kappa-interface-round2-20261022/price_profile.py": "adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb",
+  "research/kappa-owned-relation-20261023/README.md": "eb853337dfaf306808d77538e448a78f16021a2e73295078b4b2f4ff6ea835c4",
+  "research/kappa-owned-relation-20261023/RESULT.json": "1937b2e1fb4bec0fa1b0d2428a52734c554152538ac8930605bd46704f1c7320",
+  "research/kappa-owned-relation-20261023/SOURCES.json": "eca6dd5ac3028a72e016e0c8a265be702dd6c4daf481bc009524577ff5e7c831",
+  "research/kappa-owned-relation-20261023/TASK.json": "b9a9ace02d10791b49cf113dd6a19501b297920a29b9a4d5585e25ef4e8ef92f",
+  "research/kappa-owned-relation-20261023/VERIFY.json": "1fc62a3afd087aa63f8d993beb1cba944b9b441824cd14e9135e792fcd45bab8",
+  "research/kappa-owned-relation-20261023/WORD.json.gz": "8d913767ad773839995e54e4d80aeff692a86687d0f78153311c8ad62b7ba1bc",
+  "research/kappa-owned-relation-20261023/native.py": "85d994fc5661bfa53c4b42f79955ff74ffe70072163cb02fa76cd79efbcc0c97",
+  "research/kappa-owned-relation-20261023/price.py": "e228a48de6138257da7520bb57567a275c402289c90fe7e94f0ef2ad6371f836",
+  "research/kappa-owned-relation-20261023/verify.py": "c4d4fe9b74db1d47fbbfc0c602315d8256a15f0ad0e50b9fcfe2249bf65916f1",
+  "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a",
+  "research/kappa-rebuild/complex/native_extensions.py": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3",
+  "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+  "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz": "6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b",
+  "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de",
+  "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15",
+  "research/query-thinned-controllers/RESULT.json": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f",
+  "scripts/check_research_commit.py": "28fed1e156fe8601633ed453f682a158cb15e94981e6c89ed96ae72ffc9d0c6f",
+  "scripts/research_package.py": "8e07ddee4d8e1c70a278538b2758d423a298b96d5d1a18233dc29925696fc96f",
+  "docs/research/agent-task-catalog.json": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+}
diff --git a/research/owned-relation-independent-validation/evidence/cold/PRE-RUN-HASHES.json b/research/owned-relation-independent-validation/evidence/cold/PRE-RUN-HASHES.json
new file mode 100644
index 0000000000..8f98db63cf
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/PRE-RUN-HASHES.json
@@ -0,0 +1,26 @@
+{
+  "research/free-word-tensor-lift-audit/PROOF.md": "cc8ad3698a673fb225419a3636a39aa99a66c7a0676f12e329b1e76564fa1459",
+  "research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326",
+  "research/joint-helper-lattice/CONTROLLER.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f",
+  "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7",
+  "research/kappa-interface-round2-20261022/price_profile.py": "adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb",
+  "research/kappa-owned-relation-20261023/README.md": "eb853337dfaf306808d77538e448a78f16021a2e73295078b4b2f4ff6ea835c4",
+  "research/kappa-owned-relation-20261023/RESULT.json": "1937b2e1fb4bec0fa1b0d2428a52734c554152538ac8930605bd46704f1c7320",
+  "research/kappa-owned-relation-20261023/SOURCES.json": "eca6dd5ac3028a72e016e0c8a265be702dd6c4daf481bc009524577ff5e7c831",
+  "research/kappa-owned-relation-20261023/TASK.json": "b9a9ace02d10791b49cf113dd6a19501b297920a29b9a4d5585e25ef4e8ef92f",
+  "research/kappa-owned-relation-20261023/VERIFY.json": "1fc62a3afd087aa63f8d993beb1cba944b9b441824cd14e9135e792fcd45bab8",
+  "research/kappa-owned-relation-20261023/WORD.json.gz": "8d913767ad773839995e54e4d80aeff692a86687d0f78153311c8ad62b7ba1bc",
+  "research/kappa-owned-relation-20261023/native.py": "85d994fc5661bfa53c4b42f79955ff74ffe70072163cb02fa76cd79efbcc0c97",
+  "research/kappa-owned-relation-20261023/price.py": "e228a48de6138257da7520bb57567a275c402289c90fe7e94f0ef2ad6371f836",
+  "research/kappa-owned-relation-20261023/verify.py": "c4d4fe9b74db1d47fbbfc0c602315d8256a15f0ad0e50b9fcfe2249bf65916f1",
+  "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a",
+  "research/kappa-rebuild/complex/native_extensions.py": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3",
+  "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+  "research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz": "6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b",
+  "research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de",
+  "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15",
+  "research/query-thinned-controllers/RESULT.json": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f",
+  "scripts/check_research_commit.py": "28fed1e156fe8601633ed453f682a158cb15e94981e6c89ed96ae72ffc9d0c6f",
+  "scripts/research_package.py": "8e07ddee4d8e1c70a278538b2758d423a298b96d5d1a18233dc29925696fc96f",
+  "docs/research/agent-task-catalog.json": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+}
diff --git a/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COLD.stderr.log b/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COLD.stderr.log
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COLD.stdout.log b/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COLD.stdout.log
new file mode 100644
index 0000000000..bff6a67edf
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COLD.stdout.log
@@ -0,0 +1,5 @@
+CHECK Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls.
+{"gain_over_PR4610": "2871/5000000000", "kappa": "60447/20000000", "paid_calls": 64372, "productive_fields": 10912, "raw_root_interval": ["302238736347/100000000000000", "75559684087/25000000000000"], "status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION"}
+CHECK The same checks remain active with Python assertions disabled.
+{"gain_over_PR4610": "2871/5000000000", "kappa": "60447/20000000", "paid_calls": 64372, "productive_fields": 10912, "raw_root_interval": ["302238736347/100000000000000", "75559684087/25000000000000"], "status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION"}
+PASS_REGISTERED_RESEARCH_PACKAGE research/kappa-owned-relation-20261023 outcome=completed
diff --git a/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COMMIT-PREFLIGHT-CORRECTED.json b/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COMMIT-PREFLIGHT-CORRECTED.json
new file mode 100644
index 0000000000..494ff2a17f
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/REGISTERED-COMMIT-PREFLIGHT-CORRECTED.json
@@ -0,0 +1,16 @@
+{
+  "argv": [
+    "python3",
+    "-B",
+    "scripts/check_research_commit.py",
+    "--package",
+    "research/kappa-owned-relation-20261023",
+    "--check-source-history"
+  ],
+  "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/owned-relation-5377-cold-validation-20261024/snapshot",
+  "returncode": 0,
+  "stdout": "PASS_RESEARCH_COMMIT_BYTES {\"commit\": \"c448d13c71908647f968b06cddb795ce7d288139\", \"files\": 18, \"package\": \"research/kappa-owned-relation-20261023\", \"source_history_commits\": [\"7c472563474e60185e6ca101a17622133d047e56\"]}\n",
+  "stderr": "",
+  "seconds": 0.1952657009824179,
+  "object_transport": "Working bytes SHA1 checked against actual exact-head tree, then installed unchanged in isolated object store; no commit/tree object rewritten"
+}
diff --git a/research/owned-relation-independent-validation/evidence/cold/REGISTERED-PREFLIGHT.json b/research/owned-relation-independent-validation/evidence/cold/REGISTERED-PREFLIGHT.json
new file mode 100644
index 0000000000..fe9f374830
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/REGISTERED-PREFLIGHT.json
@@ -0,0 +1,32 @@
+[
+  {
+    "argv": [
+      "python3",
+      "-B",
+      "scripts/research_package.py",
+      "--package",
+      "research/kappa-owned-relation-20261023",
+      "--check-only"
+    ],
+    "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/owned-relation-5377-cold-validation-20261024/snapshot",
+    "returncode": 0,
+    "stdout": "PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)\n",
+    "stderr": "",
+    "seconds": 0.3380786839989014
+  },
+  {
+    "argv": [
+      "python3",
+      "-B",
+      "scripts/check_research_commit.py",
+      "--package",
+      "research/kappa-owned-relation-20261023",
+      "--check-source-history"
+    ],
+    "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/owned-relation-5377-cold-validation-20261024/snapshot",
+    "returncode": 1,
+    "stdout": "",
+    "stderr": "missing or non-blob Git source: 777f4e1d5114e35ba6de2a8e818b790b16aca655\n",
+    "seconds": 0.17831641901284456
+  }
+]
diff --git a/research/owned-relation-independent-validation/evidence/cold/SOURCE-HISTORY-PREFLIGHT.json b/research/owned-relation-independent-validation/evidence/cold/SOURCE-HISTORY-PREFLIGHT.json
new file mode 100644
index 0000000000..061088ea94
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/SOURCE-HISTORY-PREFLIGHT.json
@@ -0,0 +1,16 @@
+{
+  "head": "c448d13c71908647f968b06cddb795ce7d288139",
+  "base": "7c472563474e60185e6ca101a17622133d047e56",
+  "ancestry_command": [
+    "git",
+    "--no-replace-objects",
+    "merge-base",
+    "--is-ancestor",
+    "7c472563474e60185e6ca101a17622133d047e56",
+    "c448d13c71908647f968b06cddb795ce7d288139"
+  ],
+  "base_is_ancestor_exit": 0,
+  "source_manifest_rows_authenticated": 14,
+  "missing": [],
+  "git_object_store": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/integer-mult-bounds/.git/objects"
+}
diff --git a/research/owned-relation-independent-validation/evidence/cold/VALIDATION.json b/research/owned-relation-independent-validation/evidence/cold/VALIDATION.json
new file mode 100644
index 0000000000..c34bfcdb95
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/VALIDATION.json
@@ -0,0 +1,142 @@
+{
+  "status": "PASS_OWN_COMPLETE_REGISTERED_PR5377_NORMAL_AND_OPTIMIZED",
+  "utc": "2026-10-23T20:37:57.604080+00:00",
+  "head": "c448d13c71908647f968b06cddb795ce7d288139",
+  "source_base": "7c472563474e60185e6ca101a17622133d047e56",
+  "current_canonical_main_pin": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+  "package": "research/kappa-owned-relation-20261023",
+  "python": "Python 3.12.3",
+  "registered_commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "The same checks remain active with Python assertions disabled."
+    }
+  ],
+  "normal_stdout_result": {
+    "gain_over_PR4610": "2871/5000000000",
+    "kappa": "60447/20000000",
+    "paid_calls": 64372,
+    "productive_fields": 10912,
+    "raw_root_interval": [
+      "302238736347/100000000000000",
+      "75559684087/25000000000000"
+    ],
+    "status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION"
+  },
+  "optimized_stdout_result": {
+    "gain_over_PR4610": "2871/5000000000",
+    "kappa": "60447/20000000",
+    "paid_calls": 64372,
+    "productive_fields": 10912,
+    "raw_root_interval": [
+      "302238736347/100000000000000",
+      "75559684087/25000000000000"
+    ],
+    "status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION"
+  },
+  "full_result_evidence": "outputs/owned-relation-5377-cold-validation-20261024/snapshot/research/kappa-owned-relation-20261023/RESULT.json",
+  "full_result_sha256": "1937b2e1fb4bec0fa1b0d2428a52734c554152538ac8930605bd46704f1c7320",
+  "artifact_equality": "Both unmodified registered commands compare their freshly reconstructed complete result and decompressed literal WORD against the exact committed artifacts; both passed. --write was never used.",
+  "native_negative_controls": {
+    "missing_owned_input_clear": "Every independent main/helper endpoint: 0",
+    "uncleared_owned_output": "Every owned entry column is erased at return",
+    "under_or_overstated_paid_rank": "Exact paid rank and frame",
+    "wrong_copy_gauge": "Exact scalar destination frame",
+    "wrong_relation_sign": "Every independent main/helper endpoint: 0",
+    "wrong_snapshot_source": "Zero identity requires an identically zero full row",
+    "wrong_zero_input_frame": "Zero identity requires an identically zero full row"
+  },
+  "arithmetic_negative_controls": {
+    "closed_epsilon": [
+      "epsilon_below_one",
+      "global_gamma_power_slack",
+      "actual_logarithmic_gamma_guard",
+      "source_axis_superpolynomial",
+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
+    ],
+    "closed_uniform": [
+      "new_complex_uniform_saving_above_b"
+    ],
+    "old_BIT": [
+      "actual_bit_above_effective"
+    ],
+    "unearned_helper_credit": "Rejected by the independent complete census",
+    "unfunded_endpoint": [
+      "main_transform_above_kappa",
+      "global_coordinate_router_above_kappa",
+      "fused_gaussian_above_kappa",
+      "group_bit_router_above_kappa",
+      "boundary_algebraic_matrix_above_kappa"
+    ]
+  },
+  "control_count_per_mode": 12,
+  "total_control_executions": 24,
+  "all_54_strict_outer_positive": true,
+  "all_four_functional_positive": true,
+  "bound": {
+    "status": "PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED",
+    "argv": [
+      "/usr/bin/python3",
+      "-B",
+      "scripts/research_package.py",
+      "--package",
+      "research/kappa-owned-relation-20261023"
+    ],
+    "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/owned-relation-5377-cold-validation-20261024/snapshot",
+    "exit": 0,
+    "resource_stop": null,
+    "seconds": 94.34425078798085,
+    "peak_sampled_descendant_rss_kib": 153572,
+    "total_timeout_seconds": 1260,
+    "rss_limit_kib": 1048576,
+    "per_registered_command_timeout_seconds": 600,
+    "scientific_bytes_changed": [],
+    "hash_inventory_files": 24,
+    "scope": "One own execution of the registered normal then optimized commands; no independent reviewer script rerun, Lean, native build or historical archive replay."
+  },
+  "evidence_sha256": {
+    "SOURCE-HISTORY-PREFLIGHT.json": "b4f01b807f1a53bccf542e96d526d683a721e0e5848abd3a02d83d7681d1f12a",
+    "REGISTERED-PREFLIGHT.json": "cf0111b1ff06b166e0435c1587c0e9001d7d761401da9d7c1cfef84d90b01336",
+    "REGISTERED-COMMIT-PREFLIGHT-CORRECTED.json": "b99af9e62e506640a766a5d9d83a02732c1a8126593ca8ea1b06fb0847215eaf",
+    "HEAD-WORKING-BLOB-BINDINGS.json": "04d465c90bd9ccc4299f762c12c1e599cad6d29db23a5df81e5c4a29fac3de26",
+    "PRE-RUN-HASHES.json": "35aa2409a422a0f9ba3fdedca6971a88f3bc6da1a9ec83634686a3b8e0e02206",
+    "POST-RUN-HASHES.json": "35aa2409a422a0f9ba3fdedca6971a88f3bc6da1a9ec83634686a3b8e0e02206",
+    "BOUNDED-REGISTERED-RUN.json": "93a2b28e5a7b0b2720d8eefc2273925db60b5b4bd8af500b0308c92bc7607a39",
+    "REGISTERED-COLD.stdout.log": "47d795c51b65d124fd2667d42d2fe49fa51facac026e0529a7ab81b07d8b2477",
+    "REGISTERED-COLD.stderr.log": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855",
+    "PHYSICAL-EXTENSION-REVIEW.md": "1f386f91d57e349762a0e474c67997d653ff27a48a17eeab8c2e49bcd9f6a142"
+  },
+  "delegated_review_evidence": {
+    "outputs/owned-relation-5377-physical-review-20261024/independent-result.json": {
+      "sha256": "ea1f513c9288b8eb8c379158d4088d1612e2472f1f075426d324ef435abe2601",
+      "execution_owner": "separate delegated reviewer; not this cold worker"
+    },
+    "outputs/owned-relation-5377-cost-review-20261024/RESULT.json": {
+      "sha256": "c35e972b649f6004fd5706d22efa4206f29240f1569b512e4c422b54cd3cae65",
+      "execution_owner": "separate delegated reviewer; not this cold worker"
+    },
+    "outputs/owned-relation-5377-cost-review-20261024/REPORT.md": {
+      "sha256": "6c97edcbd69ffab608f6dd743071043ea53bc83687dabb82eb474229056eea03",
+      "execution_owner": "separate delegated reviewer; not this cold worker"
+    }
+  },
+  "assumptions": "Exactly five selected generic framework assumptions, source-bound PR5241 phase foundation and independently reviewed constructive relation/ownership/precision extension. No unconditional or Lean theorem.",
+  "selected_record_changed": false,
+  "external_writes": false
+}
diff --git a/research/owned-relation-independent-validation/evidence/cold/run_guarded_registered.py b/research/owned-relation-independent-validation/evidence/cold/run_guarded_registered.py
new file mode 100644
index 0000000000..c2ba986e0d
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cold/run_guarded_registered.py
@@ -0,0 +1,89 @@
+#!/usr/bin/env python3
+"""One bounded serial registered replay; local review orchestration only."""
+from pathlib import Path
+import datetime, hashlib, json, os, signal, subprocess, sys, time
+
+HERE = Path(__file__).resolve().parent
+REPO = HERE / 'snapshot'
+PACKAGE = 'research/kappa-owned-relation-20261023'
+LIMIT_SECONDS = 1260
+LIMIT_KIB = 1024 * 1024
+
+def hashes():
+    return {str(p.relative_to(REPO)): hashlib.sha256(p.read_bytes()).hexdigest()
+            for root in ('research', 'scripts', 'docs')
+            for p in sorted((REPO / root).rglob('*')) if p.is_file()}
+
+def descendants(pid):
+    found = set()
+    todo = [pid]
+    while todo:
+        current = todo.pop()
+        if current in found:
+            continue
+        found.add(current)
+        try:
+            raw = Path('/proc', str(current), 'task', str(current), 'children').read_text()
+            todo.extend(map(int, raw.split()))
+        except (FileNotFoundError, ProcessLookupError):
+            pass
+    return found
+
+def rss(pid):
+    try:
+        lines = Path('/proc', str(pid), 'status').read_text().splitlines()
+        return next((int(x.split()[1]) for x in lines if x.startswith('VmRSS:')), 0)
+    except (FileNotFoundError, ProcessLookupError):
+        return 0
+
+def main():
+    before = hashes()
+    (HERE / 'PRE-RUN-HASHES.json').write_text(json.dumps(before, indent=2) + '\n')
+    env = {k: v for k, v in os.environ.items()
+           if not k.startswith('GIT_') and k not in ('PYTHONPATH', 'PYTHONOPTIMIZE', 'LEAN_AUDIT_BIN')}
+    env.update(PYTHONDONTWRITEBYTECODE='1', PYTHONUNBUFFERED='1',
+               GIT_NO_REPLACE_OBJECTS='1', GIT_NO_LAZY_FETCH='1', GIT_GRAFT_FILE=os.devnull)
+    scratch = HERE / 'scratch'
+    scratch.mkdir(exist_ok=False)
+    env['TMPDIR'] = str(scratch)
+    command = [sys.executable, '-B', 'scripts/research_package.py', '--package', PACKAGE]
+    started = time.monotonic()
+    peak = 0
+    stop = None
+    samples = []
+    with (HERE / 'REGISTERED-COLD.stdout.log').open('wb') as out, (HERE / 'REGISTERED-COLD.stderr.log').open('wb') as err:
+        process = subprocess.Popen(command, cwd=REPO, env=env, stdout=out, stderr=err,
+                                   start_new_session=True)
+        (HERE / 'LIVE-HANDLE.json').write_text(json.dumps({'pid': process.pid, 'argv': command,
+            'cwd': str(REPO), 'utc': datetime.datetime.now(datetime.timezone.utc).isoformat()}, indent=2) + '\n')
+        while process.poll() is None:
+            seconds = time.monotonic() - started
+            members = descendants(process.pid)
+            total = sum(rss(pid) for pid in members)
+            peak = max(peak, total)
+            samples.append({'seconds': seconds, 'rss_kib': total, 'pids': sorted(members)})
+            if seconds > LIMIT_SECONDS:
+                stop = 'total_timeout'
+            if total > LIMIT_KIB:
+                stop = 'aggregate_descendant_rss'
+            if stop:
+                os.killpg(process.pid, signal.SIGKILL)
+                break
+            time.sleep(0.1)
+        code = process.wait()
+    after = hashes()
+    (HERE / 'POST-RUN-HASHES.json').write_text(json.dumps(after, indent=2) + '\n')
+    changed = sorted(k for k in before.keys() | after.keys() if before.get(k) != after.get(k))
+    result = {'status': 'PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED' if code == 0 and stop is None and not changed else 'FAIL_OR_INCOMPLETE',
+              'argv': command, 'cwd': str(REPO), 'exit': code, 'resource_stop': stop,
+              'seconds': time.monotonic() - started, 'peak_sampled_descendant_rss_kib': peak,
+              'total_timeout_seconds': LIMIT_SECONDS, 'rss_limit_kib': LIMIT_KIB,
+              'per_registered_command_timeout_seconds': 600, 'scientific_bytes_changed': changed,
+              'hash_inventory_files': len(before), 'samples': samples,
+              'scope': 'One own execution of the registered normal then optimized commands; no independent reviewer script rerun, Lean, native build or historical archive replay.'}
+    (HERE / 'BOUNDED-REGISTERED-RUN.json').write_text(json.dumps(result, indent=2) + '\n')
+    print(json.dumps({k: v for k, v in result.items() if k != 'samples'}), flush=True)
+    return 0 if result['status'].startswith('PASS_') else 1
+
+if __name__ == '__main__':
+    raise SystemExit(main())
diff --git a/research/owned-relation-independent-validation/evidence/cost/FREEZE.json b/research/owned-relation-independent-validation/evidence/cost/FREEZE.json
new file mode 100644
index 0000000000..abef8086b9
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cost/FREEZE.json
@@ -0,0 +1,135 @@
+{
+  "head": "c448d13c71908647f968b06cddb795ce7d288139",
+  "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+  "author_base": "7c472563474e60185e6ca101a17622133d047e56",
+  "selected_kappa": "15108879/5000000000",
+  "audit5241_head": "13efb5fc5f3b7c14ec2cfa181dd9eb6480972cf2",
+  "provenance": "Exact-head GitHub connector files shared by physical reviewer; price.py independently fetched by this reviewer; immutable source copied from authenticated5241 capsule and checked against5377 source pins. Main guidance from sole monitor pinned responses. Git network lazy-fetch unavailable; no ancestry claim newly established here.",
+  "files": [
+    {
+      "file": "4610-round6-ARITHMETIC.json",
+      "sha256": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de",
+      "git_blob": "0fdb65f946d557c13d8e2781b9151e2a8ddee5c3"
+    },
+    {
+      "file": "4610review-pinned.txt",
+      "sha256": "b84f833e3072cbab372fbda2ece98fbc031c15e590cf73003ddea35a5222e148",
+      "git_blob": "bf5ff049da5fa07f9bf71176dfafe3343b7ac93d"
+    },
+    {
+      "file": "4610validation-pinned.txt",
+      "sha256": "dac94ab6a32b5b8ab21282ecb25ce50e3e936196a0dfcae3d71717ceb99f3319",
+      "git_blob": "98fa64f2795dc9ba7fda012b723b6b620b153e70"
+    },
+    {
+      "file": "ACTUAL-WORD.json.gz",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e"
+    },
+    {
+      "file": "FINITE-TEMPLATE-CLOSURE.md",
+      "sha256": "3f8508c63862dd83968bd30df91b08ba5afcee1e10db15ca546cdff0caef95d9",
+      "git_blob": "9917ac5543608047fd368e5e75f0851310f53584"
+    },
+    {
+      "file": "README.md",
+      "sha256": "eb853337dfaf306808d77538e448a78f16021a2e73295078b4b2f4ff6ea835c4",
+      "git_blob": "777f4e1d5114e35ba6de2a8e818b790b16aca655"
+    },
+    {
+      "file": "RESULT.json",
+      "sha256": "1937b2e1fb4bec0fa1b0d2428a52734c554152538ac8930605bd46704f1c7320",
+      "git_blob": "27b4e5470812c2b9feaa54fbfe867b3fb68def68"
+    },
+    {
+      "file": "SOURCES.json",
+      "sha256": "eca6dd5ac3028a72e016e0c8a265be702dd6c4daf481bc009524577ff5e7c831",
+      "git_blob": "9854abbb4f66f20aad8ab5016ede8319cd47519c"
+    },
+    {
+      "file": "SPECIALIZATION.md",
+      "sha256": "70430114f744108223bc1d44b98bc25b696c4b408b7b044c2a8bbdfdb434ac5c",
+      "git_blob": "7ee84b30892f7354e1c36611f1a5e9b082dc6147"
+    },
+    {
+      "file": "TASK.json",
+      "sha256": "b9a9ace02d10791b49cf113dd6a19501b297920a29b9a4d5585e25ef4e8ef92f",
+      "git_blob": "f5df24ffe3bc51288ab57d55494b1db8684d7de9"
+    },
+    {
+      "file": "VERIFY.json",
+      "sha256": "1fc62a3afd087aa63f8d993beb1cba944b9b441824cd14e9135e792fcd45bab8",
+      "git_blob": "8098df4c806a6c6e9e2be7253ba4101744dab08d"
+    },
+    {
+      "file": "WORD.json.gz",
+      "sha256": "8d913767ad773839995e54e4d80aeff692a86687d0f78153311c8ad62b7ba1bc",
+      "git_blob": "5e79bd826c6ca1e782766ea0ae28a61d136303d1"
+    },
+    {
+      "file": "agents-initial.txt",
+      "sha256": "eb25d8ec495b80190a4b1a634710819bb74f0fae88d5203285c2b75b6f147347",
+      "git_blob": "aea5573d1b65cef7d9e08ced46d869e75da8145b"
+    },
+    {
+      "file": "autoresearch-initial.txt",
+      "sha256": "d16f0d3bb4d4b213d06c128db6d6460b0fe9ec1ac5a6c1ea1febf1db40e7b60d",
+      "git_blob": "2fe84a7b30b1e26e60ce0ec4775894eb1831c5d6"
+    },
+    {
+      "file": "compiler.py",
+      "sha256": "4ec862afb1b0c18cecebec9b04d692be37083da64814da79ad692da96fd62bb5",
+      "git_blob": "6a6f9373fe33d20e6aa7588ddcf86dde6a33a26a"
+    },
+    {
+      "file": "contributing-initial.txt",
+      "sha256": "8a49fe97e2ad088a2b2e0c5b222aaab08752783b1f9c1260790d7dd13011d215",
+      "git_blob": "fe54f23f19b082a9f8df3da9b2e205f7e230acf3"
+    },
+    {
+      "file": "controller-CONTROLLER.json",
+      "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f",
+      "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5"
+    },
+    {
+      "file": "mixed_target_probe.py",
+      "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a",
+      "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e"
+    },
+    {
+      "file": "native.py",
+      "sha256": "85d994fc5661bfa53c4b42f79955ff74ffe70072163cb02fa76cd79efbcc0c97",
+      "git_blob": "b8249ed7ba981a798ba282a6aeabd81a600bda36"
+    },
+    {
+      "file": "price.py",
+      "sha256": "e228a48de6138257da7520bb57567a275c402289c90fe7e94f0ef2ad6371f836",
+      "git_blob": "6077adf74c1a154e5f790411f774a52745eb5281"
+    },
+    {
+      "file": "priorities-pinned.txt",
+      "sha256": "7ea971a336bf526719ae1f21617038301ab95d9853a38b92c332a9ffb968297a",
+      "git_blob": "b4ece97a60dcc3a33b04d83e9f1093e60326ac4a"
+    },
+    {
+      "file": "query-thinned-RESULT.json",
+      "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f",
+      "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c"
+    },
+    {
+      "file": "selected-initial.txt",
+      "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038",
+      "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e"
+    },
+    {
+      "file": "verify.py",
+      "sha256": "c4d4fe9b74db1d47fbbfc0c602315d8256a15f0ad0e50b9fcfe2249bf65916f1",
+      "git_blob": "b19f7d0ca4a6e61a0a75595bbc413f9341e84717"
+    }
+  ],
+  "outputs": {
+    "check_cost.py": "eb66bad5d584ab29d29dd3e9f2fa7b2e71405fc1b05a659eb299c428c1332443",
+    "RESULT.json": "c35e972b649f6004fd5706d22efa4206f29240f1569b512e4c422b54cd3cae65",
+    "REPORT.md": "6c97edcbd69ffab608f6dd743071043ea53bc83687dabb82eb474229056eea03"
+  }
+}
diff --git a/research/owned-relation-independent-validation/evidence/cost/REPORT.md b/research/owned-relation-independent-validation/evidence/cost/REPORT.md
new file mode 100644
index 0000000000..aa855c967b
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cost/REPORT.md
@@ -0,0 +1,94 @@
+# Independent cost and compiler review of PR5377
+
+Static gate: **PASS for the complete invoice, directed scalar arithmetic and same-premise finite-template extension**, conditional on the separately audited COPY/zero/ownership argument and the five selected framework assumptions. This is a recommendation for one serial complete cold replay, not a selected-record update or a claim that that replay has occurred.
+
+Reviewed candidate: Ali Romman's PR5377 head `c448d13c71908647f968b06cddb795ce7d288139`, package `research/kappa-owned-relation-20261023`. Current canonical main is pinned by the sole monitor at `1ec1119972c9aefe42525172d07b332fcff81cb4`. The selected value is PR4610/PR5241 `15108879/5000000000=.0030217758`. Candidate source base is `7c472563474e60185e6ca101a17622133d047e56`; source word remains Cao Yifan's final head `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`. These three source roles are distinct.
+
+The frozen source word, round6 arithmetic, controller and supplied candidate word are identified by SHA256 and Git blob in `FREEZE.json`; `SOURCES.json` is the author's external-input manifest. Source word SHA256 is `7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05`, decompressed payload `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. Candidate word SHA256 is `8d913767ad773839995e54e4d80aeff692a86687d0f78153311c8ad62b7ba1bc`. Git network lazy-fetch was unavailable in this worker; exact-head connector materialization and authenticated source capsules were used. New canonical ancestry verification remains a root/preflight obligation.
+
+## Independently executed check
+
+`python3 -B outputs/owned-relation-5377-cost-review-20261024/check_cost.py` completed in 18.74 seconds and produced `RESULT.json` with status `PASS_INDEPENDENT_SCALAR_CENSUS_MOMENT_COMPILER_OUTER_SCREEN`.
+
+The script reads the literal candidate word and controller. It does not import either PR5377 interval engine, the candidate native verifier, or its price module. Its new directed rational engine uses an atanh logarithm series of 60 terms with a geometric tail, a 32-term positive exponential with explicit remainder and dyadic range reduction, and outward rounding to a `10^55` grid. All acceptance comparisons use fractions and integers. Only the independent PR5241 manually transcribed outer ledger function is reused, explicitly; it is frozen as `compiler.py`. Source provenance and numerical independence are separate claims.
+
+The independently derived result is:
+
+| Obligation | Result |
+| --- | --- |
+| Actual controller incidence | 16 backward full calls, 2 forward full calls, 15 thin query shears |
+| Full delta from selected PR4610 | minus 16 H1 and 16 H8 paid jobs; minus 16 H9 productive targets |
+| Complete counts | 64,372 paid jobs; 10,912 productive fields |
+| Target/paid rank masses | 239,742 / 238,990; surplus 752 |
+| Claim/tested saving | .00302235 / .00302236 |
+| Raw crossing | strict enclosure (.00302238736347,.00302238736348) |
+| Complete fixed-profile uniqueness | negative derivative on [0,.05]; negative moment on [.05,1] |
+| Charged paid ratio alpha | .999999971483293515393313955729...; below 1 minus 10^-9 |
+| Paid/completion tails gamma/delta | .9563109807264388... / .9574596897585276...; both below .97 |
+| Completion and splitting | power 1024, cutoff20, floor21, offset1/5, both charged tails and rounding pass |
+| Uniform gap | 1/700000000; uniform saving 2115651/700000000 |
+| Compiler | j=44836, H=31385200000000, N=2^H; strict integer success and preceding-grid failure |
+| Outer predicates | all 54 strict plus four functional; minimum strict slack 1/7000000000 |
+| Scalar/route allowance | backward158214, forward158120; conservative route4806000; sum below10^7 |
+| Complete raw allowance | 181098496 below10^9 |
+
+The local backward paid profile is `{1:2200,2:412,3:510,4:127,5:40,8:7}` and helper profile `{4:28,7:7,8:47,9:325}`. Forward keeps the source profiles. Full invoice reconstruction accounts for actual idle windows and diagonal main ranks, then compares to an independent substitution in the old round6 bill. The local changed scalar macros cost exactly 46 extra primitive allowances: four signed unit ADDs cost32, seven new COPY/CLEARs cost14. Across16 backward occurrences the scalar difference is736. No productive L230 output is credited. For 0<t<1, strict concavity gives `1+8^t>9^t`, so the full moment gain is `16(1+8^t-9^t)>0`.
+
+The global crossing screen is stronger than a positive sample at the claim: the derivative upper bound is below -195778.63 throughout[0,.05], and the remaining interval moment upper bound is below -6836.54. The integer grid result is a threshold for this sufficient compiler inequality, not an optimum over compilers. The concavity of `log(step*j+1)-j*log(2)/1000` gives one positive crossing, making the adjacent integer tests a valid minimum on that particular grid.
+
+Four independently applied ledger controls reject insufficient old BIT saving .0027, a closed uniform gap, charging the tested endpoint as the final claim, and epsilon=1. Productive-credit fraud is excluded by the literal census, which omits owned L230 in backward calls before assembling the full invoice. Physical review owns the separate candidate native controls.
+
+## Constructive extension of selected5241 precision and tape specialization
+
+This section supplies an implication from the selected generic contracts, rather than adding a candidate-specific premise that the new syntax is cheap. The pinned selected PR5241 `SPECIALIZATION.md` sections1,4–6 and `FINITE-TEMPLATE-CLOSURE.md` sections2–5 explicitly cover a fixed finite scalar/owned-storage program, all-column free-word evaluation, whole completed jobs, distinct suspended banks, fresh semantic constants and fixed-tape execution. They do not limit the permitted owner list to the original one center.
+
+The changed scalar instructions belong to precisely that alphabet. Four additions have coefficients plus or minus one and same exact physical frame. COPY and CLEAR act on proved owned fields. Identity on a row proved identically zero has no physical instruction; its new chart is justified by the physical review. No new monomial or phase recipe enters. Every retained paid factor, warp and main chart can therefore use the selected5241 phase-bearing catalogue and171/342 primitive-record bound. The changed algorithm contains no new gather primitive or movement exponent.
+
+The extra local scalar tariff and routes are freshly charged. Conservative routing retains every old408-helper wrapper, all old local paid jobs at their maximum direction,240 warps and448 main charts, and adds four route groups for two newly owned lifetimes. Thus the candidate does not obtain a lower tariff by relabeling L230 owned. The raw program needs one additional physical slot C1; L230 occupies its former slot. At the controller level, each backward full occurrence has three owned banks(C0,C1,L230), each forward full occurrence one(C0):50 LOCAL banks in the deliberately conservative disjoint allocation, plus the source's separately charged query, completion and compiler banks. This50 is a raw controller count, not the final expanded bank count.
+
+Now fix the candidate mixed word, the1024-fold product, charged completion/splitting, and the finite compiler at N=2^31385200000000, before allowing multiplication input width to grow. Run the retained finite emission/allocation algorithm on this new word. Define its own W as full productive arrays, P as rank-one children, and O as all physical owned banks. In counting O, allocate three banks for every instantiated backward local occurrence and one for each forward local occurrence; count all query, completion, splitting and compiler banks in addition. More conservatively, three times all LOCAL occurrences plus those additional source banks suffices. Every simultaneously suspended occurrence has a distinct bank. No factor of O contributes productive output credit, and no single-bank-per-depth reuse is allowed.
+
+Let R count every actual movement/native/normalizer/route record in the final expanded word. Define G by summing the fresh scalar primitive allowances, adding the selected conservative unit-phase charge8 per non-scalar and normalization record throughout the expanded word. The four new unit ADDs add at most four logarithmic height units per local occurrence and are already dominated by their32 primitive allowances; COPY/CLEAR add zero height but retain their14 execution allowances. Frame permutations and unit phases add no magnitude/denominator height, while retaining their movement cost in R. This is a finite algorithm for new integers W,P,O,R,G; it does not reuse an old raw or expanded cap. The old formal prefix L1/denominator numbers are optional corroboration, not a replacement for this semantic charge.
+
+Substitute these **new** integers into the unchanged source prescription:
+
+```
+Z = W+O
+E = 64*(Z+N+P+G+1)^3
+B = P+E
+C0 = 32*N*B^2
+C1 = 1
+```
+
+For positive integer N and nonnegative W,P,O,G with W>=1, putting S=Z+N+P+G+1 gives
+`2GZ^2+8P+4Z+4+32N <= 2S^3+48S <64S^3=E`.
+The same completed-child estimate then gives `A(e)<=A(floor(e/N))+P*floor(e/N)+E`, and induction yields `A(e)<=2Be`; the layer envelope is below C0*d. Correlated owned values do not weaken this norm bound: each child finishes before its parent resumes, each COPY duplicates a complete same-frame value, and permitted CLEAR deletes an owned value. No rounded or compressed child return is introduced.
+
+With this new W, use the unchanged source ordinary stock rule `q0=ceil(log2 W)*D(d)` and whole row factor at least W^D(d). O changes the fixed storage multiplier and parking passes. Simultaneous BIT and complex stocks must retain their product; taking their maximum is not licensed. The existing strict functional stock predicates are recomputed here at the candidate outer parameters. The fixed number of tapes, matrices and routing recipes uses new W,P,O,R,N. Its setup degree and coefficients may increase, but remain fixed before input growth and are absorbed by the same retained superpolynomial record fiber once epsilon<1. The new eventual threshold must use the new C0 and setup degrees. For example the source constructive fine-grid prescription with epsilon=a/b uses bitlength L of4*C0*ceil(c), t=max(4,ceil(bL/(b-a))), p0=2^t. There is no claim that old p0 or an old numerical template-size cap still applies.
+
+The independently passing alpha/tail/shifted-exit/eta/logarithmic-majorant/integer inequalities supply the retained mixed-target compiler's numerical premises for the changed bill. The old controller Laurent identity and main endpoint/chronological commutation argument remain source-identical; the physical reviewer separately checks the changed local endpoints and disjoint helper-bank interpretation. The ordinary BIT interface is unchanged with admitted saving.0034. Its authenticated conversion/stock is reused; it is not re-proved by this complex screen. All54+4 outer inequalities are freshly satisfied using C1=1 justified above.
+
+Thus the candidate's changes fit the same five selected contracts: native_all_columns, owned_erasure, compiler, precision_tape, analytic_recovery. This establishes the required generic specialization extension under those assumptions, while preserving the remaining physical/analytic theorem assumptions themselves. It neither materializes the enormous compiled word nor independently executes fixed-tape precision or integer recovery.
+
+## Remaining gate and complete obligation map
+
+| Obligation | Coverage and disposition |
+| --- | --- |
+| Exact source/head/bytes | Frozen connector bytes and source capsules; root must finish canonical ancestry/working-byte preflight |
+| Three row identities and tensor/free-word lift | Separate physical reviewer; not inferred from this invoice |
+| COPY frame/gauge and zero physical identity | Separate physical reviewer; prerequisite for replacing the two jobs |
+| Ownership, all retained arbitrary entries, private return | Separate physical reviewer; all three owned backward fields required |
+| Retained native/paid phases | Source-identical selected5241 catalogue applies; final all-phase foundation audit is separately coordinated by root |
+| p16 calls/idle/main/helper census | Fresh literal reconstruction here and physical review bank-incidence crosscheck |
+| Original main controller endpoint | Source-identical Laurent and boundary proof reused; cold registered replay also recomputes it |
+| Root, positive gain and fixed-profile ceiling | Fresh directed scalar check here |
+| Completion, reserve, splitting and tails | Fresh directed scalar check here |
+| Compiler height and uniform gap | Fresh exact rational/integer check here |
+| Additional scalar/storage/routes | Fresh raw bill and constructive new expanded constants above |
+| All-size precision, stock and fixed tapes | Same-premise constructive extension above; original physical assumptions retained |
+| BIT and outer transfer | BIT source reuse, fresh conversion domain and54+4 arithmetic here; original analytic/recovery assumptions retained |
+| Negative controls and emitted artifacts | Independent ledger controls here; physical controls separately; author complete registered normal/optimized cold replay still outstanding |
+
+Recommended next action: ONE serial complete registered cold replay after the physical gate and closed export are ready. `VERIFY.json` registers `python3 -B research/kappa-owned-relation-20261023/verify.py` and then `python3 -O -B research/kappa-owned-relation-20261023/verify.py`, each with600-second timeout, standard-library Python3.12. The standard package command is `python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023`. An export must preserve the9 exact input paths; only the small pure modules are loaded by that verifier. Do not run Lean, Docker or historical suites as a substitute. An author replay supplements these independent checks; its PASS alone would not prove the above applicability argument.
