Audit staged544 native phases and expose the binary-inverse lift defect

research/staged544-native-quadratic-audit/.gitattributes

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+frozen/* -text
+vendor/* -text
+NOTICE-PR3945.md -text
+SOURCE-CREDITS.md -text

research/staged544-native-quadratic-audit/.gitignore

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+__pycache__/
+*.pyc

research/staged544-native-quadratic-audit/LEDGER.json

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+{
+  "status": "LOCAL_NATIVE_PHASE_INTERFACES_ONLY",
+  "proved": [
+    {
+      "item": "Changed cold terminal residual widths",
+      "old": 4,
+      "new": 5,
+      "helpers_per_provider": 26,
+      "evidence": "Exact source-derived coverage and all512column signed operator equality for every unique old/new interface."
+    },
+    {
+      "item": "Actual changed native warp interfaces",
+      "per_provider": 5,
+      "binary_maps": 4,
+      "paid_recursive_rank": 0,
+      "evidence": "Both directions, old/new frames, all512columns; source lifting phase included."
+    },
+    {
+      "item": "Record-only index shifts",
+      "per_provider": 47,
+      "evidence": "G,U,E,register unchanged; chronological insertion index differs."
+    },
+    {
+      "item": "Clifford lift inverse correction",
+      "witness_G": [
+        1,
+        2,
+        8,
+        32,
+        44,
+        128,
+        59,
+        66,
+        489
+      ],
+      "character_mask": 256,
+      "flipped_columns": 256,
+      "evidence": "K_(G inverse) K_G = Z_256; correct adjoint recipe verified."
+    },
+    {
+      "item": "Computational coverage",
+      "unique_interface_classes": 40,
+      "source_occurrences": 144,
+      "basis_columns": 20480,
+      "note": "Deduplicated byte-identical descriptors with exact source coverage map; all output coefficients checked, no random probes."
+    }
+  ],
+  "inherited_not_reproved": [
+    {
+      "item": "Complete paid profile / literal owner capacity",
+      "source": "PR3969 6ff67539f1131a287eb9a9a98bf1e94a02eecba7",
+      "status": "Independent predecessor audit; not recomputed here"
+    },
+    {
+      "item": "Arbitrary dirty whole-word free-operator cleanup",
+      "source": "PR3945 andPR3969 pinned words/receipts",
+      "status": "Local all-column equality composes linearly; whole723inputfreealgebra replay not repeated"
+    }
+  ],
+  "unknown_or_outside_scope": [
+    {
+      "item": "All changed scalar frame-transition recipe classes and entire emitted program",
+      "cost": "unknown in this audit"
+    },
+    {
+      "item": "Physical hosting/allocation/owner chronology beyond inherited finite owner audit",
+      "cost": "unknown inherited full model obligation"
+    },
+    {
+      "item": "Uniform coefficient height, precision, stock and tape costs",
+      "cost": "unknown; no zero tariff assigned to monomial wrappers or Z correction"
+    },
+    {
+      "item": "All-size compiler, common mutable labels, outer/supplier, analytic and BIT H1-H5 admission",
+      "cost": "inherited conditional obligations, not admitted by this finite certificate"
+    }
+  ],
+  "selected_frontier_changed": false,
+  "new_kappa_claim": false
+}

