Independently audit cut 353 and all 35 retired P104 inputs (no κ)

research/p104-cut353-independent-audit/CASES.json

@@ -0,0 +1,22 @@
+{
+  "schema_version": 1,
+  "scope": "PR6716 cut353 fresh34 conditional LOCAL audit",
+  "source_head": "a467457692bc9e11113d9b2e2e34ea8ffb553b58",
+  "unretired_roles": 34,
+  "unretired_events": 562,
+  "final_roles": 35,
+  "final_events": 586,
+  "cut_after": 353,
+  "handoff_after": 362,
+  "fresh_first_contact": 363,
+  "pivot": 4,
+  "fresh": 34,
+  "equal_target_group": [4, 20, 21],
+  "fresh_stages": [10, 11, 12, 13],
+  "ring": "Q(i)[u]/(u^4-1)[t1^+-1,...,t18^+-1];u=sourceQ;proofq=u^-1",
+  "normalized_central": "((1+i)/2)*u^3+((1-i)/2)*u",
+  "expected_original_pivot": "u^3 without stage factors",
+  "expected_fresh_output": "t10*t11*t12*t13 without central factor",
+  "limits": {"seconds": 180, "input_bytes": 16777216, "artifact_bytes": 4194304, "simultaneous_matrix_terms": 100000},
+  "excluded": ["common_idle_physical_bank", "native_LOCAL_realization", "complete_invoice", "compiler", "outer_transfer", "frontier_admission"]
+}

research/p104-cut353-independent-audit/NOTICE

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+Independent logical cut353 audit. New material: substantial OpenAI Codex
+assistance, Apache-2.0. This is a source-bound independent audit rather than
+a new construction or frontier claim.
+
+Retain thu-nmrc/PR6716's root, two-sided witness and caller application;
+DreamingOfClouds/PR6702's native word with Claude assistance; Ali Romman's
+PR6348/6398 binary/root work and Cinna Davis's query/controller lineage;
+PR6545 and PR5599's two-sided retirement method; PR6551's rebalanced
+comparison; and all earlier native/helper, Clifford, compiler, BIT,
+precision and analytic contributors and source-specific notices.
+
+Frozen original source texts remain unmodified and retain their notices.

research/p104-cut353-independent-audit/ORACLE.json

@@ -0,0 +1,20 @@
+{
+  "artifact_sha256": "ca09e50e074afde1af921461618e2f1d8349c643a16a6db0683f2a7efcd8e579",
+  "case_manifest_sha256": "7a7e961a1971c31653770af43b0097ba55d1eb980795a050c74786e8f5c7d6c0",
+  "cut_after": 353,
+  "cut_cells": 68,
+  "final_cells": 1225,
+  "final_events": 586,
+  "final_roles": 35,
+  "fresh": 34,
+  "fresh_first_contact": 363,
+  "handoff_after": 362,
+  "ordinary_identities": 6,
+  "pivot": 4,
+  "schema_version": 1,
+  "scope": "PR6716 cut353 fresh34 conditional LOCAL audit",
+  "source_manifest_sha256": "0de615eb3eac51539567c56e85e177c91c0d3e5c2c69b8cd64abff46f68fc902",
+  "stages": 18,
+  "unretired_events": 562,
+  "unretired_roles": 34
+}

research/p104-cut353-independent-audit/PACKET.json

@@ -0,0 +1 @@
+{"a_prefix":[[],[],[],[],[[1,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[-1,2,1,2]],[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[-1,2,-1,2]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[1,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,2,-1,2]],[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,2,1,2]]],[],[],[],[],[],[],[],[],[],[],[],[],[]],"final_matrix":[[[[3,[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[[3,[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[[3,[0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[[3,[0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[[3,[0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[[3,[1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[[3,[1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[[3,[1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[[3,[1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0],[1,1,0,1]]],[],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1],[1,1,0,1]]],[],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1],[1,1,0,1]]],[],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[[3,[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0],[1,1,0,1]]],[],[],[],[],[],[]],[[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]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research/p104-cut353-independent-audit/PROOF.md