+
+No selected record, repository source, public post or Lean state was changed by this worker. Outputs are local review evidence only. Credit remains with Ali Romman for the changed relation/word, Cao Yifan for PR4610, Cinna Davis for the controller/helper lineage, zxv for native/compiler/precision machinery, Jacob Alan Sussman for mixed-target recursion, Chris R/Clear1nsight for PR5241 independent admission and all attributed physical/BIT/analytic predecessors. This review used substantial OpenAI Codex assistance and makes no independent-human acceptance claim.
diff --git a/research/owned-relation-independent-validation/evidence/cost/RESULT.json b/research/owned-relation-independent-validation/evidence/cost/RESULT.json
new file mode 100644
index 0000000000..5975458889
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cost/RESULT.json
@@ -0,0 +1,144 @@
+{
+  "H": 31385200000000,
+  "away_moment_upper": "-34182747710376247990167913998096796602246940868624236327091/5000000000000000000000000000000000000000000000000000000",
+  "capacity": {
+    "eta": true,
+    "height_domain": true,
+    "height_encoding": true,
+    "initial_range": true,
+    "integer_success": true,
+    "normalized": true,
+    "preceding_grid_fails": true,
+    "shifted_exits": true,
+    "split": true,
+    "tail_block": true,
+    "total_tails": true
+  },
+  "controls": {
+    "closed_epsilon": [
+      "epsilon_below_one",
+      "global_gamma_power_slack",
+      "actual_logarithmic_gamma_guard",
+      "source_axis_superpolynomial",
+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
+    ],
+    "closed_uniform": [
+      "new_complex_uniform_saving_above_b"
+    ],
+    "old_BIT": [
+      "actual_bit_above_effective"
+    ],
+    "unfunded_endpoint": [
+      "main_transform_above_kappa",
+      "global_coordinate_router_above_kappa",
+      "fused_gaussian_above_kappa",
+      "group_bit_router_above_kappa",
+      "boundary_algebraic_matrix_above_kappa"
+    ]
+  },
+  "derivative_upper": "-97889315019420058207499976618782634130619638823734973271109/500000000000000000000000000000000000000000000000000000",
+  "eta": [
+    "1019635281556829958140945025847885756850714643749/5000000000000000000000000000000000000000000000000000000",
+    "163141645049092793302551204135661721096114343/800000000000000000000000000000000000000000000000000"
+  ],
+  "expanded_word_materialized": false,
+  "gain": "2871/5000000000",
+  "gap": "1/700000000",
+  "head": "c448d13c71908647f968b06cddb795ce7d288139",
+  "independent_native_replay": false,
+  "j": 44836,
+  "kappa": "60447/20000000",
+  "local_routes": 4806000,
+  "local_scalar": {
+    "backward": 158214,
+    "forward": 158120
+  },
+  "normalized": "2097152001953127/2097154147483648",
+  "outer_functional_count": 4,
+  "outer_min": "1/7000000000",
+  "outer_strict_count": 54,
+  "paid": {
+    "1": 41282,
+    "16": 448,
+    "2": 7416,
+    "24": 448,
+    "3": 9180,
+    "32": 448,
+    "4": 2286,
+    "40": 448,
+    "48": 448,
+    "5": 720,
+    "56": 448,
+    "64": 448,
+    "72": 224,
+    "8": 128
+  },
+  "rank_masses": [
+    239742,
+    238990
+  ],
+  "ratios": {
+    "alpha": [
+      "4999999857416467576966569778645527061954322982193192739/5000000000000000000000000000000000000000000000000000000",
+      "9999999714832935153933139557291054123908645964386386073/10000000000000000000000000000000000000000000000000000000"
+    ],
+    "delta": [
+      "9574596897585276619213348515125306962597456984954143379/10000000000000000000000000000000000000000000000000000000",
+      "9574596897585276619213348515125306962597456984954143719/10000000000000000000000000000000000000000000000000000000"
+    ],
+    "gamma": [
+      "9563109807264388476183966069110939186746956808613120029/10000000000000000000000000000000000000000000000000000000",
+      "38252439229057553904735864276443756746987827234452483/40000000000000000000000000000000000000000000000000000"
+    ]
+  },
+  "raw": 181098496,
+  "root": [
+    "302238736347/100000000000000",
+    "75559684087/25000000000000"
+  ],
+  "root_signs": [
+    [
+      "1654180864758140801638144271742026171376018367/1250000000000000000000000000000000000000000000000000000",
+      "3308361729516281603276288543484052342785913733/2500000000000000000000000000000000000000000000000000000"
+    ],
+    [
+      "-45934963440687655168371536193650439131625933/40000000000000000000000000000000000000000000000000000",
+      "-5741870430085956896046442024206304891381449293/5000000000000000000000000000000000000000000000000000000"
+    ]
+  ],
+  "scope": "Finite scalar/census check. Physical replacement and all-f specialization reviewed separately; same five conditional assumptions retained. Raw bound is not an expanded precision/storage bound.",
+  "seconds": 18.739914530015085,
+  "sha256": {
+    "4610-round6-ARITHMETIC.json": "b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de",
+    "ACTUAL-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+    "README.md": "eb853337dfaf306808d77538e448a78f16021a2e73295078b4b2f4ff6ea835c4",
+    "RESULT.json": "1937b2e1fb4bec0fa1b0d2428a52734c554152538ac8930605bd46704f1c7320",
+    "SOURCES.json": "eca6dd5ac3028a72e016e0c8a265be702dd6c4daf481bc009524577ff5e7c831",
+    "SPECIALIZATION.md": "70430114f744108223bc1d44b98bc25b696c4b408b7b044c2a8bbdfdb434ac5c",
+    "WORD.json.gz": "8d913767ad773839995e54e4d80aeff692a86687d0f78153311c8ad62b7ba1bc",
+    "compiler.py": "4ec862afb1b0c18cecebec9b04d692be37083da64814da79ad692da96fd62bb5",
+    "controller-CONTROLLER.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f",
+    "native.py": "85d994fc5661bfa53c4b42f79955ff74ffe70072163cb02fa76cd79efbcc0c97",
+    "price.py": "e228a48de6138257da7520bb57567a275c402289c90fe7e94f0ef2ad6371f836",
+    "verify.py": "c4d4fe9b74db1d47fbbfc0c602315d8256a15f0ad0e50b9fcfe2249bf65916f1"
+  },
+  "status": "PASS_INDEPENDENT_SCALAR_CENSUS_MOMENT_COMPILER_OUTER_SCREEN",
+  "targets": {
+    "145": 224,
+    "17": 448,
+    "25": 448,
+    "33": 448,
+    "4": 504,
+    "41": 448,
+    "49": 448,
+    "57": 448,
+    "65": 448,
+    "7": 126,
+    "73": 224,
+    "8": 846,
+    "9": 5852
+  },
+  "tested": "75559/25000000",
+  "uniform_saving": "2115651/700000000"
+}
diff --git a/research/owned-relation-independent-validation/evidence/cost/pr-pinned.json b/research/owned-relation-independent-validation/evidence/cost/pr-pinned.json
new file mode 100644
index 0000000000..17bf5dc372
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/cost/pr-pinned.json
@@ -0,0 +1,55 @@
+{
+  "content": [
+    {
+      "type": "text",
+      "text": "Action completed."
+    }
+  ],
+  "structuredContent": {
+    "pull_request": {
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+      "number": 5377,
+      "state": "open",
+      "merged": false,
+      "mergeable": true,
+      "draft": false,
+      "body": "This construction gives **conditional κ = 60447/20000000 = 0.00302235**, a gain of **0.0000005742** over Cao Yifan's final [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610) value, 0.0030217758. It changes the complete paid profile and moves its raw crossing. The selected frontier is unchanged.\n\nThe [proof and complete bill](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/README.md), [exact result](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/RESULT.json), [literal word](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/WORD.json.gz) and [source pins](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/SOURCES.json) define the review scope.\n\nIn each backward call, make L230 private and prepare `h230 = h324 - h326 - h328 + h333` from four arbitrary cold helpers. Debit its rank-nine productive output. Let `Delta = h230 - h324 + h326 + h328 - h333`. Exact replay of the unrestricted source gives `C0 - saved_L92 = Delta/4` at center event 11332, and `L92 = -Delta/4` at climb event 15584. The saved value is taken just after event 11205 in the same frame as the center output. Under the prepared relation, one owned copy replaces the rank-eight job, and physical identity on a proved zero row replaces the rank-one job. All event indices are zero-based.\n\nAll 224 main inputs and the other 407 backward helper inputs remain arbitrary and independent. Every retained output keeps its complete source operator. Forward calls keep all 408 helpers. Explicit clears remove arbitrary owned entry values and erase every private output. One new private slot and 46 additional scalar operations per backward call are charged. Every retained Gaussian operator, native map, frame gauge and main adapter is unchanged.\n\nThe p16/a7 controller has 16 backward calls, two forward calls and 15 query shears. Its complete difference is **−16 H1 −16 H8 paid jobs and −16 H9 targets**. For every `0<t<1`, the target-minus-paid moment gains `16(1+8^t−9^t)>0`. The new bill has **64,372 paid jobs, 10,912 productive fields and rank surplus 752**, with every main, idle, query and completion term included.\n\nTwo rational interval engines check the complete bill. The fixed-profile crossing lies in **(0.00302238736347, 0.00302238736348)**. The claimed κ leaves more than **0.00000003736347** raw headroom. The separately tested saving is 0.00302236. Both completion tails, the finite compiler at `N=2^31385200000000`, and all **54 strict plus four functional outer predicates** pass. The complete raw nonrecursive bound remains **181,098,496 < 10^9**.\n\nBase: canonical main [7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56), priority revision 7. The source is the final [PR #4610 word](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz) at `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`; all consumed bytes are in the recorded main base. The [scoped Discussion claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737) distinguishes this changed inventory from the original-input cache and all-helper-return investigations. Live PRs and Discussions were checked again before publication.\n\nUse standard-library Python 3.12 from the repository root:\n\n```sh\npython3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023\n```\n\nBoth registered normal and optimized replays pass:\n\n```text\nPASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION\n```\n\nVerification covers exact free-word rows in both source and candidate orientations, all independent and owned entry columns, frame/rank checks, two separately computed source identities, the p16 Laurent factorization and scalar boundaries, independent full invoice counts, two rational interval engines, the fixed-profile ceiling, compiler and outer inequalities. Seven native and five cost/outer controls reject wrong relation, ownership, snapshot, gauge, rank, helper credit and compiler assumptions. Metadata, committed-byte checks, official export integrity and Git-free replay also pass. The optional full-history preflight is not claimed in this shallow checkout.\n\nThe [source absolute-phase receipt](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz) is authenticated and reused. New operations are same-frame scalar operations, owned copies/clears and identity on zero; there is no new Gaussian phase recipe. Full source phase lowering, BIT native replay, Lean, Docker, physical tape/precision execution, analytic decomposition and integer recovery were not rerun. The bound retains the source permitted-erasure, whole-job, mixed-target all-size, native, precision, tape, analytic, prime and exact-recovery contracts. It is a conditional construction with exact finite evidence, not an unconditional theorem, practical speedup or independent human acceptance. The compiled word is algorithmically specified and not materialized.\n\nCao Yifan supplied the source construction and prior κ in [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610). Cinna Davis supplied the p16 controller and helper lineage in [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470). The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py) retains zxv's completion/compiler and Jacob Alan Sussman's mixed-target credit; Dugongue's transported frames and the wider native lineage remain credited. zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283) supplied the cache-contract handoff to find actual matching rows and lifetimes; its standalone example is not used here. The new result is this helper relation, its exact native realization and its complete positive bill.\n\nPrepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. Next review task: check the three source rows and COPY/zero argument, then the inherited transfer assumptions. No broader helper-relation search is claimed.\n",
+      "title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation",
+      "base": "main",
+      "base_sha": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+      "head": "codex/kappa-owned-relation-20261023",
+      "head_sha": "c448d13c71908647f968b06cddb795ce7d288139",
+      "head_repo_id": 1413892976,
+      "head_repo_full_name": "aliromman/integer-mult-bounds",
+      "merge_commit_sha": "08e75e22ae4d39e8e3bcfafab789aa349c0ecfe6",
+      "user": {
+        "login": "aliromman",
+        "name": "aliromman",
+        "email": null,
+        "avatar_url": "https://avatars.githubusercontent.com/u/226877337?v=4",
+        "id": 226877337
+      },
+      "requested_reviewers": null,
+      "requested_team_reviewers": null,
+      "diff": "@@ -0,0 +1,249 @@\n+# Conditional kappa 0.00302235 from one owned helper relation\n+\n+This construction gives **conditional kappa = 60447/20000000 = 0.00302235**.\n+The gain over Cao Yifan's final\n+[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+value, 0.0030217758, is **2871/5000000000 = 0.0000005742**.\n+The construction changes the complete paid profile. It does not obtain the\n+gain by taking more digits of the old root.\n+\n+One helper becomes owned storage in each backward call. A prepared relation\n+then makes one paid rank-eight center equal to an earlier saved value. The same\n+relation makes one later rank-one job act on zero. Both jobs can be removed,\n+with the rank-nine helper credit also removed. All other independent outputs\n+and all main interfaces keep their source operators.\n+\n+[WORD.json.gz](WORD.json.gz) is the complete emitted word.\n+[RESULT.json](RESULT.json) records the exact native checks, the two source\n+identities, both full profiles, completion, compiler and outer calculations.\n+[SOURCES.json](SOURCES.json) pins every external input by Git blob and SHA256.\n+The proof below explains why the changed word has the stated contract.\n+\n+## Source and scope\n+\n+The base is canonical main\n+[7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56).\n+The native source is the final PR #4610 word at\n+[20bb93cd990d2ff683e4d0fc56b87a42cd5d3296](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz).\n+Its decompressed SHA256 is\n+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.\n+The comparison value and old crossing come from its\n+[final compiler arithmetic](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json).\n+All consumed bytes are already in the recorded main base.\n+\n+This is one instance of the current `complex-new-helper-inventory` priority.\n+The [scoped claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737)\n+reserves only the relation and two replacements below.\n+[Discussion #5355](https://github.com/CrocSwap/integer-mult-bounds/discussions/5355)\n+retains all 632 independent inputs and all eight centers.\n+[Discussion #4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930)\n+retains every original helper endpoint. This construction removes the\n+independent L230 job in backward calls. It does not claim those broader scopes.\n+The selected certificate is unchanged. A fresh check at 20:20 UTC found that\n+Discussion #5355 had released its original-input scope without a saving.\n+Canonical main still had the recorded base commit.\n+\n+## Exact replacement proof\n+\n+All indices below are zero-based indices in the frozen backward program.\n+Let `h_r` be the source logical input of helper `Lr`. The five helpers in\n+\n+```math\n+\\Delta=h_{230}-h_{324}+h_{326}+h_{328}-h_{333}\n+```\n+\n+all start in frame 0 and finish in frame 1, of rank nine. The new backward\n+contract has 224 independent main fields and 407 independent helper fields.\n+L230 is private. Clear it, then use four same-frame ADDs to prepare\n+\n+```math\n+h_{230}=h_{324}-h_{326}-h_{328}+h_{333}.\n+```\n+\n+The other helper inputs remain arbitrary and independent. This preparation\n+sets Delta to zero for every input. It uses no recursive job. It removes one\n+rank-nine productive target; the dependent field receives no output credit.\n+\n+Run the original source program on unrestricted inputs. Let `q` be the\n+logical row of L92 just after event 11205, a paid climb into frame 254.\n+The separate predecessor row engine gives these exact identities:\n+\n+| Source position | Exact logical row |\n+| --- | --- |\n+| C0 at the rank-eight center, event 11332 | `q + Delta/4` |\n+| L92 at the rank-one climb, event 15584 | `-Delta/4` |\n+\n+These identities are over rational coefficients and free native operator\n+words. They hold for every value of every source input and for every invertible\n+interpretation of the native symbols. They do not use numerical samples or an\n+assumed relation between distinct native maps.\n+\n+For every positive tensor width f, substitute each native generator by its\n+source operator tensor power and each inverse by the inverse tensor power.\n+This defines a representation of the free group. Keep the rational scalar\n+coefficients outside the substitution. The two row identities therefore hold\n+at every such width. In particular, Delta/4 remains a scalar linear form; it\n+is not a tensor power of that sum. This uses the termwise argument recorded in\n+the [free-word tensor audit](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/free-word-tensor-lift-audit/PROOF.md),\n+which credits Cinna Davis's proposal and ToikY's scoped audit. Physical frame\n+realization and the complete all-size compiler retain their source contracts.\n+\n+Immediately after event 11205, clear a new private field C1 in frame 254 and\n+COPY L92 into it. C1 is not written until the replacement of event 11332. At\n+that event, clear owned C0, set its frame to 254, COPY C1 into C0, then clear C1.\n+The copy coefficient is exactly one. Under Delta = 0, the copied field is the\n+same physical value as the old center output: the logical rows and the exact\n+frame gauge are equal. The old C0 input can be erased because C0 is owned.\n+This removes one rank-eight recursive job.\n+\n+At event 15584, L92 is exactly zero in every input column. The physical\n+identity therefore has the same result as the old rank-one frame change.\n+`zero_retag` records this fact. It performs no physical write and is accepted\n+only when the full exact row is empty and the current frame is 254. It then\n+records frame 1. This removes one rank-one recursive job. It does not erase a\n+main input or replace a nonzero transform with a free frame change.\n+\n+Every other event stays in source order. Clear private L230 at return. The\n+source clears C0, and the new program has already cleared C1. The original\n+linear endpoint identity, restricted by the prepared relation, gives all 224\n+main outputs and all 407 retained helper outputs. The literal new-word replay\n+checks these outputs separately, with all 631 retained inputs and all three\n+owned entry fields initially arbitrary. It also checks every scalar frame,\n+paid rank, native frame transition and final frame.\n+\n+The 4,429 source frames, 72 native maps, all remaining paid operators, and main\n+adapters are unchanged. The source\n+[absolute-phase certificate](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz)\n+is authenticated and reused. Same-frame COPY and identity on zero introduce no\n+phase recipe. The source's amplitude and Clifford-lowering checks are not\n+rerun by this package. The new free-word identities prove equivalence for the\n+source operators with their full phases, not just their projective classes.\n+\n+## Complete cost and conditional compiler\n+\n+The forward word is unchanged. Each backward call has these counts:\n+\n+```text\n+paid:    {1:2200, 2:412, 3:510, 4:127, 5:40, 8:7}\n+helpers: {4:28, 7:7, 8:47, 9:325}\n+```\n+\n+The full p16/a7 controller contains 16 backward calls, two forward calls and\n+15 query shears. Thus the complete difference is **minus 16 H1 and 16 H8 paid\n+jobs, and minus 16 H9 productive targets**. It includes every idle and main\n+target. There are 64,372 paid jobs and 10,912 productive fields. Their rank\n+masses are 238,990 and 239,742; the surplus remains 752.\n+\n+For every real `0 < t < 1`, the complete target-minus-paid moment increases by\n+\n+```math\n+16(1+8^t-9^t)>0.\n+```\n+\n+For a direct proof, both `(1/9)^t > 1/9` and `(8/9)^t > 8/9`; multiply their\n+sum by `9^t`. The improvement is strict throughout the required range.\n+\n+The backward word has 158,214 real scalar operations under the source macro\n+allowance, exactly 46 more than its source. Its maximum formal prefix L1 norm\n+is 169, with maximum denominator 64; both equal the source bounds. The forward\n+bounds remain 457 and 32. One extra physical private slot holds C1. L230 uses\n+an existing slot. The route bound also charges two routes for each of the two\n+new owned lifetimes. The local scalar-plus-route bound stays below 10^7, and\n+the complete raw nonrecursive bound stays **181,098,496 < 10^9**. Preparation,\n+COPY, CLEAR and storage therefore do not introduce an unpaid recursive cost.\n+\n+Two rational interval engines check the complete moment. Its unique crossing\n+in `0 < kappa < 1` lies in\n+**(0.00302238736347, 0.00302238736348)**. The verifier proves the moment decreases\n+on `[0,0.05]` and remains negative on `[0.05,1]`. This is a ceiling for this\n+fixed complete profile, not an optimum over circuits or helper relations.\n+The claimed kappa leaves more than **0.00000003736347** raw headroom.\n+\n+The separately tested saving is 0.00302236. The paid/target ratio is below\n+`0.999999971483293515393313955730`, with reserve `1e-9`. Both charged tails are\n+below `0.97`. The source power 1024, cutoff 20, floor 21, tail offset 1/5,\n+complement factor 63/64 and logarithm power 1000 still pass. The compiler gap\n+is `1/700000000`, with `j=44836`, `H=31385200000000` and `N=2^31385200000000`.\n+The exact integer test `(H+1)^1000 < 2^44836` passes; the preceding grid integer\n+fails. The uniform complex saving is `2115651/700000000`. All 54 strict outer\n+predicates and four functional predicates pass, using the retained ordinary\n+BIT saving 0.0034.\n+\n+## Verification and reproduction\n+\n+Use Python 3.12 or 3.14, with the standard library only. From the repository root:\n+\n+```sh\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023 --check-only\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023\n+```\n+\n+The registered commands run normal and optimized Python. The direct command,\n+also used for a Git-free export, is:\n+\n+```sh\n+python3 -B research/kappa-owned-relation-20261023/verify.py\n+python3 -O -B research/kappa-owned-relation-20261023/verify.py\n+```\n+\n+Each prints status\n+`PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION`.\n+The verifier reconstructs the word and compares its bytes and exact result with\n+the published artifacts. `--write` is a separate authoring command. It changes\n+only this package's word and result after all checks pass.\n+\n+Fresh checks cover both source words, both candidate words, every independent\n+entry column and owned return, the two unrestricted source identities, retained\n+phase bindings, the p16 rational Laurent factorization, both scalar boundary\n+programs, two complete invoice counts, two rational interval engines, the fixed\n+profile ceiling, completion, compiler, BIT conversion and all outer predicates.\n+The emitted word replaces the old single `canonical.local_profile` metadata\n+field with explicit `paid_profiles` for the two directions.\n+\n+Seven native controls reject a wrong relation sign, omitted input clear, wrong\n+snapshot, wrong zero frame, wrong paid rank, wrong copy gauge, and omitted\n+output clear. Five cost/outer controls reject the lost helper's output credit,\n+old BIT stock, closed uniform gap, unfunded endpoint and closed epsilon.\n+\n+Normal and optimized registered replays passed on CPython 3.12.14. The direct\n+author check also passed on CPython 3.14. Source metadata and pins passed.\n+The optional full-history preflight is not claimed in the shallow checkout.\n+The publication handoff records export and committed-byte checks.\n+\n+The full source phase lowering, BIT native replay, Lean, Docker, physical tape\n+execution, numerical precision execution, analytic decomposition and integer\n+recovery are not rerun here. The complete bound retains those predecessor\n+contracts, including permitted owned erasure, whole-job normalizers, mixed\n+productive-target recursion and all-size closure. The expanded compiled word\n+is specified by a finite algorithm, not materialized. This is a conditional\n+construction with exact finite evidence, not an unconditional multiplication\n+theorem, a practical timing result or independent human acceptance.\n+\n+## Credit\n+\n+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.\n+Cao Yifan's [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+supplies the exact source word, phase evidence and previous compiler value.\n+Cinna Davis's [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470)\n+supplies the p16 controller and helper-interface lineage. The source code keeps\n+credit for Dugongue's transported frames, zxv's native and finite-compiler\n+work, Jacob Alan Sussman's mixed-target recursion and their predecessors.\n+The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py)\n+and [literal native source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-rebuild/complex/native_extensions.py)\n+are pinned as provenance for the adapted checks.\n+\n+zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283)\n+supplies the related cache contract and the explicit handoff to find actual\n+matching rows and their lifetimes. Its standalone cache example is not part of\n+this word. The new contribution is the five-helper relation, its actual cache\n+and zero identities, the full owned-field replacement and the complete positive\n+bill. No priority is claimed for the general cache or paid-history ideas.\n+\n+## Open next questions\n+\n+Independent review should first check the three source rows and the physical\n+COPY/zero argument above, then the retained all-size and phase premises.\n+A later construction could test a different helper relation, but it must claim\n+a disjoint scope and pay every lost target and owned field. This package does\n+not classify such relations. [TASK.json](TASK.json) records the first steps,\n+relevance and blockers for both questions.\n@@ -0,0 +1,373 @@\n+{\n+  \"arithmetic\": {\n+    \"compiler\": {\n+      \"H\": 31385200000000,\n+      \"N\": \"2^31385200000000\",\n+      \"eta\": {\n+        \"lower\": \"0.000000203927056311365991628189\",\n+        \"upper\": \"0.000000203927056311365991628190\"\n+      },\n+      \"gap\": \"1/700000000\",\n+      \"integer_test_exponent\": 44836,\n+      \"logarithm_power\": 1000,\n+      \"theta\": \"63/64\",\n+      \"uniform_saving\": \"2115651/700000000\",\n+      \"word_materialized\": false\n+    },\n+    \"fixed_profile_ceiling\": {\n+      \"decreasing_through\": \"1/20\",\n+      \"derivative_upper\": {\n+        \"lower\": \"-195778.630038840116414999953237565269\",\n+        \"upper\": \"-195778.630038840116414999953237565268\"\n+      },\n+      \"remaining_interval_moment_upper\": {\n+        \"lower\": \"-6836.549542075249598033582799619360\",\n+        \"upper\": \"-6836.549542075249598033582799619359\"\n+      }\n+    },\n+    \"full_backward\": 16,\n+    \"full_forward\": 2,\n+    \"gain_over_PR4610\": \"2871/5000000000\",\n+    \"kappa\": \"60447/20000000\",\n+    \"kappa_decimal\": \".00302235\",\n+    \"margin_at_previous_kappa\": {\n+      \"lower\": \"0.151161494385402651700356241377\",\n+      \"upper\": \"0.151161494385402651700356241378\"\n+    },\n+    \"margin_at_previous_root_upper\": {\n+      \"lower\": \"0.151143999513185007311808491175\",\n+      \"upper\": \"0.151143999513185007311808491176\"\n+    },\n+    \"negative_controls\": {\n+      \"closed_epsilon\": [\n+        \"epsilon_below_one\",\n+        \"global_gamma_power_slack\",\n+        \"actual_logarithmic_gamma_guard\",\n+        \"source_axis_superpolynomial\",\n+        \"gaussian_above_main\",\n+        \"new_semantic_guard_with_C1_one\"\n+      ],\n+      \"closed_uniform\": [\n+        \"new_complex_uniform_saving_above_b\"\n+      ],\n+      \"old_BIT\": [\n+        \"actual_bit_above_effective\"\n+      ],\n+      \"unearned_helper_credit\": \"Rejected by the independent complete census\",\n+      \"unfunded_endpoint\": [\n+        \"main_transform_above_kappa\",\n+        \"global_coordinate_router_above_kappa\",\n+        \"fused_gaussian_above_kappa\",\n+        \"group_bit_router_above_kappa\",\n+        \"boundary_algebraic_matrix_above_kappa\"\n+      ]\n+    },\n+    \"nonrecursive\": {\n+      \"additional_private_slots\": 1,\n+      \"local_routes\": 4806000,\n+      \"local_scalar\": 158214,\n+      \"owned_slots_backward\": 3,\n+      \"raw_budget\": 1000000000,\n+      \"raw_scalar_upper\": 181098496\n+    },\n+    \"ordinary_BIT\": {\n+      \"admitted\": \"17/5000\",\n+      \"after_cover\": \"69/20000\",\n+      \"atom\": \"1/250\",\n+      \"before_cover\": \"3459/1000000\",\n+      \"ordinary_saving\": \"8590884599/2500000000000\",\n+      \"prime_rule\": \"odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses\"\n+    },\n+    \"outer\": {\n+      \"functional_checks\": {\n+        \"actual_new_BIT_stock_sublinear\": \"174299999253/175000000000\",\n+        \"fixed_halo_explicit_metadata_branch\": \"13475000001/175000000\",\n+        \"new_BIT_row_stock_sublinear_in_active_group\": \"697899997009/700000000000\",\n+        \"new_semantic_group_guard\": \"3/700000000\"\n+      },\n+      \"margins\": {\n+        \"boundary_algebraic_matrix\": \"23139910904443/7656250000000000\",\n+        \"fused_gaussian\": \"23139910838329/7656250000000000\",\n+        \"global_coordinate_router\": \"2115649/700000000\",\n+        \"group_bit_router\": \"1480954993653053/490000000000000000\",\n+        \"group_scans\": \"349999999/350000000\",\n+        \"main_transform\": \"23139899966943/7656250000000000\",\n+        \"microbox_face_corrections\": \"13475000001/175000000\",\n+        \"polynomial_products\": \"699999999/700000000\",\n+        \"sparse_union_movement\": \"3133491473404443/7656250000000000\"\n+      },\n+      \"parameters\": {\n+        \"a\": \"2115649/700000000\",\n+        \"b\": \"42313/14000000\",\n+        \"beta\": \"699999997/700000000\",\n+        \"bit_saving\": \"17/5000\",\n+        \"cap_xi\": \"6961616462466943/7656250000000000\",\n+        \"complex_uniform_saving\": \"2115651/700000000\",\n+        \"d\": \"1/700000000\",\n+        \"epsilon\": \"699999999/700000000\",\n+        \"kappa\": \"60447/20000000\",\n+        \"lambda_\": \"199395529/200000000\",\n+        \"lambda_prime\": \"10904443/10937500\",\n+        \"layout\": \"1/700000000\",\n+        \"q\": \"33057/10937500\",\n+        \"r0\": \"1/7000000000\",\n+        \"stop\": \"1/700000000\",\n+        \"tested_saving\": \"75559/25000000\"\n+      },\n+      \"strict_checks\": {\n+        \"actual_bit_above_effective\": \"264351/700000000\",\n+        \"actual_logarithmic_gamma_guard\": \"1/700000000\",\n+        \"actual_logarithmic_group_guard\": \"694633553939307/3828125000000000\",\n+        \"alpha_logarithm_absorption\": \"1/7000000000\",\n+        \"boundary_algebraic_matrix_above_kappa\": \"43716943/7656250000000000\",\n+        \"cap_above_band\": \"3133491462466943/7656250000000000\",\n+        \"cap_below_cell\": \"694633526595557/7656250000000000\",\n+        \"cap_below_phase_cell_power\": \"8350883537533057/7656250000000000\",\n+        \"complex_above_effective\": \"1/700000000\",\n+        \"complex_below_one_over_32\": \"395187/14000000\",\n+        \"complex_endpoint\": \"1/350000000\",\n+        \"epsilon_below_one\": \"1/700000000\",\n+        \"epsilon_positive\": \"699999999/700000000\",\n+        \"fine_prime_halo_umbrella\": \"7/2\",\n+        \"fused_gaussian_above_kappa\": \"43650829/7656250000000000\",\n+        \"gaussian_above_main\": \"5435693/3828125000000000\",\n+        \"global_coordinate_router_above_kappa\": \"1/175000000\",\n+        \"global_gamma_power_slack\": \"9/7000000000\",\n+        \"group_below_dimension\": \"1/350000000\",\n+        \"group_bit_router_above_kappa\": \"3493653053/490000000000000000\",\n+        \"group_gauge_power_slack\": \"43414597087027/239257812500000\",\n+        \"group_key_fits_record\": \"1/350000000\",\n+        \"group_positive\": \"699999997/700000000\",\n+        \"group_scans_above_kappa\": \"697884353/700000000\",\n+        \"halo_covers_generic_inverse_radius\": \"5\",\n+        \"improvement_over_user_baseline\": \"645689790400418148631/500000000000000000000000\",\n+        \"lambda_above_internal\": \"1/1400000000\",\n+        \"lambda_above_sigma\": \"3/1400000000\",\n+        \"lambda_above_tau\": \"1/1400000000\",\n+        \"lambda_prime_above_lambda\": \"1/1400000000\",\n+        \"lambda_prime_above_leaf\": \"27957687/9800000000000000\",\n+        \"leaf_saving_above_effective\": \"13957687/9800000000000000\",\n+        \"main_transform_above_kappa\": \"32779443/7656250000000000\",\n+        \"membership_arithmetic_fits_record\": \"1/700000000\",\n+        \"microbox_face_corrections_above_kappa\": \"53897884359/700000000\",\n+        \"microbox_halo_volume\": \"55300000003/700000000\",\n+        \"new_complex_uniform_saving_above_b\": \"1/700000000\",\n+        \"new_semantic_guard_with_C1_one\": \"1/700000000\",\n+        \"polynomial_products_above_kappa\": \"348942177/350000000\",\n+        \"positive_layout_slack\": \"1/700000000\",\n+        \"q_below_effective\": \"1/700000000\",\n+        \"q_below_internal\": \"1/700000000\",\n+        \"q_below_leaf\": \"27957687/9800000000000000\",\n+        \"q_positive\": \"33057/10937500\",\n+        \"short_record_fallback\": \"13957687/14000000\",\n+        \"source_axis_superpolynomial\": \"1/700000000\",\n+        \"sparse_union_movement_above_kappa\": \"3110351606216943/7656250000000000\",\n+        \"stop_below_one\": \"699999999/700000000\",\n+        \"stop_positive\": \"1/700000000\",\n+        \"strassen_integer_power_gap\": \"1951441519231\",\n+        \"support_router_span\": \"3/700000000\",\n+        \"theta_positive_polynomial_power\": \"2\",\n+        \"union_header_fits_record\": \"3/700000000\",\n+        \"union_tag_work_per_visit_fits_record\": \"3/700000000\"\n+      }\n+    },\n+    \"paid\": {\n+      \"1\": 41282,\n+      \"16\": 448,\n+      \"2\": 7416,\n+      \"24\": 448,\n+      \"3\": 9180,\n+      \"32\": 448,\n+      \"4\": 2286,\n+      \"40\": 448,\n+      \"48\": 448,\n+      \"5\": 720,\n+      \"56\": 448,\n+      \"64\": 448,\n+      \"72\": 224,\n+      \"8\": 128\n+    },\n+    \"paid_calls\": 64372,\n+    \"productive_fields\": 10912,\n+    \"query_shears\": 15,\n+    \"rank_mass_surplus\": 752,\n+    \"raw_headroom\": [\n+      \"3736347/100000000000000\",\n+      \"934087/25000000000000\"\n+    ],\n+    \"raw_root_interval\": [\n+      \"302238736347/100000000000000\",\n+      \"75559684087/25000000000000\"\n+    ],\n+    \"strictification\": {\n+      \"alpha\": {\n+        \"lower\": \"0.999999971483293515393313955729\",\n+        \"upper\": \"0.999999971483293515393313955730\"\n+      },\n+      \"cutoff\": 20,\n+      \"delta\": {\n+        \"lower\": \"0.957459689758527661921334851512\",\n+        \"upper\": \"0.957459689758527661921334851513\"\n+      },\n+      \"floor\": 21,\n+      \"gamma\": {\n+        \"lower\": \"0.956310980726438847618396606911\",\n+        \"upper\": \"0.956310980726438847618396606912\"\n+      },\n+      \"normalized_paid_upper\": \"2097152001953127/2097154147483648\",\n+      \"power\": 1024,\n+      \"reserve\": \"1/1000000000\",\n+      \"tail_offset\": \"1/5\",\n+      \"tested\": \"75559/25000000\"\n+    },\n+    \"targets\": {\n+      \"145\": 224,\n+      \"17\": 448,\n+      \"25\": 448,\n+      \"33\": 448,\n+      \"4\": 504,\n+      \"41\": 448,\n+      \"49\": 448,\n+      \"57\": 448,\n+      \"65\": 448,\n+      \"7\": 126,\n+      \"73\": 224,\n+      \"8\": 846,\n+      \"9\": 5852\n+    }\n+  },\n+  \"candidate_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 325\n+      },\n+      \"independent_owned_entry_columns\": 3,\n+      \"independent_persistent_columns\": 631,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2200,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 7\n+      },\n+      \"real_scalar_allowance\": 158214,\n+      \"zero_identities\": 1\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"independent_source_identities\": {\n+    \"center_minus_snapshot\": \"Delta/4\",\n+    \"center_replaced\": 11332,\n+    \"copy_coefficient\": \"1\",\n+    \"relation\": {\n+      \"230\": 1,\n+      \"324\": -1,\n+      \"326\": 1,\n+      \"328\": 1,\n+      \"333\": -1\n+    },\n+    \"snapshot_after\": 11205,\n+    \"snapshot_terms_before_substitution\": 61,\n+    \"source_event_indices_are_zero_based\": true,\n+    \"zero_identity_at\": 15584,\n+    \"zero_site_row\": \"-Delta/4\"\n+  },\n+  \"native_negative_controls\": {\n+    \"missing_owned_input_clear\": \"Every independent main/helper endpoint: 0\",\n+    \"uncleared_owned_output\": \"Every owned entry column is erased at return\",\n+    \"under_or_overstated_paid_rank\": \"Exact paid rank and frame\",\n+    \"wrong_copy_gauge\": \"Exact scalar destination frame\",\n+    \"wrong_relation_sign\": \"Every independent main/helper endpoint: 0\",\n+    \"wrong_snapshot_source\": \"Zero identity requires an identically zero full row\",\n+    \"wrong_zero_input_frame\": \"Zero identity requires an identically zero full row\"\n+  },\n+  \"phase_inheritance\": {\n+    \"absolute_phase_receipt_reused\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"all_retained_paid_events_and_warps_from_source\": true,\n+    \"new_gaussian_operators\": 0,\n+    \"new_native_maps\": 0,\n+    \"new_operations\": \"Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.\",\n+    \"source_amplitudes_and_phase_lowering_freshly_replayed\": false\n+  },\n+  \"scope\": \"Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.\",\n+  \"source_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158168,\n+      \"zero_identities\": 0\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"source_payload_sha256\": \"cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd\",\n+  \"status\": \"PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION\",\n+  \"word_payload_sha256\": \"645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35\"\n+}\n@@ -0,0 +1,90 @@\n+{\n+  \"schema_version\": 1,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"files\": [\n+    {\n+      \"path\": \"certificates/selected-result.json\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"c35482cd9035843b15a634cc8276a7e1e40e8395\",\n+      \"sha256\": \"6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375\"\n+    },\n+    {\n+      \"path\": \"docs/research/agent-task-catalog.json\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"f126dd2e2dad2b669e75d1d0d0bd05c600725602\",\n+      \"sha256\": \"f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72\"\n+    },\n+    {\n+      \"path\": \"research/free-word-tensor-lift-audit/PROOF.md\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"69c337a7704ce589798269ab4b8606189c070c4e\",\n+      \"sha256\": \"cc8ad3698a673fb225419a3636a39aa99a66c7a0676f12e329b1e76564fa1459\"\n+    },\n+    {\n+      \"path\": \"research/higher-moment-strictification/verify.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"4b24a5096154736ce060474eb8c72dc64c303699\",\n+      \"sha256\": \"0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326\"\n+    },\n+    {\n+      \"path\": \"research/joint-helper-lattice/CONTROLLER.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"49a2f0675819f9deeea27ed77be2c2b6ff2e87e5\",\n+      \"sha256\": \"1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f\"\n+    },\n+    {\n+      \"path\": \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"5a55034ec9e6185d981e16c28e1e2e455069e2cb\",\n+      \"sha256\": \"106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7\"\n+    },\n+    {\n+      \"path\": \"research/kappa-interface-round2-20261022/price_profile.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"1d93e43d1cb888d128c2faa2be83a96d85b84295\",\n+      \"sha256\": \"adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"4fc05ab08138218ba9f09e5c89b649afae7c914e\",\n+      \"sha256\": \"011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/complex/native_extensions.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"7f84894efc309546a903d314c7ac1473e7f594a8\",\n+      \"sha256\": \"50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"46d929df83817b85a5387bcdb9745e0627d6366e\",\n+      \"sha256\": \"7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"ac77b78547d6dbf2e6bd102e1047c5b16c1bca88\",\n+      \"sha256\": \"6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"0fdb65f946d557c13d8e2781b9151e2a8ddee5c3\",\n+      \"sha256\": \"b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de\"\n+    },\n+    {\n+      \"path\": \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59\",\n+      \"sha256\": \"d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15\"\n+    },\n+    {\n+      \"path\": \"research/query-thinned-controllers/RESULT.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"e0695152c98d727edfd0d2034b58a1c7e8682c0c\",\n+      \"sha256\": \"6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f\"\n+    }\n+  ]\n+}\n@@ -0,0 +1,80 @@\n+{\n+  \"schema_version\": 1,\n+  \"task_id\": \"complex-new-helper-inventory\",\n+  \"priority_revision\": 7,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"original_card\": {\n+    \"id\": \"complex-new-helper-inventory\",\n+    \"question\": \"Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?\",\n+    \"starting_points\": [\n+      \"docs/research/research-family-status.md\",\n+      \"research/complex-local-word-ceiling/README.md\",\n+      \"research/heterogeneous-owner-assembly/README.md\",\n+      \"certificates/selected-result.json\",\n+      \"research/selected-k8-unrestricted-ends/README.md\"\n+    ],\n+    \"methods\": [\n+      \"Propose a changed helper inventory and derive an optimistic exact moment.\",\n+      \"Design a small completed instance and independently verify its endpoint and rank bill.\"\n+    ],\n+    \"acceptance_gate\": \"A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.\",\n+    \"first_step\": {\n+      \"command\": [\n+        \"python3\",\n+        \"-B\",\n+        \"research/complex-local-word-ceiling/verify.py\"\n+      ],\n+      \"expected\": \"PASS_COMPLEX_LOCAL_WORD_CEILING\",\n+      \"inspect\": \"Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.\",\n+      \"scope\": \"Positive control and planning budget only; this is not a new construction or full cold replay.\"\n+    },\n+    \"first_experiment\": \"Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.\",\n+    \"bottleneck_link\": \"Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.\",\n+    \"allowed_variations\": [\n+      \"Narrow to one changed boundary or helper type with explicit counts.\",\n+      \"If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope.\"\n+    ],\n+    \"scope_change_triggers\": [\n+      \"Mixing only providers already inside the pinned catalogue.\",\n+      \"Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.\",\n+      \"Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts.\"\n+    ],\n+    \"overlap_terms\": [\n+      \"helper inventory\",\n+      \"heterogeneous-owner\",\n+      \"mutable leaver\"\n+    ]\n+  },\n+  \"scope_status\": \"refined\",\n+  \"actual_scope\": \"Make helper L230 owned in each backward call, prepare one five-helper relation, retain one exact frame-254 snapshot, remove one rank-eight center and one rank-one zero job, and debit one rank-nine target.\",\n+  \"scope_change_reason\": \"This uses the current helper-inventory priority. It changes the independent input inventory and scalar word; all physical native maps and the p16 controller remain fixed.\",\n+  \"bottleneck_link\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+  \"budget_minutes\": 240,\n+  \"stop_rule\": \"Publish one exact complete-profile kappa improvement after native, ownership, phase-inheritance, compiler and cold-export checks.\",\n+  \"outcome\": \"completed\",\n+  \"evidence\": \"README.md, WORD.json.gz, RESULT.json and verify.py. The complete conditional kappa is 60447/20000000.\",\n+  \"author\": \"Ali Romman\",\n+  \"ai_assistance\": \"Substantial OpenAI Codex assistance in discovery, code, proof, verification and publication.\",\n+  \"open_questions\": [\n+    {\n+      \"question\": \"Can a separate reviewer validate this one-relation restriction and the inherited physical transfer premises?\",\n+      \"why_it_matters\": \"The new finite construction is exact, but the complete bound still uses the source phase and all-size contracts.\",\n+      \"first_step\": \"Replay the three unrestricted source rows in native.py and check the COPY and zero-identity argument in README.md.\",\n+      \"blocked_by\": \"Independent review has not yet occurred.\"\n+    },\n+    {\n+      \"question\": \"Can a different helper relation give another complete positive bill?\",\n+      \"why_it_matters\": \"This construction gives one positive instance, not an optimum for changed helper inventories.\",\n+      \"first_step\": \"Claim a disjoint relation in Discussions, derive its exact rows, and include every lost target and owned-storage cost.\",\n+      \"blocked_by\": \"Current active cache and paid-history scopes must be checked first.\"\n+    }\n+  ],\n+  \"coordination\": {\n+    \"claim\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+    \"distinct_scopes\": [\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5355\",\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/4930\"\n+    ],\n+    \"boundary\": \"The first scope retains 632 arbitrary inputs and eight centers. The second retains every original helper endpoint. This package removes the independent L230 job only in backward calls and claims only the stated relation and two event replacements.