Independent verification: quadratic-phase certificate for a selected cold wrapper

[jsnider3]

Change and mathematical scope

Independent finite verification; no new κ. This contribution checks one selected #626 rank-4 cold-wrapper identity using an affine-support certificate and symbolic quadratic phases over Z/4Z. The object is helper 442 with terminal basis [268,140,45,30], recipe 0:429 in CK and 0:413 in JP8.

The output map reduces to c = D x + P delta + e over F2, with an invertible four-bit P and five identically zero spectator displacements. The difference of the two operator phases is a square-free quadratic polynomial in 13 Boolean variables. Every coefficient in its 92 possible positions cancels exactly. EXPECTED.json preserves the six component polynomials and the affine maps. The written derivation connects this certificate to the exact finite operator identity for arbitrary complex payloads.

PR #702 appeared during this run and already verifies all 14 selected cold wrappers with direct amplitudes. I retired the initial one-pair amplitude replay and made the allowed single pivot to this symbolic method. This corroborates one identity covered by #702 with a separate implementation; it does not import #702, the Clifford compiler, tableaus, or the state-vector executor. Credit to #702 is explicit, pinned at 27db45ac6befa99d6c06be920a93845023e81937.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Selected #626 source: 660de893d27bb7abd1d5b01b1640207528a5c851. SOURCES.json pins both provider artifacts, the selected record and inherited definitions; the transcribed instance is checked against the full archived recipes and helper labels. Conditional project κ remains 51110230636731/31250000000000000.

This is one finite identity, not a Lean proof or complete multiplication theorem. Scalar-word/tail correctness, full dirty restoration, owner hosting and cost, compiler/realization, residual, precision/tape/recovery and analytic obligations remain inherited. Only the new research package is added.

Validation

python3 -I -B research/cold-wrapper-quadratic81/verify.py
python3 -I -O -B research/cold-wrapper-quadratic81/test_verify.py

Expected: PASS_COLD_WRAPPER_QUADRATIC_CERTIFICATE 13 variables, 92 coefficient positions, 13 rejection controls, then five passing tests.

• Normal and optimized isolated runs reproduce the same exact certificate.
• Five test groups check all used XOR lifts and complements, every phase component against direct arithmetic on all 8,192 assignments, 276 nonzero single-coefficient witnesses, rejection controls, and optimized subprocess execution.
• Thirteen controls cover phase, translation, quadratic terms, omitted/swapped wrappers, wrong geometry and width. The input-Z8 control produces exactly 2*x8, documenting the zero-input-column blind spot without alleging a production defect.
• A separate committed-files-only worktree reproduces the result. make selected-record-check and staged whitespace checks pass. The unchanged producer/global suites were not rebuilt for this standalone verification package.

Assignment seed 81, independent verification. No pinned coordination issue exists; the claim and pivot are local in CLAIM.md. The final scope was checked against current PRs through #711.

Credits to Chafik Boukhalfa, Jeremy Kothe, DreamingOfClouds, icekylinx, Douglas Colkitt, BigCactusLabs (#702), and the retained supplier/compiler lineage are preserved. Prepared by Joshua Snider (jsnider3) with substantial OpenAI Codex assistance; Apache-2.0, no independent human peer review claimed.

[Mister-Meeseeks]

100-PR batch review at 4773b879a1087540f5919c726ec8c670dadfa0c5.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent affine/quadratic phase certificate for a fixed cold wrapper; exact symbolic phase identity, not a whole supplier replay.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.