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+# Conditional independent audit of the cut353 retirement
+
+This note audits the logical independent-input boundary in PR6716 at
+`a467457692bc9e11113d9b2e2e34ea8ffb553b58`. It does not audit the common-idle
+physical bank, native realization, complete invoice, claimed exponent,
+compiler or outer transfer. The author-side construction and all earlier
+methods retain their credit. The exact serialized controller data, rather
+than the source's checker or constructor, are the executable audit inputs.
+
+## Algebra and conventions
+
+Write `u` for the source's operator `Q`, and retain only `u^4=1`. In the
+source proof, `q=Q^-1=u^3`. All eighteen stage variables remain distinct
+commuting invertible indeterminates. Computation takes place over
+
+`Q(i)[u]/(u^4-1)[t1^+-1,...,t18^+-1]`.
+
+There is no specialization of `u^2` to identity, no merging of stage
+variables and no numerical evaluation. Every matrix cell is a finite
+canonical Laurent polynomial with exact rational real and imaginary
+coefficients. Put
+
+`lambda=((1+i)/2)+((1-i)/2)u^2`,
+
+`S=lambda*u^3=((1+i)/2)u^3+((1-i)/2)u`.
+
+The LOCAL opcode is an assumed algebraic interface: first add `u^3` times
+the source row to the destination row, then multiply both rows by their
+named fresh stage variable. Its native physical implementation is not
+executed or proved by this audit. LAMBDA, QUERY, ordinary row operations
+and the one- or two-row IDLE actions use the literal source opcode
+specification retained as inert text. An IDLE on two rows is two algebraic
+actions; this audit supplies no license to merge two independent arrays.
+
+## Why two-sided separation is sufficient
+
+Let `P` denote the unretired prefix through event353 inclusive. The ordinary
+vectors in the actual witness satisfy
+
+`ab=cd=1`, `aP=S c`, `Pd=S b`.
+
+Let `G,J` be the literal ordinary basis words in that witness. Their
+required identities are
+
+`e4^T G=c`, `Gd=e4`, `e4^T J=a`, `Jb=e4`.
+
+Consequently `e4^T J P G^-1=S e4^T` and
+`J P G^-1 e4=S e4`. Both off-diagonal couplings at the pivot vanish.
+Thus this transformed prefix is exactly `S` on pivot4 and an independent
+operator on the other 33 inputs. A row identity alone would not establish
+this conclusion; the column identity is independently required.
+
+The input basis uses only roles4,20,21. Their complete declared endpoint
+targets are identical, so this ordinary basis commutes with that endpoint.
+The full final-controller check below independently verifies the resulting
+endpoints, rather than inferring them merely from this commutation argument.
+
+## Literal handoff and full endpoint
+
+The audit compares every event of the serialized retired word with the
+following surgery on the serialized unretired word: inverse input basis;
+prefix through353; middle basis `J`; inverse middle basis with pivot4
+renamed to fresh34; remaining unretired suffix with that same renaming;
+the three recorded lambda returns; renamed final `G`; and the three
+recorded original-group lambda adapters. This is an exact event comparison,
+including scalar signs and chronology.
+
+No event through retired index362 uses role34; its first contact is363.
+Its arbitrary input therefore remains independent until the handoff.
+The original pivot receives `u^3` without stage factors. The new role
+receives `t10*t11*t12*t13` without a central factor. All other targets
+are taken from the unretired declaration. The final declaration is checked
+against this independently assembled list.
+
+The independently implemented forward matrix calculation checks all
+35 by35 cells of the actual final word against that diagonal list. The
+unretired controller is computed only through the prefix; its remaining
+declared targets are the contract used to assemble that expected list.
+The entire final controller is checked directly. This
+establishes the stated logical endpoint simultaneously for arbitrary
+independent inputs, conditional on the declared LOCAL interface and ring
+relations. It is stronger than testing selected numerical inputs, but is
+not a native supplier or all-size multiplication theorem.
+
+The artifact retains all 68 prefix row/column cells and all 1,225 final
+matrix cells. Default replay recomputes and compares those actual cells.
+The ordered list of paid-opcode kinds, stage sets and central query signs
+is also compared before and after surgery. That structural check is not
+a complete price, native-caller or resource audit.
+
+## Evidence boundary and credit
+
+Both separately implemented blind first executions passed on
+2026-11-04, finishing at 19:59:36 and 19:59:45 UTC. Every typed common
+receipt field and every actual canonical polynomial cell agreed. The
+common receipt SHA256 is
+`9e9a7b5f05fc9e8824fc6206771625f91acf0aead53aae461cb0fdaf9afff6ef`;
+the canonical packet SHA256 is
+`ca09e50e074afde1af921461618e2f1d8349c643a16a6db0683f2a7efcd8e579`.
+These are complete-value comparisons, not only selected summary counts.
+
+The primary has ten rejection controls. Three execute actual changed
+controllers through the full polynomial engine and require the intended
+endpoint failure: reverse the first QUERY central sign, change the first
+input-basis coefficient to -2, or append a central operation to fresh34.
+Before the first execution, static review corrected a no-op dual-pair
+control and replaced two expected-object controls with these actual-engine
+mutants. Both earlier unexecuted code versions were preserved. These
+changes were not reactions to a failed scientific execution.
+
+Execution status and retained receipts are recorded separately in
+`VALIDATION.md` and `RUN-RECORDS.json`; this written argument does not
+substitute for an execution receipt. The source's existing independent
+checker was not imported or executed. Reading its source during task
+selection is disclosed in the scout record; the new implementation uses
+fresh whole forward matrices rather than that checker's per-column and
+reverse-row architecture. Independent AI work is not independent human
+acceptance or proof-kernel verification.
+
+Credit thu-nmrc/PR6716 for the exact root, witness, caller application and
+complete claimed budget; DreamingOfClouds/PR6702 for the inherited native
+word; Ali Romman/PR6348 andPR6398 and Cinna Davis's query/controller lineage
+for the binary supplier and normalization; PR6545 and PR5599's dual-pair
+retirement lineage for the method; and PR6551 for the earlier rebalanced
+comparison. No invention of dual-pair retirement, native normalization,
+productive recursion or binary refinement is claimed here. New audit
+material was prepared with substantial OpenAI Codex assistance and is
+Apache-2.0. The frozen source texts retain their original notices.