\"\n+  }\n+}\n@@ -0,0 +1,38 @@\n+{\n+  \"schema_version\": 1,\n+  \"status\": \"ready\",\n+  \"python\": \"3.12\",\n+  \"requirements\": [],\n+  \"inputs\": [\n+    \"research/higher-moment-strictification/verify.py\",\n+    \"research/joint-helper-lattice/CONTROLLER.json\",\n+    \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+    \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+    \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+    \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+    \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+    \"research/query-thinned-controllers/RESULT.json\"\n+  ],\n+  \"commands\": [\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls.\"\n+    },\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-O\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"The same checks remain active with Python assertions disabled.\"\n+    }\n+  ]\n+}\n\n@@ -0,0 +1,299 @@\n+\"\"\"One prepared helper removes two paid jobs in the PR4610 backward word.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+The source word is by Cao Yifan. The row convention and scalar allowance\n+follow the credited native work of Cinna Davis and zxv.\n+\"\"\"\n+from collections import Counter\n+from copy import deepcopy\n+from fractions import Fraction as Q\n+from hashlib import sha1, sha256\n+from pathlib import Path\n+import gzip\n+import importlib.util\n+import json\n+import sys\n+\n+HERE = Path(__file__).resolve().parent\n+ROOT = HERE.parents[1]\n+SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'\n+PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz'\n+PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'\n+RELATION = {230: 1, 324: -1, 326: 1, 328: 1, 333: -1}\n+OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}\n+NEW_PAID = dict(OLD_PAID)\n+NEW_PAID[1] -= 1\n+NEW_PAID[8] -= 1\n+OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326}\n+\n+\n+def need(ok, why):\n+    if not ok:\n+        raise ValueError(why)\n+\n+\n+def read(path):\n+    data = path.read_bytes()\n+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)\n+\n+\n+def encode(x):\n+    if isinstance(x, Q):\n+        return str(x)\n+    if isinstance(x, dict):\n+        return {str(k): encode(v) for k, v in x.items()}\n+    if isinstance(x, (list, tuple)):\n+        return [encode(v) for v in x]\n+    return x\n+\n+\n+def load(relative, name):\n+    spec = importlib.util.spec_from_file_location(name, ROOT / relative)\n+    module = importlib.util.module_from_spec(spec)\n+    sys.modules[name] = module\n+    spec.loader.exec_module(module)\n+    return module\n+\n+\n+def authenticate():\n+    pins = read(HERE / 'SOURCES.json')\n+    for row in pins['files']:\n+        if row['usage'] != 'input':\n+            continue\n+        p = ROOT\n+        for part in Path(row['path']).parts:\n+            p /= part\n+            need(not p.is_symlink(), 'No source aliases')\n+        raw = p.read_bytes()\n+        need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path'])\n+        need(sha1(b'blob ' + str(len(raw)).encode() + b'\\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob')\n+    need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload')\n+    return pins\n+\n+\n+def span(basis):\n+    out = {0}\n+    for vector in basis:\n+        need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate')\n+        out |= {v ^ vector for v in tuple(out)}\n+    need(len(out) == 2 ** len(basis), 'Independent frame basis')\n+    return out\n+\n+\n+def add(dst, src, q):\n+    for k, v in tuple(src.items()):\n+        value = dst.get(k, Q(0)) + q * v\n+        if value:\n+            dst[k] = value\n+        else:\n+            dst.pop(k, None)\n+\n+\n+def allowance(g):\n+    if g[0] in ('clear', 'copy'):\n+        return 2\n+    q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:])\n+    n, d = abs(q.numerator), q.denominator\n+    need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar')\n+    if g[0] == 'scale':\n+        need(n & (n - 1) == 0, 'Dyadic unit SCALE')\n+        return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0))\n+    need(g[0] == 'add', 'Known scalar operation')\n+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)\n+\n+\n+def construct(source):\n+    c = source['canonical']\n+    old = source['programs']['backward']\n+    need(old[11205] == ['climb', 'warp_retimed', 92, 310, 254, 4], 'Snapshot source event')\n+    need(old[11332] == ['center', 0, 0, 254, 8], 'Center source event')\n+    need(old[15584] == ['climb', 'warp_retimed', 92, 254, 1, 1], 'Zero source event')\n+    need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in RELATION), 'Five cold full-ended helpers')\n+    word = [['scalar', ['clear', ['L', 230]], 0]]\n+    word += [['scalar', ['add', ['L', 230], ['L', h], -q, 1], 0]\n+             for h, q in RELATION.items() if h != 230]\n+    for i, event in enumerate(old):\n+        if i == 11332:\n+            word += [['scalar', ['clear', ['C', 0]], 254],\n+                     ['scalar', ['copy', ['C', 0], ['C', 1]], 254],\n+                     ['scalar', ['clear', ['C', 1]], 254]]\n+        elif i == 15584:\n+            word.append(['zero_retag', ['L', 92], 254, 1])\n+        else:\n+            word.append(deepcopy(event))\n+        if i == 11205:\n+            word += [['scalar', ['clear', ['C', 1]], 254],\n+                     ['scalar', ['copy', ['C', 1], ['L', 92]], 254]]\n+    word.append(['scalar', ['clear', ['L', 230]], 1])\n+    physical = deepcopy(c)\n+    physical.pop('local_profile')\n+    return {'schema': 'owned-helper-relation-word/1', 'canonical': physical,\n+            'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID},\n+            'owned': {'forward': [['C', 0]], 'backward': [['C', 0], ['C', 1], ['L', 230]]},\n+            'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}}\n+\n+\n+def replay(c, program, backward, specialized):\n+    \"\"\"Run every event on all independent entry columns and exact frames.\"\"\"\n+    owned = {('C', 0)} | ({('C', 1), ('L', 230)} if specialized else set())\n+    roles = {('L', i) for i in range(632)} | owned\n+    rows = {r: {(r, ()): Q(1)} for r in roles}\n+    frames = {('L', i): f for i, f in enumerate(c['start'])}\n+    frames.update({r: None for r in owned if r[0] == 'C'})\n+    spaces = [span(b) for b in c['frames']]\n+    paid = Counter()\n+    cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0\n+    for e in program:\n+        kind, touched = e[0], None\n+        if kind == 'scalar':\n+            g, frame = e[1:]\n+            dst = tuple(g[1]); touched = dst\n+            need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame')\n+            cost += allowance(g)\n+            if g[0] == 'clear':\n+                need(dst in owned, 'Only owned fields can be erased')\n+                rows[dst] = {}; frames[dst] = frame\n+            else:\n+                need(frames[dst] == frame, 'Exact scalar destination frame')\n+                if g[0] in ('add', 'copy'):\n+                    src = tuple(g[2])\n+                    need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame')\n+                    if g[0] == 'copy':\n+                        need(dst in owned and not rows[dst], 'COPY into cleared owned storage')\n+                        rows[dst] = dict(rows[src])\n+                    else:\n+                        add(rows[dst], rows[src], Q(g[3], g[4]))\n+                else:\n+                    need(g[0] == 'scale', 'Known scalar operation')\n+                    rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()}\n+        elif kind == 'warp':\n+            _, role, op, old, new = e\n+            dst = tuple(role); touched = dst\n+            need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input')\n+            symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0))\n+            rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q\n+                         for (r, w), q in rows[dst].items()}\n+            frames[dst] = new\n+        elif kind in ('climb', 'center'):\n+            if kind == 'climb':\n+                _, _, i, old, new, rank = e\n+                dst = ('L', i)\n+                need(spaces[old] < spaces[new], 'Ascending paid climb')\n+            else:\n+                _, i, old, new, rank = e\n+                dst = ('C', i)\n+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center')\n+            need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame')\n+            frames[dst] = new; paid[rank] += 1\n+        elif kind == 'zero_retag':\n+            _, role, old, new = e\n+            dst = tuple(role)\n+            need(specialized and backward and dst == ('L', 92), 'Declared zero identity')\n+            need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row')\n+            need((old, new) == (254, 1), 'Declared zero frame change')\n+            frames[dst] = new; zero_count += 1\n+        else:\n+            need(kind in ('phase', 'adapter'), 'Known inert source marker')\n+        if touched is not None:\n+            max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0)))\n+            denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1))\n+    need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame')\n+    for i in range(632):\n+        r = ('L', i)\n+        if r in owned:\n+            continue\n+        expected = {(r, ()): Q(1)}\n+        if i < 112 if backward else 112 <= i < 224:\n+            expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1)\n+        need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i))\n+    need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return')\n+    need(zero_count == int(specialized), 'Exactly one checked zero identity')\n+    helpers = Counter()\n+    for i in range(224, 632):\n+        if ('L', i) in owned:\n+            continue\n+        a, b = c['start'][i], c['final'][i]\n+        need(spaces[a] < spaces[b], 'Strict independent productive helper')\n+        helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1\n+    return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())),\n+            'independent_persistent_columns': 631 if specialized else 632,\n+            'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True,\n+            'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1),\n+            'max_denominator': denominator, 'zero_identities': zero_count}\n+\n+\n+def independent_source_identities(source):\n+    \"\"\"Use the predecessor row engine on the unrestricted original word.\"\"\"\n+    v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'owned_relation_source_rows')\n+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}\n+    rows['C', 0] = v.identity(('C', 0))\n+    delta = {(('L', i), ()): Q(q) for i, q in RELATION.items()}\n+    saved = None\n+    for index, e in enumerate(source['programs']['backward']):\n+        if e[0] == 'scalar':\n+            g = e[1]; dst = tuple(g[1])\n+            if g[0] == 'clear': rows[dst] = {}\n+            elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])])\n+            elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()}\n+            else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4]))\n+        elif e[0] == 'warp':\n+            dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True)\n+        if index == 11205: saved = dict(rows['L', 92])\n+        if index == 11332:\n+            diff = dict(rows['C', 0]); v.add(diff, saved, -1)\n+            need(diff == {k: q / 4 for k, q in delta.items()}, 'Independent exact center minus snapshot = Delta/4')\n+        if index == 15584:\n+            need(rows['L', 92] == {k: -q / 4 for k, q in delta.items()}, 'Independent exact zero-site row = -Delta/4')\n+    need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints')\n+    return {'source_event_indices_are_zero_based': True, 'snapshot_after': 11205,\n+            'center_replaced': 11332, 'zero_identity_at': 15584,\n+            'snapshot_terms_before_substitution': len(saved), 'copy_coefficient': '1',\n+            'center_minus_snapshot': 'Delta/4', 'zero_site_row': '-Delta/4', 'relation': RELATION}\n+\n+\n+def phase_inheritance(source, candidate):\n+    receipt = read(ROOT / PHASE)\n+    need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and\n+         receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt')\n+    physical = deepcopy(source['canonical']); physical.pop('local_profile')\n+    need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged')\n+    for direction, program in candidate['programs'].items():\n+        old = source['programs'][direction]\n+        for kind in ('warp', 'adapter', 'phase'):\n+            need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence')\n+        old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center'))\n+        new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center'))\n+        expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for i in (11332, 15584))\n+        need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the two proved jobs are removed')\n+    return {'new_gaussian_operators': 0, 'new_native_maps': 0,\n+            'all_retained_paid_events_and_warps_from_source': True,\n+            'absolute_phase_receipt_reused': PHASE,\n+            'source_amplitudes_and_phase_lowering_freshly_replayed': False,\n+            'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'}\n+\n+\n+def controls(c, candidate):\n+    controls = {}\n+    base = candidate['programs']['backward']\n+    variants = {}\n+    bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad\n+    variants['missing_owned_input_clear'] = deepcopy(base[1:])\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63]\n+    variants['wrong_snapshot_source'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0\n+    variants['wrong_zero_input_frame'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1\n+    variants['under_or_overstated_paid_rank'] = bad\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0\n+    variants['wrong_copy_gauge'] = bad\n+    variants['uncleared_owned_output'] = deepcopy(base[:-1])\n+    for name, program in variants.items():\n+        try:\n+            replay(c, program, True, True)\n+        except ValueError as err:\n+            controls[name] = str(err)\n+        else:\n+            raise ValueError('Control accepted: ' + name)\n+    return controls\n@@ -0,0 +1,196 @@\n+\"\"\"Complete p16 bill and finite compiler for one owned helper relation.\n+\n+The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna\n+Davis's PR4470 controller, zxv's completion and logarithmic majorant, and\n+Jacob Alan Sussman's mixed-target recursion. Apache-2.0.\n+Ali Romman, with substantial OpenAI Codex assistance.\n+\"\"\"\n+from collections import Counter\n+from fractions import Fraction as Q\n+from native import ROOT, read, load, need, encode, OLD_PAID, OLD_HELPERS\n+\n+KAPPA = Q('.00302235')\n+TESTED = Q('.00302236')\n+PREVIOUS = Q('.0030217758')\n+OLD_ROOT_UPPER = Q('.00302177587078')\n+\n+\n+def controller():\n+    \"\"\"Check the literal p16 word and both rational boundary programs.\"\"\"\n+    word = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json')\n+    need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller')\n+    zero = (0,) * 34\n+    def plus(dst, src, q):\n+        for k, v in src.items():\n+            value = dst.get(k, Q(0)) + q * v\n+            if value: dst[k] = value\n+            else: dst.pop(k, None)\n+    def shifted(row, term, sign=1):\n+        return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row]\n+    for side in ('left', 'right'):\n+        matrix = [[Q(i == j) for j in range(32)] for i in range(32)]\n+        for e in word['boundaries'][side + '_program']:\n+            if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]]\n+            elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]]\n+            else:\n+                need(e[0] == 'ADD', 'Boundary scalar opcode')\n+                matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])]\n+        need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program')\n+    rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']]\n+    for e in word['physical_events']:\n+        if e[0] in ('LOCAL', 'QUERY_SHEAR'):\n+            _, stage, pair, back = e\n+            x, y = 2 * pair, 2 * pair + 1\n+            if back: x, y = y, x\n+            term = (1 if back else -1,) + (0,) * 33\n+            for dst, src in zip(rows[y], shifted(rows[x], term)):\n+                plus(dst, src, Q(-1 if back else 1))\n+            if e[0] == 'LOCAL':\n+                term = (0,) + tuple(int(s == stage) for s in range(33))\n+                for r in (x, y): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'IDLE':\n+            term = (0,) + tuple(int(s in e[2]) for s in range(33))\n+            for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'ADD':\n+            for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3]))\n+        else:\n+            need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode')\n+            rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1)\n+    out = [[{} for _ in range(32)] for _ in range(32)]\n+    for i, row in enumerate(word['boundaries']['left']):\n+        for k, q in enumerate(row):\n+            if Q(q):\n+                for j in range(32): plus(out[i][j], rows[k][j], Q(q))\n+    expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)]\n+    need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors')\n+    return word\n+\n+\n+def assemble(native, word):\n+    T, P = Counter(), Counter()\n+    orientations = Counter(); thin = 0\n+    for e in word['physical_events']:\n+        if e[0] == 'LOCAL':\n+            direction = 'backward' if e[3] else 'forward'\n+            orientations[direction] += 1\n+            T.update(native[direction]['helpers']); P.update(native[direction]['paid'])\n+        elif e[0] == 'QUERY_SHEAR': thin += 1; P[1] += 112\n+        elif e[0] == 'IDLE': P[8 * len(e[2])] += 224\n+    main = Counter()\n+    for term in word['diagonal']:\n+        need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole Gaussian main target')\n+        main[1 + 8 * sum(term[1:])] += 112\n+    T.update(main)\n+    need(orientations == {'backward': 16, 'forward': 2} and thin == 15, 'Every actual call orientation')\n+    # This second census uses the source invoice and the two local deltas.\n+    check_T = Counter({int(r): n for r, n in word['invoice']['main'].items()})\n+    check_T.update({r: 18 * n for r, n in OLD_HELPERS.items()}); check_T[9] -= 16\n+    check_P = Counter({int(r): n for r, n in word['invoice']['whole_idle'].items()})\n+    check_P.update({r: 18 * n for r, n in OLD_PAID.items()}); check_P[1] += 1680 - 16; check_P[8] -= 16\n+    need(T == check_T and P == check_P, 'Independent full invoice substitution')\n+    need(sum(T.values()) == 10912 and sum(P.values()) == 64372, 'Complete productive and paid counts')\n+    need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Unchanged complete rank surplus')\n+    return T, P\n+\n+\n+def run(native):\n+    word = controller(); T, P = assemble(native, word)\n+    prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json')\n+    need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing')\n+    prior_T = Counter({int(r): n for r, n in prior['targets'].items()})\n+    prior_P = Counter({int(r): n for r, n in prior['paid'].items()})\n+    prior_T[9] -= 16; prior_P[1] -= 16; prior_P[8] -= 16\n+    need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill')\n+    E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals')\n+    other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals')\n+    def margin(c):\n+        t, p = E.moment(T, 1 - c), E.moment(P, 1 - c)\n+        return t[0] - p[1], t[1] - p[0]\n+    need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint')\n+    lo, hi, grid = 0, 10**12, 10**14\n+    while hi - lo > 1:\n+        mid = (lo + hi) // 2\n+        if margin(Q(mid, grid))[0] > 0: lo = mid\n+        else: hi = mid\n+    root_low, root_high = Q(lo, grid), Q(hi, grid)\n+    need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure')\n+    need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom')\n+    # The complete signed profile decreases on [0, .05], and stays negative\n+    # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling.\n+    signed = {r: T[r] - P[r] for r in T.keys() | P.keys()}\n+    derivative, upper = None, None\n+    for i in range(16):\n+        l, r = Q(i, 320), Q(i + 1, 320); low = Q(0)\n+        for rank, n in signed.items():\n+            term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank))\n+            low += n * term[0 if n > 0 else 1]\n+        derivative = low if derivative is None else min(derivative, low)\n+    for i in range(128):\n+        l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560)\n+        value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items())\n+        upper = value if upper is None else max(upper, value)\n+    need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1')\n+    t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21\n+    target, paid = E.moment(T, t), E.moment(P, t)\n+    tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED)\n+    need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree')\n+    alpha = E.divide(paid, target)\n+    gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target))\n+    delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target))\n+    reserve = Q(1, 10**9); g = d = Q(97, 100)\n+    need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged')\n+    need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks')\n+    normalized = 1 / (1 + v * reserve) + Q(4, 2**32)\n+    need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding')\n+    theta, power = Q(63, 64), 1000\n+    eta = E.scale(E.power(145, -v * TESTED), t)\n+    need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')\n+    need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range')\n+    gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid')\n+    step = gap.denominator\n+    def wins(j): return (step * j + 1)**power < 2**j\n+    left, right = 1, 2\n+    while not wins(right): left, right = right, 2 * right\n+    while right - left > 1:\n+        mid = (left + right) // 2\n+        if wins(mid): right = mid\n+        else: left = mid\n+    height = step * right\n+    need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold')\n+    local_scalar = max(x['real_scalar_allowance'] for x in native.values())\n+    # The old route allowance is retained. Charge two additional owned field\n+    # lifetimes at two routes each, even though L230 uses an existing slot.\n+    routes = (max(sum(x['paid'].values()) for x in native.values()) + 2 * 408 + 688 + 4) * 1000\n+    need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit')\n+    scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right')))\n+    need(scalar_upper < 10**9, 'Complete raw nonrecursive bound')\n+    bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']\n+    atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted'])\n+    need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock')\n+    L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer')\n+    params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap,\n+              'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted,\n+              'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap}\n+    outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom)\n+    need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')\n+    need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict')\n+    controls = {}\n+    for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]:\n+        bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0]\n+        need(failed, 'Reject outer patch ' + name); controls[name] = failed\n+    bad_native = {d: dict(x) for d, x in native.items()}\n+    bad_native['backward']['helpers'] = OLD_HELPERS\n+    try: assemble(bad_native, word)\n+    except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census'\n+    else: raise ValueError('Unowned helper credit was accepted')\n+    return encode({'kappa': KAPPA, 'kappa_decimal': '.00302235', 'gain_over_PR4610': KAPPA - PREVIOUS,\n+                   'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA],\n+                   'margin_at_previous_kappa': E.display(margin(PREVIOUS)),\n+                   'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)),\n+                   'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)},\n+                   'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752,\n+                   'full_backward': 16, 'full_forward': 2, 'query_shears': 15,\n+                   'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized},\n+                   'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False},\n+                   'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': 1, 'owned_slots_backward': 3},\n+                   'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls})\n@@ -0,0 +1,64 @@\n+#!/usr/bin/env python3\n+\"\"\"Replay the one-relation native word and its complete conditional kappa.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+Read README.md for the source credit and inherited proof obligations.\n+\"\"\"\n+from hashlib import sha256\n+import argparse\n+import gzip\n+import json\n+from pathlib import Path\n+import sys\n+sys.dont_write_bytecode = True\n+import native as N\n+import price\n+\n+\n+def run():\n+    N.authenticate()\n+    source = N.read(N.ROOT / N.SOURCE)\n+    candidate = N.construct(source)\n+    c = candidate['canonical']\n+    before, after = {}, {}\n+    for direction in ('forward', 'backward'):\n+        back = direction == 'backward'\n+        before[direction] = N.replay(c, source['programs'][direction], back, False)\n+        after[direction] = N.replay(c, candidate['programs'][direction], back, back)\n+        N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Pinned source census')\n+        N.need(after[direction]['paid'] == candidate['paid_profiles'][direction], 'Emitted direction-specific paid profile')\n+        helpers = dict(N.OLD_HELPERS)\n+        if back: helpers[9] -= 1\n+        N.need(after[direction]['paid'] == (N.NEW_PAID if back else N.OLD_PAID) and after[direction]['helpers'] == helpers, 'Actual complete changed native census')\n+    identities = N.independent_source_identities(source)\n+    phase = N.phase_inheritance(source, candidate)\n+    controls = N.controls(c, candidate)\n+    arithmetic = price.run(after)\n+    data = (json.dumps(candidate, sort_keys=True, separators=(',', ':')) + '\\n').encode()\n+    result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION',\n+                       'source_payload_sha256': N.PAYLOAD, 'word_payload_sha256': sha256(data).hexdigest(),\n+                       'source_native': before, 'candidate_native': after, 'independent_source_identities': identities,\n+                       'phase_inheritance': phase, 'native_negative_controls': controls, 'arithmetic': arithmetic,\n+                       'scope': 'Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.'})\n+    return data, result\n+\n+\n+def main():\n+    ap = argparse.ArgumentParser(description=__doc__)\n+    ap.add_argument('--write', action='store_true', help='Write only this package word and result after all checks pass.')\n+    ap.add_argument('--out', type=Path, help='Write a replay result to a separate path.')\n+    args = ap.parse_args()\n+    data, result = run()\n+    if args.write:\n+        (N.HERE / 'WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))\n+        (N.HERE / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    else:\n+        N.need(gzip.decompress((N.HERE / 'WORD.json.gz').read_bytes()) == data, 'Exact literal published word')\n+        N.need(N.read(N.HERE / 'RESULT.json') == result, 'Exact published replay result')\n+    if args.out:\n+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR4610', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True))\n+\n+\n+if __name__ == '__main__':\n+    main()",
+      "comments": [],
+      "created_at": "2026-10-23T20:26:27Z",
+      "updated_at": "2026-10-23T20:26:27Z",
+      "closed_at": null,
+      "merged_at": null,
+      "commits": 1,
+      "changed_files": 9,
+      "additions": 1389,
+      "deletions": 0,
+      "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+      "display_title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation"
+    },
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+    "title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation",
+    "diff": "@@ -0,0 +1,249 @@\n+# Conditional kappa 0.00302235 from one owned helper relation\n+\n+This construction gives **conditional kappa = 60447/20000000 = 0.00302235**.\n+The gain over Cao Yifan's final\n+[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+value, 0.0030217758, is **2871/5000000000 = 0.0000005742**.\n+The construction changes the complete paid profile. It does not obtain the\n+gain by taking more digits of the old root.\n+\n+One helper becomes owned storage in each backward call. A prepared relation\n+then makes one paid rank-eight center equal to an earlier saved value. The same\n+relation makes one later rank-one job act on zero. Both jobs can be removed,\n+with the rank-nine helper credit also removed. All other independent outputs\n+and all main interfaces keep their source operators.\n+\n+[WORD.json.gz](WORD.json.gz) is the complete emitted word.\n+[RESULT.json](RESULT.json) records the exact native checks, the two source\n+identities, both full profiles, completion, compiler and outer calculations.\n+[SOURCES.json](SOURCES.json) pins every external input by Git blob and SHA256.\n+The proof below explains why the changed word has the stated contract.\n+\n+## Source and scope\n+\n+The base is canonical main\n+[7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56).\n+The native source is the final PR #4610 word at\n+[20bb93cd990d2ff683e4d0fc56b87a42cd5d3296](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz).\n+Its decompressed SHA256 is\n+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.\n+The comparison value and old crossing come from its\n+[final compiler arithmetic](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json).\n+All consumed bytes are already in the recorded main base.\n+\n+This is one instance of the current `complex-new-helper-inventory` priority.\n+The [scoped claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737)\n+reserves only the relation and two replacements below.\n+[Discussion #5355](https://github.com/CrocSwap/integer-mult-bounds/discussions/5355)\n+retains all 632 independent inputs and all eight centers.\n+[Discussion #4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930)\n+retains every original helper endpoint. This construction removes the\n+independent L230 job in backward calls. It does not claim those broader scopes.\n+The selected certificate is unchanged. A fresh check at 20:20 UTC found that\n+Discussion #5355 had released its original-input scope without a saving.\n+Canonical main still had the recorded base commit.\n+\n+## Exact replacement proof\n+\n+All indices below are zero-based indices in the frozen backward program.\n+Let `h_r` be the source logical input of helper `Lr`. The five helpers in\n+\n+```math\n+\\Delta=h_{230}-h_{324}+h_{326}+h_{328}-h_{333}\n+```\n+\n+all start in frame 0 and finish in frame 1, of rank nine. The new backward\n+contract has 224 independent main fields and 407 independent helper fields.\n+L230 is private. Clear it, then use four same-frame ADDs to prepare\n+\n+```math\n+h_{230}=h_{324}-h_{326}-h_{328}+h_{333}.\n+```\n+\n+The other helper inputs remain arbitrary and independent. This preparation\n+sets Delta to zero for every input. It uses no recursive job. It removes one\n+rank-nine productive target; the dependent field receives no output credit.\n+\n+Run the original source program on unrestricted inputs. Let `q` be the\n+logical row of L92 just after event 11205, a paid climb into frame 254.\n+The separate predecessor row engine gives these exact identities:\n+\n+| Source position | Exact logical row |\n+| --- | --- |\n+| C0 at the rank-eight center, event 11332 | `q + Delta/4` |\n+| L92 at the rank-one climb, event 15584 | `-Delta/4` |\n+\n+These identities are over rational coefficients and free native operator\n+words. They hold for every value of every source input and for every invertible\n+interpretation of the native symbols. They do not use numerical samples or an\n+assumed relation between distinct native maps.\n+\n+For every positive tensor width f, substitute each native generator by its\n+source operator tensor power and each inverse by the inverse tensor power.\n+This defines a representation of the free group. Keep the rational scalar\n+coefficients outside the substitution. The two row identities therefore hold\n+at every such width. In particular, Delta/4 remains a scalar linear form; it\n+is not a tensor power of that sum. This uses the termwise argument recorded in\n+the [free-word tensor audit](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/free-word-tensor-lift-audit/PROOF.md),\n+which credits Cinna Davis's proposal and ToikY's scoped audit. Physical frame\n+realization and the complete all-size compiler retain their source contracts.\n+\n+Immediately after event 11205, clear a new private field C1 in frame 254 and\n+COPY L92 into it. C1 is not written until the replacement of event 11332. At\n+that event, clear owned C0, set its frame to 254, COPY C1 into C0, then clear C1.\n+The copy coefficient is exactly one. Under Delta = 0, the copied field is the\n+same physical value as the old center output: the logical rows and the exact\n+frame gauge are equal. The old C0 input can be erased because C0 is owned.\n+This removes one rank-eight recursive job.\n+\n+At event 15584, L92 is exactly zero in every input column. The physical\n+identity therefore has the same result as the old rank-one frame change.\n+`zero_retag` records this fact. It performs no physical write and is accepted\n+only when the full exact row is empty and the current frame is 254. It then\n+records frame 1. This removes one rank-one recursive job. It does not erase a\n+main input or replace a nonzero transform with a free frame change.\n+\n+Every other event stays in source order. Clear private L230 at return. The\n+source clears C0, and the new program has already cleared C1. The original\n+linear endpoint identity, restricted by the prepared relation, gives all 224\n+main outputs and all 407 retained helper outputs. The literal new-word replay\n+checks these outputs separately, with all 631 retained inputs and all three\n+owned entry fields initially arbitrary. It also checks every scalar frame,\n+paid rank, native frame transition and final frame.\n+\n+The 4,429 source frames, 72 native maps, all remaining paid operators, and main\n+adapters are unchanged. The source\n+[absolute-phase certificate](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz)\n+is authenticated and reused. Same-frame COPY and identity on zero introduce no\n+phase recipe. The source's amplitude and Clifford-lowering checks are not\n+rerun by this package. The new free-word identities prove equivalence for the\n+source operators with their full phases, not just their projective classes.\n+\n+## Complete cost and conditional compiler\n+\n+The forward word is unchanged. Each backward call has these counts:\n+\n+```text\n+paid:    {1:2200, 2:412, 3:510, 4:127, 5:40, 8:7}\n+helpers: {4:28, 7:7, 8:47, 9:325}\n+```\n+\n+The full p16/a7 controller contains 16 backward calls, two forward calls and\n+15 query shears. Thus the complete difference is **minus 16 H1 and 16 H8 paid\n+jobs, and minus 16 H9 productive targets**. It includes every idle and main\n+target. There are 64,372 paid jobs and 10,912 productive fields. Their rank\n+masses are 238,990 and 239,742; the surplus remains 752.\n+\n+For every real `0 < t < 1`, the complete target-minus-paid moment increases by\n+\n+```math\n+16(1+8^t-9^t)>0.\n+```\n+\n+For a direct proof, both `(1/9)^t > 1/9` and `(8/9)^t > 8/9`; multiply their\n+sum by `9^t`. The improvement is strict throughout the required range.\n+\n+The backward word has 158,214 real scalar operations under the source macro\n+allowance, exactly 46 more than its source. Its maximum formal prefix L1 norm\n+is 169, with maximum denominator 64; both equal the source bounds. The forward\n+bounds remain 457 and 32. One extra physical private slot holds C1. L230 uses\n+an existing slot. The route bound also charges two routes for each of the two\n+new owned lifetimes. The local scalar-plus-route bound stays below 10^7, and\n+the complete raw nonrecursive bound stays **181,098,496 < 10^9**. Preparation,\n+COPY, CLEAR and storage therefore do not introduce an unpaid recursive cost.\n+\n+Two rational interval engines check the complete moment. Its unique crossing\n+in `0 < kappa < 1` lies in\n+**(0.00302238736347, 0.00302238736348)**. The verifier proves the moment decreases\n+on `[0,0.05]` and remains negative on `[0.05,1]`. This is a ceiling for this\n+fixed complete profile, not an optimum over circuits or helper relations.\n+The claimed kappa leaves more than **0.00000003736347** raw headroom.\n+\n+The separately tested saving is 0.00302236. The paid/target ratio is below\n+`0.999999971483293515393313955730`, with reserve `1e-9`. Both charged tails are\n+below `0.97`. The source power 1024, cutoff 20, floor 21, tail offset 1/5,\n+complement factor 63/64 and logarithm power 1000 still pass. The compiler gap\n+is `1/700000000`, with `j=44836`, `H=31385200000000` and `N=2^31385200000000`.\n+The exact integer test `(H+1)^1000 < 2^44836` passes; the preceding grid integer\n+fails. The uniform complex saving is `2115651/700000000`. All 54 strict outer\n+predicates and four functional predicates pass, using the retained ordinary\n+BIT saving 0.0034.\n+\n+## Verification and reproduction\n+\n+Use Python 3.12 or 3.14, with the standard library only. From the repository root:\n+\n+```sh\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023 --check-only\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023\n+```\n+\n+The registered commands run normal and optimized Python. The direct command,\n+also used for a Git-free export, is:\n+\n+```sh\n+python3 -B research/kappa-owned-relation-20261023/verify.py\n+python3 -O -B research/kappa-owned-relation-20261023/verify.py\n+```\n+\n+Each prints status\n+`PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION`.\n+The verifier reconstructs the word and compares its bytes and exact result with\n+the published artifacts. `--write` is a separate authoring command. It changes\n+only this package's word and result after all checks pass.\n+\n+Fresh checks cover both source words, both candidate words, every independent\n+entry column and owned return, the two unrestricted source identities, retained\n+phase bindings, the p16 rational Laurent factorization, both scalar boundary\n+programs, two complete invoice counts, two rational interval engines, the fixed\n+profile ceiling, completion, compiler, BIT conversion and all outer predicates.\n+The emitted word replaces the old single `canonical.local_profile` metadata\n+field with explicit `paid_profiles` for the two directions.\n+\n+Seven native controls reject a wrong relation sign, omitted input clear, wrong\n+snapshot, wrong zero frame, wrong paid rank, wrong copy gauge, and omitted\n+output clear. Five cost/outer controls reject the lost helper's output credit,\n+old BIT stock, closed uniform gap, unfunded endpoint and closed epsilon.\n+\n+Normal and optimized registered replays passed on CPython 3.12.14. The direct\n+author check also passed on CPython 3.14. Source metadata and pins passed.\n+The optional full-history preflight is not claimed in the shallow checkout.\n+The publication handoff records export and committed-byte checks.\n+\n+The full source phase lowering, BIT native replay, Lean, Docker, physical tape\n+execution, numerical precision execution, analytic decomposition and integer\n+recovery are not rerun here. The complete bound retains those predecessor\n+contracts, including permitted owned erasure, whole-job normalizers, mixed\n+productive-target recursion and all-size closure. The expanded compiled word\n+is specified by a finite algorithm, not materialized. This is a conditional\n+construction with exact finite evidence, not an unconditional multiplication\n+theorem, a practical timing result or independent human acceptance.\n+\n+## Credit\n+\n+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.\n+Cao Yifan's [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+supplies the exact source word, phase evidence and previous compiler value.\n+Cinna Davis's [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470)\n+supplies the p16 controller and helper-interface lineage. The source code keeps\n+credit for Dugongue's transported frames, zxv's native and finite-compiler\n+work, Jacob Alan Sussman's mixed-target recursion and their predecessors.\n+The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py)\n+and [literal native source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-rebuild/complex/native_extensions.py)\n+are pinned as provenance for the adapted checks.\n+\n+zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283)\n+supplies the related cache contract and the explicit handoff to find actual\n+matching rows and their lifetimes. Its standalone cache example is not part of\n+this word. The new contribution is the five-helper relation, its actual cache\n+and zero identities, the full owned-field replacement and the complete positive\n+bill. No priority is claimed for the general cache or paid-history ideas.\n+\n+## Open next questions\n+\n+Independent review should first check the three source rows and the physical\n+COPY/zero argument above, then the retained all-size and phase premises.\n+A later construction could test a different helper relation, but it must claim\n+a disjoint scope and pay every lost target and owned field. This package does\n+not classify such relations. [TASK.json](TASK.json) records the first steps,\n+relevance and blockers for both questions.