research/staged544-native-quadratic-audit/NOTICE-PR3945.md

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+# Attribution and scope
+
+New terminal-width/frame construction, idle-gap absorption proof, source-guarded recipe, independent finite checks and integration: Dugongue with substantial OpenAI Codex assistance, including three parallel Codex agents. Apache-2.0. AI implementation separation is not independent human review.
+
+Retain the following predecessor credit and all native/vendor notices:
+
+- dataisfire, PR3734: actual staged544 supplier and retained full source closure. zxv, PR3682: staged pair. Ross Richardson, PR3605: staged entrance, cleanup and residual checks.
+- Erwan Secousses / ChaloupeMusic, PR3815, with retained PR3638 lineage: attained T360 owner clock and fill. The new allocation changes widths and offsets on that placement; it does not invent the source clock.
+- hexapode, PR3802 and PR3875: previous complete endpoint combination and refinement. Dugongue, PR3857: prior general proof/evaluator work; PR3929: transported-frame compiler and concrete nonimproving example.
+- Sagar Thakrar, PR3687: audit_core.py, retained byte for byte. Its header explicitly credits Arham Tahir's coupled-carrier audit, which it reimplements. roger-sato, PR3693: whole-word audit adapter in the inherited closure. Retained exact rational-price evaluator and source notices are unchanged.
+- Jeremy Kothe: frame/preload machinery and PR2833 native rewrite; Lyy-iiis, PR2857; Dugongue, PR2863; philippeVV, PR2853, and all retained provider, owner, native/admission and outer contributors.
+- Cinna Davis (@1337isnot1337), PR2226, with OpenAI Codex assistance: native exact Clifford/operator machinery. icekylinx, PR514/433, and retained native ancestry.
+- DreamingOfClouds with Claude Opus 5.5: inherited wrapper/outer machinery; chafreaky, PR458, and its retained lineage.
+- Tekalign (@tekuuu): sparse native acceleration; retain SPARSE-NOTICE, SPARSE-PROOF, Rohan Arun and all earlier authors/PRs listed by those files. The accelerator changes replay representation, not the certified word.
+
+The original contributor names already present in upstream sources are attribution. They are not new identification of the submitting GitHub account. All original licenses and source headers remain in place. No broad mathematical novelty, independent human approval, unconditional all-size multiplication bound or fresh Lean/kernel certification is claimed.
+
+Adjacent reviews were compared and credited: Chris R / Clear1nsight PR3883/3936, with substantial OpenAI Codex assistance, supplies the completed T385 execution/COPY-contract audit precedent; retain its ai-nanachi PR3647, Sagar Thakrar PR3700 and PR2809 physical-caller lineage. These are scoped comparison sources, not a new admission receipt for our changed T360 words.
+
+Also compare and credit Chris R / Clear1nsight PR3941 for its distinct neutral-first enumeration/middle-cut reduction, following PR3886/3734, Jeremy Kothe PR2957/2979 and Dugongue PR3863/ranked-pair/MathProof predecessors. Rohan Arun's PR3939 bit-pooling draft and its explicitly conditional PR3934 stack are acknowledged as higher draft endpoints on a different route; their data and extra assumptions are not imported into this supplier.

