Independently validate κ = 0.00302235 and the owned-relation price ceiling

research/owned-relation-independent-validation/.gitattributes

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+# Preserve every retained source/report byte, including original CRLF.
+* -text

research/owned-relation-independent-validation/README.md

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+# 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.

research/owned-relation-independent-validation/REGISTERED-REPLAY.stdout.log

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+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

research/owned-relation-independent-validation/REPLAY.json

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+{
+  "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."
+}