\n@@ -0,0 +1,373 @@\n+{\n+  \"arithmetic\": {\n+    \"compiler\": {\n+      \"H\": 31385200000000,\n+      \"N\": \"2^31385200000000\",\n+      \"eta\": {\n+        \"lower\": \"0.000000203927056311365991628189\",\n+        \"upper\": \"0.000000203927056311365991628190\"\n+      },\n+      \"gap\": \"1/700000000\",\n+      \"integer_test_exponent\": 44836,\n+      \"logarithm_power\": 1000,\n+      \"theta\": \"63/64\",\n+      \"uniform_saving\": \"2115651/700000000\",\n+      \"word_materialized\": false\n+    },\n+    \"fixed_profile_ceiling\": {\n+      \"decreasing_through\": \"1/20\",\n+      \"derivative_upper\": {\n+        \"lower\": \"-195778.630038840116414999953237565269\",\n+        \"upper\": \"-195778.630038840116414999953237565268\"\n+      },\n+      \"remaining_interval_moment_upper\": {\n+        \"lower\": \"-6836.549542075249598033582799619360\",\n+        \"upper\": \"-6836.549542075249598033582799619359\"\n+      }\n+    },\n+    \"full_backward\": 16,\n+    \"full_forward\": 2,\n+    \"gain_over_PR4610\": \"2871/5000000000\",\n+    \"kappa\": \"60447/20000000\",\n+    \"kappa_decimal\": \".00302235\",\n+    \"margin_at_previous_kappa\": {\n+      \"lower\": \"0.151161494385402651700356241377\",\n+      \"upper\": \"0.151161494385402651700356241378\"\n+    },\n+    \"margin_at_previous_root_upper\": {\n+      \"lower\": \"0.151143999513185007311808491175\",\n+      \"upper\": \"0.151143999513185007311808491176\"\n+    },\n+    \"negative_controls\": {\n+      \"closed_epsilon\": [\n+        \"epsilon_below_one\",\n+        \"global_gamma_power_slack\",\n+        \"actual_logarithmic_gamma_guard\",\n+        \"source_axis_superpolynomial\",\n+        \"gaussian_above_main\",\n+        \"new_semantic_guard_with_C1_one\"\n+      ],\n+      \"closed_uniform\": [\n+        \"new_complex_uniform_saving_above_b\"\n+      ],\n+      \"old_BIT\": [\n+        \"actual_bit_above_effective\"\n+      ],\n+      \"unearned_helper_credit\": \"Rejected by the independent complete census\",\n+      \"unfunded_endpoint\": [\n+        \"main_transform_above_kappa\",\n+        \"global_coordinate_router_above_kappa\",\n+        \"fused_gaussian_above_kappa\",\n+        \"group_bit_router_above_kappa\",\n+        \"boundary_algebraic_matrix_above_kappa\"\n+      ]\n+    },\n+    \"nonrecursive\": {\n+      \"additional_private_slots\": 1,\n+      \"local_routes\": 4806000,\n+      \"local_scalar\": 158214,\n+      \"owned_slots_backward\": 3,\n+      \"raw_budget\": 1000000000,\n+      \"raw_scalar_upper\": 181098496\n+    },\n+    \"ordinary_BIT\": {\n+      \"admitted\": \"17/5000\",\n+      \"after_cover\": \"69/20000\",\n+      \"atom\": \"1/250\",\n+      \"before_cover\": \"3459/1000000\",\n+      \"ordinary_saving\": \"8590884599/2500000000000\",\n+      \"prime_rule\": \"odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses\"\n+    },\n+    \"outer\": {\n+      \"functional_checks\": {\n+        \"actual_new_BIT_stock_sublinear\": \"174299999253/175000000000\",\n+        \"fixed_halo_explicit_metadata_branch\": \"13475000001/175000000\",\n+        \"new_BIT_row_stock_sublinear_in_active_group\": \"697899997009/700000000000\",\n+        \"new_semantic_group_guard\": \"3/700000000\"\n+      },\n+      \"margins\": {\n+        \"boundary_algebraic_matrix\": \"23139910904443/7656250000000000\",\n+        \"fused_gaussian\": \"23139910838329/7656250000000000\",\n+        \"global_coordinate_router\": \"2115649/700000000\",\n+        \"group_bit_router\": \"1480954993653053/490000000000000000\",\n+        \"group_scans\": \"349999999/350000000\",\n+        \"main_transform\": \"23139899966943/7656250000000000\",\n+        \"microbox_face_corrections\": \"13475000001/175000000\",\n+        \"polynomial_products\": \"699999999/700000000\",\n+        \"sparse_union_movement\": \"3133491473404443/7656250000000000\"\n+      },\n+      \"parameters\": {\n+        \"a\": \"2115649/700000000\",\n+        \"b\": \"42313/14000000\",\n+        \"beta\": \"699999997/700000000\",\n+        \"bit_saving\": \"17/5000\",\n+        \"cap_xi\": \"6961616462466943/7656250000000000\",\n+        \"complex_uniform_saving\": \"2115651/700000000\",\n+        \"d\": \"1/700000000\",\n+        \"epsilon\": \"699999999/700000000\",\n+        \"kappa\": \"60447/20000000\",\n+        \"lambda_\": \"199395529/200000000\",\n+        \"lambda_prime\": \"10904443/10937500\",\n+        \"layout\": \"1/700000000\",\n+        \"q\": \"33057/10937500\",\n+        \"r0\": \"1/7000000000\",\n+        \"stop\": \"1/700000000\",\n+        \"tested_saving\": \"75559/25000000\"\n+      },\n+      \"strict_checks\": {\n+        \"actual_bit_above_effective\": \"264351/700000000\",\n+        \"actual_logarithmic_gamma_guard\": \"1/700000000\",\n+        \"actual_logarithmic_group_guard\": \"694633553939307/3828125000000000\",\n+        \"alpha_logarithm_absorption\": \"1/7000000000\",\n+        \"boundary_algebraic_matrix_above_kappa\": \"43716943/7656250000000000\",\n+        \"cap_above_band\": \"3133491462466943/7656250000000000\",\n+        \"cap_below_cell\": \"694633526595557/7656250000000000\",\n+        \"cap_below_phase_cell_power\": \"8350883537533057/7656250000000000\",\n+        \"complex_above_effective\": \"1/700000000\",\n+        \"complex_below_one_over_32\": \"395187/14000000\",\n+        \"complex_endpoint\": \"1/350000000\",\n+        \"epsilon_below_one\": \"1/700000000\",\n+        \"epsilon_positive\": \"699999999/700000000\",\n+        \"fine_prime_halo_umbrella\": \"7/2\",\n+        \"fused_gaussian_above_kappa\": \"43650829/7656250000000000\",\n+        \"gaussian_above_main\": \"5435693/3828125000000000\",\n+        \"global_coordinate_router_above_kappa\": \"1/175000000\",\n+        \"global_gamma_power_slack\": \"9/7000000000\",\n+        \"group_below_dimension\": \"1/350000000\",\n+        \"group_bit_router_above_kappa\": \"3493653053/490000000000000000\",\n+        \"group_gauge_power_slack\": \"43414597087027/239257812500000\",\n+        \"group_key_fits_record\": \"1/350000000\",\n+        \"group_positive\": \"699999997/700000000\",\n+        \"group_scans_above_kappa\": \"697884353/700000000\",\n+        \"halo_covers_generic_inverse_radius\": \"5\",\n+        \"improvement_over_user_baseline\": \"645689790400418148631/500000000000000000000000\",\n+        \"lambda_above_internal\": \"1/1400000000\",\n+        \"lambda_above_sigma\": \"3/1400000000\",\n+        \"lambda_above_tau\": \"1/1400000000\",\n+        \"lambda_prime_above_lambda\": \"1/1400000000\",\n+        \"lambda_prime_above_leaf\": \"27957687/9800000000000000\",\n+        \"leaf_saving_above_effective\": \"13957687/9800000000000000\",\n+        \"main_transform_above_kappa\": \"32779443/7656250000000000\",\n+        \"membership_arithmetic_fits_record\": \"1/700000000\",\n+        \"microbox_face_corrections_above_kappa\": \"53897884359/700000000\",\n+        \"microbox_halo_volume\": \"55300000003/700000000\",\n+        \"new_complex_uniform_saving_above_b\": \"1/700000000\",\n+        \"new_semantic_guard_with_C1_one\": \"1/700000000\",\n+        \"polynomial_products_above_kappa\": \"348942177/350000000\",\n+        \"positive_layout_slack\": \"1/700000000\",\n+        \"q_below_effective\": \"1/700000000\",\n+        \"q_below_internal\": \"1/700000000\",\n+        \"q_below_leaf\": \"27957687/9800000000000000\",\n+        \"q_positive\": \"33057/10937500\",\n+        \"short_record_fallback\": \"13957687/14000000\",\n+        \"source_axis_superpolynomial\": \"1/700000000\",\n+        \"sparse_union_movement_above_kappa\": \"3110351606216943/7656250000000000\",\n+        \"stop_below_one\": \"699999999/700000000\",\n+        \"stop_positive\": \"1/700000000\",\n+        \"strassen_integer_power_gap\": \"1951441519231\",\n+        \"support_router_span\": \"3/700000000\",\n+        \"theta_positive_polynomial_power\": \"2\",\n+        \"union_header_fits_record\": \"3/700000000\",\n+        \"union_tag_work_per_visit_fits_record\": \"3/700000000\"\n+      }\n+    },\n+    \"paid\": {\n+      \"1\": 41282,\n+      \"16\": 448,\n+      \"2\": 7416,\n+      \"24\": 448,\n+      \"3\": 9180,\n+      \"32\": 448,\n+      \"4\": 2286,\n+      \"40\": 448,\n+      \"48\": 448,\n+      \"5\": 720,\n+      \"56\": 448,\n+      \"64\": 448,\n+      \"72\": 224,\n+      \"8\": 128\n+    },\n+    \"paid_calls\": 64372,\n+    \"productive_fields\": 10912,\n+    \"query_shears\": 15,\n+    \"rank_mass_surplus\": 752,\n+    \"raw_headroom\": [\n+      \"3736347/100000000000000\",\n+      \"934087/25000000000000\"\n+    ],\n+    \"raw_root_interval\": [\n+      \"302238736347/100000000000000\",\n+      \"75559684087/25000000000000\"\n+    ],\n+    \"strictification\": {\n+      \"alpha\": {\n+        \"lower\": \"0.999999971483293515393313955729\",\n+        \"upper\": \"0.999999971483293515393313955730\"\n+      },\n+      \"cutoff\": 20,\n+      \"delta\": {\n+        \"lower\": \"0.957459689758527661921334851512\",\n+        \"upper\": \"0.957459689758527661921334851513\"\n+      },\n+      \"floor\": 21,\n+      \"gamma\": {\n+        \"lower\": \"0.956310980726438847618396606911\",\n+        \"upper\": \"0.956310980726438847618396606912\"\n+      },\n+      \"normalized_paid_upper\": \"2097152001953127/2097154147483648\",\n+      \"power\": 1024,\n+      \"reserve\": \"1/1000000000\",\n+      \"tail_offset\": \"1/5\",\n+      \"tested\": \"75559/25000000\"\n+    },\n+    \"targets\": {\n+      \"145\": 224,\n+      \"17\": 448,\n+      \"25\": 448,\n+      \"33\": 448,\n+      \"4\": 504,\n+      \"41\": 448,\n+      \"49\": 448,\n+      \"57\": 448,\n+      \"65\": 448,\n+      \"7\": 126,\n+      \"73\": 224,\n+      \"8\": 846,\n+      \"9\": 5852\n+    }\n+  },\n+  \"candidate_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 325\n+      },\n+      \"independent_owned_entry_columns\": 3,\n+      \"independent_persistent_columns\": 631,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2200,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 7\n+      },\n+      \"real_scalar_allowance\": 158214,\n+      \"zero_identities\": 1\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"independent_source_identities\": {\n+    \"center_minus_snapshot\": \"Delta/4\",\n+    \"center_replaced\": 11332,\n+    \"copy_coefficient\": \"1\",\n+    \"relation\": {\n+      \"230\": 1,\n+      \"324\": -1,\n+      \"326\": 1,\n+      \"328\": 1,\n+      \"333\": -1\n+    },\n+    \"snapshot_after\": 11205,\n+    \"snapshot_terms_before_substitution\": 61,\n+    \"source_event_indices_are_zero_based\": true,\n+    \"zero_identity_at\": 15584,\n+    \"zero_site_row\": \"-Delta/4\"\n+  },\n+  \"native_negative_controls\": {\n+    \"missing_owned_input_clear\": \"Every independent main/helper endpoint: 0\",\n+    \"uncleared_owned_output\": \"Every owned entry column is erased at return\",\n+    \"under_or_overstated_paid_rank\": \"Exact paid rank and frame\",\n+    \"wrong_copy_gauge\": \"Exact scalar destination frame\",\n+    \"wrong_relation_sign\": \"Every independent main/helper endpoint: 0\",\n+    \"wrong_snapshot_source\": \"Zero identity requires an identically zero full row\",\n+    \"wrong_zero_input_frame\": \"Zero identity requires an identically zero full row\"\n+  },\n+  \"phase_inheritance\": {\n+    \"absolute_phase_receipt_reused\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"all_retained_paid_events_and_warps_from_source\": true,\n+    \"new_gaussian_operators\": 0,\n+    \"new_native_maps\": 0,\n+    \"new_operations\": \"Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.\",\n+    \"source_amplitudes_and_phase_lowering_freshly_replayed\": false\n+  },\n+  \"scope\": \"Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.\",\n+  \"source_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158168,\n+      \"zero_identities\": 0\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"source_payload_sha256\": \"cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd\",\n+  \"status\": \"PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION\",\n+  \"word_payload_sha256\": \"645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35\"\n+}\n@@ -0,0 +1,90 @@\n+{\n+  \"schema_version\": 1,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"files\": [\n+    {\n+      \"path\": \"certificates/selected-result.json\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"c35482cd9035843b15a634cc8276a7e1e40e8395\",\n+      \"sha256\": \"6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375\"\n+    },\n+    {\n+      \"path\": \"docs/research/agent-task-catalog.json\",\n+ 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\"1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f\"\n+    },\n+    {\n+      \"path\": \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"5a55034ec9e6185d981e16c28e1e2e455069e2cb\",\n+      \"sha256\": \"106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7\"\n+    },\n+    {\n+      \"path\": \"research/kappa-interface-round2-20261022/price_profile.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"1d93e43d1cb888d128c2faa2be83a96d85b84295\",\n+      \"sha256\": \"adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"4fc05ab08138218ba9f09e5c89b649afae7c914e\",\n+      \"sha256\": \"011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/complex/native_extensions.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"7f84894efc309546a903d314c7ac1473e7f594a8\",\n+      \"sha256\": \"50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"46d929df83817b85a5387bcdb9745e0627d6366e\",\n+      \"sha256\": \"7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"ac77b78547d6dbf2e6bd102e1047c5b16c1bca88\",\n+      \"sha256\": \"6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"0fdb65f946d557c13d8e2781b9151e2a8ddee5c3\",\n+      \"sha256\": \"b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de\"\n+    },\n+    {\n+      \"path\": \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59\",\n+      \"sha256\": \"d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15\"\n+    },\n+    {\n+      \"path\": \"research/query-thinned-controllers/RESULT.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"e0695152c98d727edfd0d2034b58a1c7e8682c0c\",\n+      \"sha256\": \"6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f\"\n+    }\n+  ]\n+}\n@@ -0,0 +1,80 @@\n+{\n+  \"schema_version\": 1,\n+  \"task_id\": \"complex-new-helper-inventory\",\n+  \"priority_revision\": 7,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"original_card\": {\n+    \"id\": \"complex-new-helper-inventory\",\n+    \"question\": \"Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?\",\n+    \"starting_points\": [\n+      \"docs/research/research-family-status.md\",\n+      \"research/complex-local-word-ceiling/README.md\",\n+      \"research/heterogeneous-owner-assembly/README.md\",\n+      \"certificates/selected-result.json\",\n+      \"research/selected-k8-unrestricted-ends/README.md\"\n+    ],\n+    \"methods\": [\n+      \"Propose a changed helper inventory and derive an optimistic exact moment.\",\n+      \"Design a small completed instance and independently verify its endpoint and rank bill.\"\n+    ],\n+    \"acceptance_gate\": \"A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.\",\n+    \"first_step\": {\n+      \"command\": [\n+        \"python3\",\n+        \"-B\",\n+        \"research/complex-local-word-ceiling/verify.py\"\n+      ],\n+      \"expected\": \"PASS_COMPLEX_LOCAL_WORD_CEILING\",\n+      \"inspect\": \"Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.\",\n+      \"scope\": \"Positive control and planning budget only; this is not a new construction or full cold replay.\"\n+    },\n+    \"first_experiment\": \"Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.\",\n+    \"bottleneck_link\": \"Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.\",\n+    \"allowed_variations\": [\n+      \"Narrow to one changed boundary or helper type with explicit counts.\",\n+      \"If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope.\"\n+    ],\n+    \"scope_change_triggers\": [\n+      \"Mixing only providers already inside the pinned catalogue.\",\n+      \"Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.\",\n+      \"Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts.\"\n+    ],\n+    \"overlap_terms\": [\n+      \"helper inventory\",\n+      \"heterogeneous-owner\",\n+      \"mutable leaver\"\n+    ]\n+  },\n+  \"scope_status\": \"refined\",\n+  \"actual_scope\": \"Make helper L230 owned in each backward call, prepare one five-helper relation, retain one exact frame-254 snapshot, remove one rank-eight center and one rank-one zero job, and debit one rank-nine target.\",\n+  \"scope_change_reason\": \"This uses the current helper-inventory priority. It changes the independent input inventory and scalar word; all physical native maps and the p16 controller remain fixed.\",\n+  \"bottleneck_link\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+  \"budget_minutes\": 240,\n+  \"stop_rule\": \"Publish one exact complete-profile kappa improvement after native, ownership, phase-inheritance, compiler and cold-export checks.\",\n+  \"outcome\": \"completed\",\n+  \"evidence\": \"README.md, WORD.json.gz, RESULT.json and verify.py. The complete conditional kappa is 60447/20000000.\",\n+  \"author\": \"Ali Romman\",\n+  \"ai_assistance\": \"Substantial OpenAI Codex assistance in discovery, code, proof, verification and publication.\",\n+  \"open_questions\": [\n+    {\n+      \"question\": \"Can a separate reviewer validate this one-relation restriction and the inherited physical transfer premises?\",\n+      \"why_it_matters\": \"The new finite construction is exact, but the complete bound still uses the source phase and all-size contracts.\",\n+      \"first_step\": \"Replay the three unrestricted source rows in native.py and check the COPY and zero-identity argument in README.md.\",\n+      \"blocked_by\": \"Independent review has not yet occurred.\"\n+    },\n+    {\n+      \"question\": \"Can a different helper relation give another complete positive bill?\",\n+      \"why_it_matters\": \"This construction gives one positive instance, not an optimum for changed helper inventories.\",\n+      \"first_step\": \"Claim a disjoint relation in Discussions, derive its exact rows, and include every lost target and owned-storage cost.\",\n+      \"blocked_by\": \"Current active cache and paid-history scopes must be checked first.\"\n+    }\n+  ],\n+  \"coordination\": {\n+    \"claim\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+    \"distinct_scopes\": [\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5355\",\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/4930\"\n+    ],\n+    \"boundary\": \"The first scope retains 632 arbitrary inputs and eight centers. The second retains every original helper endpoint. This package removes the independent L230 job only in backward calls and claims only the stated relation and two event replacements.\"\n+  }\n+}\n@@ -0,0 +1,38 @@\n+{\n+  \"schema_version\": 1,\n+  \"status\": \"ready\",\n+  \"python\": \"3.12\",\n+  \"requirements\": [],\n+  \"inputs\": [\n+    \"research/higher-moment-strictification/verify.py\",\n+    \"research/joint-helper-lattice/CONTROLLER.json\",\n+    \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+    \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+    \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+    \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+    \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+    \"research/query-thinned-controllers/RESULT.json\"\n+  ],\n+  \"commands\": [\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls.\"\n+    },\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-O\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"The same checks remain active with Python assertions disabled.\"\n+    }\n+  ]\n+}\n\n@@ -0,0 +1,299 @@\n+\"\"\"One prepared helper removes two paid jobs in the PR4610 backward word.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+The source word is by Cao Yifan. The row convention and scalar allowance\n+follow the credited native work of Cinna Davis and zxv.\n+\"\"\"\n+from collections import Counter\n+from copy import deepcopy\n+from fractions import Fraction as Q\n+from hashlib import sha1, sha256\n+from pathlib import Path\n+import gzip\n+import importlib.util\n+import json\n+import sys\n+\n+HERE = Path(__file__).resolve().parent\n+ROOT = HERE.parents[1]\n+SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'\n+PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz'\n+PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'\n+RELATION = {230: 1, 324: -1, 326: 1, 328: 1, 333: -1}\n+OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}\n+NEW_PAID = dict(OLD_PAID)\n+NEW_PAID[1] -= 1\n+NEW_PAID[8] -= 1\n+OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326}\n+\n+\n+def need(ok, why):\n+    if not ok:\n+        raise ValueError(why)\n+\n+\n+def read(path):\n+    data = path.read_bytes()\n+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)\n+\n+\n+def encode(x):\n+    if isinstance(x, Q):\n+        return str(x)\n+    if isinstance(x, dict):\n+        return {str(k): encode(v) for k, v in x.items()}\n+    if isinstance(x, (list, tuple)):\n+        return [encode(v) for v in x]\n+    return x\n+\n+\n+def load(relative, name):\n+    spec = importlib.util.spec_from_file_location(name, ROOT / relative)\n+    module = importlib.util.module_from_spec(spec)\n+    sys.modules[name] = module\n+    spec.loader.exec_module(module)\n+    return module\n+\n+\n+def authenticate():\n+    pins = read(HERE / 'SOURCES.json')\n+    for row in pins['files']:\n+        if row['usage'] != 'input':\n+            continue\n+        p = ROOT\n+        for part in Path(row['path']).parts:\n+            p /= part\n+            need(not p.is_symlink(), 'No source aliases')\n+        raw = p.read_bytes()\n+        need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path'])\n+        need(sha1(b'blob ' + str(len(raw)).encode() + b'\\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob')\n+    need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload')\n+    return pins\n+\n+\n+def span(basis):\n+    out = {0}\n+    for vector in basis:\n+        need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate')\n+        out |= {v ^ vector for v in tuple(out)}\n+    need(len(out) == 2 ** len(basis), 'Independent frame basis')\n+    return out\n+\n+\n+def add(dst, src, q):\n+    for k, v in tuple(src.items()):\n+        value = dst.get(k, Q(0)) + q * v\n+        if value:\n+            dst[k] = value\n+        else:\n+            dst.pop(k, None)\n+\n+\n+def allowance(g):\n+    if g[0] in ('clear', 'copy'):\n+        return 2\n+    q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:])\n+    n, d = abs(q.numerator), q.denominator\n+    need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar')\n+    if g[0] == 'scale':\n+        need(n & (n - 1) == 0, 'Dyadic unit SCALE')\n+        return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0))\n+    need(g[0] == 'add', 'Known scalar operation')\n+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)\n+\n+\n+def construct(source):\n+    c = source['canonical']\n+    old = source['programs']['backward']\n+    need(old[11205] == ['climb', 'warp_retimed', 92, 310, 254, 4], 'Snapshot source event')\n+    need(old[11332] == ['center', 0, 0, 254, 8], 'Center source event')\n+    need(old[15584] == ['climb', 'warp_retimed', 92, 254, 1, 1], 'Zero source event')\n+    need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in RELATION), 'Five cold full-ended helpers')\n+    word = [['scalar', ['clear', ['L', 230]], 0]]\n+    word += [['scalar', ['add', ['L', 230], ['L', h], -q, 1], 0]\n+             for h, q in RELATION.items() if h != 230]\n+    for i, event in enumerate(old):\n+        if i == 11332:\n+            word += [['scalar', ['clear', ['C', 0]], 254],\n+                     ['scalar', ['copy', ['C', 0], ['C', 1]], 254],\n+                     ['scalar', ['clear', ['C', 1]], 254]]\n+        elif i == 15584:\n+            word.append(['zero_retag', ['L', 92], 254, 1])\n+        else:\n+            word.append(deepcopy(event))\n+        if i == 11205:\n+            word += [['scalar', ['clear', ['C', 1]], 254],\n+                     ['scalar', ['copy', ['C', 1], ['L', 92]], 254]]\n+    word.append(['scalar', ['clear', ['L', 230]], 1])\n+    physical = deepcopy(c)\n+    physical.pop('local_profile')\n+    return {'schema': 'owned-helper-relation-word/1', 'canonical': physical,\n+            'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID},\n+            'owned': {'forward': [['C', 0]], 'backward': [['C', 0], ['C', 1], ['L', 230]]},\n+            'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}}\n+\n+\n+def replay(c, program, backward, specialized):\n+    \"\"\"Run every event on all independent entry columns and exact frames.\"\"\"\n+    owned = {('C', 0)} | ({('C', 1), ('L', 230)} if specialized else set())\n+    roles = {('L', i) for i in range(632)} | owned\n+    rows = {r: {(r, ()): Q(1)} for r in roles}\n+    frames = {('L', i): f for i, f in enumerate(c['start'])}\n+    frames.update({r: None for r in owned if r[0] == 'C'})\n+    spaces = [span(b) for b in c['frames']]\n+    paid = Counter()\n+    cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0\n+    for e in program:\n+        kind, touched = e[0], None\n+        if kind == 'scalar':\n+            g, frame = e[1:]\n+            dst = tuple(g[1]); touched = dst\n+            need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame')\n+            cost += allowance(g)\n+            if g[0] == 'clear':\n+                need(dst in owned, 'Only owned fields can be erased')\n+                rows[dst] = {}; frames[dst] = frame\n+            else:\n+                need(frames[dst] == frame, 'Exact scalar destination frame')\n+                if g[0] in ('add', 'copy'):\n+                    src = tuple(g[2])\n+                    need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame')\n+                    if g[0] == 'copy':\n+                        need(dst in owned and not rows[dst], 'COPY into cleared owned storage')\n+                        rows[dst] = dict(rows[src])\n+                    else:\n+                        add(rows[dst], rows[src], Q(g[3], g[4]))\n+                else:\n+                    need(g[0] == 'scale', 'Known scalar operation')\n+                    rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()}\n+        elif kind == 'warp':\n+            _, role, op, old, new = e\n+            dst = tuple(role); touched = dst\n+            need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input')\n+            symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0))\n+            rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q\n+                         for (r, w), q in rows[dst].items()}\n+            frames[dst] = new\n+        elif kind in ('climb', 'center'):\n+            if kind == 'climb':\n+                _, _, i, old, new, rank = e\n+                dst = ('L', i)\n+                need(spaces[old] < spaces[new], 'Ascending paid climb')\n+            else:\n+                _, i, old, new, rank = e\n+                dst = ('C', i)\n+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center')\n+            need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame')\n+            frames[dst] = new; paid[rank] += 1\n+        elif kind == 'zero_retag':\n+            _, role, old, new = e\n+            dst = tuple(role)\n+            need(specialized and backward and dst == ('L', 92), 'Declared zero identity')\n+            need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row')\n+            need((old, new) == (254, 1), 'Declared zero frame change')\n+            frames[dst] = new; zero_count += 1\n+        else:\n+            need(kind in ('phase', 'adapter'), 'Known inert source marker')\n+        if touched is not None:\n+            max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0)))\n+            denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1))\n+    need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame')\n+    for i in range(632):\n+        r = ('L', i)\n+        if r in owned:\n+            continue\n+        expected = {(r, ()): Q(1)}\n+        if i < 112 if backward else 112 <= i < 224:\n+            expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1)\n+        need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i))\n+    need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return')\n+    need(zero_count == int(specialized), 'Exactly one checked zero identity')\n+    helpers = Counter()\n+    for i in range(224, 632):\n+        if ('L', i) in owned:\n+            continue\n+        a, b = c['start'][i], c['final'][i]\n+        need(spaces[a] < spaces[b], 'Strict independent productive helper')\n+        helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1\n+    return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())),\n+            'independent_persistent_columns': 631 if specialized else 632,\n+            'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True,\n+            'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1),\n+            'max_denominator': denominator, 'zero_identities': zero_count}\n+\n+\n+def independent_source_identities(source):\n+    \"\"\"Use the predecessor row engine on the unrestricted original word.\"\"\"\n+    v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'owned_relation_source_rows')\n+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}\n+    rows['C', 0] = v.identity(('C', 0))\n+    delta = {(('L', i), ()): Q(q) for i, q in RELATION.items()}\n+    saved = None\n+    for index, e in enumerate(source['programs']['backward']):\n+        if e[0] == 'scalar':\n+            g = e[1]; dst = tuple(g[1])\n+            if g[0] == 'clear': rows[dst] = {}\n+            elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])])\n+            elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()}\n+            else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4]))\n+        elif e[0] == 'warp':\n+            dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True)\n+        if index == 11205: saved = dict(rows['L', 92])\n+        if index == 11332:\n+            diff = dict(rows['C', 0]); v.add(diff, saved, -1)\n+            need(diff == {k: q / 4 for k, q in delta.items()}, 'Independent exact center minus snapshot = Delta/4')\n+        if index == 15584:\n+            need(rows['L', 92] == {k: -q / 4 for k, q in delta.items()}, 'Independent exact zero-site row = -Delta/4')\n+    need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints')\n+    return {'source_event_indices_are_zero_based': True, 'snapshot_after': 11205,\n+            'center_replaced': 11332, 'zero_identity_at': 15584,\n+            'snapshot_terms_before_substitution': len(saved), 'copy_coefficient': '1',\n+            'center_minus_snapshot': 'Delta/4', 'zero_site_row': '-Delta/4', 'relation': RELATION}\n+\n+\n+def phase_inheritance(source, candidate):\n+    receipt = read(ROOT / PHASE)\n+    need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and\n+         receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt')\n+    physical = deepcopy(source['canonical']); physical.pop('local_profile')\n+    need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged')\n+    for direction, program in candidate['programs'].items():\n+        old = source['programs'][direction]\n+        for kind in ('warp', 'adapter', 'phase'):\n+            need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence')\n+        old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center'))\n+        new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center'))\n+        expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for i in (11332, 15584))\n+        need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the two proved jobs are removed')\n+    return {'new_gaussian_operators': 0, 'new_native_maps': 0,\n+            'all_retained_paid_events_and_warps_from_source': True,\n+            'absolute_phase_receipt_reused': PHASE,\n+            'source_amplitudes_and_phase_lowering_freshly_replayed': False,\n+            'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'}\n+\n+\n+def controls(c, candidate):\n+    controls = {}\n+    base = candidate['programs']['backward']\n+    variants = {}\n+    bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad\n+    variants['missing_owned_input_clear'] = deepcopy(base[1:])\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63]\n+    variants['wrong_snapshot_source'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0\n+    variants['wrong_zero_input_frame'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1\n+    variants['under_or_overstated_paid_rank'] = bad\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0\n+    variants['wrong_copy_gauge'] = bad\n+    variants['uncleared_owned_output'] = deepcopy(base[:-1])\n+    for name, program in variants.items():\n+        try:\n+            replay(c, program, True, True)\n+        except ValueError as err:\n+            controls[name] = str(err)\n+        else:\n+            raise ValueError('Control accepted: ' + name)\n+    return controls\n@@ -0,0 +1,196 @@\n+\"\"\"Complete p16 bill and finite compiler for one owned helper relation.\n+\n+The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna\n+Davis's PR4470 controller, zxv's completion and logarithmic majorant, and\n+Jacob Alan Sussman's mixed-target recursion. Apache-2.0.\n+Ali Romman, with substantial OpenAI Codex assistance.\n+\"\"\"\n+from collections import Counter\n+from fractions import Fraction as Q\n+from native import ROOT, read, load, need, encode, OLD_PAID, OLD_HELPERS\n+\n+KAPPA = Q('.00302235')\n+TESTED = Q('.00302236')\n+PREVIOUS = Q('.0030217758')\n+OLD_ROOT_UPPER = Q('.00302177587078')\n+\n+\n+def controller():\n+    \"\"\"Check the literal p16 word and both rational boundary programs.\"\"\"\n+    word = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json')\n+    need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller')\n+    zero = (0,) * 34\n+    def plus(dst, src, q):\n+        for k, v in src.items():\n+            value = dst.get(k, Q(0)) + q * v\n+            if value: dst[k] = value\n+            else: dst.pop(k, None)\n+    def shifted(row, term, sign=1):\n+        return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row]\n+    for side in ('left', 'right'):\n+        matrix = [[Q(i == j) for j in range(32)] for i in range(32)]\n+        for e in word['boundaries'][side + '_program']:\n+            if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]]\n+            elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]]\n+            else:\n+                need(e[0] == 'ADD', 'Boundary scalar opcode')\n+                matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])]\n+        need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program')\n+    rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']]\n+    for e in word['physical_events']:\n+        if e[0] in ('LOCAL', 'QUERY_SHEAR'):\n+            _, stage, pair, back = e\n+            x, y = 2 * pair, 2 * pair + 1\n+            if back: x, y = y, x\n+            term = (1 if back else -1,) + (0,) * 33\n+            for dst, src in zip(rows[y], shifted(rows[x], term)):\n+                plus(dst, src, Q(-1 if back else 1))\n+            if e[0] == 'LOCAL':\n+                term = (0,) + tuple(int(s == stage) for s in range(33))\n+                for r in (x, y): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'IDLE':\n+            term = (0,) + tuple(int(s in e[2]) for s in range(33))\n+            for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'ADD':\n+            for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3]))\n+        else:\n+            need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode')\n+            rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1)\n+    out = [[{} for _ in range(32)] for _ in range(32)]\n+    for i, row in enumerate(word['boundaries']['left']):\n+        for k, q in enumerate(row):\n+            if Q(q):\n+                for j in range(32): plus(out[i][j], rows[k][j], Q(q))\n+    expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)]\n+    need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors')\n+    return word\n+\n+\n+def assemble(native, word):\n+    T, P = Counter(), Counter()\n+    orientations = Counter(); thin = 0\n+    for e in word['physical_events']:\n+        if e[0] == 'LOCAL':\n+            direction = 'backward' if e[3] else 'forward'\n+            orientations[direction] += 1\n+            T.update(native[direction]['helpers']); P.update(native[direction]['paid'])\n+        elif e[0] == 'QUERY_SHEAR': thin += 1; P[1] += 112\n+        elif e[0] == 'IDLE': P[8 * len(e[2])] += 224\n+    main = Counter()\n+    for term in word['diagonal']:\n+        need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole Gaussian main target')\n+        main[1 + 8 * sum(term[1:])] += 112\n+    T.update(main)\n+    need(orientations == {'backward': 16, 'forward': 2} and thin == 15, 'Every actual call orientation')\n+    # This second census uses the source invoice and the two local deltas.\n+    check_T = Counter({int(r): n for r, n in word['invoice']['main'].items()})\n+    check_T.update({r: 18 * n for r, n in OLD_HELPERS.items()}); check_T[9] -= 16\n+    check_P = Counter({int(r): n for r, n in word['invoice']['whole_idle'].items()})\n+    check_P.update({r: 18 * n for r, n in OLD_PAID.items()}); check_P[1] += 1680 - 16; check_P[8] -= 16\n+    need(T == check_T and P == check_P, 'Independent full invoice substitution')\n+    need(sum(T.values()) == 10912 and sum(P.values()) == 64372, 'Complete productive and paid counts')\n+    need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Unchanged complete rank surplus')\n+    return T, P\n+\n+\n+def run(native):\n+    word = controller(); T, P = assemble(native, word)\n+    prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json')\n+    need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing')\n+    prior_T = Counter({int(r): n for r, n in prior['targets'].items()})\n+    prior_P = Counter({int(r): n for r, n in prior['paid'].items()})\n+    prior_T[9] -= 16; prior_P[1] -= 16; prior_P[8] -= 16\n+    need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill')\n+    E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals')\n+    other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals')\n+    def margin(c):\n+        t, p = E.moment(T, 1 - c), E.moment(P, 1 - c)\n+        return t[0] - p[1], t[1] - p[0]\n+    need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint')\n+    lo, hi, grid = 0, 10**12, 10**14\n+    while hi - lo > 1:\n+        mid = (lo + hi) // 2\n+        if margin(Q(mid, grid))[0] > 0: lo = mid\n+        else: hi = mid\n+    root_low, root_high = Q(lo, grid), Q(hi, grid)\n+    need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure')\n+    need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom')\n+    # The complete signed profile decreases on [0, .05], and stays negative\n+    # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling.\n+    signed = {r: T[r] - P[r] for r in T.keys() | P.keys()}\n+    derivative, upper = None, None\n+    for i in range(16):\n+        l, r = Q(i, 320), Q(i + 1, 320); low = Q(0)\n+        for rank, n in signed.items():\n+            term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank))\n+            low += n * term[0 if n > 0 else 1]\n+        derivative = low if derivative is None else min(derivative, low)\n+    for i in range(128):\n+        l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560)\n+        value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items())\n+        upper = value if upper is None else max(upper, value)\n+    need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1')\n+    t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21\n+    target, paid = E.moment(T, t), E.moment(P, t)\n+    tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED)\n+    need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree')\n+    alpha = E.divide(paid, target)\n+    gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target))\n+    delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target))\n+    reserve = Q(1, 10**9); g = d = Q(97, 100)\n+    need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged')\n+    need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks')\n+    normalized = 1 / (1 + v * reserve) + Q(4, 2**32)\n+    need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding')\n+    theta, power = Q(63, 64), 1000\n+    eta = E.scale(E.power(145, -v * TESTED), t)\n+    need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')\n+    need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range')\n+    gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid')\n+    step = gap.denominator\n+    def wins(j): return (step * j + 1)**power < 2**j\n+    left, right = 1, 2\n+    while not wins(right): left, right = right, 2 * right\n+    while right - left > 1:\n+        mid = (left + right) // 2\n+        if wins(mid): right = mid\n+        else: left = mid\n+    height = step * right\n+    need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold')\n+    local_scalar = max(x['real_scalar_allowance'] for x in native.values())\n+    # The old route allowance is retained. Charge two additional owned field\n+    # lifetimes at two routes each, even though L230 uses an existing slot.\n+    routes = (max(sum(x['paid'].values()) for x in native.values()) + 2 * 408 + 688 + 4) * 1000\n+    need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit')\n+    scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right')))\n+    need(scalar_upper < 10**9, 'Complete raw nonrecursive bound')\n+    bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']\n+    atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted'])\n+    need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock')\n+    L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer')\n+    params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap,\n+              'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted,\n+              'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap}\n+    outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom)\n+    need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')\n+    need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict')\n+    controls = {}\n+    for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]:\n+        bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0]\n+        need(failed, 'Reject outer patch ' + name); controls[name] = failed\n+    bad_native = {d: dict(x) for d, x in native.items()}\n+    bad_native['backward']['helpers'] = OLD_HELPERS\n+    try: assemble(bad_native, word)\n+    except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census'\n+    else: raise ValueError('Unowned helper credit was accepted')\n+    return encode({'kappa': KAPPA, 'kappa_decimal': '.00302235', 'gain_over_PR4610': KAPPA - PREVIOUS,\n+                   'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA],\n+                   'margin_at_previous_kappa': E.display(margin(PREVIOUS)),\n+                   'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)),\n+                   'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)},\n+                   'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752,\n+                   'full_backward': 16, 'full_forward': 2, 'query_shears': 15,\n+                   'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized},\n+                   'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False},\n+                   'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': 1, 'owned_slots_backward': 3},\n+                   'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls})\n@@ -0,0 +1,64 @@\n+#!/usr/bin/env python3\n+\"\"\"Replay the one-relation native word and its complete conditional kappa.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+Read README.md for the source credit and inherited proof obligations.\n+\"\"\"\n+from hashlib import sha256\n+import argparse\n+import gzip\n+import json\n+from pathlib import Path\n+import sys\n+sys.dont_write_bytecode = True\n+import native as N\n+import price\n+\n+\n+def run():\n+    N.authenticate()\n+    source = N.read(N.ROOT / N.SOURCE)\n+    candidate = N.construct(source)\n+    c = candidate['canonical']\n+    before, after = {}, {}\n+    for direction in ('forward', 'backward'):\n+        back = direction == 'backward'\n+        before[direction] = N.replay(c, source['programs'][direction], back, False)\n+        after[direction] = N.replay(c, candidate['programs'][direction], back, back)\n+        N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Pinned source census')\n+        N.need(after[direction]['paid'] == candidate['paid_profiles'][direction], 'Emitted direction-specific paid profile')\n+        helpers = dict(N.OLD_HELPERS)\n+        if back: helpers[9] -= 1\n+        N.need(after[direction]['paid'] == (N.NEW_PAID if back else N.OLD_PAID) and after[direction]['helpers'] == helpers, 'Actual complete changed native census')\n+    identities = N.independent_source_identities(source)\n+    phase = N.phase_inheritance(source, candidate)\n+    controls = N.controls(c, candidate)\n+    arithmetic = price.run(after)\n+    data = (json.dumps(candidate, sort_keys=True, separators=(',', ':')) + '\\n').encode()\n+    result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION',\n+                       'source_payload_sha256': N.PAYLOAD, 'word_payload_sha256': sha256(data).hexdigest(),\n+                       'source_native': before, 'candidate_native': after, 'independent_source_identities': identities,\n+                       'phase_inheritance': phase, 'native_negative_controls': controls, 'arithmetic': arithmetic,\n+                       'scope': 'Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.'})\n+    return data, result\n+\n+\n+def main():\n+    ap = argparse.ArgumentParser(description=__doc__)\n+    ap.add_argument('--write', action='store_true', help='Write only this package word and result after all checks pass.')\n+    ap.add_argument('--out', type=Path, help='Write a replay result to a separate path.')\n+    args = ap.parse_args()\n+    data, result = run()\n+    if args.write:\n+        (N.HERE / 'WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))\n+        (N.HERE / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    else:\n+        N.need(gzip.decompress((N.HERE / 'WORD.json.gz').read_bytes()) == data, 'Exact literal published word')\n+        N.need(N.read(N.HERE / 'RESULT.json') == result, 'Exact published replay result')\n+    if args.out:\n+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR4610', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True))\n+\n+\n+if __name__ == '__main__':\n+    main()",
+    "comments": null,
+    "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+    "display_title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation"
+  },
+  "isError": false
+}
diff --git a/research/owned-relation-independent-validation/evidence/physical/CONNECTOR-PINS.json b/research/owned-relation-independent-validation/evidence/physical/CONNECTOR-PINS.json
new file mode 100644
index 0000000000..28c84c15fa
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/physical/CONNECTOR-PINS.json
@@ -0,0 +1,99 @@
+[
+  {
+    "path": "research/kappa-owned-relation-20261023/native.py",
+    "local": "pinned/native.py",
+    "git_blob": "b8249ed7ba981a798ba282a6aeabd81a600bda36",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/native.py"
+  },
+  {
+    "path": "research/kappa-owned-relation-20261023/verify.py",
+    "local": "pinned/verify.py",
+    "git_blob": "b19f7d0ca4a6e61a0a75595bbc413f9341e84717",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/verify.py"
+  },
+  {
+    "path": "research/kappa-owned-relation-20261023/price.py",
+    "local": "pinned/price.py",
+    "git_blob": "6077adf74c1a154e5f790411f774a52745eb5281",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/price.py"
+  },
+  {
+    "path": "research/kappa-owned-relation-20261023/SOURCES.json",
+    "local": "pinned/SOURCES.json",
+    "git_blob": "9854abbb4f66f20aad8ab5016ede8319cd47519c",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/SOURCES.json"
+  },
+  {
+    "path": "research/kappa-owned-relation-20261023/RESULT.json",
+    "local": "pinned/RESULT.json",
+    "git_blob": "27b4e5470812c2b9feaa54fbfe867b3fb68def68",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/RESULT.json"
+  },
+  {
+    "path": "research/kappa-owned-relation-20261023/README.md",
+    "local": "pinned/README.md",
+    "git_blob": "777f4e1d5114e35ba6de2a8e818b790b16aca655",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/README.md"
+  },
+  {
+    "path": "research/joint-helper-lattice/CONTROLLER.json",
+    "local": "pinned/controller-CONTROLLER.json",
+    "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5",
+    "ref": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/CONTROLLER.json"
+  },
+  {
+    "path": "research/joint-helper-lattice/README.md",
+    "local": "pinned/controller-README.md",
+    "git_blob": "8c9bd69cd445bd05f18ffcf86d6feb556d634b14",
+    "ref": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/README.md"
+  },
+  {
+    "path": "research/joint-helper-lattice/PROOF.md",
+    "local": "pinned/controller-PROOF.md",
+    "git_blob": "e41106031da41fade7a7419c17a32c1bd9aa103b",
+    "ref": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/joint-helper-lattice/PROOF.md"
+  },
+  {
+    "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+    "local": "pinned/verify_buffers.py",
+    "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb",
+    "ref": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py"
+  },
+  {
+    "path": "research/free-word-tensor-lift-audit/PROOF.md",
+    "local": "pinned/PROOF.md",
+    "git_blob": "69c337a7704ce589798269ab4b8606189c070c4e",
+    "ref": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/free-word-tensor-lift-audit/PROOF.md"
+  },
+  {
+    "path": "research/final4610-independent-admission/SPECIALIZATION.md",
+    "local": "pinned/source4610-SPECIALIZATION.md",
+    "git_blob": "7ee84b30892f7354e1c36611f1a5e9b082dc6147",
+    "ref": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/research/final4610-independent-admission/SPECIALIZATION.md"
+  },
+  {
+    "path": "certificates/selected-result.json",
+    "local": "pinned/selected-current.json",
+    "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e",
+    "ref": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1ec1119972c9aefe42525172d07b332fcff81cb4/certificates/selected-result.json"
+  },
+  {
+    "path": "research/kappa-owned-relation-20261023/WORD.json.gz",
+    "local": "pinned/WORD.json.gz",
+    "git_blob": "5e79bd826c6ca1e782766ea0ae28a61d136303d1",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139"
+  }
+]
diff --git a/research/owned-relation-independent-validation/evidence/physical/PHYSICAL-REVIEW.md b/research/owned-relation-independent-validation/evidence/physical/PHYSICAL-REVIEW.md
new file mode 100644
index 0000000000..8c0d8f0965
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/physical/PHYSICAL-REVIEW.md
@@ -0,0 +1,106 @@
+# PR5377: independent bounded physical/operator/ownership review
+
+**Decision: the changed local physical witness passes this bounded review.** No counterexample or new physical primitive is needed for the two replacements. The saving genuinely changes the independent helper contract: one rank-nine output is surrendered per backward call. This is a local conditional proof and independent finite check; it does not independently admit the complete claimed kappa or rerun the source phase/physical foundations.