research/staged544-native-quadratic-audit/PROOF.md

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+# Exact quadratic-phase interface certificate
+
+Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance.
+Apache-2.0. This is an independent finite audit of Dugongue's PR3945, not a
+claim that its native checker is wrong or a new multiplication theorem.
+
+## Domain and conventions
+
+The logical coordinate space has dimension 512, indexed by `x in F_2^9`.
+Write `X^u |x> = |x+u>` and `Z^v |x> = (-1)^(v dot x)|x>`.
+Products act right to left. Every scalar coefficient below is an exact Gaussian
+integer divided by an explicit power of two. The verifier uses Python integers,
+not floating point, sampled states, the predecessor tableau compiler, or numpy.
+
+For invertible binary columns G, set Q_G = I + G^(-T)G^(-1) over F_2.
+Its specified Z4 quadratic refinement is
+
+    q_G(y) = sum_i (Q_G)_ii y_i + 2 sum_(i<j) (Q_G)_ij y_i y_j mod 4.
+    K_G |x> = i^(q_G(Gx)) |Gx>.
+
+The source's canonical frame T_U is K_B C_[r] K_B^adjoint, where B completes
+the given ordered basis U by successive coordinate vectors, r=dim U, and
+C_j=((1+i)I+(1-i)X_j)/2. Its inverse conjugates the Gaussian coefficients.
+The local warp is T_E K_G^(sign) T_U^adjoint. The cold terminal residual is
+T_E, since its entrance U is empty. These definitions preserve global phase.
+
+The new evaluator finds inverse columns by exhaustive permutation inversion,
+constructs the quadratic form from their binary dot products, and propagates
+sparse Gaussian numerator dictionaries one coordinate at a time. It independently
+decodes a serialized monomial's binary rows, translation, Z4 linear coefficients,
+symmetric quadratic rows and global phase. A compiler recipe is R, C_[rank], L
+in chronological order. Reference recipes are generated by the frozen source
+compiler; the verifier never imports that compiler or its dependent checkers.
+A shared mathematical convention is unavoidable and is stated above; no claim
+of independently deriving the construction's physical model is made.
+
+## Complete finite interface equality
+
+Both frozen providers have exactly 26 helper terminal extensions from width 4
+to width 5; every one has the same empty entrance in old and new words. Their
+first helper is 277:
+
+    old [388,75,41,26]
+    new [388,74,40,26,1]
+
+Exactly 5 of the 72 warp records per provider change their entrance/exit frame;
+the binary map and register identity are unchanged. Another 47 records change
+only their chronological index. We compare both signs of each genuinely changed
+warp, at old and new interfaces. We do not confuse these 47 index shifts with
+new native operators.
+
+The 144 source occurrences deduplicate to 40 exact descriptors: 24 residuals
+and 16 signed warp interfaces. Each descriptor includes the actual ordered
+frames and, for a warp, its binary columns and sign. Coverage is reconstructed
+from the four frozen words by verify.py, independently of the recipe generator.
+Every descriptor is evaluated on all 512 input basis columns, comparing every
+output coefficient after exact dyadic normalization: 20,480 column equalities.
+RESULT.json commits a digest of the normalized complete action of each class.
+
+Equality on a basis proves equality for arbitrary complex input, hence for any
+arbitrary dirty coordinate state at this local interface, including relative
+and global phases. It also tensors with untouched registers. This does not
+by itself reprove the whole emitted program's chronological composition,
+all dirty-buffer restoration, or the supplier contract. The old terminal
+recipes are calibration controls; they are not proposed substitutes for the
+promoted width-5 interfaces. All signed warps have zero recursive rank; the
+residual recipe ranks are exactly 4 and 5 respectively. Zero recursive rank
+does not mean zero physical or uniform precision cost.
+
+## Why the binary inverse is insufficient: the lift cocycle
+
+The binary symplectic action of K_G on Pauli labels (x,z) is
+
+    M(G) = [[G, 0], [G + G^(-T), G^(-T)]].
+
+Direct multiplication gives M(H)M(G)=M(HG). This does not determine the signed
+lift. The exact phase difference
+
+    d_(G,H)(x) = q_G(Gx) + q_H(HGx) - q_(HG)(HGx) mod 4
+
+is an even linear character, 2 ell dot x. One way to see this is to use
+q_Q(a+b)-q_Q(a)-q_Q(b)=2 a^T Q b mod 4, noting that all binary operations
+inside q use XOR. The composed quadratic polarizations cancel under the
+identity for M. The parity cancels as well; since d(0)=0, the remaining even
+additive function is exactly a binary linear character. Consequently
+
+    K_H K_G = K_(HG) Z_ell.
+
+The certificate calculates ell from the nine coordinate inputs and then
+checks this identity on every one of the 512 inputs for each ordered pair of
+the four actual changed binary maps. These 16 algebraic pair controls are not
+asserted to occur adjacently in either word.
+
+For an actual map in the changed interfaces,
+
+    G = [1,2,8,32,44,128,59,66,489],
+    G^(-1) = [1,2,28,4,79,8,130,32,431],
+
+our exact certificate finds
+
+    K_(G^(-1)) K_G = Z_256.
+
+This is a relative sign on exactly 256 of the 512 basis coordinates, not a
+removable global phase. In particular the input x=256 is sent to its negative
+by this binary-identity product. The phase-correct inverse is
+
+    K_G^adjoint = Z_256 K_(G^(-1)).
+
+The source uses the correct adjoint; it passes the signed audit. This witness
+rejects the tempting implementation shortcut of substituting the canonical
+lift of the binary inverse. It is a precise source-bound warning, not a
+counterexample to the author's construction. A physical implementation of the
+Z correction needs its own paid contract; this audit supplies an exact local
+operator identity and assigns no free implementation tariff.
+
+## Failure controls and limits
+
+Fourteen controls reject wrong residual left/right global phases, warp global,
+linear and quadratic phase changes, translation, signed inverse, terminal,
+singular binary map, wrong charged residual rank, swapped residual wrappers,
+an omitted descriptor and a relabelled provider. A global-phase mutant preserves
+all 512 permutation columns while failing the exact phase comparison. Every
+serialized monomial is also composed with its independently decoded inverse
+on every input column. Normal and optimized Python must give the same result.
+
+The frozen author NATIVE receipts bind the literal changed word hashes and
+native source hashes and report all five native stages passed. Their status
+is authenticated historical evidence. Fresh equality here covers the stated
+40 classes only. Full changed scalar frame-transition recipes, the complete
+CLIFFORD-RECIPES serialization, whole emitted program, ordinary/outer release
+replay, and all-size or uniform resource admission remain outside this proof.
+See LEDGER.json and RELEASE-BINDING.json for the exact inherited/unknown split.