research/p104-cut353-independent-audit/README.md

@@ -0,0 +1,67 @@
+# Independent logical audit of PR6716's cut353
+
+This package independently checks the two-sided fresh-input retirement in
+PR6716 at `a467457692bc9e11113d9b2e2e34ea8ffb553b58`. It interprets the actual
+serialized controllers over exact Gaussian-rational Laurent polynomials,
+retaining an order-four central operator and all eighteen stage variables.
+
+The scope is the ordinary dual-pair identities, their actual prefix,
+literal event surgery, the first fresh-input contact and all 1,225 final
+coefficient positions. It assumes the source's LOCAL algebraic interface.
+It gives no new construction, invoice, conditional exponent, scientific
+admission or frontier change.
+
+Both separately implemented blind first runs passed on 2026-11-04 at
+19:59:36 and 19:59:45 UTC. Their complete receipts and all 68 prefix plus
+1,225 final polynomial cells agree. The original pivot receives `Q^-1`
+with no stage factor; fresh input34 receives the product of stages10–13
+with no central factor. These statements concern the declared logical
+LOCAL interface, not its physical native implementation.
+
+The primary checks ten rejection controls, including three actual
+full-matrix executions with a reversed query sign, wrong input-basis
+coefficient and unearned central factor on the fresh output. Each must
+fail at the polynomial endpoint check. Two unexecuted control drafts were
+corrected before the first run and preserved separately; scientific
+code and first artifacts were unchanged after that first execution.
+
+The unretired controller is evaluated only through its cut prefix. Its
+declared target list supplies the unchanged endpoint contract; the entire
+retired controller is checked directly against the independently assembled
+35-input target list. This does not claim a second full unretired replay.
+
+`PROOF.md` states the argument and boundary. `SOURCE-PINS.json` binds six
+inert original source objects. No predecessor checker is imported or
+executed. Default verification is read-only and compares every retained
+proof-relevant field of `PACKET.json` and `RESULT.json`.
+
+```sh
+python3.12 -I -B verify.py
+python3.12 -I -O -B verify.py
+```
+
+The explicitly mutating `--emit --write-packet PATH` mode regenerates an
+audit packet and emits its receipt. Execution evidence belongs in
+`VALIDATION.md` and `RUN-RECORDS.json`; an unexecuted prototype is not a
+passing audit. Canonical JSON values determine mathematical equality;
+file-container hashes are separate provenance evidence.
+
+Credit thu-nmrc/PR6716, DreamingOfClouds/PR6702, Ali Romman's PR6348/6398,
+Cinna Davis's query/controller lineage, PR6545/5599's dual-pair method and
+PR6551's rebalanced comparison, with all retained earlier native/helper,
+Clifford, compiler, BIT, precision and analytic notices. New material has
+substantial OpenAI Codex assistance. Separate AI checks do not imply
+independent human acceptance or proof-kernel certification.
+
+## Open next questions
+
+1. Independently bind the actual common-idle bank and native absolute
+   phases to this logical caller. Start from the shared ordinary basis
+   and the exact source invocations; this audit does not price or replay
+   that physical supplier.
+2. Audit the complete invoice, completion/compiler and outer transfer at
+   this same source head. Logical separation alone cannot certify their
+   costs, assumptions or claimed saving.
+3. Discharge the consumed framework assumptions for the full recursive
+   interface. Finite symbolic coefficients do not establish the required
+   all-size native, ownership, stock, precision or analytic contracts.

research/p104-cut353-independent-audit/RESULT.json

@@ -0,0 +1 @@
+{"artifact_sha256":"ca09e50e074afde1af921461618e2f1d8349c643a16a6db0683f2a7efcd8e579","case_manifest_sha256":"7a7e961a1971c31653770af43b0097ba55d1eb980795a050c74786e8f5c7d6c0","cut_after":353,"cut_cells":68,"final_cells":1225,"final_events":586,"final_roles":35,"fresh":34,"fresh_first_contact":363,"handoff_after":362,"ordinary_identities":6,"pivot":4,"schema_version":1,"scope":"PR6716 cut353 fresh34 conditional LOCAL audit","source_manifest_sha256":"0de615eb3eac51539567c56e85e177c91c0d3e5c2c69b8cd64abff46f68fc902","stages":18,"unretired_events":562,"unretired_roles":34}