+
+Reviewed PR: <https://github.com/CrocSwap/integer-mult-bounds/pull/5377>. The read-only GitHub connector authenticated head `c448d13c71908647f968b06cddb795ce7d288139`, with current base `1ec1119972c9aefe42525172d07b332fcff81cb4`. The sole upstream monitor separately confirmed that head unchanged. The current selected record is still final PR4610, kappa `.0030217758`, independently admitted through PR5241, with the same five PR4470 framework assumptions. This review changes no selected record and publishes nothing.
+
+The author is Ali Romman, with substantial OpenAI Codex assistance. Cao Yifan supplied the final PR4610 native word; Cinna Davis supplied the p16 controller and helper lineage. The predecessor native, physical, compiler and free-word credit is retained. This independent check was also prepared with OpenAI Codex assistance.
+
+## Exact inputs and reproducibility
+
+`VERIFIED-PINS.json` records 16 consumed artifacts with source commits, Git blobs, SHA256 and local file names. Every fetched text file was checked to have the connector-reported Git blob after local materialization. The two source gzip files were copied read-only from the parallel final4610 review snapshot, then checked against both Git blobs and SHA256 in PR5377's connector-authenticated SOURCES.json.
+
+Principal pins:
+
+| Object | Git blob |
+|---|---|
+| PR5377 literal WORD.json.gz | `5e79bd826c6ca1e782766ea0ae28a61d136303d1` |
+| PR5377 native.py | `b8249ed7ba981a798ba282a6aeabd81a600bda36` |
+| PR5377 README.md proof | `777f4e1d5114e35ba6de2a8e818b790b16aca655` |
+| PR5377 SOURCES.json | `9854abbb4f66f20aad8ab5016ede8319cd47519c` |
+| Final PR4610 ACTUAL-WORD.json.gz | `46d929df83817b85a5387bcdb9745e0627d6366e` |
+| Final PR4610 PHASE-VALIDATION.json.gz | `ac77b78547d6dbf2e6bd102e1047c5b16c1bca88` |
+| Literal p16 CONTROLLER.json | `49a2f0675819f9deeea27ed77be2c2b6ff2e87e5` |
+| Controller PROOF.md | `e41106031da41fade7a7419c17a32c1bd9aa103b` |
+| Accepted source SPECIALIZATION.md | `7ee84b30892f7354e1c36611f1a5e9b082dc6147` |
+
+The source decompressed payload is `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`; the candidate gzip SHA256 is `8d913767ad773839995e54e4d80aeff692a86687d0f78153311c8ad62b7ba1bc`. The source phase receipt explicitly binds that source payload. No physical recipe is inferred from a matching rank alone.
+
+Run from the project workspace:
+
+```sh
+python3 -B outputs/owned-relation-5377-physical-review-20261024/independent_physical_check.py
+```
+
+The check completed in 3.581 seconds with `PASS_BOUNDED_INDEPENDENT_PHYSICAL_DELTA`. It imports no submitted or predecessor evaluator. `independent-result.json` is the actual output. There was no solver, emitter, Lean build, source phase lowering, full compiler run or full-history preflight in this task. The separate registered cold-run and cost reviewers own those validation decisions.
+
+## What changes, and why the copies are physical
+
+Use the backward source word and its exact inherited orientation convention. All event indices in the next paragraph refer to the zero-based original source, before new events are inserted. All five helpers in
+
+`Delta = h230 - h324 + h326 + h328 - h333`
+
+start in frame 0 (dimension zero) and finish in frame 1 (dimension nine). The candidate clears L230 and forms `h230=h324-h326-h328+h333` by four same-frame ADDs. The retained four inputs remain unrestricted. L230 has ceased to be an independent productive input and is explicitly private.
+
+An independent reverse functional propagation through the source word gives, over the exact rational free group algebra,
+
+* `C0 at event 11332 - L92 just after event 11205 = Delta/4`;
+* `L92 at event 15584 = -Delta/4`.
+
+The saved L92 row has 61 terms before subtraction. Reverse propagation appends native symbols on the right and cancels only adjacent inverse symbols. This is different from the submitted forward row interpreter; it does not substitute a finite numerical native matrix or assume distinct generators commute. Controls changing the relation sign and snapshot owner fail the equalities.
+
+The paid event 11205 places L92 in the exact frame 254, whose dimension is eight. Candidate C1 is first cleared in frame 254 and then receives L92 by COPY. It remains untouched until the center replacement. The old center event 11332 is the rank-eight transition from frame 0 to frame 254. Under Delta=0, its old output and the saved C1 have the same logical value **and the same exact oriented frame operator**, so copying C1 into cleared C0 reproduces the old physical output, including scalar coefficient one and the inherited absolute gauge. Equality of dimensions alone would not suffice; equality of the actual frame label is checked.
+
+The later rank-one event 15584 changes L92 from frame 254 to frame 1. Its full logical row is zero under the prepared relation. Every linear frame operator maps zero to zero, so physical identity has the required output. `zero_retag` is bookkeeping for this state-specific identity; it is not an uncharged transform of a general nonzero field. The candidate's shifted index for this marker is 15593. Subsequent operations use frame 1 as required by the source itinerary.
+
+The literal-word comparison proves that these are the only event changes: initial relation preparation, the C1 snapshot, center replacement, zero identity and final L230 clear. All retained events remain in source order. Every canonical frame, native map, main chart, and signed native occurrence is unchanged; the forward program is byte-equivalent as a parsed literal event list. Therefore no new Gaussian phase circuit or new native map needs to be invented for this delta.
+
+## Arbitrary inputs, raw orientations and returned storage
+
+A separate exact forward propagation checks source and candidate words in **both orientations**, including every initial independent column, all scalar gauges, nested paid transitions, paid ranks, final gauges and owned returns.
+
+| Word/orientation | Independent retained fields | Arbitrary owned entry fields | Result |
+|---|---:|---:|---|
+| Source forward | 632 | 1 | Main forward shear, all helpers retained, owned C0 zero |
+| Source backward | 632 | 1 | Main backward shear, all helpers retained, owned C0 zero |
+| Candidate forward | 632 | 1 | Identical forward contract |
+| Candidate backward | 631 | 3 | 224 main plus 407 helpers retained; C0, C1 and L230 zero |
+
+For each retained main/helper output, the complete logical row is exactly its required identity/shear row. No output contains an owned entry column. In the backward direction the main shear is `(x,y)->(x-y,y)`; forward is `(x,y)->(x,y+x)`. The helpers have their same complete physical source residuals because both their logical endpoint identity and ordered entrance/exit frame bases are unchanged.
+
+The inverse-transpose/raw-dual convention is inherited from the actual source oriented operators. The free symbols for the backward word denote those full operators, not a guessed normalized Gaussian transpose. Treating them as separate abstract generators is legitimate because the identities hold for every invertible substitution. The exact source absolute phases are reused; this task did not independently lower them. The current PR4610 admission includes the full actual phase-bearing classes, beyond the author's original changed-pair phase receipt. Candidate retained recipes are a subset of that same source catalogue.
+
+The candidate backward supplier is not required to retain all forward helpers or be the inverse transpose of the entire forward input/output map on 632 independent productive fields: it explicitly has a smaller independent helper contract. What the controller needs is the same main oriented interface and the listed independent helper residuals. Both are established. Importing an obstruction that assumes all 408 original helpers remain productive would not address this changed contract.
+
+C0 and C1 are owned, so the old C0 value can be erased at replacement and the copied C1 value erased afterward. C1's arbitrary entry value is cleared before first read. L230's arbitrary entry value is cleared before preparing the relation, and its dependent output is cleared at return. No retained input is erased. Borrowed temporary fields are not reclassified silently; the one reclassification is the explicitly surrendered L230 job.
+
+## Actual 18-call incidence and unique productive owners
+
+The literal controller has forward LOCAL stages 0 and 32, backward LOCAL stages `1,3,...,31`, and 15 QUERY_SHEAR events. The improvement therefore applies 16 times, not 18. The controller proof section 4 explicitly assigns a fresh disjoint helper bank to every full call. These 18 banks are separate from the main banks and query scratch.
+
+Label a helper by `(LOCAL stage, helper role)`. Remove exactly `(stage,230)` for the 16 backward stages. The other 407 helper roles at each such stage remain distinct arbitrary inputs and outputs. Both forward banks retain all 408 helpers, including L230. Consequently there are
+
+`16*407 + 2*408 = 7,328`
+
+independent helper outputs, plus the unchanged `32*112 = 3,584` controller main fields: **10,912 independent productive fields, each once**. The new C1, C0, private L230 and query scratch receive no productive credit. The scalar controller and diagonal main outputs are inherited because every LOCAL main interface is unchanged.
+
+The exact local paid profiles independently counted from candidate events are:
+
+* forward: `{1:2201,2:412,3:510,4:127,5:40,8:8}`;
+* backward: `{1:2200,2:412,3:510,4:127,5:40,8:7}`.
+
+The local target difference is minus one rank-nine helper only in backward calls. Thus the full delta is minus 16 paid rank-one jobs, minus 16 paid rank-eight jobs and minus 16 rank-nine productive targets. The total rank mass balance is unchanged because `1+8=9`; the concave moment gain is positive as stated in the author proof. The separate cost review checks the complete bill and kappa transfer.
+
+## Finite cost, tensor lift and inherited contracts
+
+The new scalar operations use the source alphabet: four ADDs with coefficients +/-1, owned COPY/CLEAR and physical identity on zero. Under the source scalar macro formula the added work is 46 real scalar operations: 32 for the four ADDs and 14 for seven COPY/CLEAR operations. There is one extra raw private slot C1; L230 reuses an existing physical slot but no longer earns helper credit. The author's route allowance additionally charges four route groups for the two new owned lifetimes. These are finite paid scalar/storage/route changes, not free initialization of a productive input.
+
+The source specialization explicitly permits owned COPY/CLEAR, distinct suspended center banks, and newly counted finite template constants. In recursive substitution each suspended occurrence must retain its own relevant owned bank until return; sequential raw-call reuse is not permission to alias simultaneous suspended occurrences. The candidate can use this same allocation rule with C1 and private L230 included in the owned count. No different ownership theorem is required.
+
+For every positive tensor width, evaluate the formal free generators at their source tensor lifts while retaining scalar coefficients outside the substitution. The source identities and Delta=0 then hold on every vector, including correlated/nonseparable inputs. The relation is a linear combination of whole fields, not a tensor power of a sum. Same-frame COPY and identity on zero commute with this substitution. This proves the algebraic lift of the local replacements; it does not provide a physical runtime theorem from finite tests.
+
+For physical costs, precision and tape storage, the source's domain and finite-template prescriptions must remain intact. The raw source `10^9` allowance is not the expanded compiler's storage or error constant. Expanded W,P,O,R,G,N must describe the changed construction, including extra suspended owned banks; then the source fixed-template formulas apply before multiplication input size grows. Formal prefix L1 bounds are useful checks, not a substitute for that source precision contract. Approximate intermediate zero values are handled by the error bound for the actual changed program, rather than by assuming numerical error disappears at `zero_retag`.
+
+The five inherited selected assumptions remain: native all-column/phase/whole-job realization; permitted owned allocation/erasure; chronological product/completion/splitting and mixed-target uniform compiler closure; fixed-tape movement and precision/storage; analytic decomposition, prime avoidance and exact recovery. This review establishes the candidate-specific local operator/ownership implication within that grammar. It does not discharge those generic foundations, audit the full numerical compiler/outer predicates, or supply independent human/formal-kernel acceptance.
+
+**Recommended disposition for this review slice:** positive scoped physical-delta evidence. Combine it with the separate exact complete-cost/compiler review and registered cold validation before any broader admission decision. The changed word has a valid source-bound local mechanism; no need to repeat the older full-helper or two-H1 cross-register searches to decide this proposal.
diff --git a/research/owned-relation-independent-validation/evidence/physical/VERIFIED-PINS.json b/research/owned-relation-independent-validation/evidence/physical/VERIFIED-PINS.json
new file mode 100644
index 0000000000..af8d7ff840
--- /dev/null
+++ b/research/owned-relation-independent-validation/evidence/physical/VERIFIED-PINS.json
@@ -0,0 +1,177 @@
+[
+  {
+    "path": "research/kappa-owned-relation-20261023/native.py",
+    "local": "pinned/native.py",
+    "git_blob": "b8249ed7ba981a798ba282a6aeabd81a600bda36",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/native.py",
+    "sha256": "85d994fc5661bfa53c4b42f79955ff74ffe70072163cb02fa76cd79efbcc0c97",
+    "bytes": 14132,
+    "verified_blob": "b8249ed7ba981a798ba282a6aeabd81a600bda36",
+    "exact": true
+  },
+  {
+    "path": "research/kappa-owned-relation-20261023/verify.py",
+    "local": "pinned/verify.py",
+    "git_blob": "b19f7d0ca4a6e61a0a75595bbc413f9341e84717",
+    "ref": "c448d13c71908647f968b06cddb795ce7d288139",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/verify.py",
+    "sha256": "c4d4fe9b74db1d47fbbfc0c602315d8256a15f0ad0e50b9fcfe2249bf65916f1",
+    "bytes": 3443,
+    "verified_blob": "b19f7d0ca4a6e61a0a75595bbc413f9341e84717",
+    "exact": true
+  },
+  {
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+    "pull_request": {
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+      "number": 5377,
+      "state": "open",
+      "merged": false,
+      "mergeable": true,
+      "draft": false,
+      "body": "This construction gives **conditional κ = 60447/20000000 = 0.00302235**, a gain of **0.0000005742** over Cao Yifan's final [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610) value, 0.0030217758. It changes the complete paid profile and moves its raw crossing. The selected frontier is unchanged.\n\nThe [proof and complete bill](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/README.md), [exact result](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/RESULT.json), [literal word](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/WORD.json.gz) and [source pins](https://github.com/aliromman/integer-mult-bounds/blob/c448d13c71908647f968b06cddb795ce7d288139/research/kappa-owned-relation-20261023/SOURCES.json) define the review scope.\n\nIn each backward call, make L230 private and prepare `h230 = h324 - h326 - h328 + h333` from four arbitrary cold helpers. Debit its rank-nine productive output. Let `Delta = h230 - h324 + h326 + h328 - h333`. Exact replay of the unrestricted source gives `C0 - saved_L92 = Delta/4` at center event 11332, and `L92 = -Delta/4` at climb event 15584. The saved value is taken just after event 11205 in the same frame as the center output. Under the prepared relation, one owned copy replaces the rank-eight job, and physical identity on a proved zero row replaces the rank-one job. All event indices are zero-based.\n\nAll 224 main inputs and the other 407 backward helper inputs remain arbitrary and independent. Every retained output keeps its complete source operator. Forward calls keep all 408 helpers. Explicit clears remove arbitrary owned entry values and erase every private output. One new private slot and 46 additional scalar operations per backward call are charged. Every retained Gaussian operator, native map, frame gauge and main adapter is unchanged.\n\nThe p16/a7 controller has 16 backward calls, two forward calls and 15 query shears. Its complete difference is **−16 H1 −16 H8 paid jobs and −16 H9 targets**. For every `0<t<1`, the target-minus-paid moment gains `16(1+8^t−9^t)>0`. The new bill has **64,372 paid jobs, 10,912 productive fields and rank surplus 752**, with every main, idle, query and completion term included.\n\nTwo rational interval engines check the complete bill. The fixed-profile crossing lies in **(0.00302238736347, 0.00302238736348)**. The claimed κ leaves more than **0.00000003736347** raw headroom. The separately tested saving is 0.00302236. Both completion tails, the finite compiler at `N=2^31385200000000`, and all **54 strict plus four functional outer predicates** pass. The complete raw nonrecursive bound remains **181,098,496 < 10^9**.\n\nBase: canonical main [7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56), priority revision 7. The source is the final [PR #4610 word](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz) at `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`; all consumed bytes are in the recorded main base. The [scoped Discussion claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737) distinguishes this changed inventory from the original-input cache and all-helper-return investigations. Live PRs and Discussions were checked again before publication.\n\nUse standard-library Python 3.12 from the repository root:\n\n```sh\npython3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023\n```\n\nBoth registered normal and optimized replays pass:\n\n```text\nPASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION\n```\n\nVerification covers exact free-word rows in both source and candidate orientations, all independent and owned entry columns, frame/rank checks, two separately computed source identities, the p16 Laurent factorization and scalar boundaries, independent full invoice counts, two rational interval engines, the fixed-profile ceiling, compiler and outer inequalities. Seven native and five cost/outer controls reject wrong relation, ownership, snapshot, gauge, rank, helper credit and compiler assumptions. Metadata, committed-byte checks, official export integrity and Git-free replay also pass. The optional full-history preflight is not claimed in this shallow checkout.\n\nThe [source absolute-phase receipt](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz) is authenticated and reused. New operations are same-frame scalar operations, owned copies/clears and identity on zero; there is no new Gaussian phase recipe. Full source phase lowering, BIT native replay, Lean, Docker, physical tape/precision execution, analytic decomposition and integer recovery were not rerun. The bound retains the source permitted-erasure, whole-job, mixed-target all-size, native, precision, tape, analytic, prime and exact-recovery contracts. It is a conditional construction with exact finite evidence, not an unconditional theorem, practical speedup or independent human acceptance. The compiled word is algorithmically specified and not materialized.\n\nCao Yifan supplied the source construction and prior κ in [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610). Cinna Davis supplied the p16 controller and helper lineage in [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470). The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py) retains zxv's completion/compiler and Jacob Alan Sussman's mixed-target credit; Dugongue's transported frames and the wider native lineage remain credited. zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283) supplied the cache-contract handoff to find actual matching rows and lifetimes; its standalone example is not used here. The new result is this helper relation, its exact native realization and its complete positive bill.\n\nPrepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. Next review task: check the three source rows and COPY/zero argument, then the inherited transfer assumptions. No broader helper-relation search is claimed.\n",
+      "title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation",
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+      "requested_reviewers": null,
+      "requested_team_reviewers": null,
+      "diff": "@@ -0,0 +1,249 @@\n+# Conditional kappa 0.00302235 from one owned helper relation\n+\n+This construction gives **conditional kappa = 60447/20000000 = 0.00302235**.\n+The gain over Cao Yifan's final\n+[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+value, 0.0030217758, is **2871/5000000000 = 0.0000005742**.\n+The construction changes the complete paid profile. It does not obtain the\n+gain by taking more digits of the old root.\n+\n+One helper becomes owned storage in each backward call. A prepared relation\n+then makes one paid rank-eight center equal to an earlier saved value. The same\n+relation makes one later rank-one job act on zero. Both jobs can be removed,\n+with the rank-nine helper credit also removed. All other independent outputs\n+and all main interfaces keep their source operators.\n+\n+[WORD.json.gz](WORD.json.gz) is the complete emitted word.\n+[RESULT.json](RESULT.json) records the exact native checks, the two source\n+identities, both full profiles, completion, compiler and outer calculations.\n+[SOURCES.json](SOURCES.json) pins every external input by Git blob and SHA256.\n+The proof below explains why the changed word has the stated contract.\n+\n+## Source and scope\n+\n+The base is canonical main\n+[7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56).\n+The native source is the final PR #4610 word at\n+[20bb93cd990d2ff683e4d0fc56b87a42cd5d3296](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz).\n+Its decompressed SHA256 is\n+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.\n+The comparison value and old crossing come from its\n+[final compiler arithmetic](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json).\n+All consumed bytes are already in the recorded main base.\n+\n+This is one instance of the current `complex-new-helper-inventory` priority.\n+The [scoped claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737)\n+reserves only the relation and two replacements below.\n+[Discussion #5355](https://github.com/CrocSwap/integer-mult-bounds/discussions/5355)\n+retains all 632 independent inputs and all eight centers.\n+[Discussion #4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930)\n+retains every original helper endpoint. This construction removes the\n+independent L230 job in backward calls. It does not claim those broader scopes.\n+The selected certificate is unchanged. A fresh check at 20:20 UTC found that\n+Discussion #5355 had released its original-input scope without a saving.\n+Canonical main still had the recorded base commit.\n+\n+## Exact replacement proof\n+\n+All indices below are zero-based indices in the frozen backward program.\n+Let `h_r` be the source logical input of helper `Lr`. The five helpers in\n+\n+```math\n+\\Delta=h_{230}-h_{324}+h_{326}+h_{328}-h_{333}\n+```\n+\n+all start in frame 0 and finish in frame 1, of rank nine. The new backward\n+contract has 224 independent main fields and 407 independent helper fields.\n+L230 is private. Clear it, then use four same-frame ADDs to prepare\n+\n+```math\n+h_{230}=h_{324}-h_{326}-h_{328}+h_{333}.\n+```\n+\n+The other helper inputs remain arbitrary and independent. This preparation\n+sets Delta to zero for every input. It uses no recursive job. It removes one\n+rank-nine productive target; the dependent field receives no output credit.\n+\n+Run the original source program on unrestricted inputs. Let `q` be the\n+logical row of L92 just after event 11205, a paid climb into frame 254.\n+The separate predecessor row engine gives these exact identities:\n+\n+| Source position | Exact logical row |\n+| --- | --- |\n+| C0 at the rank-eight center, event 11332 | `q + Delta/4` |\n+| L92 at the rank-one climb, event 15584 | `-Delta/4` |\n+\n+These identities are over rational coefficients and free native operator\n+words. They hold for every value of every source input and for every invertible\n+interpretation of the native symbols. They do not use numerical samples or an\n+assumed relation between distinct native maps.\n+\n+For every positive tensor width f, substitute each native generator by its\n+source operator tensor power and each inverse by the inverse tensor power.\n+This defines a representation of the free group. Keep the rational scalar\n+coefficients outside the substitution. The two row identities therefore hold\n+at every such width. In particular, Delta/4 remains a scalar linear form; it\n+is not a tensor power of that sum. This uses the termwise argument recorded in\n+the [free-word tensor audit](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/free-word-tensor-lift-audit/PROOF.md),\n+which credits Cinna Davis's proposal and ToikY's scoped audit. Physical frame\n+realization and the complete all-size compiler retain their source contracts.\n+\n+Immediately after event 11205, clear a new private field C1 in frame 254 and\n+COPY L92 into it. C1 is not written until the replacement of event 11332. At\n+that event, clear owned C0, set its frame to 254, COPY C1 into C0, then clear C1.\n+The copy coefficient is exactly one. Under Delta = 0, the copied field is the\n+same physical value as the old center output: the logical rows and the exact\n+frame gauge are equal. The old C0 input can be erased because C0 is owned.\n+This removes one rank-eight recursive job.\n+\n+At event 15584, L92 is exactly zero in every input column. The physical\n+identity therefore has the same result as the old rank-one frame change.\n+`zero_retag` records this fact. It performs no physical write and is accepted\n+only when the full exact row is empty and the current frame is 254. It then\n+records frame 1. This removes one rank-one recursive job. It does not erase a\n+main input or replace a nonzero transform with a free frame change.\n+\n+Every other event stays in source order. Clear private L230 at return. The\n+source clears C0, and the new program has already cleared C1. The original\n+linear endpoint identity, restricted by the prepared relation, gives all 224\n+main outputs and all 407 retained helper outputs. The literal new-word replay\n+checks these outputs separately, with all 631 retained inputs and all three\n+owned entry fields initially arbitrary. It also checks every scalar frame,\n+paid rank, native frame transition and final frame.\n+\n+The 4,429 source frames, 72 native maps, all remaining paid operators, and main\n+adapters are unchanged. The source\n+[absolute-phase certificate](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz)\n+is authenticated and reused. Same-frame COPY and identity on zero introduce no\n+phase recipe. The source's amplitude and Clifford-lowering checks are not\n+rerun by this package. The new free-word identities prove equivalence for the\n+source operators with their full phases, not just their projective classes.\n+\n+## Complete cost and conditional compiler\n+\n+The forward word is unchanged. Each backward call has these counts:\n+\n+```text\n+paid:    {1:2200, 2:412, 3:510, 4:127, 5:40, 8:7}\n+helpers: {4:28, 7:7, 8:47, 9:325}\n+```\n+\n+The full p16/a7 controller contains 16 backward calls, two forward calls and\n+15 query shears. Thus the complete difference is **minus 16 H1 and 16 H8 paid\n+jobs, and minus 16 H9 productive targets**. It includes every idle and main\n+target. There are 64,372 paid jobs and 10,912 productive fields. Their rank\n+masses are 238,990 and 239,742; the surplus remains 752.\n+\n+For every real `0 < t < 1`, the complete target-minus-paid moment increases by\n+\n+```math\n+16(1+8^t-9^t)>0.\n+```\n+\n+For a direct proof, both `(1/9)^t > 1/9` and `(8/9)^t > 8/9`; multiply their\n+sum by `9^t`. The improvement is strict throughout the required range.\n+\n+The backward word has 158,214 real scalar operations under the source macro\n+allowance, exactly 46 more than its source. Its maximum formal prefix L1 norm\n+is 169, with maximum denominator 64; both equal the source bounds. The forward\n+bounds remain 457 and 32. One extra physical private slot holds C1. L230 uses\n+an existing slot. The route bound also charges two routes for each of the two\n+new owned lifetimes. The local scalar-plus-route bound stays below 10^7, and\n+the complete raw nonrecursive bound stays **181,098,496 < 10^9**. Preparation,\n+COPY, CLEAR and storage therefore do not introduce an unpaid recursive cost.\n+\n+Two rational interval engines check the complete moment. Its unique crossing\n+in `0 < kappa < 1` lies in\n+**(0.00302238736347, 0.00302238736348)**. The verifier proves the moment decreases\n+on `[0,0.05]` and remains negative on `[0.05,1]`. This is a ceiling for this\n+fixed complete profile, not an optimum over circuits or helper relations.\n+The claimed kappa leaves more than **0.00000003736347** raw headroom.\n+\n+The separately tested saving is 0.00302236. The paid/target ratio is below\n+`0.999999971483293515393313955730`, with reserve `1e-9`. Both charged tails are\n+below `0.97`. The source power 1024, cutoff 20, floor 21, tail offset 1/5,\n+complement factor 63/64 and logarithm power 1000 still pass. The compiler gap\n+is `1/700000000`, with `j=44836`, `H=31385200000000` and `N=2^31385200000000`.\n+The exact integer test `(H+1)^1000 < 2^44836` passes; the preceding grid integer\n+fails. The uniform complex saving is `2115651/700000000`. All 54 strict outer\n+predicates and four functional predicates pass, using the retained ordinary\n+BIT saving 0.0034.\n+\n+## Verification and reproduction\n+\n+Use Python 3.12 or 3.14, with the standard library only. From the repository root:\n+\n+```sh\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023 --check-only\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023\n+```\n+\n+The registered commands run normal and optimized Python. The direct command,\n+also used for a Git-free export, is:\n+\n+```sh\n+python3 -B research/kappa-owned-relation-20261023/verify.py\n+python3 -O -B research/kappa-owned-relation-20261023/verify.py\n+```\n+\n+Each prints status\n+`PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION`.\n+The verifier reconstructs the word and compares its bytes and exact result with\n+the published artifacts. `--write` is a separate authoring command. It changes\n+only this package's word and result after all checks pass.\n+\n+Fresh checks cover both source words, both candidate words, every independent\n+entry column and owned return, the two unrestricted source identities, retained\n+phase bindings, the p16 rational Laurent factorization, both scalar boundary\n+programs, two complete invoice counts, two rational interval engines, the fixed\n+profile ceiling, completion, compiler, BIT conversion and all outer predicates.\n+The emitted word replaces the old single `canonical.local_profile` metadata\n+field with explicit `paid_profiles` for the two directions.\n+\n+Seven native controls reject a wrong relation sign, omitted input clear, wrong\n+snapshot, wrong zero frame, wrong paid rank, wrong copy gauge, and omitted\n+output clear. Five cost/outer controls reject the lost helper's output credit,\n+old BIT stock, closed uniform gap, unfunded endpoint and closed epsilon.\n+\n+Normal and optimized registered replays passed on CPython 3.12.14. The direct\n+author check also passed on CPython 3.14. Source metadata and pins passed.\n+The optional full-history preflight is not claimed in the shallow checkout.\n+The publication handoff records export and committed-byte checks.\n+\n+The full source phase lowering, BIT native replay, Lean, Docker, physical tape\n+execution, numerical precision execution, analytic decomposition and integer\n+recovery are not rerun here. The complete bound retains those predecessor\n+contracts, including permitted owned erasure, whole-job normalizers, mixed\n+productive-target recursion and all-size closure. The expanded compiled word\n+is specified by a finite algorithm, not materialized. This is a conditional\n+construction with exact finite evidence, not an unconditional multiplication\n+theorem, a practical timing result or independent human acceptance.\n+\n+## Credit\n+\n+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.\n+Cao Yifan's [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+supplies the exact source word, phase evidence and previous compiler value.\n+Cinna Davis's [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470)\n+supplies the p16 controller and helper-interface lineage. The source code keeps\n+credit for Dugongue's transported frames, zxv's native and finite-compiler\n+work, Jacob Alan Sussman's mixed-target recursion and their predecessors.\n+The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py)\n+and [literal native source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-rebuild/complex/native_extensions.py)\n+are pinned as provenance for the adapted checks.\n+\n+zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283)\n+supplies the related cache contract and the explicit handoff to find actual\n+matching rows and their lifetimes. Its standalone cache example is not part of\n+this word. The new contribution is the five-helper relation, its actual cache\n+and zero identities, the full owned-field replacement and the complete positive\n+bill. No priority is claimed for the general cache or paid-history ideas.\n+\n+## Open next questions\n+\n+Independent review should first check the three source rows and the physical\n+COPY/zero argument above, then the retained all-size and phase premises.\n+A later construction could test a different helper relation, but it must claim\n+a disjoint scope and pay every lost target and owned field. This package does\n+not classify such relations. [TASK.json](TASK.json) records the first steps,\n+relevance and blockers for both questions.\n@@ -0,0 +1,373 @@\n+{\n+  \"arithmetic\": {\n+    \"compiler\": {\n+      \"H\": 31385200000000,\n+      \"N\": \"2^31385200000000\",\n+      \"eta\": {\n+        \"lower\": \"0.000000203927056311365991628189\",\n+        \"upper\": \"0.000000203927056311365991628190\"\n+      },\n+      \"gap\": \"1/700000000\",\n+      \"integer_test_exponent\": 44836,\n+      \"logarithm_power\": 1000,\n+      \"theta\": \"63/64\",\n+      \"uniform_saving\": \"2115651/700000000\",\n+      \"word_materialized\": false\n+    },\n+    \"fixed_profile_ceiling\": {\n+      \"decreasing_through\": \"1/20\",\n+      \"derivative_upper\": {\n+        \"lower\": \"-195778.630038840116414999953237565269\",\n+        \"upper\": \"-195778.630038840116414999953237565268\"\n+      },\n+      \"remaining_interval_moment_upper\": {\n+        \"lower\": \"-6836.549542075249598033582799619360\",\n+        \"upper\": \"-6836.549542075249598033582799619359\"\n+      }\n+    },\n+    \"full_backward\": 16,\n+    \"full_forward\": 2,\n+    \"gain_over_PR4610\": \"2871/5000000000\",\n+    \"kappa\": \"60447/20000000\",\n+    \"kappa_decimal\": \".00302235\",\n+    \"margin_at_previous_kappa\": {\n+      \"lower\": \"0.151161494385402651700356241377\",\n+      \"upper\": \"0.151161494385402651700356241378\"\n+    },\n+    \"margin_at_previous_root_upper\": {\n+      \"lower\": \"0.151143999513185007311808491175\",\n+      \"upper\": \"0.151143999513185007311808491176\"\n+    },\n+    \"negative_controls\": {\n+      \"closed_epsilon\": [\n+        \"epsilon_below_one\",\n+        \"global_gamma_power_slack\",\n+        \"actual_logarithmic_gamma_guard\",\n+        \"source_axis_superpolynomial\",\n+        \"gaussian_above_main\",\n+        \"new_semantic_guard_with_C1_one\"\n+      ],\n+      \"closed_uniform\": [\n+        \"new_complex_uniform_saving_above_b\"\n+      ],\n+      \"old_BIT\": [\n+        \"actual_bit_above_effective\"\n+      ],\n+      \"unearned_helper_credit\": \"Rejected by the independent complete census\",\n+      \"unfunded_endpoint\": [\n+        \"main_transform_above_kappa\",\n+        \"global_coordinate_router_above_kappa\",\n+        \"fused_gaussian_above_kappa\",\n+        \"group_bit_router_above_kappa\",\n+        \"boundary_algebraic_matrix_above_kappa\"\n+      ]\n+    },\n+    \"nonrecursive\": {\n+      \"additional_private_slots\": 1,\n+      \"local_routes\": 4806000,\n+      \"local_scalar\": 158214,\n+      \"owned_slots_backward\": 3,\n+      \"raw_budget\": 1000000000,\n+      \"raw_scalar_upper\": 181098496\n+    },\n+    \"ordinary_BIT\": {\n+      \"admitted\": \"17/5000\",\n+      \"after_cover\": \"69/20000\",\n+      \"atom\": \"1/250\",\n+      \"before_cover\": \"3459/1000000\",\n+      \"ordinary_saving\": \"8590884599/2500000000000\",\n+      \"prime_rule\": \"odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses\"\n+    },\n+    \"outer\": {\n+      \"functional_checks\": {\n+        \"actual_new_BIT_stock_sublinear\": \"174299999253/175000000000\",\n+        \"fixed_halo_explicit_metadata_branch\": \"13475000001/175000000\",\n+        \"new_BIT_row_stock_sublinear_in_active_group\": \"697899997009/700000000000\",\n+        \"new_semantic_group_guard\": \"3/700000000\"\n+      },\n+      \"margins\": {\n+        \"boundary_algebraic_matrix\": \"23139910904443/7656250000000000\",\n+        \"fused_gaussian\": \"23139910838329/7656250000000000\",\n+        \"global_coordinate_router\": \"2115649/700000000\",\n+        \"group_bit_router\": \"1480954993653053/490000000000000000\",\n+        \"group_scans\": \"349999999/350000000\",\n+        \"main_transform\": \"23139899966943/7656250000000000\",\n+        \"microbox_face_corrections\": \"13475000001/175000000\",\n+        \"polynomial_products\": \"699999999/700000000\",\n+        \"sparse_union_movement\": \"3133491473404443/7656250000000000\"\n+      },\n+      \"parameters\": {\n+        \"a\": \"2115649/700000000\",\n+        \"b\": \"42313/14000000\",\n+        \"beta\": \"699999997/700000000\",\n+        \"bit_saving\": \"17/5000\",\n+        \"cap_xi\": \"6961616462466943/7656250000000000\",\n+        \"complex_uniform_saving\": \"2115651/700000000\",\n+        \"d\": \"1/700000000\",\n+        \"epsilon\": \"699999999/700000000\",\n+        \"kappa\": \"60447/20000000\",\n+        \"lambda_\": \"199395529/200000000\",\n+        \"lambda_prime\": \"10904443/10937500\",\n+        \"layout\": \"1/700000000\",\n+        \"q\": \"33057/10937500\",\n+        \"r0\": \"1/7000000000\",\n+        \"stop\": \"1/700000000\",\n+        \"tested_saving\": \"75559/25000000\"\n+      },\n+      \"strict_checks\": {\n+        \"actual_bit_above_effective\": \"264351/700000000\",\n+        \"actual_logarithmic_gamma_guard\": \"1/700000000\",\n+        \"actual_logarithmic_group_guard\": \"694633553939307/3828125000000000\",\n+        \"alpha_logarithm_absorption\": \"1/7000000000\",\n+        \"boundary_algebraic_matrix_above_kappa\": \"43716943/7656250000000000\",\n+        \"cap_above_band\": \"3133491462466943/7656250000000000\",\n+        \"cap_below_cell\": \"694633526595557/7656250000000000\",\n+        \"cap_below_phase_cell_power\": \"8350883537533057/7656250000000000\",\n+        \"complex_above_effective\": \"1/700000000\",\n+        \"complex_below_one_over_32\": \"395187/14000000\",\n+        \"complex_endpoint\": \"1/350000000\",\n+        \"epsilon_below_one\": \"1/700000000\",\n+        \"epsilon_positive\": \"699999999/700000000\",\n+        \"fine_prime_halo_umbrella\": \"7/2\",\n+        \"fused_gaussian_above_kappa\": \"43650829/7656250000000000\",\n+        \"gaussian_above_main\": \"5435693/3828125000000000\",\n+        \"global_coordinate_router_above_kappa\": \"1/175000000\",\n+        \"global_gamma_power_slack\": \"9/7000000000\",\n+        \"group_below_dimension\": \"1/350000000\",\n+        \"group_bit_router_above_kappa\": \"3493653053/490000000000000000\",\n+        \"group_gauge_power_slack\": \"43414597087027/239257812500000\",\n+        \"group_key_fits_record\": \"1/350000000\",\n+        \"group_positive\": \"699999997/700000000\",\n+        \"group_scans_above_kappa\": \"697884353/700000000\",\n+        \"halo_covers_generic_inverse_radius\": \"5\",\n+        \"improvement_over_user_baseline\": \"645689790400418148631/500000000000000000000000\",\n+        \"lambda_above_internal\": \"1/1400000000\",\n+        \"lambda_above_sigma\": \"3/1400000000\",\n+        \"lambda_above_tau\": \"1/1400000000\",\n+        \"lambda_prime_above_lambda\": \"1/1400000000\",\n+        \"lambda_prime_above_leaf\": \"27957687/9800000000000000\",\n+        \"leaf_saving_above_effective\": \"13957687/9800000000000000\",\n+        \"main_transform_above_kappa\": \"32779443/7656250000000000\",\n+        \"membership_arithmetic_fits_record\": \"1/700000000\",\n+        \"microbox_face_corrections_above_kappa\": \"53897884359/700000000\",\n+        \"microbox_halo_volume\": \"55300000003/700000000\",\n+        \"new_complex_uniform_saving_above_b\": \"1/700000000\",\n+        \"new_semantic_guard_with_C1_one\": \"1/700000000\",\n+        \"polynomial_products_above_kappa\": \"348942177/350000000\",\n+        \"positive_layout_slack\": \"1/700000000\",\n+        \"q_below_effective\": \"1/700000000\",\n+        \"q_below_internal\": \"1/700000000\",\n+        \"q_below_leaf\": \"27957687/9800000000000000\",\n+        \"q_positive\": \"33057/10937500\",\n+        \"short_record_fallback\": \"13957687/14000000\",\n+        \"source_axis_superpolynomial\": \"1/700000000\",\n+        \"sparse_union_movement_above_kappa\": \"3110351606216943/7656250000000000\",\n+        \"stop_below_one\": \"699999999/700000000\",\n+        \"stop_positive\": \"1/700000000\",\n+        \"strassen_integer_power_gap\": \"1951441519231\",\n+        \"support_router_span\": \"3/700000000\",\n+        \"theta_positive_polynomial_power\": \"2\",\n+        \"union_header_fits_record\": \"3/700000000\",\n+        \"union_tag_work_per_visit_fits_record\": \"3/700000000\"\n+      }\n+    },\n+    \"paid\": {\n+      \"1\": 41282,\n+      \"16\": 448,\n+      \"2\": 7416,\n+      \"24\": 448,\n+      \"3\": 9180,\n+      \"32\": 448,\n+      \"4\": 2286,\n+      \"40\": 448,\n+      \"48\": 448,\n+      \"5\": 720,\n+      \"56\": 448,\n+      \"64\": 448,\n+      \"72\": 224,\n+      \"8\": 128\n+    },\n+    \"paid_calls\": 64372,\n+    \"productive_fields\": 10912,\n+    \"query_shears\": 15,\n+    \"rank_mass_surplus\": 752,\n+    \"raw_headroom\": [\n+      \"3736347/100000000000000\",\n+      \"934087/25000000000000\"\n+    ],\n+    \"raw_root_interval\": [\n+      \"302238736347/100000000000000\",\n+      \"75559684087/25000000000000\"\n+    ],\n+    \"strictification\": {\n+      \"alpha\": {\n+        \"lower\": \"0.999999971483293515393313955729\",\n+        \"upper\": \"0.999999971483293515393313955730\"\n+      },\n+      \"cutoff\": 20,\n+      \"delta\": {\n+        \"lower\": \"0.957459689758527661921334851512\",\n+        \"upper\": \"0.957459689758527661921334851513\"\n+      },\n+      \"floor\": 21,\n+      \"gamma\": {\n+        \"lower\": \"0.956310980726438847618396606911\",\n+        \"upper\": \"0.956310980726438847618396606912\"\n+      },\n+      \"normalized_paid_upper\": \"2097152001953127/2097154147483648\",\n+      \"power\": 1024,\n+      \"reserve\": \"1/1000000000\",\n+      \"tail_offset\": \"1/5\",\n+      \"tested\": \"75559/25000000\"\n+    },\n+    \"targets\": {\n+      \"145\": 224,\n+      \"17\": 448,\n+      \"25\": 448,\n+      \"33\": 448,\n+      \"4\": 504,\n+      \"41\": 448,\n+      \"49\": 448,\n+      \"57\": 448,\n+      \"65\": 448,\n+      \"7\": 126,\n+      \"73\": 224,\n+      \"8\": 846,\n+      \"9\": 5852\n+    }\n+  },\n+  \"candidate_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 325\n+      },\n+      \"independent_owned_entry_columns\": 3,\n+      \"independent_persistent_columns\": 631,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2200,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 7\n+      },\n+      \"real_scalar_allowance\": 158214,\n+      \"zero_identities\": 1\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"independent_source_identities\": {\n+    \"center_minus_snapshot\": \"Delta/4\",\n+    \"center_replaced\": 11332,\n+    \"copy_coefficient\": \"1\",\n+    \"relation\": {\n+      \"230\": 1,\n+      \"324\": -1,\n+      \"326\": 1,\n+      \"328\": 1,\n+      \"333\": -1\n+    },\n+    \"snapshot_after\": 11205,\n+    \"snapshot_terms_before_substitution\": 61,\n+    \"source_event_indices_are_zero_based\": true,\n+    \"zero_identity_at\": 15584,\n+    \"zero_site_row\": \"-Delta/4\"\n+  },\n+  \"native_negative_controls\": {\n+    \"missing_owned_input_clear\": \"Every independent main/helper endpoint: 0\",\n+    \"uncleared_owned_output\": \"Every owned entry column is erased at return\",\n+    \"under_or_overstated_paid_rank\": \"Exact paid rank and frame\",\n+    \"wrong_copy_gauge\": \"Exact scalar destination frame\",\n+    \"wrong_relation_sign\": \"Every independent main/helper endpoint: 0\",\n+    \"wrong_snapshot_source\": \"Zero identity requires an identically zero full row\",\n+    \"wrong_zero_input_frame\": \"Zero identity requires an identically zero full row\"\n+  },\n+  \"phase_inheritance\": {\n+    \"absolute_phase_receipt_reused\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"all_retained_paid_events_and_warps_from_source\": true,\n+    \"new_gaussian_operators\": 0,\n+    \"new_native_maps\": 0,\n+    \"new_operations\": \"Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.