research/staged544-native-quadratic-audit/README.md

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+# Native quadratic-phase audit of the staged544 terminal promotion
+
+This independently corroborates the signed native action at every promoted
+terminal residual and every genuinely changed warp interface in the two
+PR3945 providers. It also exhibits an actual binary inverse whose canonical
+Clifford lift differs from the correct adjoint by a nonconstant sign character.
+The result is a finite local operator certificate; it makes no new κ claim.
+
+**Result:** 40 unique interfaces cover 144 source occurrences, checked on all
+20,480 basis columns with every Gaussian coefficient and global phase retained.
+Each provider contributes 26 cold terminal promotions, old and new residuals,
+and 5 changed warp interfaces in both directions, old and new. The other 47
+changed warp records only shift chronological indices. All equalities pass.
+
+The mathematical pairing is framed arithmetic with finite symplectic geometry
+and Z4 quadratic refinements. For the actual map
+`G=[1,2,8,32,44,128,59,66,489]`, the canonical lift obeys
+`K_(G inverse) K_G = Z_256`: a sign change on 256 of 512 basis coordinates.
+Thus replacing a signed adjoint with the canonical lift of the binary inverse
+would be wrong. The source uses the correct adjoint and passes. This is a
+phase-discipline witness, not an author bug. The correction is a nonconstant
+Pauli character; it is not merely a global scalar phase.
+
+## Sources and independence
+
+Scientific input: [Dugongue PR3945](https://github.com/CrocSwap/integer-mult-bounds/pull/3945),
+head `91f81d131252db704f945891da1ea54e29d46b8b`. The four exact frozen words and
+native source/receipt hashes are authenticated by SOURCES.json. Source words
+are not edited. The nearest predecessor is the independent owner audit
+[PR3969](https://github.com/CrocSwap/integer-mult-bounds/pull/3969), head
+`6ff67539f1131a287eb9a9a98bf1e94a02eecba7`, which explicitly excluded phases.
+
+`generate.py` optionally uses the byte-pinned predecessor compiler to generate
+RECIPES.json. `verify.py` and `exact_phase.py` execute no predecessor code.
+The new standard-library verifier independently inverts binary permutations,
+constructs quadratic forms, propagates scalar Gaussian integers and decodes
+the serialized recipe. It checks coverage directly against both old/new words.
+The all-column checks prove local equality on arbitrary complex dirty state;
+whole-word dirty restoration and physical admission remain inherited obligations.
+
+Fresh frozen release crosslinks connect these exact words, the author native
+recipe inventories, the final package manifest and the reported release receipt.
+All crosslink files are included and checked. This does not replay the full
+archive or complete native recipe payload. The retained complete recipe hashes
+are recorded separately from our newly generated subset. The author evidence
+explicitly discloses corrected frozen-spec bindings and reused successful
+prefixes; this package does not describe that history as an uninterrupted run.
+
+## Reproduce
+
+Python 3.12, standard library only; no network or Git needed for the standalone
+scientific verifier:
+
+```sh
+python3 -B research/staged544-native-quadratic-audit/verify.py
+python3 -O -B research/staged544-native-quadratic-audit/verify.py
+```
+
+The registered repository check is:
+
+```sh
+python3 scripts/research_package.py --package research/staged544-native-quadratic-audit
+```
+
+The verifier is read-only. To obtain a new comparison receipt, pass `--emit`
+with a path outside the package. Optional source-compiler recipe regeneration:
+
+```sh
+python3 -B research/staged544-native-quadratic-audit/generate.py /tmp/phase-recipes.json
+```
+
+Compare that JSON with RECIPES.json. Generation is not the independent check.
+Fourteen semantic mutations reject, including phases invisible to binary-map
+checks; all serialized monomials also pass exact inverse-column controls.
+Both ordinary and optimized independent verifier runs are registered.
+
+## Costs, scope and attribution
+
+LEDGER.json lists proved, inherited and unknown obligations. Terminal recursive
+ranks are 4 before and 5 after promotion; changed native warps have rank zero.
+These statements assign no zero physical, precision, stock or tape tariff to
+monomial wrappers or to the corrective sign. The complete owner bill is inherited
+from PR3969. All changed scalar frame-transition classes, complete emitted
+program, full release and uniform supplier conditions are outside this audit.
+
+Credit: Dugongue's terminal promotion and native frame work (PR3945/3929),
+dataisfire's literal providers (PR3734), Cinna Davis's PR2226 dirty-borrowing
+operators, Tekalign's native replay, and the retained native compiler and phase
+lineage including icekylinx, DreamingOfClouds and upstream contributors. The
+source audit lineage includes Sagar Thakrar, roger-sato and Arham Tahir. Exact
+retained notices are in SOURCE-CREDITS.md, NOTICE-PR3945.md and
+frozen/NATIVE-LINEAGE-NOTICE. Chris R / Clear1nsight prepared this independent
+audit with substantial OpenAI Codex assistance. Root-agent coordination supplied
+an independently authenticated release crosslink inspection; this verifier
+rechecks those links from the included raw bytes. Apache-2.0.
+
+## Open next questions
+
+Regenerate the complete source-bound canonical word and native recipe payload,
+match the retained complete recipe hashes, and extend independent exact action
+to every changed scalar frame-transition class and complete emitted program.
+This would connect the local equality here to the remaining native admission
+boundary. It requires explicit coverage of all emitted interfaces and the
+retained uniform model obligations; a fresh subset hash or owner bill alone
+cannot discharge it. TASK.json records the bounded first step and stop rule.