\",\n+    \"source_amplitudes_and_phase_lowering_freshly_replayed\": false\n+  },\n+  \"scope\": \"Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.\",\n+  \"source_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158168,\n+      \"zero_identities\": 0\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"source_payload_sha256\": \"cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd\",\n+  \"status\": \"PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION\",\n+  \"word_payload_sha256\": \"645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35\"\n+}\n@@ -0,0 +1,90 @@\n+{\n+  \"schema_version\": 1,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"files\": [\n+    {\n+      \"path\": \"certificates/selected-result.json\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"c35482cd9035843b15a634cc8276a7e1e40e8395\",\n+      \"sha256\": \"6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375\"\n+    },\n+    {\n+      \"path\": \"docs/research/agent-task-catalog.json\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"f126dd2e2dad2b669e75d1d0d0bd05c600725602\",\n+      \"sha256\": \"f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72\"\n+    },\n+    {\n+      \"path\": \"research/free-word-tensor-lift-audit/PROOF.md\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"69c337a7704ce589798269ab4b8606189c070c4e\",\n+      \"sha256\": \"cc8ad3698a673fb225419a3636a39aa99a66c7a0676f12e329b1e76564fa1459\"\n+    },\n+    {\n+      \"path\": \"research/higher-moment-strictification/verify.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"4b24a5096154736ce060474eb8c72dc64c303699\",\n+      \"sha256\": \"0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326\"\n+    },\n+    {\n+      \"path\": \"research/joint-helper-lattice/CONTROLLER.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"49a2f0675819f9deeea27ed77be2c2b6ff2e87e5\",\n+      \"sha256\": \"1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f\"\n+    },\n+    {\n+      \"path\": \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"5a55034ec9e6185d981e16c28e1e2e455069e2cb\",\n+      \"sha256\": \"106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7\"\n+    },\n+    {\n+      \"path\": \"research/kappa-interface-round2-20261022/price_profile.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"1d93e43d1cb888d128c2faa2be83a96d85b84295\",\n+      \"sha256\": \"adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"4fc05ab08138218ba9f09e5c89b649afae7c914e\",\n+      \"sha256\": \"011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/complex/native_extensions.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"7f84894efc309546a903d314c7ac1473e7f594a8\",\n+      \"sha256\": \"50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"46d929df83817b85a5387bcdb9745e0627d6366e\",\n+      \"sha256\": \"7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"ac77b78547d6dbf2e6bd102e1047c5b16c1bca88\",\n+      \"sha256\": \"6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"0fdb65f946d557c13d8e2781b9151e2a8ddee5c3\",\n+      \"sha256\": \"b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de\"\n+    },\n+    {\n+      \"path\": \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59\",\n+      \"sha256\": \"d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15\"\n+    },\n+    {\n+      \"path\": \"research/query-thinned-controllers/RESULT.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"e0695152c98d727edfd0d2034b58a1c7e8682c0c\",\n+      \"sha256\": \"6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f\"\n+    }\n+  ]\n+}\n@@ -0,0 +1,80 @@\n+{\n+  \"schema_version\": 1,\n+  \"task_id\": \"complex-new-helper-inventory\",\n+  \"priority_revision\": 7,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"original_card\": {\n+    \"id\": \"complex-new-helper-inventory\",\n+    \"question\": \"Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?\",\n+    \"starting_points\": [\n+      \"docs/research/research-family-status.md\",\n+      \"research/complex-local-word-ceiling/README.md\",\n+      \"research/heterogeneous-owner-assembly/README.md\",\n+      \"certificates/selected-result.json\",\n+      \"research/selected-k8-unrestricted-ends/README.md\"\n+    ],\n+    \"methods\": [\n+      \"Propose a changed helper inventory and derive an optimistic exact moment.\",\n+      \"Design a small completed instance and independently verify its endpoint and rank bill.\"\n+    ],\n+    \"acceptance_gate\": \"A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.\",\n+    \"first_step\": {\n+      \"command\": [\n+        \"python3\",\n+        \"-B\",\n+        \"research/complex-local-word-ceiling/verify.py\"\n+      ],\n+      \"expected\": \"PASS_COMPLEX_LOCAL_WORD_CEILING\",\n+      \"inspect\": \"Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.\",\n+      \"scope\": \"Positive control and planning budget only; this is not a new construction or full cold replay.\"\n+    },\n+    \"first_experiment\": \"Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.\",\n+    \"bottleneck_link\": \"Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.\",\n+    \"allowed_variations\": [\n+      \"Narrow to one changed boundary or helper type with explicit counts.\",\n+      \"If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope.\"\n+    ],\n+    \"scope_change_triggers\": [\n+      \"Mixing only providers already inside the pinned catalogue.\",\n+      \"Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.\",\n+      \"Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts.\"\n+    ],\n+    \"overlap_terms\": [\n+      \"helper inventory\",\n+      \"heterogeneous-owner\",\n+      \"mutable leaver\"\n+    ]\n+  },\n+  \"scope_status\": \"refined\",\n+  \"actual_scope\": \"Make helper L230 owned in each backward call, prepare one five-helper relation, retain one exact frame-254 snapshot, remove one rank-eight center and one rank-one zero job, and debit one rank-nine target.\",\n+  \"scope_change_reason\": \"This uses the current helper-inventory priority. It changes the independent input inventory and scalar word; all physical native maps and the p16 controller remain fixed.\",\n+  \"bottleneck_link\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+  \"budget_minutes\": 240,\n+  \"stop_rule\": \"Publish one exact complete-profile kappa improvement after native, ownership, phase-inheritance, compiler and cold-export checks.\",\n+  \"outcome\": \"completed\",\n+  \"evidence\": \"README.md, WORD.json.gz, RESULT.json and verify.py. The complete conditional kappa is 60447/20000000.\",\n+  \"author\": \"Ali Romman\",\n+  \"ai_assistance\": \"Substantial OpenAI Codex assistance in discovery, code, proof, verification and publication.\",\n+  \"open_questions\": [\n+    {\n+      \"question\": \"Can a separate reviewer validate this one-relation restriction and the inherited physical transfer premises?\",\n+      \"why_it_matters\": \"The new finite construction is exact, but the complete bound still uses the source phase and all-size contracts.\",\n+      \"first_step\": \"Replay the three unrestricted source rows in native.py and check the COPY and zero-identity argument in README.md.\",\n+      \"blocked_by\": \"Independent review has not yet occurred.\"\n+    },\n+    {\n+      \"question\": \"Can a different helper relation give another complete positive bill?\",\n+      \"why_it_matters\": \"This construction gives one positive instance, not an optimum for changed helper inventories.\",\n+      \"first_step\": \"Claim a disjoint relation in Discussions, derive its exact rows, and include every lost target and owned-storage cost.\",\n+      \"blocked_by\": \"Current active cache and paid-history scopes must be checked first.\"\n+    }\n+  ],\n+  \"coordination\": {\n+    \"claim\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+    \"distinct_scopes\": [\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5355\",\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/4930\"\n+    ],\n+    \"boundary\": \"The first scope retains 632 arbitrary inputs and eight centers. The second retains every original helper endpoint. This package removes the independent L230 job only in backward calls and claims only the stated relation and two event replacements.\"\n+  }\n+}\n@@ -0,0 +1,38 @@\n+{\n+  \"schema_version\": 1,\n+  \"status\": \"ready\",\n+  \"python\": \"3.12\",\n+  \"requirements\": [],\n+  \"inputs\": [\n+    \"research/higher-moment-strictification/verify.py\",\n+    \"research/joint-helper-lattice/CONTROLLER.json\",\n+    \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+    \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+    \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+    \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+    \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+    \"research/query-thinned-controllers/RESULT.json\"\n+  ],\n+  \"commands\": [\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls.\"\n+    },\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-O\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"The same checks remain active with Python assertions disabled.\"\n+    }\n+  ]\n+}\n\n@@ -0,0 +1,299 @@\n+\"\"\"One prepared helper removes two paid jobs in the PR4610 backward word.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+The source word is by Cao Yifan. The row convention and scalar allowance\n+follow the credited native work of Cinna Davis and zxv.\n+\"\"\"\n+from collections import Counter\n+from copy import deepcopy\n+from fractions import Fraction as Q\n+from hashlib import sha1, sha256\n+from pathlib import Path\n+import gzip\n+import importlib.util\n+import json\n+import sys\n+\n+HERE = Path(__file__).resolve().parent\n+ROOT = HERE.parents[1]\n+SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'\n+PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz'\n+PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'\n+RELATION = {230: 1, 324: -1, 326: 1, 328: 1, 333: -1}\n+OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}\n+NEW_PAID = dict(OLD_PAID)\n+NEW_PAID[1] -= 1\n+NEW_PAID[8] -= 1\n+OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326}\n+\n+\n+def need(ok, why):\n+    if not ok:\n+        raise ValueError(why)\n+\n+\n+def read(path):\n+    data = path.read_bytes()\n+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)\n+\n+\n+def encode(x):\n+    if isinstance(x, Q):\n+        return str(x)\n+    if isinstance(x, dict):\n+        return {str(k): encode(v) for k, v in x.items()}\n+    if isinstance(x, (list, tuple)):\n+        return [encode(v) for v in x]\n+    return x\n+\n+\n+def load(relative, name):\n+    spec = importlib.util.spec_from_file_location(name, ROOT / relative)\n+    module = importlib.util.module_from_spec(spec)\n+    sys.modules[name] = module\n+    spec.loader.exec_module(module)\n+    return module\n+\n+\n+def authenticate():\n+    pins = read(HERE / 'SOURCES.json')\n+    for row in pins['files']:\n+        if row['usage'] != 'input':\n+            continue\n+        p = ROOT\n+        for part in Path(row['path']).parts:\n+            p /= part\n+            need(not p.is_symlink(), 'No source aliases')\n+        raw = p.read_bytes()\n+        need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path'])\n+        need(sha1(b'blob ' + str(len(raw)).encode() + b'\\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob')\n+    need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload')\n+    return pins\n+\n+\n+def span(basis):\n+    out = {0}\n+    for vector in basis:\n+        need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate')\n+        out |= {v ^ vector for v in tuple(out)}\n+    need(len(out) == 2 ** len(basis), 'Independent frame basis')\n+    return out\n+\n+\n+def add(dst, src, q):\n+    for k, v in tuple(src.items()):\n+        value = dst.get(k, Q(0)) + q * v\n+        if value:\n+            dst[k] = value\n+        else:\n+            dst.pop(k, None)\n+\n+\n+def allowance(g):\n+    if g[0] in ('clear', 'copy'):\n+        return 2\n+    q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:])\n+    n, d = abs(q.numerator), q.denominator\n+    need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar')\n+    if g[0] == 'scale':\n+        need(n & (n - 1) == 0, 'Dyadic unit SCALE')\n+        return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0))\n+    need(g[0] == 'add', 'Known scalar operation')\n+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)\n+\n+\n+def construct(source):\n+    c = source['canonical']\n+    old = source['programs']['backward']\n+    need(old[11205] == ['climb', 'warp_retimed', 92, 310, 254, 4], 'Snapshot source event')\n+    need(old[11332] == ['center', 0, 0, 254, 8], 'Center source event')\n+    need(old[15584] == ['climb', 'warp_retimed', 92, 254, 1, 1], 'Zero source event')\n+    need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in RELATION), 'Five cold full-ended helpers')\n+    word = [['scalar', ['clear', ['L', 230]], 0]]\n+    word += [['scalar', ['add', ['L', 230], ['L', h], -q, 1], 0]\n+             for h, q in RELATION.items() if h != 230]\n+    for i, event in enumerate(old):\n+        if i == 11332:\n+            word += [['scalar', ['clear', ['C', 0]], 254],\n+                     ['scalar', ['copy', ['C', 0], ['C', 1]], 254],\n+                     ['scalar', ['clear', ['C', 1]], 254]]\n+        elif i == 15584:\n+            word.append(['zero_retag', ['L', 92], 254, 1])\n+        else:\n+            word.append(deepcopy(event))\n+        if i == 11205:\n+            word += [['scalar', ['clear', ['C', 1]], 254],\n+                     ['scalar', ['copy', ['C', 1], ['L', 92]], 254]]\n+    word.append(['scalar', ['clear', ['L', 230]], 1])\n+    physical = deepcopy(c)\n+    physical.pop('local_profile')\n+    return {'schema': 'owned-helper-relation-word/1', 'canonical': physical,\n+            'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID},\n+            'owned': {'forward': [['C', 0]], 'backward': [['C', 0], ['C', 1], ['L', 230]]},\n+            'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}}\n+\n+\n+def replay(c, program, backward, specialized):\n+    \"\"\"Run every event on all independent entry columns and exact frames.\"\"\"\n+    owned = {('C', 0)} | ({('C', 1), ('L', 230)} if specialized else set())\n+    roles = {('L', i) for i in range(632)} | owned\n+    rows = {r: {(r, ()): Q(1)} for r in roles}\n+    frames = {('L', i): f for i, f in enumerate(c['start'])}\n+    frames.update({r: None for r in owned if r[0] == 'C'})\n+    spaces = [span(b) for b in c['frames']]\n+    paid = Counter()\n+    cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0\n+    for e in program:\n+        kind, touched = e[0], None\n+        if kind == 'scalar':\n+            g, frame = e[1:]\n+            dst = tuple(g[1]); touched = dst\n+            need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame')\n+            cost += allowance(g)\n+            if g[0] == 'clear':\n+                need(dst in owned, 'Only owned fields can be erased')\n+                rows[dst] = {}; frames[dst] = frame\n+            else:\n+                need(frames[dst] == frame, 'Exact scalar destination frame')\n+                if g[0] in ('add', 'copy'):\n+                    src = tuple(g[2])\n+                    need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame')\n+                    if g[0] == 'copy':\n+                        need(dst in owned and not rows[dst], 'COPY into cleared owned storage')\n+                        rows[dst] = dict(rows[src])\n+                    else:\n+                        add(rows[dst], rows[src], Q(g[3], g[4]))\n+                else:\n+                    need(g[0] == 'scale', 'Known scalar operation')\n+                    rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()}\n+        elif kind == 'warp':\n+            _, role, op, old, new = e\n+            dst = tuple(role); touched = dst\n+            need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input')\n+            symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0))\n+            rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q\n+                         for (r, w), q in rows[dst].items()}\n+            frames[dst] = new\n+        elif kind in ('climb', 'center'):\n+            if kind == 'climb':\n+                _, _, i, old, new, rank = e\n+                dst = ('L', i)\n+                need(spaces[old] < spaces[new], 'Ascending paid climb')\n+            else:\n+                _, i, old, new, rank = e\n+                dst = ('C', i)\n+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center')\n+            need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame')\n+            frames[dst] = new; paid[rank] += 1\n+        elif kind == 'zero_retag':\n+            _, role, old, new = e\n+            dst = tuple(role)\n+            need(specialized and backward and dst == ('L', 92), 'Declared zero identity')\n+            need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row')\n+            need((old, new) == (254, 1), 'Declared zero frame change')\n+            frames[dst] = new; zero_count += 1\n+        else:\n+            need(kind in ('phase', 'adapter'), 'Known inert source marker')\n+        if touched is not None:\n+            max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0)))\n+            denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1))\n+    need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame')\n+    for i in range(632):\n+        r = ('L', i)\n+        if r in owned:\n+            continue\n+        expected = {(r, ()): Q(1)}\n+        if i < 112 if backward else 112 <= i < 224:\n+            expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1)\n+        need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i))\n+    need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return')\n+    need(zero_count == int(specialized), 'Exactly one checked zero identity')\n+    helpers = Counter()\n+    for i in range(224, 632):\n+        if ('L', i) in owned:\n+            continue\n+        a, b = c['start'][i], c['final'][i]\n+        need(spaces[a] < spaces[b], 'Strict independent productive helper')\n+        helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1\n+    return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())),\n+            'independent_persistent_columns': 631 if specialized else 632,\n+            'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True,\n+            'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1),\n+            'max_denominator': denominator, 'zero_identities': zero_count}\n+\n+\n+def independent_source_identities(source):\n+    \"\"\"Use the predecessor row engine on the unrestricted original word.\"\"\"\n+    v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'owned_relation_source_rows')\n+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}\n+    rows['C', 0] = v.identity(('C', 0))\n+    delta = {(('L', i), ()): Q(q) for i, q in RELATION.items()}\n+    saved = None\n+    for index, e in enumerate(source['programs']['backward']):\n+        if e[0] == 'scalar':\n+            g = e[1]; dst = tuple(g[1])\n+            if g[0] == 'clear': rows[dst] = {}\n+            elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])])\n+            elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()}\n+            else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4]))\n+        elif e[0] == 'warp':\n+            dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True)\n+        if index == 11205: saved = dict(rows['L', 92])\n+        if index == 11332:\n+            diff = dict(rows['C', 0]); v.add(diff, saved, -1)\n+            need(diff == {k: q / 4 for k, q in delta.items()}, 'Independent exact center minus snapshot = Delta/4')\n+        if index == 15584:\n+            need(rows['L', 92] == {k: -q / 4 for k, q in delta.items()}, 'Independent exact zero-site row = -Delta/4')\n+    need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints')\n+    return {'source_event_indices_are_zero_based': True, 'snapshot_after': 11205,\n+            'center_replaced': 11332, 'zero_identity_at': 15584,\n+            'snapshot_terms_before_substitution': len(saved), 'copy_coefficient': '1',\n+            'center_minus_snapshot': 'Delta/4', 'zero_site_row': '-Delta/4', 'relation': RELATION}\n+\n+\n+def phase_inheritance(source, candidate):\n+    receipt = read(ROOT / PHASE)\n+    need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and\n+         receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt')\n+    physical = deepcopy(source['canonical']); physical.pop('local_profile')\n+    need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged')\n+    for direction, program in candidate['programs'].items():\n+        old = source['programs'][direction]\n+        for kind in ('warp', 'adapter', 'phase'):\n+            need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence')\n+        old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center'))\n+        new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center'))\n+        expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for i in (11332, 15584))\n+        need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the two proved jobs are removed')\n+    return {'new_gaussian_operators': 0, 'new_native_maps': 0,\n+            'all_retained_paid_events_and_warps_from_source': True,\n+            'absolute_phase_receipt_reused': PHASE,\n+            'source_amplitudes_and_phase_lowering_freshly_replayed': False,\n+            'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'}\n+\n+\n+def controls(c, candidate):\n+    controls = {}\n+    base = candidate['programs']['backward']\n+    variants = {}\n+    bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad\n+    variants['missing_owned_input_clear'] = deepcopy(base[1:])\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63]\n+    variants['wrong_snapshot_source'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0\n+    variants['wrong_zero_input_frame'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1\n+    variants['under_or_overstated_paid_rank'] = bad\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0\n+    variants['wrong_copy_gauge'] = bad\n+    variants['uncleared_owned_output'] = deepcopy(base[:-1])\n+    for name, program in variants.items():\n+        try:\n+            replay(c, program, True, True)\n+        except ValueError as err:\n+            controls[name] = str(err)\n+        else:\n+            raise ValueError('Control accepted: ' + name)\n+    return controls\n@@ -0,0 +1,196 @@\n+\"\"\"Complete p16 bill and finite compiler for one owned helper relation.\n+\n+The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna\n+Davis's PR4470 controller, zxv's completion and logarithmic majorant, and\n+Jacob Alan Sussman's mixed-target recursion. Apache-2.0.\n+Ali Romman, with substantial OpenAI Codex assistance.\n+\"\"\"\n+from collections import Counter\n+from fractions import Fraction as Q\n+from native import ROOT, read, load, need, encode, OLD_PAID, OLD_HELPERS\n+\n+KAPPA = Q('.00302235')\n+TESTED = Q('.00302236')\n+PREVIOUS = Q('.0030217758')\n+OLD_ROOT_UPPER = Q('.00302177587078')\n+\n+\n+def controller():\n+    \"\"\"Check the literal p16 word and both rational boundary programs.\"\"\"\n+    word = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json')\n+    need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller')\n+    zero = (0,) * 34\n+    def plus(dst, src, q):\n+        for k, v in src.items():\n+            value = dst.get(k, Q(0)) + q * v\n+            if value: dst[k] = value\n+            else: dst.pop(k, None)\n+    def shifted(row, term, sign=1):\n+        return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row]\n+    for side in ('left', 'right'):\n+        matrix = [[Q(i == j) for j in range(32)] for i in range(32)]\n+        for e in word['boundaries'][side + '_program']:\n+            if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]]\n+            elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]]\n+            else:\n+                need(e[0] == 'ADD', 'Boundary scalar opcode')\n+                matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])]\n+        need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program')\n+    rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']]\n+    for e in word['physical_events']:\n+        if e[0] in ('LOCAL', 'QUERY_SHEAR'):\n+            _, stage, pair, back = e\n+            x, y = 2 * pair, 2 * pair + 1\n+            if back: x, y = y, x\n+            term = (1 if back else -1,) + (0,) * 33\n+            for dst, src in zip(rows[y], shifted(rows[x], term)):\n+                plus(dst, src, Q(-1 if back else 1))\n+            if e[0] == 'LOCAL':\n+                term = (0,) + tuple(int(s == stage) for s in range(33))\n+                for r in (x, y): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'IDLE':\n+            term = (0,) + tuple(int(s in e[2]) for s in range(33))\n+            for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'ADD':\n+            for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3]))\n+        else:\n+            need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode')\n+            rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1)\n+    out = [[{} for _ in range(32)] for _ in range(32)]\n+    for i, row in enumerate(word['boundaries']['left']):\n+        for k, q in enumerate(row):\n+            if Q(q):\n+                for j in range(32): plus(out[i][j], rows[k][j], Q(q))\n+    expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)]\n+    need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors')\n+    return word\n+\n+\n+def assemble(native, word):\n+    T, P = Counter(), Counter()\n+    orientations = Counter(); thin = 0\n+    for e in word['physical_events']:\n+        if e[0] == 'LOCAL':\n+            direction = 'backward' if e[3] else 'forward'\n+            orientations[direction] += 1\n+            T.update(native[direction]['helpers']); P.update(native[direction]['paid'])\n+        elif e[0] == 'QUERY_SHEAR': thin += 1; P[1] += 112\n+        elif e[0] == 'IDLE': P[8 * len(e[2])] += 224\n+    main = Counter()\n+    for term in word['diagonal']:\n+        need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole Gaussian main target')\n+        main[1 + 8 * sum(term[1:])] += 112\n+    T.update(main)\n+    need(orientations == {'backward': 16, 'forward': 2} and thin == 15, 'Every actual call orientation')\n+    # This second census uses the source invoice and the two local deltas.\n+    check_T = Counter({int(r): n for r, n in word['invoice']['main'].items()})\n+    check_T.update({r: 18 * n for r, n in OLD_HELPERS.items()}); check_T[9] -= 16\n+    check_P = Counter({int(r): n for r, n in word['invoice']['whole_idle'].items()})\n+    check_P.update({r: 18 * n for r, n in OLD_PAID.items()}); check_P[1] += 1680 - 16; check_P[8] -= 16\n+    need(T == check_T and P == check_P, 'Independent full invoice substitution')\n+    need(sum(T.values()) == 10912 and sum(P.values()) == 64372, 'Complete productive and paid counts')\n+    need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Unchanged complete rank surplus')\n+    return T, P\n+\n+\n+def run(native):\n+    word = controller(); T, P = assemble(native, word)\n+    prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json')\n+    need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing')\n+    prior_T = Counter({int(r): n for r, n in prior['targets'].items()})\n+    prior_P = Counter({int(r): n for r, n in prior['paid'].items()})\n+    prior_T[9] -= 16; prior_P[1] -= 16; prior_P[8] -= 16\n+    need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill')\n+    E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals')\n+    other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals')\n+    def margin(c):\n+        t, p = E.moment(T, 1 - c), E.moment(P, 1 - c)\n+        return t[0] - p[1], t[1] - p[0]\n+    need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint')\n+    lo, hi, grid = 0, 10**12, 10**14\n+    while hi - lo > 1:\n+        mid = (lo + hi) // 2\n+        if margin(Q(mid, grid))[0] > 0: lo = mid\n+        else: hi = mid\n+    root_low, root_high = Q(lo, grid), Q(hi, grid)\n+    need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure')\n+    need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom')\n+    # The complete signed profile decreases on [0, .05], and stays negative\n+    # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling.\n+    signed = {r: T[r] - P[r] for r in T.keys() | P.keys()}\n+    derivative, upper = None, None\n+    for i in range(16):\n+        l, r = Q(i, 320), Q(i + 1, 320); low = Q(0)\n+        for rank, n in signed.items():\n+            term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank))\n+            low += n * term[0 if n > 0 else 1]\n+        derivative = low if derivative is None else min(derivative, low)\n+    for i in range(128):\n+        l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560)\n+        value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items())\n+        upper = value if upper is None else max(upper, value)\n+    need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1')\n+    t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21\n+    target, paid = E.moment(T, t), E.moment(P, t)\n+    tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED)\n+    need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree')\n+    alpha = E.divide(paid, target)\n+    gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target))\n+    delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target))\n+    reserve = Q(1, 10**9); g = d = Q(97, 100)\n+    need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged')\n+    need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks')\n+    normalized = 1 / (1 + v * reserve) + Q(4, 2**32)\n+    need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding')\n+    theta, power = Q(63, 64), 1000\n+    eta = E.scale(E.power(145, -v * TESTED), t)\n+    need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')\n+    need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range')\n+    gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid')\n+    step = gap.denominator\n+    def wins(j): return (step * j + 1)**power < 2**j\n+    left, right = 1, 2\n+    while not wins(right): left, right = right, 2 * right\n+    while right - left > 1:\n+        mid = (left + right) // 2\n+        if wins(mid): right = mid\n+        else: left = mid\n+    height = step * right\n+    need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold')\n+    local_scalar = max(x['real_scalar_allowance'] for x in native.values())\n+    # The old route allowance is retained. Charge two additional owned field\n+    # lifetimes at two routes each, even though L230 uses an existing slot.\n+    routes = (max(sum(x['paid'].values()) for x in native.values()) + 2 * 408 + 688 + 4) * 1000\n+    need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit')\n+    scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right')))\n+    need(scalar_upper < 10**9, 'Complete raw nonrecursive bound')\n+    bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']\n+    atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted'])\n+    need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock')\n+    L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer')\n+    params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap,\n+              'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted,\n+              'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap}\n+    outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom)\n+    need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')\n+    need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict')\n+    controls = {}\n+    for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]:\n+        bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0]\n+        need(failed, 'Reject outer patch ' + name); controls[name] = failed\n+    bad_native = {d: dict(x) for d, x in native.items()}\n+    bad_native['backward']['helpers'] = OLD_HELPERS\n+    try: assemble(bad_native, word)\n+    except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census'\n+    else: raise ValueError('Unowned helper credit was accepted')\n+    return encode({'kappa': KAPPA, 'kappa_decimal': '.00302235', 'gain_over_PR4610': KAPPA - PREVIOUS,\n+                   'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA],\n+                   'margin_at_previous_kappa': E.display(margin(PREVIOUS)),\n+                   'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)),\n+                   'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)},\n+                   'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752,\n+                   'full_backward': 16, 'full_forward': 2, 'query_shears': 15,\n+                   'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized},\n+                   'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False},\n+                   'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': 1, 'owned_slots_backward': 3},\n+                   'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls})\n@@ -0,0 +1,64 @@\n+#!/usr/bin/env python3\n+\"\"\"Replay the one-relation native word and its complete conditional kappa.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+Read README.md for the source credit and inherited proof obligations.\n+\"\"\"\n+from hashlib import sha256\n+import argparse\n+import gzip\n+import json\n+from pathlib import Path\n+import sys\n+sys.dont_write_bytecode = True\n+import native as N\n+import price\n+\n+\n+def run():\n+    N.authenticate()\n+    source = N.read(N.ROOT / N.SOURCE)\n+    candidate = N.construct(source)\n+    c = candidate['canonical']\n+    before, after = {}, {}\n+    for direction in ('forward', 'backward'):\n+        back = direction == 'backward'\n+        before[direction] = N.replay(c, source['programs'][direction], back, False)\n+        after[direction] = N.replay(c, candidate['programs'][direction], back, back)\n+        N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Pinned source census')\n+        N.need(after[direction]['paid'] == candidate['paid_profiles'][direction], 'Emitted direction-specific paid profile')\n+        helpers = dict(N.OLD_HELPERS)\n+        if back: helpers[9] -= 1\n+        N.need(after[direction]['paid'] == (N.NEW_PAID if back else N.OLD_PAID) and after[direction]['helpers'] == helpers, 'Actual complete changed native census')\n+    identities = N.independent_source_identities(source)\n+    phase = N.phase_inheritance(source, candidate)\n+    controls = N.controls(c, candidate)\n+    arithmetic = price.run(after)\n+    data = (json.dumps(candidate, sort_keys=True, separators=(',', ':')) + '\\n').encode()\n+    result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION',\n+                       'source_payload_sha256': N.PAYLOAD, 'word_payload_sha256': sha256(data).hexdigest(),\n+                       'source_native': before, 'candidate_native': after, 'independent_source_identities': identities,\n+                       'phase_inheritance': phase, 'native_negative_controls': controls, 'arithmetic': arithmetic,\n+                       'scope': 'Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.'})\n+    return data, result\n+\n+\n+def main():\n+    ap = argparse.ArgumentParser(description=__doc__)\n+    ap.add_argument('--write', action='store_true', help='Write only this package word and result after all checks pass.')\n+    ap.add_argument('--out', type=Path, help='Write a replay result to a separate path.')\n+    args = ap.parse_args()\n+    data, result = run()\n+    if args.write:\n+        (N.HERE / 'WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))\n+        (N.HERE / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    else:\n+        N.need(gzip.decompress((N.HERE / 'WORD.json.gz').read_bytes()) == data, 'Exact literal published word')\n+        N.need(N.read(N.HERE / 'RESULT.json') == result, 'Exact published replay result')\n+    if args.out:\n+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR4610', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True))\n+\n+\n+if __name__ == '__main__':\n+    main()",
+      "comments": [],
+      "created_at": "2026-10-23T20:26:27Z",
+      "updated_at": "2026-10-23T20:26:27Z",
+      "closed_at": null,
+      "merged_at": null,
+      "commits": 1,
+      "changed_files": 9,
+      "additions": 1389,
+      "deletions": 0,
+      "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+      "display_title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation"
+    },
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+    "title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation",
+    "diff": "@@ -0,0 +1,249 @@\n+# Conditional kappa 0.00302235 from one owned helper relation\n+\n+This construction gives **conditional kappa = 60447/20000000 = 0.00302235**.\n+The gain over Cao Yifan's final\n+[PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+value, 0.0030217758, is **2871/5000000000 = 0.0000005742**.\n+The construction changes the complete paid profile. It does not obtain the\n+gain by taking more digits of the old root.\n+\n+One helper becomes owned storage in each backward call. A prepared relation\n+then makes one paid rank-eight center equal to an earlier saved value. The same\n+relation makes one later rank-one job act on zero. Both jobs can be removed,\n+with the rank-nine helper credit also removed. All other independent outputs\n+and all main interfaces keep their source operators.\n+\n+[WORD.json.gz](WORD.json.gz) is the complete emitted word.\n+[RESULT.json](RESULT.json) records the exact native checks, the two source\n+identities, both full profiles, completion, compiler and outer calculations.\n+[SOURCES.json](SOURCES.json) pins every external input by Git blob and SHA256.\n+The proof below explains why the changed word has the stated contract.\n+\n+## Source and scope\n+\n+The base is canonical main\n+[7c472563474e60185e6ca101a17622133d047e56](https://github.com/CrocSwap/integer-mult-bounds/commit/7c472563474e60185e6ca101a17622133d047e56).\n+The native source is the final PR #4610 word at\n+[20bb93cd990d2ff683e4d0fc56b87a42cd5d3296](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz).\n+Its decompressed SHA256 is\n+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.\n+The comparison value and old crossing come from its\n+[final compiler arithmetic](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json).\n+All consumed bytes are already in the recorded main base.\n+\n+This is one instance of the current `complex-new-helper-inventory` priority.\n+The [scoped claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737)\n+reserves only the relation and two replacements below.\n+[Discussion #5355](https://github.com/CrocSwap/integer-mult-bounds/discussions/5355)\n+retains all 632 independent inputs and all eight centers.\n+[Discussion #4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930)\n+retains every original helper endpoint. This construction removes the\n+independent L230 job in backward calls. It does not claim those broader scopes.\n+The selected certificate is unchanged. A fresh check at 20:20 UTC found that\n+Discussion #5355 had released its original-input scope without a saving.\n+Canonical main still had the recorded base commit.\n+\n+## Exact replacement proof\n+\n+All indices below are zero-based indices in the frozen backward program.\n+Let `h_r` be the source logical input of helper `Lr`. The five helpers in\n+\n+```math\n+\\Delta=h_{230}-h_{324}+h_{326}+h_{328}-h_{333}\n+```\n+\n+all start in frame 0 and finish in frame 1, of rank nine. The new backward\n+contract has 224 independent main fields and 407 independent helper fields.\n+L230 is private. Clear it, then use four same-frame ADDs to prepare\n+\n+```math\n+h_{230}=h_{324}-h_{326}-h_{328}+h_{333}.\n+```\n+\n+The other helper inputs remain arbitrary and independent. This preparation\n+sets Delta to zero for every input. It uses no recursive job. It removes one\n+rank-nine productive target; the dependent field receives no output credit.\n+\n+Run the original source program on unrestricted inputs. Let `q` be the\n+logical row of L92 just after event 11205, a paid climb into frame 254.\n+The separate predecessor row engine gives these exact identities:\n+\n+| Source position | Exact logical row |\n+| --- | --- |\n+| C0 at the rank-eight center, event 11332 | `q + Delta/4` |\n+| L92 at the rank-one climb, event 15584 | `-Delta/4` |\n+\n+These identities are over rational coefficients and free native operator\n+words. They hold for every value of every source input and for every invertible\n+interpretation of the native symbols. They do not use numerical samples or an\n+assumed relation between distinct native maps.\n+\n+For every positive tensor width f, substitute each native generator by its\n+source operator tensor power and each inverse by the inverse tensor power.\n+This defines a representation of the free group. Keep the rational scalar\n+coefficients outside the substitution. The two row identities therefore hold\n+at every such width. In particular, Delta/4 remains a scalar linear form; it\n+is not a tensor power of that sum. This uses the termwise argument recorded in\n+the [free-word tensor audit](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/free-word-tensor-lift-audit/PROOF.md),\n+which credits Cinna Davis's proposal and ToikY's scoped audit. Physical frame\n+realization and the complete all-size compiler retain their source contracts.\n+\n+Immediately after event 11205, clear a new private field C1 in frame 254 and\n+COPY L92 into it. C1 is not written until the replacement of event 11332. At\n+that event, clear owned C0, set its frame to 254, COPY C1 into C0, then clear C1.\n+The copy coefficient is exactly one. Under Delta = 0, the copied field is the\n+same physical value as the old center output: the logical rows and the exact\n+frame gauge are equal. The old C0 input can be erased because C0 is owned.\n+This removes one rank-eight recursive job.\n+\n+At event 15584, L92 is exactly zero in every input column. The physical\n+identity therefore has the same result as the old rank-one frame change.\n+`zero_retag` records this fact. It performs no physical write and is accepted\n+only when the full exact row is empty and the current frame is 254. It then\n+records frame 1. This removes one rank-one recursive job. It does not erase a\n+main input or replace a nonzero transform with a free frame change.\n+\n+Every other event stays in source order. Clear private L230 at return. The\n+source clears C0, and the new program has already cleared C1. The original\n+linear endpoint identity, restricted by the prepared relation, gives all 224\n+main outputs and all 407 retained helper outputs. The literal new-word replay\n+checks these outputs separately, with all 631 retained inputs and all three\n+owned entry fields initially arbitrary. It also checks every scalar frame,\n+paid rank, native frame transition and final frame.\n+\n+The 4,429 source frames, 72 native maps, all remaining paid operators, and main\n+adapters are unchanged. The source\n+[absolute-phase certificate](https://github.com/intqwq/integer-mult-bounds/blob/20bb93cd990d2ff683e4d0fc56b87a42cd5d3296/research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz)\n+is authenticated and reused. Same-frame COPY and identity on zero introduce no\n+phase recipe. The source's amplitude and Clifford-lowering checks are not\n+rerun by this package. The new free-word identities prove equivalence for the\n+source operators with their full phases, not just their projective classes.\n+\n+## Complete cost and conditional compiler\n+\n+The forward word is unchanged. Each backward call has these counts:\n+\n+```text\n+paid:    {1:2200, 2:412, 3:510, 4:127, 5:40, 8:7}\n+helpers: {4:28, 7:7, 8:47, 9:325}\n+```\n+\n+The full p16/a7 controller contains 16 backward calls, two forward calls and\n+15 query shears. Thus the complete difference is **minus 16 H1 and 16 H8 paid\n+jobs, and minus 16 H9 productive targets**. It includes every idle and main\n+target. There are 64,372 paid jobs and 10,912 productive fields. Their rank\n+masses are 238,990 and 239,742; the surplus remains 752.\n+\n+For every real `0 < t < 1`, the complete target-minus-paid moment increases by\n+\n+```math\n+16(1+8^t-9^t)>0.\n+```\n+\n+For a direct proof, both `(1/9)^t > 1/9` and `(8/9)^t > 8/9`; multiply their\n+sum by `9^t`. The improvement is strict throughout the required range.\n+\n+The backward word has 158,214 real scalar operations under the source macro\n+allowance, exactly 46 more than its source. Its maximum formal prefix L1 norm\n+is 169, with maximum denominator 64; both equal the source bounds. The forward\n+bounds remain 457 and 32. One extra physical private slot holds C1. L230 uses\n+an existing slot. The route bound also charges two routes for each of the two\n+new owned lifetimes. The local scalar-plus-route bound stays below 10^7, and\n+the complete raw nonrecursive bound stays **181,098,496 < 10^9**. Preparation,\n+COPY, CLEAR and storage therefore do not introduce an unpaid recursive cost.\n+\n+Two rational interval engines check the complete moment. Its unique crossing\n+in `0 < kappa < 1` lies in\n+**(0.00302238736347, 0.00302238736348)**. The verifier proves the moment decreases\n+on `[0,0.05]` and remains negative on `[0.05,1]`. This is a ceiling for this\n+fixed complete profile, not an optimum over circuits or helper relations.\n+The claimed kappa leaves more than **0.00000003736347** raw headroom.\n+\n+The separately tested saving is 0.00302236. The paid/target ratio is below\n+`0.999999971483293515393313955730`, with reserve `1e-9`. Both charged tails are\n+below `0.97`. The source power 1024, cutoff 20, floor 21, tail offset 1/5,\n+complement factor 63/64 and logarithm power 1000 still pass. The compiler gap\n+is `1/700000000`, with `j=44836`, `H=31385200000000` and `N=2^31385200000000`.\n+The exact integer test `(H+1)^1000 < 2^44836` passes; the preceding grid integer\n+fails. The uniform complex saving is `2115651/700000000`. All 54 strict outer\n+predicates and four functional predicates pass, using the retained ordinary\n+BIT saving 0.0034.\n+\n+## Verification and reproduction\n+\n+Use Python 3.12 or 3.14, with the standard library only. From the repository root:\n+\n+```sh\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023 --check-only\n+python3 -B scripts/research_package.py --package research/kappa-owned-relation-20261023\n+```\n+\n+The registered commands run normal and optimized Python. The direct command,\n+also used for a Git-free export, is:\n+\n+```sh\n+python3 -B research/kappa-owned-relation-20261023/verify.py\n+python3 -O -B research/kappa-owned-relation-20261023/verify.py\n+```\n+\n+Each prints status\n+`PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION`.\n+The verifier reconstructs the word and compares its bytes and exact result with\n+the published artifacts. `--write` is a separate authoring command. It changes\n+only this package's word and result after all checks pass.\n+\n+Fresh checks cover both source words, both candidate words, every independent\n+entry column and owned return, the two unrestricted source identities, retained\n+phase bindings, the p16 rational Laurent factorization, both scalar boundary\n+programs, two complete invoice counts, two rational interval engines, the fixed\n+profile ceiling, completion, compiler, BIT conversion and all outer predicates.\n+The emitted word replaces the old single `canonical.local_profile` metadata\n+field with explicit `paid_profiles` for the two directions.\n+\n+Seven native controls reject a wrong relation sign, omitted input clear, wrong\n+snapshot, wrong zero frame, wrong paid rank, wrong copy gauge, and omitted\n+output clear. Five cost/outer controls reject the lost helper's output credit,\n+old BIT stock, closed uniform gap, unfunded endpoint and closed epsilon.\n+\n+Normal and optimized registered replays passed on CPython 3.12.14. The direct\n+author check also passed on CPython 3.14. Source metadata and pins passed.\n+The optional full-history preflight is not claimed in the shallow checkout.\n+The publication handoff records export and committed-byte checks.\n+\n+The full source phase lowering, BIT native replay, Lean, Docker, physical tape\n+execution, numerical precision execution, analytic decomposition and integer\n+recovery are not rerun here. The complete bound retains those predecessor\n+contracts, including permitted owned erasure, whole-job normalizers, mixed\n+productive-target recursion and all-size closure. The expanded compiled word\n+is specified by a finite algorithm, not materialized. This is a conditional\n+construction with exact finite evidence, not an unconditional multiplication\n+theorem, a practical timing result or independent human acceptance.\n+\n+## Credit\n+\n+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.\n+Cao Yifan's [PR #4610](https://github.com/CrocSwap/integer-mult-bounds/pull/4610)\n+supplies the exact source word, phase evidence and previous compiler value.\n+Cinna Davis's [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470)\n+supplies the p16 controller and helper-interface lineage. The source code keeps\n+credit for Dugongue's transported frames, zxv's native and finite-compiler\n+work, Jacob Alan Sussman's mixed-target recursion and their predecessors.\n+The [pricing source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-interface-round2-20261022/price_profile.py)\n+and [literal native source](https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/research/kappa-rebuild/complex/native_extensions.py)\n+are pinned as provenance for the adapted checks.\n+\n+zxv's [PR #5283](https://github.com/CrocSwap/integer-mult-bounds/pull/5283)\n+supplies the related cache contract and the explicit handoff to find actual\n+matching rows and their lifetimes. Its standalone cache example is not part of\n+this word. The new contribution is the five-helper relation, its actual cache\n+and zero identities, the full owned-field replacement and the complete positive\n+bill. No priority is claimed for the general cache or paid-history ideas.\n+\n+## Open next questions\n+\n+Independent review should first check the three source rows and the physical\n+COPY/zero argument above, then the retained all-size and phase premises.\n+A later construction could test a different helper relation, but it must claim\n+a disjoint scope and pay every lost target and owned field. This package does\n+not classify such relations. [TASK.json](TASK.json) records the first steps,\n+relevance and blockers for both questions.\n@@ -0,0 +1,373 @@\n+{\n+  \"arithmetic\": {\n+    \"compiler\": {\n+      \"H\": 31385200000000,\n+      \"N\": \"2^31385200000000\",\n+      \"eta\": {\n+        \"lower\": \"0.000000203927056311365991628189\",\n+        \"upper\": \"0.000000203927056311365991628190\"\n+      },\n+      \"gap\": \"1/700000000\",\n+      \"integer_test_exponent\": 44836,\n+      \"logarithm_power\": 1000,\n+      \"theta\": \"63/64\",\n+      \"uniform_saving\": \"2115651/700000000\",\n+      \"word_materialized\": false\n+    },\n+    \"fixed_profile_ceiling\": {\n+      \"decreasing_through\": \"1/20\",\n+      \"derivative_upper\": {\n+        \"lower\": \"-195778.630038840116414999953237565269\",\n+        \"upper\": \"-195778.630038840116414999953237565268\"\n+      },\n+      \"remaining_interval_moment_upper\": {\n+        \"lower\": \"-6836.549542075249598033582799619360\",\n+        \"upper\": \"-6836.549542075249598033582799619359\"\n+      }\n+    },\n+    \"full_backward\": 16,\n+    \"full_forward\": 2,\n+    \"gain_over_PR4610\": \"2871/5000000000\",\n+    \"kappa\": \"60447/20000000\",\n+    \"kappa_decimal\": \".00302235\",\n+    \"margin_at_previous_kappa\": {\n+      \"lower\": \"0.151161494385402651700356241377\",\n+      \"upper\": \"0.151161494385402651700356241378\"\n+    },\n+    \"margin_at_previous_root_upper\": {\n+      \"lower\": \"0.151143999513185007311808491175\",\n+      \"upper\": \"0.151143999513185007311808491176\"\n+    },\n+    \"negative_controls\": {\n+      \"closed_epsilon\": [\n+        \"epsilon_below_one\",\n+        \"global_gamma_power_slack\",\n+        \"actual_logarithmic_gamma_guard\",\n+        \"source_axis_superpolynomial\",\n+        \"gaussian_above_main\",\n+        \"new_semantic_guard_with_C1_one\"\n+      ],\n+      \"closed_uniform\": [\n+        \"new_complex_uniform_saving_above_b\"\n+      ],\n+      \"old_BIT\": [\n+        \"actual_bit_above_effective\"\n+      ],\n+      \"unearned_helper_credit\": \"Rejected by the independent complete census\",\n+      \"unfunded_endpoint\": [\n+        \"main_transform_above_kappa\",\n+        \"global_coordinate_router_above_kappa\",\n+        \"fused_gaussian_above_kappa\",\n+        \"group_bit_router_above_kappa\",\n+        \"boundary_algebraic_matrix_above_kappa\"\n+      ]\n+    },\n+    \"nonrecursive\": {\n+      \"additional_private_slots\": 1,\n+      \"local_routes\": 4806000,\n+      \"local_scalar\": 158214,\n+      \"owned_slots_backward\": 3,\n+      \"raw_budget\": 1000000000,\n+      \"raw_scalar_upper\": 181098496\n+    },\n+    \"ordinary_BIT\": {\n+      \"admitted\": \"17/5000\",\n+      \"after_cover\": \"69/20000\",\n+      \"atom\": \"1/250\",\n+      \"before_cover\": \"3459/1000000\",\n+      \"ordinary_saving\": \"8590884599/2500000000000\",\n+      \"prime_rule\": \"odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses\"\n+    },\n+    \"outer\": {\n+      \"functional_checks\": {\n+        \"actual_new_BIT_stock_sublinear\": \"174299999253/175000000000\",\n+        \"fixed_halo_explicit_metadata_branch\": \"13475000001/175000000\",\n+        \"new_BIT_row_stock_sublinear_in_active_group\": \"697899997009/700000000000\",\n+        \"new_semantic_group_guard\": \"3/700000000\"\n+      },\n+      \"margins\": {\n+        \"boundary_algebraic_matrix\": \"23139910904443/7656250000000000\",\n+        \"fused_gaussian\": \"23139910838329/7656250000000000\",\n+        \"global_coordinate_router\": \"2115649/700000000\",\n+        \"group_bit_router\": \"1480954993653053/490000000000000000\",\n+        \"group_scans\": \"349999999/350000000\",\n+        \"main_transform\": \"23139899966943/7656250000000000\",\n+        \"microbox_face_corrections\": \"13475000001/175000000\",\n+        \"polynomial_products\": \"699999999/700000000\",\n+        \"sparse_union_movement\": \"3133491473404443/7656250000000000\"\n+      },\n+      \"parameters\": {\n+        \"a\": \"2115649/700000000\",\n+        \"b\": \"42313/14000000\",\n+        \"beta\": \"699999997/700000000\",\n+        \"bit_saving\": \"17/5000\",\n+        \"cap_xi\": \"6961616462466943/7656250000000000\",\n+        \"complex_uniform_saving\": \"2115651/700000000\",\n+        \"d\": \"1/700000000\",\n+        \"epsilon\": \"699999999/700000000\",\n+        \"kappa\": \"60447/20000000\",\n+        \"lambda_\": \"199395529/200000000\",\n+        \"lambda_prime\": \"10904443/10937500\",\n+        \"layout\": \"1/700000000\",\n+        \"q\": \"33057/10937500\",\n+        \"r0\": \"1/7000000000\",\n+        \"stop\": \"1/700000000\",\n+        \"tested_saving\": \"75559/25000000\"\n+      },\n+      \"strict_checks\": {\n+        \"actual_bit_above_effective\": \"264351/700000000\",\n+        \"actual_logarithmic_gamma_guard\": \"1/700000000\",\n+        \"actual_logarithmic_group_guard\": \"694633553939307/3828125000000000\",\n+        \"alpha_logarithm_absorption\": \"1/7000000000\",\n+        \"boundary_algebraic_matrix_above_kappa\": \"43716943/7656250000000000\",\n+        \"cap_above_band\": \"3133491462466943/7656250000000000\",\n+        \"cap_below_cell\": \"694633526595557/7656250000000000\",\n+        \"cap_below_phase_cell_power\": \"8350883537533057/7656250000000000\",\n+        \"complex_above_effective\": \"1/700000000\",\n+        \"complex_below_one_over_32\": \"395187/14000000\",\n+        \"complex_endpoint\": \"1/350000000\",\n+        \"epsilon_below_one\": \"1/700000000\",\n+        \"epsilon_positive\": \"699999999/700000000\",\n+        \"fine_prime_halo_umbrella\": \"7/2\",\n+        \"fused_gaussian_above_kappa\": \"43650829/7656250000000000\",\n+        \"gaussian_above_main\": \"5435693/3828125000000000\",\n+        \"global_coordinate_router_above_kappa\": \"1/175000000\",\n+        \"global_gamma_power_slack\": \"9/7000000000\",\n+        \"group_below_dimension\": \"1/350000000\",\n+        \"group_bit_router_above_kappa\": \"3493653053/490000000000000000\",\n+        \"group_gauge_power_slack\": \"43414597087027/239257812500000\",\n+        \"group_key_fits_record\": \"1/350000000\",\n+        \"group_positive\": \"699999997/700000000\",\n+        \"group_scans_above_kappa\": \"697884353/700000000\",\n+        \"halo_covers_generic_inverse_radius\": \"5\",\n+        \"improvement_over_user_baseline\": \"645689790400418148631/500000000000000000000000\",\n+        \"lambda_above_internal\": \"1/1400000000\",\n+        \"lambda_above_sigma\": \"3/1400000000\",\n+        \"lambda_above_tau\": \"1/1400000000\",\n+        \"lambda_prime_above_lambda\": \"1/1400000000\",\n+        \"lambda_prime_above_leaf\": \"27957687/9800000000000000\",\n+        \"leaf_saving_above_effective\": \"13957687/9800000000000000\",\n+        \"main_transform_above_kappa\": \"32779443/7656250000000000\",\n+        \"membership_arithmetic_fits_record\": \"1/700000000\",\n+        \"microbox_face_corrections_above_kappa\": \"53897884359/700000000\",\n+        \"microbox_halo_volume\": \"55300000003/700000000\",\n+        \"new_complex_uniform_saving_above_b\": \"1/700000000\",\n+        \"new_semantic_guard_with_C1_one\": \"1/700000000\",\n+        \"polynomial_products_above_kappa\": \"348942177/350000000\",\n+        \"positive_layout_slack\": \"1/700000000\",\n+        \"q_below_effective\": \"1/700000000\",\n+        \"q_below_internal\": \"1/700000000\",\n+        \"q_below_leaf\": \"27957687/9800000000000000\",\n+        \"q_positive\": \"33057/10937500\",\n+        \"short_record_fallback\": \"13957687/14000000\",\n+        \"source_axis_superpolynomial\": \"1/700000000\",\n+        \"sparse_union_movement_above_kappa\": \"3110351606216943/7656250000000000\",\n+        \"stop_below_one\": \"699999999/700000000\",\n+        \"stop_positive\": \"1/700000000\",\n+        \"strassen_integer_power_gap\": \"1951441519231\",\n+        \"support_router_span\": \"3/700000000\",\n+        \"theta_positive_polynomial_power\": \"2\",\n+        \"union_header_fits_record\": \"3/700000000\",\n+        \"union_tag_work_per_visit_fits_record\": \"3/700000000\"\n+      }\n+    },\n+    \"paid\": {\n+      \"1\": 41282,\n+      \"16\": 448,\n+      \"2\": 7416,\n+      \"24\": 448,\n+      \"3\": 9180,\n+      \"32\": 448,\n+      \"4\": 2286,\n+      \"40\": 448,\n+      \"48\": 448,\n+      \"5\": 720,\n+      \"56\": 448,\n+      \"64\": 448,\n+      \"72\": 224,\n+      \"8\": 128\n+    },\n+    \"paid_calls\": 64372,\n+    \"productive_fields\": 10912,\n+    \"query_shears\": 15,\n+    \"rank_mass_surplus\": 752,\n+    \"raw_headroom\": [\n+      \"3736347/100000000000000\",\n+      \"934087/25000000000000\"\n+    ],\n+    \"raw_root_interval\": [\n+      \"302238736347/100000000000000\",\n+      \"75559684087/25000000000000\"\n+    ],\n+    \"strictification\": {\n+      \"alpha\": {\n+        \"lower\": \"0.999999971483293515393313955729\",\n+        \"upper\": \"0.999999971483293515393313955730\"\n+      },\n+      \"cutoff\": 20,\n+      \"delta\": {\n+        \"lower\": \"0.957459689758527661921334851512\",\n+        \"upper\": \"0.957459689758527661921334851513\"\n+      },\n+      \"floor\": 21,\n+      \"gamma\": {\n+        \"lower\": \"0.956310980726438847618396606911\",\n+        \"upper\": \"0.956310980726438847618396606912\"\n+      },\n+      \"normalized_paid_upper\": \"2097152001953127/2097154147483648\",\n+      \"power\": 1024,\n+      \"reserve\": \"1/1000000000\",\n+      \"tail_offset\": \"1/5\",\n+      \"tested\": \"75559/25000000\"\n+    },\n+    \"targets\": {\n+      \"145\": 224,\n+      \"17\": 448,\n+      \"25\": 448,\n+      \"33\": 448,\n+      \"4\": 504,\n+      \"41\": 448,\n+      \"49\": 448,\n+      \"57\": 448,\n+      \"65\": 448,\n+      \"7\": 126,\n+      \"73\": 224,\n+      \"8\": 846,\n+      \"9\": 5852\n+    }\n+  },\n+  \"candidate_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 325\n+      },\n+      \"independent_owned_entry_columns\": 3,\n+      \"independent_persistent_columns\": 631,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2200,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 7\n+      },\n+      \"real_scalar_allowance\": 158214,\n+      \"zero_identities\": 1\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"independent_source_identities\": {\n+    \"center_minus_snapshot\": \"Delta/4\",\n+    \"center_replaced\": 11332,\n+    \"copy_coefficient\": \"1\",\n+    \"relation\": {\n+      \"230\": 1,\n+      \"324\": -1,\n+      \"326\": 1,\n+      \"328\": 1,\n+      \"333\": -1\n+    },\n+    \"snapshot_after\": 11205,\n+    \"snapshot_terms_before_substitution\": 61,\n+    \"source_event_indices_are_zero_based\": true,\n+    \"zero_identity_at\": 15584,\n+    \"zero_site_row\": \"-Delta/4\"\n+  },\n+  \"native_negative_controls\": {\n+    \"missing_owned_input_clear\": \"Every independent main/helper endpoint: 0\",\n+    \"uncleared_owned_output\": \"Every owned entry column is erased at return\",\n+    \"under_or_overstated_paid_rank\": \"Exact paid rank and frame\",\n+    \"wrong_copy_gauge\": \"Exact scalar destination frame\",\n+    \"wrong_relation_sign\": \"Every independent main/helper endpoint: 0\",\n+    \"wrong_snapshot_source\": \"Zero identity requires an identically zero full row\",\n+    \"wrong_zero_input_frame\": \"Zero identity requires an identically zero full row\"\n+  },\n+  \"phase_inheritance\": {\n+    \"absolute_phase_receipt_reused\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"all_retained_paid_events_and_warps_from_source\": true,\n+    \"new_gaussian_operators\": 0,\n+    \"new_native_maps\": 0,\n+    \"new_operations\": \"Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.\",\n+    \"source_amplitudes_and_phase_lowering_freshly_replayed\": false\n+  },\n+  \"scope\": \"Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.\",\n+  \"source_native\": {\n+    \"backward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 64,\n+      \"max_formal_prefix_l1\": \"169\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158168,\n+      \"zero_identities\": 0\n+    },\n+    \"forward\": {\n+      \"helpers\": {\n+        \"4\": 28,\n+        \"7\": 7,\n+        \"8\": 47,\n+        \"9\": 326\n+      },\n+      \"independent_owned_entry_columns\": 1,\n+      \"independent_persistent_columns\": 632,\n+      \"max_denominator\": 32,\n+      \"max_formal_prefix_l1\": \"457\",\n+      \"owned_outputs_zero\": true,\n+      \"paid\": {\n+        \"1\": 2201,\n+        \"2\": 412,\n+        \"3\": 510,\n+        \"4\": 127,\n+        \"5\": 40,\n+        \"8\": 8\n+      },\n+      \"real_scalar_allowance\": 158120,\n+      \"zero_identities\": 0\n+    }\n+  },\n+  \"source_payload_sha256\": \"cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd\",\n+  \"status\": \"PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION\",\n+  \"word_payload_sha256\": \"645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35\"\n+}\n@@ -0,0 +1,90 @@\n+{\n+  \"schema_version\": 1,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"files\": [\n+    {\n+      \"path\": \"certificates/selected-result.json\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"c35482cd9035843b15a634cc8276a7e1e40e8395\",\n+      \"sha256\": \"6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375\"\n+    },\n+    {\n+      \"path\": \"docs/research/agent-task-catalog.json\",\n+ 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\"1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f\"\n+    },\n+    {\n+      \"path\": \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"5a55034ec9e6185d981e16c28e1e2e455069e2cb\",\n+      \"sha256\": \"106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7\"\n+    },\n+    {\n+      \"path\": \"research/kappa-interface-round2-20261022/price_profile.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"1d93e43d1cb888d128c2faa2be83a96d85b84295\",\n+      \"sha256\": \"adde619968d3ac37147d239e25145b28150650e9ce0f76035f680f22589adcbb\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"4fc05ab08138218ba9f09e5c89b649afae7c914e\",\n+      \"sha256\": \"011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a\"\n+    },\n+    {\n+      \"path\": \"research/kappa-rebuild/complex/native_extensions.py\",\n+      \"usage\": \"provenance\",\n+      \"git_blob\": \"7f84894efc309546a903d314c7ac1473e7f594a8\",\n+      \"sha256\": \"50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"46d929df83817b85a5387bcdb9745e0627d6366e\",\n+      \"sha256\": \"7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"ac77b78547d6dbf2e6bd102e1047c5b16c1bca88\",\n+      \"sha256\": \"6eae66ed3cfa8a1533e89b9660a57276908e6646640a12f8b1e3489f4ea1354b\"\n+    },\n+    {\n+      \"path\": \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"0fdb65f946d557c13d8e2781b9151e2a8ddee5c3\",\n+      \"sha256\": \"b4f720a7ccbb5b46e472eaf85dc8739a40598986f19b37d26c4f9ecfbd31f0de\"\n+    },\n+    {\n+      \"path\": \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59\",\n+      \"sha256\": \"d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15\"\n+    },\n+    {\n+      \"path\": \"research/query-thinned-controllers/RESULT.json\",\n+      \"usage\": \"input\",\n+      \"git_blob\": \"e0695152c98d727edfd0d2034b58a1c7e8682c0c\",\n+      \"sha256\": \"6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f\"\n+    }\n+  ]\n+}\n@@ -0,0 +1,80 @@\n+{\n+  \"schema_version\": 1,\n+  \"task_id\": \"complex-new-helper-inventory\",\n+  \"priority_revision\": 7,\n+  \"base_commit\": \"7c472563474e60185e6ca101a17622133d047e56\",\n+  \"original_card\": {\n+    \"id\": \"complex-new-helper-inventory\",\n+    \"question\": \"Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?\",\n+    \"starting_points\": [\n+      \"docs/research/research-family-status.md\",\n+      \"research/complex-local-word-ceiling/README.md\",\n+      \"research/heterogeneous-owner-assembly/README.md\",\n+      \"certificates/selected-result.json\",\n+      \"research/selected-k8-unrestricted-ends/README.md\"\n+    ],\n+    \"methods\": [\n+      \"Propose a changed helper inventory and derive an optimistic exact moment.\",\n+      \"Design a small completed instance and independently verify its endpoint and rank bill.\"\n+    ],\n+    \"acceptance_gate\": \"A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.\",\n+    \"first_step\": {\n+      \"command\": [\n+        \"python3\",\n+        \"-B\",\n+        \"research/complex-local-word-ceiling/verify.py\"\n+      ],\n+      \"expected\": \"PASS_COMPLEX_LOCAL_WORD_CEILING\",\n+      \"inspect\": \"Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.\",\n+      \"scope\": \"Positive control and planning budget only; this is not a new construction or full cold replay.\"\n+    },\n+    \"first_experiment\": \"Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.\",\n+    \"bottleneck_link\": \"Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.\",\n+    \"allowed_variations\": [\n+      \"Narrow to one changed boundary or helper type with explicit counts.\",\n+      \"If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope.\"\n+    ],\n+    \"scope_change_triggers\": [\n+      \"Mixing only providers already inside the pinned catalogue.\",\n+      \"Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.\",\n+      \"Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts.\"\n+    ],\n+    \"overlap_terms\": [\n+      \"helper inventory\",\n+      \"heterogeneous-owner\",\n+      \"mutable leaver\"\n+    ]\n+  },\n+  \"scope_status\": \"refined\",\n+  \"actual_scope\": \"Make helper L230 owned in each backward call, prepare one five-helper relation, retain one exact frame-254 snapshot, remove one rank-eight center and one rank-one zero job, and debit one rank-nine target.\",\n+  \"scope_change_reason\": \"This uses the current helper-inventory priority. It changes the independent input inventory and scalar word; all physical native maps and the p16 controller remain fixed.\",\n+  \"bottleneck_link\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+  \"budget_minutes\": 240,\n+  \"stop_rule\": \"Publish one exact complete-profile kappa improvement after native, ownership, phase-inheritance, compiler and cold-export checks.\",\n+  \"outcome\": \"completed\",\n+  \"evidence\": \"README.md, WORD.json.gz, RESULT.json and verify.py. The complete conditional kappa is 60447/20000000.\",\n+  \"author\": \"Ali Romman\",\n+  \"ai_assistance\": \"Substantial OpenAI Codex assistance in discovery, code, proof, verification and publication.\",\n+  \"open_questions\": [\n+    {\n+      \"question\": \"Can a separate reviewer validate this one-relation restriction and the inherited physical transfer premises?\",\n+      \"why_it_matters\": \"The new finite construction is exact, but the complete bound still uses the source phase and all-size contracts.\",\n+      \"first_step\": \"Replay the three unrestricted source rows in native.py and check the COPY and zero-identity argument in README.md.\",\n+      \"blocked_by\": \"Independent review has not yet occurred.\"\n+    },\n+    {\n+      \"question\": \"Can a different helper relation give another complete positive bill?\",\n+      \"why_it_matters\": \"This construction gives one positive instance, not an optimum for changed helper inventories.\",\n+      \"first_step\": \"Claim a disjoint relation in Discussions, derive its exact rows, and include every lost target and owned-storage cost.\",\n+      \"blocked_by\": \"Current active cache and paid-history scopes must be checked first.\"\n+    }\n+  ],\n+  \"coordination\": {\n+    \"claim\": \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5125#discussioncomment-19153737\",\n+    \"distinct_scopes\": [\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/5355\",\n+      \"https://github.com/CrocSwap/integer-mult-bounds/discussions/4930\"\n+    ],\n+    \"boundary\": \"The first scope retains 632 arbitrary inputs and eight centers. The second retains every original helper endpoint. This package removes the independent L230 job only in backward calls and claims only the stated relation and two event replacements.\"\n+  }\n+}\n@@ -0,0 +1,38 @@\n+{\n+  \"schema_version\": 1,\n+  \"status\": \"ready\",\n+  \"python\": \"3.12\",\n+  \"requirements\": [],\n+  \"inputs\": [\n+    \"research/higher-moment-strictification/verify.py\",\n+    \"research/joint-helper-lattice/CONTROLLER.json\",\n+    \"research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py\",\n+    \"research/kappa-rebuild/architecture/mixed_target_probe.py\",\n+    \"research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz\",\n+    \"research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz\",\n+    \"research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json\",\n+    \"research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py\",\n+    \"research/query-thinned-controllers/RESULT.json\"\n+  ],\n+  \"commands\": [\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"Exact native rows, owned entry columns, event ranks, independent source identities, p16 Laurent controller, complete asymmetric invoice, two interval engines, compiler and outer predicates, negative controls.\"\n+    },\n+    {\n+      \"argv\": [\n+        \"{python}\",\n+        \"-O\",\n+        \"-B\",\n+        \"{package}/verify.py\"\n+      ],\n+      \"timeout_seconds\": 600,\n+      \"checks\": \"The same checks remain active with Python assertions disabled.\"\n+    }\n+  ]\n+}\n\n@@ -0,0 +1,299 @@\n+\"\"\"One prepared helper removes two paid jobs in the PR4610 backward word.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+The source word is by Cao Yifan. The row convention and scalar allowance\n+follow the credited native work of Cinna Davis and zxv.\n+\"\"\"\n+from collections import Counter\n+from copy import deepcopy\n+from fractions import Fraction as Q\n+from hashlib import sha1, sha256\n+from pathlib import Path\n+import gzip\n+import importlib.util\n+import json\n+import sys\n+\n+HERE = Path(__file__).resolve().parent\n+ROOT = HERE.parents[1]\n+SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz'\n+PHASE = 'research/kappa-round3-warp-20261022/PHASE-VALIDATION.json.gz'\n+PAYLOAD = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'\n+RELATION = {230: 1, 324: -1, 326: 1, 328: 1, 333: -1}\n+OLD_PAID = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}\n+NEW_PAID = dict(OLD_PAID)\n+NEW_PAID[1] -= 1\n+NEW_PAID[8] -= 1\n+OLD_HELPERS = {4: 28, 7: 7, 8: 47, 9: 326}\n+\n+\n+def need(ok, why):\n+    if not ok:\n+        raise ValueError(why)\n+\n+\n+def read(path):\n+    data = path.read_bytes()\n+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)\n+\n+\n+def encode(x):\n+    if isinstance(x, Q):\n+        return str(x)\n+    if isinstance(x, dict):\n+        return {str(k): encode(v) for k, v in x.items()}\n+    if isinstance(x, (list, tuple)):\n+        return [encode(v) for v in x]\n+    return x\n+\n+\n+def load(relative, name):\n+    spec = importlib.util.spec_from_file_location(name, ROOT / relative)\n+    module = importlib.util.module_from_spec(spec)\n+    sys.modules[name] = module\n+    spec.loader.exec_module(module)\n+    return module\n+\n+\n+def authenticate():\n+    pins = read(HERE / 'SOURCES.json')\n+    for row in pins['files']:\n+        if row['usage'] != 'input':\n+            continue\n+        p = ROOT\n+        for part in Path(row['path']).parts:\n+            p /= part\n+            need(not p.is_symlink(), 'No source aliases')\n+        raw = p.read_bytes()\n+        need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: ' + row['path'])\n+        need(sha1(b'blob ' + str(len(raw)).encode() + b'\\0' + raw).hexdigest() == row['git_blob'], 'Source Git blob')\n+    need(sha256(gzip.decompress((ROOT / SOURCE).read_bytes())).hexdigest() == PAYLOAD, 'Exact source payload')\n+    return pins\n+\n+\n+def span(basis):\n+    out = {0}\n+    for vector in basis:\n+        need(isinstance(vector, int) and 0 <= vector < 512, 'Binary frame coordinate')\n+        out |= {v ^ vector for v in tuple(out)}\n+    need(len(out) == 2 ** len(basis), 'Independent frame basis')\n+    return out\n+\n+\n+def add(dst, src, q):\n+    for k, v in tuple(src.items()):\n+        value = dst.get(k, Q(0)) + q * v\n+        if value:\n+            dst[k] = value\n+        else:\n+            dst.pop(k, None)\n+\n+\n+def allowance(g):\n+    if g[0] in ('clear', 'copy'):\n+        return 2\n+    q = Q(*g[3:]) if g[0] == 'add' else Q(*g[2:])\n+    n, d = abs(q.numerator), q.denominator\n+    need(n > 0 and d & (d - 1) == 0, 'Nonzero dyadic scalar')\n+    if g[0] == 'scale':\n+        need(n & (n - 1) == 0, 'Dyadic unit SCALE')\n+        return 2 * (abs(n.bit_length() - d.bit_length()) + int(q < 0))\n+    need(g[0] == 'add', 'Known scalar operation')\n+    return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1)\n+\n+\n+def construct(source):\n+    c = source['canonical']\n+    old = source['programs']['backward']\n+    need(old[11205] == ['climb', 'warp_retimed', 92, 310, 254, 4], 'Snapshot source event')\n+    need(old[11332] == ['center', 0, 0, 254, 8], 'Center source event')\n+    need(old[15584] == ['climb', 'warp_retimed', 92, 254, 1, 1], 'Zero source event')\n+    need(all(c['start'][h] == 0 and c['final'][h] == 1 for h in RELATION), 'Five cold full-ended helpers')\n+    word = [['scalar', ['clear', ['L', 230]], 0]]\n+    word += [['scalar', ['add', ['L', 230], ['L', h], -q, 1], 0]\n+             for h, q in RELATION.items() if h != 230]\n+    for i, event in enumerate(old):\n+        if i == 11332:\n+            word += [['scalar', ['clear', ['C', 0]], 254],\n+                     ['scalar', ['copy', ['C', 0], ['C', 1]], 254],\n+                     ['scalar', ['clear', ['C', 1]], 254]]\n+        elif i == 15584:\n+            word.append(['zero_retag', ['L', 92], 254, 1])\n+        else:\n+            word.append(deepcopy(event))\n+        if i == 11205:\n+            word += [['scalar', ['clear', ['C', 1]], 254],\n+                     ['scalar', ['copy', ['C', 1], ['L', 92]], 254]]\n+    word.append(['scalar', ['clear', ['L', 230]], 1])\n+    physical = deepcopy(c)\n+    physical.pop('local_profile')\n+    return {'schema': 'owned-helper-relation-word/1', 'canonical': physical,\n+            'paid_profiles': {'forward': OLD_PAID, 'backward': NEW_PAID},\n+            'owned': {'forward': [['C', 0]], 'backward': [['C', 0], ['C', 1], ['L', 230]]},\n+            'programs': {'forward': deepcopy(source['programs']['forward']), 'backward': word}}\n+\n+\n+def replay(c, program, backward, specialized):\n+    \"\"\"Run every event on all independent entry columns and exact frames.\"\"\"\n+    owned = {('C', 0)} | ({('C', 1), ('L', 230)} if specialized else set())\n+    roles = {('L', i) for i in range(632)} | owned\n+    rows = {r: {(r, ()): Q(1)} for r in roles}\n+    frames = {('L', i): f for i, f in enumerate(c['start'])}\n+    frames.update({r: None for r in owned if r[0] == 'C'})\n+    spaces = [span(b) for b in c['frames']]\n+    paid = Counter()\n+    cost, max_l1, denominator, zero_count = 0, Q(1), 1, 0\n+    for e in program:\n+        kind, touched = e[0], None\n+        if kind == 'scalar':\n+            g, frame = e[1:]\n+            dst = tuple(g[1]); touched = dst\n+            need(dst in rows and 0 <= frame < len(spaces), 'Declared scalar destination and frame')\n+            cost += allowance(g)\n+            if g[0] == 'clear':\n+                need(dst in owned, 'Only owned fields can be erased')\n+                rows[dst] = {}; frames[dst] = frame\n+            else:\n+                need(frames[dst] == frame, 'Exact scalar destination frame')\n+                if g[0] in ('add', 'copy'):\n+                    src = tuple(g[2])\n+                    need(src in rows and frames[src] == frame and dst != src, 'Exact scalar source frame')\n+                    if g[0] == 'copy':\n+                        need(dst in owned and not rows[dst], 'COPY into cleared owned storage')\n+                        rows[dst] = dict(rows[src])\n+                    else:\n+                        add(rows[dst], rows[src], Q(g[3], g[4]))\n+                else:\n+                    need(g[0] == 'scale', 'Known scalar operation')\n+                    rows[dst] = {k: Q(g[2], g[3]) * v for k, v in rows[dst].items()}\n+        elif kind == 'warp':\n+            _, role, op, old, new = e\n+            dst = tuple(role); touched = dst\n+            need(frames[dst] == old and 1 <= abs(op) <= len(c['warps']), 'Exact warp input')\n+            symbol = (1 if op > 0 else -1) * (abs(op) + (10**6 if backward else 0))\n+            rows[dst] = {(r, w[1:] if w and w[0] == -symbol else (symbol,) + w): q\n+                         for (r, w), q in rows[dst].items()}\n+            frames[dst] = new\n+        elif kind in ('climb', 'center'):\n+            if kind == 'climb':\n+                _, _, i, old, new, rank = e\n+                dst = ('L', i)\n+                need(spaces[old] < spaces[new], 'Ascending paid climb')\n+            else:\n+                _, i, old, new, rank = e\n+                dst = ('C', i)\n+                need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested paid center')\n+            need(frames[dst] == old and rank == abs(len(c['frames'][new]) - len(c['frames'][old])), 'Exact paid rank and frame')\n+            frames[dst] = new; paid[rank] += 1\n+        elif kind == 'zero_retag':\n+            _, role, old, new = e\n+            dst = tuple(role)\n+            need(specialized and backward and dst == ('L', 92), 'Declared zero identity')\n+            need(frames[dst] == old and not rows[dst], 'Zero identity requires an identically zero full row')\n+            need((old, new) == (254, 1), 'Declared zero frame change')\n+            frames[dst] = new; zero_count += 1\n+        else:\n+            need(kind in ('phase', 'adapter'), 'Known inert source marker')\n+        if touched is not None:\n+            max_l1 = max(max_l1, sum(map(abs, rows[touched].values()), Q(0)))\n+            denominator = max(denominator, max((q.denominator for q in rows[touched].values()), default=1))\n+    need([frames['L', i] for i in range(632)] == c['final'], 'Every final native frame')\n+    for i in range(632):\n+        r = ('L', i)\n+        if r in owned:\n+            continue\n+        expected = {(r, ()): Q(1)}\n+        if i < 112 if backward else 112 <= i < 224:\n+            expected[(('L', i + 112 if backward else i - 112), ())] = Q(-1 if backward else 1)\n+        need(rows[r] == expected, 'Every independent main/helper endpoint: ' + str(i))\n+    need(all(not rows[r] for r in owned), 'Every owned entry column is erased at return')\n+    need(zero_count == int(specialized), 'Exactly one checked zero identity')\n+    helpers = Counter()\n+    for i in range(224, 632):\n+        if ('L', i) in owned:\n+            continue\n+        a, b = c['start'][i], c['final'][i]\n+        need(spaces[a] < spaces[b], 'Strict independent productive helper')\n+        helpers[len(c['frames'][b]) - len(c['frames'][a])] += 1\n+    return {'paid': dict(sorted(paid.items())), 'helpers': dict(sorted(helpers.items())),\n+            'independent_persistent_columns': 631 if specialized else 632,\n+            'independent_owned_entry_columns': len(owned), 'owned_outputs_zero': True,\n+            'real_scalar_allowance': cost, 'max_formal_prefix_l1': str(max_l1),\n+            'max_denominator': denominator, 'zero_identities': zero_count}\n+\n+\n+def independent_source_identities(source):\n+    \"\"\"Use the predecessor row engine on the unrestricted original word.\"\"\"\n+    v = load('research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'owned_relation_source_rows')\n+    rows = {('L', i): v.identity(('L', i)) for i in range(632)}\n+    rows['C', 0] = v.identity(('C', 0))\n+    delta = {(('L', i), ()): Q(q) for i, q in RELATION.items()}\n+    saved = None\n+    for index, e in enumerate(source['programs']['backward']):\n+        if e[0] == 'scalar':\n+            g = e[1]; dst = tuple(g[1])\n+            if g[0] == 'clear': rows[dst] = {}\n+            elif g[0] == 'copy': rows[dst] = dict(rows[tuple(g[2])])\n+            elif g[0] == 'scale': rows[dst] = {k: Q(g[2], g[3]) * a for k, a in rows[dst].items()}\n+            else: v.add(rows[dst], rows[tuple(g[2])], Q(g[3], g[4]))\n+        elif e[0] == 'warp':\n+            dst = tuple(e[1]); rows[dst] = v.warp(rows[dst], e[2], True)\n+        if index == 11205: saved = dict(rows['L', 92])\n+        if index == 11332:\n+            diff = dict(rows['C', 0]); v.add(diff, saved, -1)\n+            need(diff == {k: q / 4 for k, q in delta.items()}, 'Independent exact center minus snapshot = Delta/4')\n+        if index == 15584:\n+            need(rows['L', 92] == {k: -q / 4 for k, q in delta.items()}, 'Independent exact zero-site row = -Delta/4')\n+    need(all(rows['L', i] == v.expected(('L', i), [], True, False) for i in range(632)), 'Independent unrestricted source endpoints')\n+    return {'source_event_indices_are_zero_based': True, 'snapshot_after': 11205,\n+            'center_replaced': 11332, 'zero_identity_at': 15584,\n+            'snapshot_terms_before_substitution': len(saved), 'copy_coefficient': '1',\n+            'center_minus_snapshot': 'Delta/4', 'zero_site_row': '-Delta/4', 'relation': RELATION}\n+\n+\n+def phase_inheritance(source, candidate):\n+    receipt = read(ROOT / PHASE)\n+    need(receipt['status'] == 'PASS_JOINT_HELPER_MAPS_ALL_ACTUAL_ABSOLUTE_PHASES' and\n+         receipt['actual_word_canonical_sha256'] == PAYLOAD, 'Authenticated source absolute-phase receipt')\n+    physical = deepcopy(source['canonical']); physical.pop('local_profile')\n+    need(candidate['canonical'] == physical, 'Every frame, native map and main adapter unchanged')\n+    for direction, program in candidate['programs'].items():\n+        old = source['programs'][direction]\n+        for kind in ('warp', 'adapter', 'phase'):\n+            need([e for e in program if e[0] == kind] == [e for e in old if e[0] == kind], 'Exact inherited ' + kind + ' sequence')\n+        old_paid = Counter(tuple(e) for e in old if e[0] in ('climb', 'center'))\n+        new_paid = Counter(tuple(e) for e in program if e[0] in ('climb', 'center'))\n+        expected = Counter() if direction == 'forward' else Counter(tuple(old[i]) for i in (11332, 15584))\n+        need(old_paid - new_paid == expected and not new_paid - old_paid, 'Only the two proved jobs are removed')\n+    return {'new_gaussian_operators': 0, 'new_native_maps': 0,\n+            'all_retained_paid_events_and_warps_from_source': True,\n+            'absolute_phase_receipt_reused': PHASE,\n+            'source_amplitudes_and_phase_lowering_freshly_replayed': False,\n+            'new_operations': 'Same-frame COPY, owned CLEAR/ADD, and physical identity on a proved zero row.'}\n+\n+\n+def controls(c, candidate):\n+    controls = {}\n+    base = candidate['programs']['backward']\n+    variants = {}\n+    bad = deepcopy(base); bad[1][1][3] *= -1; variants['wrong_relation_sign'] = bad\n+    variants['missing_owned_input_clear'] = deepcopy(base[1:])\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 1]])[1][2] = ['L', 63]\n+    variants['wrong_snapshot_source'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'zero_retag')[2] = 0\n+    variants['wrong_zero_input_frame'] = bad\n+    bad = deepcopy(base); next(e for e in bad if e[0] == 'climb')[5] += 1\n+    variants['under_or_overstated_paid_rank'] = bad\n+    bad = deepcopy(base)\n+    next(e for e in bad if e[0] == 'scalar' and e[1][:2] == ['copy', ['C', 0]])[2] = 0\n+    variants['wrong_copy_gauge'] = bad\n+    variants['uncleared_owned_output'] = deepcopy(base[:-1])\n+    for name, program in variants.items():\n+        try:\n+            replay(c, program, True, True)\n+        except ValueError as err:\n+            controls[name] = str(err)\n+        else:\n+            raise ValueError('Control accepted: ' + name)\n+    return controls\n@@ -0,0 +1,196 @@\n+\"\"\"Complete p16 bill and finite compiler for one owned helper relation.\n+\n+The interval and compiler proof follows Cao Yifan's PR4610 pricing, Cinna\n+Davis's PR4470 controller, zxv's completion and logarithmic majorant, and\n+Jacob Alan Sussman's mixed-target recursion. Apache-2.0.\n+Ali Romman, with substantial OpenAI Codex assistance.\n+\"\"\"\n+from collections import Counter\n+from fractions import Fraction as Q\n+from native import ROOT, read, load, need, encode, OLD_PAID, OLD_HELPERS\n+\n+KAPPA = Q('.00302235')\n+TESTED = Q('.00302236')\n+PREVIOUS = Q('.0030217758')\n+OLD_ROOT_UPPER = Q('.00302177587078')\n+\n+\n+def controller():\n+    \"\"\"Check the literal p16 word and both rational boundary programs.\"\"\"\n+    word = read(ROOT / 'research/joint-helper-lattice/CONTROLLER.json')\n+    need((word['kind'], word['pairs'], word['prefix_pairs'], word['ambient_rank']) == ('complex', 16, 7, 145), 'Source p16/a7 controller')\n+    zero = (0,) * 34\n+    def plus(dst, src, q):\n+        for k, v in src.items():\n+            value = dst.get(k, Q(0)) + q * v\n+            if value: dst[k] = value\n+            else: dst.pop(k, None)\n+    def shifted(row, term, sign=1):\n+        return [{tuple(a + b for a, b in zip(k, term)): sign * v for k, v in cell.items()} for cell in row]\n+    for side in ('left', 'right'):\n+        matrix = [[Q(i == j) for j in range(32)] for i in range(32)]\n+        for e in word['boundaries'][side + '_program']:\n+            if e[0] == 'SWAP': matrix[e[1]], matrix[e[2]] = matrix[e[2]], matrix[e[1]]\n+            elif e[0] == 'SCALE': matrix[e[1]] = [Q(e[2]) * x for x in matrix[e[1]]]\n+            else:\n+                need(e[0] == 'ADD', 'Boundary scalar opcode')\n+                matrix[e[1]] = [x + Q(e[3]) * y for x, y in zip(matrix[e[1]], matrix[e[2]])]\n+        need(matrix == [[Q(x) for x in row] for row in word['boundaries'][side]], 'Exact scalar boundary program')\n+    rows = [[{zero: Q(x)} if Q(x) else {} for x in row] for row in word['boundaries']['right']]\n+    for e in word['physical_events']:\n+        if e[0] in ('LOCAL', 'QUERY_SHEAR'):\n+            _, stage, pair, back = e\n+            x, y = 2 * pair, 2 * pair + 1\n+            if back: x, y = y, x\n+            term = (1 if back else -1,) + (0,) * 33\n+            for dst, src in zip(rows[y], shifted(rows[x], term)):\n+                plus(dst, src, Q(-1 if back else 1))\n+            if e[0] == 'LOCAL':\n+                term = (0,) + tuple(int(s == stage) for s in range(33))\n+                for r in (x, y): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'IDLE':\n+            term = (0,) + tuple(int(s in e[2]) for s in range(33))\n+            for r in (2 * e[1], 2 * e[1] + 1): rows[r] = shifted(rows[r], term)\n+        elif e[0] == 'ADD':\n+            for dst, src in zip(rows[e[1]], rows[e[2]]): plus(dst, src, Q(e[3]))\n+        else:\n+            need(e[0] in ('SWAP', 'SIGNED_SWAP'), 'Controller physical opcode')\n+            rows[e[1]], rows[e[2]] = rows[e[2]], shifted(rows[e[1]], zero, -1 if e[0] == 'SIGNED_SWAP' else 1)\n+    out = [[{} for _ in range(32)] for _ in range(32)]\n+    for i, row in enumerate(word['boundaries']['left']):\n+        for k, q in enumerate(row):\n+            if Q(q):\n+                for j in range(32): plus(out[i][j], rows[k][j], Q(q))\n+    expected = [[{tuple(word['diagonal'][i]): Q(1)} if i == j else {} for j in range(32)] for i in range(32)]\n+    need(out == expected, 'All p16 Laurent coefficients, central signs and boundary factors')\n+    return word\n+\n+\n+def assemble(native, word):\n+    T, P = Counter(), Counter()\n+    orientations = Counter(); thin = 0\n+    for e in word['physical_events']:\n+        if e[0] == 'LOCAL':\n+            direction = 'backward' if e[3] else 'forward'\n+            orientations[direction] += 1\n+            T.update(native[direction]['helpers']); P.update(native[direction]['paid'])\n+        elif e[0] == 'QUERY_SHEAR': thin += 1; P[1] += 112\n+        elif e[0] == 'IDLE': P[8 * len(e[2])] += 224\n+    main = Counter()\n+    for term in word['diagonal']:\n+        need(term[0] in (-1, 1) and all(x in (0, 1) for x in term[1:]), 'Whole Gaussian main target')\n+        main[1 + 8 * sum(term[1:])] += 112\n+    T.update(main)\n+    need(orientations == {'backward': 16, 'forward': 2} and thin == 15, 'Every actual call orientation')\n+    # This second census uses the source invoice and the two local deltas.\n+    check_T = Counter({int(r): n for r, n in word['invoice']['main'].items()})\n+    check_T.update({r: 18 * n for r, n in OLD_HELPERS.items()}); check_T[9] -= 16\n+    check_P = Counter({int(r): n for r, n in word['invoice']['whole_idle'].items()})\n+    check_P.update({r: 18 * n for r, n in OLD_PAID.items()}); check_P[1] += 1680 - 16; check_P[8] -= 16\n+    need(T == check_T and P == check_P, 'Independent full invoice substitution')\n+    need(sum(T.values()) == 10912 and sum(P.values()) == 64372, 'Complete productive and paid counts')\n+    need(sum(r * n for r, n in T.items()) - sum(r * n for r, n in P.items()) == 752, 'Unchanged complete rank surplus')\n+    return T, P\n+\n+\n+def run(native):\n+    word = controller(); T, P = assemble(native, word)\n+    prior = read(ROOT / 'research/kappa-round6-compiler-tightening-20261022/ARITHMETIC.json')\n+    need(Q(prior['kappa']) == PREVIOUS and Q(prior['raw_root_interval'][1]) == OLD_ROOT_UPPER, 'Pinned prior conditional bound and raw crossing')\n+    prior_T = Counter({int(r): n for r, n in prior['targets'].items()})\n+    prior_P = Counter({int(r): n for r, n in prior['paid'].items()})\n+    prior_T[9] -= 16; prior_P[1] -= 16; prior_P[8] -= 16\n+    need(T == prior_T and P == prior_P, 'Complete delta from the final PR4610 bill')\n+    E = load('research/higher-moment-strictification/verify.py', 'owned_relation_intervals')\n+    other = load('research/kappa-rebuild/architecture/mixed_target_probe.py', 'owned_relation_second_intervals')\n+    def margin(c):\n+        t, p = E.moment(T, 1 - c), E.moment(P, 1 - c)\n+        return t[0] - p[1], t[1] - p[0]\n+    need(margin(OLD_ROOT_UPPER)[0] > 0, 'Changed invoice beats the prior raw root upper endpoint')\n+    lo, hi, grid = 0, 10**12, 10**14\n+    while hi - lo > 1:\n+        mid = (lo + hi) // 2\n+        if margin(Q(mid, grid))[0] > 0: lo = mid\n+        else: hi = mid\n+    root_low, root_high = Q(lo, grid), Q(hi, grid)\n+    need(margin(root_low)[0] > 0 and margin(root_high)[1] < 0, 'Strict rational root enclosure')\n+    need(PREVIOUS < KAPPA < TESTED < root_low, 'New bound and explicit compiler headroom')\n+    # The complete signed profile decreases on [0, .05], and stays negative\n+    # on [.05, 1]. This proves a fixed-profile ceiling, not a circuit ceiling.\n+    signed = {r: T[r] - P[r] for r in T.keys() | P.keys()}\n+    derivative, upper = None, None\n+    for i in range(16):\n+        l, r = Q(i, 320), Q(i + 1, 320); low = Q(0)\n+        for rank, n in signed.items():\n+            term = E.mul(E.power(rank, 1 - r if n > 0 else 1 - l), E.log_bounds(rank))\n+            low += n * term[0 if n > 0 else 1]\n+        derivative = low if derivative is None else min(derivative, low)\n+    for i in range(128):\n+        l, r = Q(1, 20) + Q(19 * i, 2560), Q(1, 20) + Q(19 * (i + 1), 2560)\n+        value = sum(n * E.power(rank, 1 - l if n > 0 else 1 - r)[1 if n > 0 else 0] for rank, n in signed.items())\n+        upper = value if upper is None else max(upper, value)\n+    need(derivative > 0 and upper < 0, 'Fixed-profile ceiling on all 0 < kappa < 1')\n+    t, u, v, c, b = 1 - TESTED, Q(1, 5), 1024, 20, 21\n+    target, paid = E.moment(T, t), E.moment(P, t)\n+    tl, th = other.moment(T, TESTED); pl, ph = other.moment(P, TESTED)\n+    need(tl > ph and max(tl, target[0]) <= min(th, target[1]) and max(pl, paid[0]) <= min(ph, paid[1]), 'Two exact interval engines agree')\n+    alpha = E.divide(paid, target)\n+    gamma = E.divide(E.moment(P, t + u), E.mul(E.power(c, u), target))\n+    delta = E.divide((Q(sum(T.values()) * b),) * 2, E.mul(E.power(c, TESTED), target))\n+    reserve = Q(1, 10**9); g = d = Q(97, 100)\n+    need(alpha[1] < 1 - reserve and gamma[1] < g and delta[1] < d, 'Original and completion tails charged')\n+    need(g**128 < Q(1, 16) and d**128 < Q(1, 16), 'Two strict tail decay blocks')\n+    normalized = 1 / (1 + v * reserve) + Q(4, 2**32)\n+    need(normalized < 1 and c**64 < b**63, 'Paid completion, splitting and rounding')\n+    theta, power = Q(63, 64), 1000\n+    eta = E.scale(E.power(145, -v * TESTED), t)\n+    need(2 * (20**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity')\n+    need(E.power(145, v * TESTED)[1] < 2**power, 'Compiler initial range')\n+    gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'Finite integer grid')\n+    step = gap.denominator\n+    def wins(j): return (step * j + 1)**power < 2**j\n+    left, right = 1, 2\n+    while not wins(right): left, right = right, 2 * right\n+    while right - left > 1:\n+        mid = (left + right) // 2\n+        if wins(mid): right = mid\n+        else: left = mid\n+    height = step * right\n+    need(height > 8 * v and wins(right) and not wins(right - 1), 'Finite uniform-rank threshold')\n+    local_scalar = max(x['real_scalar_allowance'] for x in native.values())\n+    # The old route allowance is retained. Charge two additional owned field\n+    # lifetimes at two routes each, even though L230 uses an existing slot.\n+    routes = (max(sum(x['paid'].values()) for x in native.values()) + 2 * 408 + 688 + 4) * 1000\n+    need(local_scalar + routes < 10**7, 'All new preparation, COPY, CLEAR and fixed routes fit')\n+    scalar_upper = 18 * 10**7 + 15 * 1792 + 32 * 112 * (len(word['physical_events']) + sum(len(word['boundaries'][k + '_program']) for k in ('left', 'right')))\n+    need(scalar_upper < 10**9, 'Complete raw nonrecursive bound')\n+    bit = read(ROOT / 'research/query-thinned-controllers/RESULT.json')['ordinary_BIT']\n+    atom = Q(bit['atom']); ordinary = (1 - atom) * Q(bit['after_cover']) + atom * Q('.0000384599'); admitted = Q(bit['admitted'])\n+    need(atom == Q('.004') and atom > ordinary > admitted > TESTED and atom < 1 - ordinary, 'Retained stronger BIT admission and stock')\n+    L = load('research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'owned_relation_outer')\n+    params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap,\n+              'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': admitted,\n+              'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap}\n+    outer = L.ledger(params); outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - atom)\n+    need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory')\n+    need(all(x > 0 for key in ('strict_checks', 'functional_checks') for x in outer[key].values()), 'Every outer inequality is strict')\n+    controls = {}\n+    for name, patch in [('old_BIT', {'bit_saving': Q('.0027')}), ('closed_uniform', {'complex_uniform_saving': params['b']}), ('unfunded_endpoint', {'kappa': TESTED}), ('closed_epsilon', {'epsilon': Q(1)})]:\n+        bad = L.ledger(dict(params, **patch)); failed = [k for k, x in bad['strict_checks'].items() if x <= 0]\n+        need(failed, 'Reject outer patch ' + name); controls[name] = failed\n+    bad_native = {d: dict(x) for d, x in native.items()}\n+    bad_native['backward']['helpers'] = OLD_HELPERS\n+    try: assemble(bad_native, word)\n+    except ValueError: controls['unearned_helper_credit'] = 'Rejected by the independent complete census'\n+    else: raise ValueError('Unowned helper credit was accepted')\n+    return encode({'kappa': KAPPA, 'kappa_decimal': '.00302235', 'gain_over_PR4610': KAPPA - PREVIOUS,\n+                   'raw_root_interval': [root_low, root_high], 'raw_headroom': [root_low - KAPPA, root_high - KAPPA],\n+                   'margin_at_previous_kappa': E.display(margin(PREVIOUS)),\n+                   'margin_at_previous_root_upper': E.display(margin(OLD_ROOT_UPPER)),\n+                   'fixed_profile_ceiling': {'decreasing_through': Q(1, 20), 'derivative_upper': E.display((-derivative,) * 2), 'remaining_interval_moment_upper': E.display((upper,) * 2)},\n+                   'targets': T, 'paid': P, 'productive_fields': sum(T.values()), 'paid_calls': sum(P.values()), 'rank_mass_surplus': 752,\n+                   'full_backward': 16, 'full_forward': 2, 'query_shears': 15,\n+                   'strictification': {'tested': TESTED, 'power': v, 'cutoff': c, 'floor': b, 'tail_offset': u, 'reserve': reserve, 'alpha': E.display(alpha), 'gamma': E.display(gamma), 'delta': E.display(delta), 'normalized_paid_upper': normalized},\n+                   'compiler': {'theta': theta, 'logarithm_power': power, 'eta': E.display(eta), 'gap': gap, 'uniform_saving': params['complex_uniform_saving'], 'H': height, 'N': '2^' + str(height), 'integer_test_exponent': right, 'word_materialized': False},\n+                   'nonrecursive': {'local_scalar': local_scalar, 'local_routes': routes, 'raw_scalar_upper': scalar_upper, 'raw_budget': 10**9, 'additional_private_slots': 1, 'owned_slots_backward': 3},\n+                   'ordinary_BIT': bit, 'outer': outer, 'negative_controls': controls})\n@@ -0,0 +1,64 @@\n+#!/usr/bin/env python3\n+\"\"\"Replay the one-relation native word and its complete conditional kappa.\n+\n+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.\n+Read README.md for the source credit and inherited proof obligations.\n+\"\"\"\n+from hashlib import sha256\n+import argparse\n+import gzip\n+import json\n+from pathlib import Path\n+import sys\n+sys.dont_write_bytecode = True\n+import native as N\n+import price\n+\n+\n+def run():\n+    N.authenticate()\n+    source = N.read(N.ROOT / N.SOURCE)\n+    candidate = N.construct(source)\n+    c = candidate['canonical']\n+    before, after = {}, {}\n+    for direction in ('forward', 'backward'):\n+        back = direction == 'backward'\n+        before[direction] = N.replay(c, source['programs'][direction], back, False)\n+        after[direction] = N.replay(c, candidate['programs'][direction], back, back)\n+        N.need(before[direction]['paid'] == N.OLD_PAID and before[direction]['helpers'] == N.OLD_HELPERS, 'Pinned source census')\n+        N.need(after[direction]['paid'] == candidate['paid_profiles'][direction], 'Emitted direction-specific paid profile')\n+        helpers = dict(N.OLD_HELPERS)\n+        if back: helpers[9] -= 1\n+        N.need(after[direction]['paid'] == (N.NEW_PAID if back else N.OLD_PAID) and after[direction]['helpers'] == helpers, 'Actual complete changed native census')\n+    identities = N.independent_source_identities(source)\n+    phase = N.phase_inheritance(source, candidate)\n+    controls = N.controls(c, candidate)\n+    arithmetic = price.run(after)\n+    data = (json.dumps(candidate, sort_keys=True, separators=(',', ':')) + '\\n').encode()\n+    result = N.encode({'status': 'PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION',\n+                       'source_payload_sha256': N.PAYLOAD, 'word_payload_sha256': sha256(data).hexdigest(),\n+                       'source_native': before, 'candidate_native': after, 'independent_source_identities': identities,\n+                       'phase_inheritance': phase, 'native_negative_controls': controls, 'arithmetic': arithmetic,\n+                       'scope': 'Exact finite word, full all-column endpoints, ownership, p16 bill and compiler arithmetic. Retains source native phase, allowed owned erasure, mixed-target all-size, analytic, precision, tape, prime and exact-recovery contracts. No selected-frontier update.'})\n+    return data, result\n+\n+\n+def main():\n+    ap = argparse.ArgumentParser(description=__doc__)\n+    ap.add_argument('--write', action='store_true', help='Write only this package word and result after all checks pass.')\n+    ap.add_argument('--out', type=Path, help='Write a replay result to a separate path.')\n+    args = ap.parse_args()\n+    data, result = run()\n+    if args.write:\n+        (N.HERE / 'WORD.json.gz').write_bytes(gzip.compress(data, mtime=0))\n+        (N.HERE / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    else:\n+        N.need(gzip.decompress((N.HERE / 'WORD.json.gz').read_bytes()) == data, 'Exact literal published word')\n+        N.need(N.read(N.HERE / 'RESULT.json') == result, 'Exact published replay result')\n+    if args.out:\n+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\\n', encoding='utf-8')\n+    print(json.dumps({'status': result['status'], **{k: result['arithmetic'][k] for k in ('kappa', 'gain_over_PR4610', 'raw_root_interval', 'paid_calls', 'productive_fields')}}, sort_keys=True))\n+\n+\n+if __name__ == '__main__':\n+    main()",
+    "comments": null,
+    "display_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377",
+    "display_title": "Conditional κ = 0.00302235 (+5.742e-7 over #4610): one owned helper relation"
+  },
+  "isError": false
+}
diff --git a/research/owned-relation-independent-validation/git-evidence/commit/1ec1119972c9aefe42525172d07b332fcff81cb4 b/research/owned-relation-independent-validation/git-evidence/commit/1ec1119972c9aefe42525172d07b332fcff81cb4
new file mode 100644
index 0000000000..87c53f7af1
--- /dev/null
+++ b/research/owned-relation-independent-validation/git-evidence/commit/1ec1119972c9aefe42525172d07b332fcff81cb4
@@ -0,0 +1,6 @@
+tree bfb420045d2bc04dd026b5020aea84d547873ef4
+parent 7c472563474e60185e6ca101a17622133d047e56
+author Douglas R. Colkitt <douglas.colkitt@gmail.com> 1792786762 -0400
+committer Douglas R. Colkitt <douglas.colkitt@gmail.com> 1792786762 -0400
+
+Admit conditional PR4610 frontier through independent PR5241 audit [skip ci]
diff --git a/research/owned-relation-independent-validation/git-evidence/commit/7c472563474e60185e6ca101a17622133d047e56 b/research/owned-relation-independent-validation/git-evidence/commit/7c472563474e60185e6ca101a17622133d047e56
new file mode 100644
index 0000000000..644749f746
--- /dev/null
+++ b/research/owned-relation-independent-validation/git-evidence/commit/7c472563474e60185e6ca101a17622133d047e56
@@ -0,0 +1,6 @@
+tree 32f0a466021c5f549d7a538a0807b30c7ca9f25a
+parent 3b785d5197a073ea3304f19587fd65f2b670928f
+author Douglas R. Colkitt <douglas.colkitt@gmail.com> 1792780698 -0400
+committer Douglas R. Colkitt <douglas.colkitt@gmail.com> 1792780698 -0400
+
+Record 91 confirmed PR merges and empty actionable queue [skip ci]
diff --git a/research/owned-relation-independent-validation/git-evidence/commit/c448d13c71908647f968b06cddb795ce7d288139 b/research/owned-relation-independent-validation/git-evidence/commit/c448d13c71908647f968b06cddb795ce7d288139
new file mode 100644
index 0000000000..4d1d1ea199
--- /dev/null
+++ b/research/owned-relation-independent-validation/git-evidence/commit/c448d13c71908647f968b06cddb795ce7d288139
@@ -0,0 +1,6 @@
+tree e4370e0bff125a6575ed3c073d24aa1a984323d1
+parent 7c472563474e60185e6ca101a17622133d047e56
+author Ali Romman <226877337+aliromman@users.noreply.github.com> 1792786992 -0500
+committer Ali Romman <226877337+aliromman@users.noreply.github.com> 1792786992 -0500
+
+Improve conditional kappa to 0.00302235 with one owned helper relation
diff --git a/research/owned-relation-independent-validation/git-evidence/tree/02fdbbad293e674b3e2300ee89b37ed4dc623f6f b/research/owned-relation-independent-validation/git-evidence/tree/02fdbbad293e674b3e2300ee89b37ed4dc623f6f
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diff --git a/research/owned-relation-independent-validation/verify.py b/research/owned-relation-independent-validation/verify.py
new file mode 100644
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--- /dev/null
+++ b/research/owned-relation-independent-validation/verify.py
@@ -0,0 +1,172 @@
+#!/usr/bin/env python3
+"""Independent PR5377 packet replay, standard-library Python, no Git/network.
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+The two frozen review engines retain their attribution and exact source bytes.
+"""
+from pathlib import Path, PurePosixPath
+import argparse, gzip, hashlib, json, os, shutil, subprocess, sys, tempfile, time
+
+HERE = Path(__file__).resolve().parent
+CAPSULE_SHA256 = '3351f3826dff8c1b39aa63f15a1f8d2764111ae61ffb4d49a2ebd3ed658471e6'
+HEAD = 'c448d13c71908647f968b06cddb795ce7d288139'
+MAIN = '1ec1119972c9aefe42525172d07b332fcff81cb4'
+BASE = '7c472563474e60185e6ca101a17622133d047e56'
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+def digest(raw, kind='blob'):
+    return hashlib.sha1(kind.encode()+b' '+str(len(raw)).encode()+b'\0'+raw).hexdigest()
+
+def read(path):
+    return json.loads(path.read_bytes())
+
+def file_at(root, name):
+    parts=PurePosixPath(name)
+    need(not parts.is_absolute() and '..' not in parts.parts and str(parts)==name, 'unsafe packet path')
+    current=root
+    for part in parts.parts:
+        current=current/part
+        need(not current.is_symlink(), 'symlink in packet path '+name)
+    need(current.is_file(), 'missing packet file '+name)
+    return current
+
+def inventory(root, manifest):
+    seen=set()
+    for row in manifest['files']:
+        name=row['path'];need(name not in seen,'duplicate inventory path');seen.add(name)
+        raw=file_at(root,name).read_bytes()
+        need(len(raw)==row['bytes'] and hashlib.sha256(raw).hexdigest()==row['sha256'] and digest(raw)==row['git_blob'], 'source/receipt byte guard: '+name)
+    actual={q.relative_to(root).as_posix() for folder in ['capsule','engines','evidence','git-evidence'] for q in (root/folder).rglob('*') if q.is_file()}
+    need(actual==seen-{'SOURCE-GUARDS.json'}, 'extra/missing capsule inventory file')
+    return len(seen)
+
+def object_at(root,kind,sha):
+    raw=file_at(root,'git-evidence/'+kind+'/'+sha).read_bytes()
+    need(digest(raw,kind)==sha,'raw Git object hash '+sha)
+    return raw
+
+def tree_entries(raw):
+    result={};i=0
+    while i<len(raw):
+        j=raw.index(b' ',i);k=raw.index(b'\0',j);name=raw[j+1:k].decode('utf-8')
+        need(name not in result and k+21<=len(raw),'malformed raw Git tree')
+        result[name]=(raw[i:j].decode(),raw[k+1:k+21].hex());i=k+21
+    return result
+
+def source_guards(root):
+    guards=read(root/'SOURCE-GUARDS.json')['rows']
+    for row in guards:
+        raw=object_at(root,'commit',row['commit']);first=raw.split(b'\n',1)[0].split()
+        need(first[0]==b'tree','commit tree header');tree=first[1].decode()
+        parts=row['path'].split('/')
+        for i,part in enumerate(parts):
+            mode,sha=tree_entries(object_at(root,'tree',tree))[part]
+            if i==len(parts)-1:
+                need(mode=='100644' and sha==row['git_blob'],'raw committed blob identity '+row['path'])
+                need(digest(file_at(root,row['local']).read_bytes())==sha,'source alias mismatch '+row['local'])
+            else:
+                need(mode=='40000','non-tree source ancestor');tree=sha
+    # Both commits are sibling children of the author source base. The candidate
+    # head is expressly not used as SOURCES.json canonical provenance.
+    for commit in [HEAD,MAIN]:
+        raw=object_at(root,'commit',commit)
+        need(('parent '+BASE+'\n').encode() in raw.split(b'\n\n',1)[0]+b'\n','source base parent relation')
+    author=read(root/'capsule/research/kappa-owned-relation-20261023/SOURCES.json')
+    need(author['base_commit']==BASE,'original author base')
+    need(sum(r['usage']=='input' for r in author['files'])==9 and len(author['files'])==14,'original9input14rowcontract')
+    need(sum(r['local'].startswith('capsule/research/kappa-owned-relation-20261023/') for r in guards)==9,'original9filepayload')
+    return len(guards)
+
+def cold_receipt(root):
+    cold=root/'evidence/cold';v=read(cold/'VALIDATION.json');bound=read(cold/'BOUNDED-REGISTERED-RUN.json')
+    need(v['head']==HEAD and v['current_canonical_main_pin']==MAIN,'cold exact source pins')
+    need(v['status']=='PASS_OWN_COMPLETE_REGISTERED_PR5377_NORMAL_AND_OPTIMIZED','full frozen cold result')
+    need(bound['status']=='PASS_COMPLETE_REGISTERED_NORMAL_AND_OPTIMIZED' and bound['exit']==0 and bound['resource_stop'] is None and not bound['scientific_bytes_changed'],'frozen bounded execution result')
+    need(read(cold/'PRE-RUN-HASHES.json')==read(cold/'POST-RUN-HASHES.json'),'cold input immutability')
+    for name,sha in v['evidence_sha256'].items():
+        need(hashlib.sha256(file_at(cold,name).read_bytes()).hexdigest()==sha,'complete cold receipt '+name)
+    original=root/'capsule/research/kappa-owned-relation-20261023/RESULT.json'
+    need(hashlib.sha256(original.read_bytes()).hexdigest()==v['full_result_sha256'],'cold full scientific artifact')
+    need(v['normal_stdout_result']==v['optimized_stdout_result'],'cold mode result equality')
+    need(v['total_control_executions']==24 and v['all_54_strict_outer_positive'] and v['all_four_functional_positive'],'cold complete registered coverage')
+    log=(cold/'REGISTERED-COLD.stdout.log').read_text()
+    need(log.count('"status": "PASS_CONDITIONAL_KAPPA_00302235_ONE_OWNED_RELATION"')==2 and 'PASS_REGISTERED_RESEARCH_PACKAGE' in log,'cold complete stdout')
+    return dict(status=bound['status'],seconds=bound['seconds'],fresh_here=False,source_files_unchanged=bound['hash_inventory_files'],controls=v['total_control_executions'])
+
+def make_engine(root,name,dest):
+    shutil.copytree(root/'engines'/name,dest)
+    # The engine program can write its result in dest; its source inputs and
+    # nested directories are read-only. No package evidence is overwritten.
+    sub=dest/('pinned' if name=='physical' else 'frozen')
+    for q in sub.rglob('*'):
+        if q.is_file():q.chmod(0o444)
+    sub.chmod(0o555)
+    return sub
+
+def launch(dest,script):
+    argv=[sys.executable]
+    if sys.flags.optimize:argv+=['-O']
+    argv+=['-B',str(dest/script)]
+    env=dict(os.environ);env.pop('PYTHONOPTIMIZE',None);env['PYTHONPYCACHEPREFIX']=str(dest/'private-bytecode')
+    return subprocess.run(argv,cwd=dest,env=env,stdout=subprocess.PIPE,stderr=subprocess.PIPE,text=True,timeout=110)
+
+def stable(result):
+    result=dict(result);result.pop('seconds',None);return result
+
+def run_engines(root,tmp):
+    results={}
+    for name,script,expected in [('physical','independent_physical_check.py','evidence/physical/independent-result.json'),('cost','check_cost.py','evidence/cost/RESULT.json')]:
+        dest=tmp/name;inputs=make_engine(root,name,dest);before={q.name:hashlib.sha256(q.read_bytes()).hexdigest() for q in inputs.iterdir() if q.is_file()}
+        run=launch(dest,script);need(run.returncode==0,'independent '+name+' engine failed: '+run.stderr[-2500:])
+        fresh=json.loads(run.stdout);old=read(root/expected)
+        # The initial cost receipt predates later provenance captures in its
+        # frozen folder. Bind every current hash by CAPSULE+Merkle guards, then
+        # require all original receipt hashes and every mathematical field.
+        if name=='cost':
+            hashes=fresh.pop('sha256');oldhash=dict(old.pop('sha256'))
+            need(hashes==before and all(hashes[k]==v for k,v in oldhash.items()),'cost complete frozen source map')
+        need(stable(fresh)==stable(old),'complete stable '+name+' result differs')
+        need(before=={q.name:hashlib.sha256(q.read_bytes()).hexdigest() for q in inputs.iterdir() if q.is_file()},'engine changed frozen input')
+        results[name]=dict(status=fresh['status'],seconds=fresh['seconds'],complete_stable_result_equal=True,source_hashes=len(before))
+    return results
+
+def semantic_controls(root,tmp,manifest):
+    # A raw byte mutation must fail before evaluator execution.
+    row=next(r for r in manifest['files'] if r['path']=='capsule/research/kappa-owned-relation-20261023/README.md')
+    changed_root=tmp/'control-source';changed_root.mkdir()
+    target=changed_root/row['path'];target.parent.mkdir(parents=True)
+    target.write_bytes((root/row['path']).read_bytes()+b'\n')
+    try:
+        inventory(changed_root,{'files':[row]})
+    except ValueError as error:
+        need('source/receipt byte guard: '+row['path'] in str(error),'source control wrong failure')
+    else:
+        raise ValueError('altered source byte accepted')
+    out=['altered source byte rejected by actual inventory guard']
+    dest=tmp/'control-cost';shutil.copytree(root/'engines/cost',dest)
+    path=dest/'frozen/RESULT.json';receipt=read(path)
+    receipt['arithmetic']['targets']['9']+=16
+    path.write_text(json.dumps(receipt))
+    run=launch(dest,'check_cost.py')
+    need(run.returncode!=0 and 'author invoice crosscheck' in run.stderr,
+         'productive-credit control wrong failure: '+run.stderr[-2000:])
+    out.append('unearned16rank9productive-targets rejected by literal census')
+    out.append('fresh physical engine executes its intrinsic wrong-relation and wrong-snapshot controls')
+    return out
+
+def main():
+    parser=argparse.ArgumentParser();parser.add_argument('--integrity-only',action='store_true');args=parser.parse_args();start=time.monotonic()
+    raw=(HERE/'CAPSULE.json').read_bytes();need(hashlib.sha256(raw).hexdigest()==CAPSULE_SHA256,'capsule manifest immutable hash')
+    manifest=json.loads(raw);need(manifest['frozen_cold_complete'] and manifest['canonical_base']==MAIN and manifest['author_head']==HEAD,'complete packet pins')
+    count=inventory(HERE,manifest);guards=source_guards(HERE);cold=cold_receipt(HERE)
+    result=dict(status='PASS_INDEPENDENT_PR5377_CAPSULE_INTEGRITY',head=HEAD,inventory_files=count,raw_merkle_source_paths=guards,cold_frozen_receipt=cold)
+    if not args.integrity_only:
+        with tempfile.TemporaryDirectory(prefix='pr5377-independent-') as folder:
+            tmp=Path(folder);result['independent_engines']=run_engines(HERE,tmp);result['wrapper_controls']=semantic_controls(HERE,tmp,manifest)
+        inventory(HERE,manifest)
+        result.update(status='PASS_INDEPENDENT_PR5377_CONDITIONAL_VALIDATION',kappa='60447/20000000',gain_over_selected4610='2871/5000000000',fixed_profile_root=['302238736347/100000000000000','75559684087/25000000000000'],framework_assumptions=5,selected_record_changed=False)
+    result['seconds']=round(time.monotonic()-start,3);print(json.dumps(result,indent=2,sort_keys=True))
+if __name__=='__main__':main()