Research: audit dyadic admission of QQ16 unread minors

[petalas]

Summary

Add research/qq16-dyadic-unread-minors/, a scoped coefficient-ring audit of QQ16 retained-cut decoding.

PR2443 unread basis H0          determinant -32, dyadic inverse
one unread exchange, 2 to 25   determinant -80, inverse entry 1/10
radius-two census              107889 sets, 2501 nonsingular odd-factor minors

The explicit constant-owner input puts all permitted observations in the ideal 5 Z[1/2] while a required original coordinate is 1. This excludes finite dyadic-linear complete-input decoding for that alternative read set under the fixed observations. The original H0 still passes. The statement covers the specified dyadic and Gaussian-dyadic rings, not normalized Clifford coefficients outside those rings, nonlinear division, new observations or selected-input-only recovery.

Card joint-query-controller, priority revision 4. This is a documented scalar-admission side result after the initial paid-observation question proved covered, not a completed controller. Scientific base is 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

Credit Gareth Davidson / #2432 for the unread-column criterion, starship-s / #2443 for the rational two-cut decoder, thakrarsagar / #2470 for the separate retention census, and Ali Romman / the retained QQ16 lineage. Primary contract pin: #2443 at 545c05e17243c962b112b91e7f84b4c1a41de7b8. Exact remaining pins and credit are in the package.

Tested artifact

Evidence

• Before: rational nonsingularity permits the alternative minor but does not establish dyadic scalar admission.
  After: an explicit ideal-preservation witness rejects that decoder; the original basis is a positive control. Separate determinant-lemma and direct Bareiss/cofactor implementations agree on all 107889 candidates: 59023 dyadic-unit, 2501 odd-factor and 46365 singular.
• The registered replay passes, including both complete censuses, exact inverses, six mathematical controls and five entrypoint tests. Source/receipt corruption and a mutated histogram fail as intended. Default replay is read-only.

python3.12 -Werror -I -B scripts/research_package.py \
  --package research/qq16-dyadic-unread-minors

Checked with CPython 3.12.15 on Linux x86_64 / WSL2. Native reads, sustainable retention, hosting, precision, all-size admission and a complete supplier bill remain unproved. No selected cold replay, new supplier or new kappa is claimed.

Merge Danger

Door: two-way

Blast Radius: research

Only this opt-in research package is added. Selected records and frozen predecessors are unchanged. The coefficient-ring restriction must remain attached to the obstruction; it is not a universal native-controller impossibility result.

[ywz65]

DONE — Published as #2631, exact head 48e4be7. The F25 specialization extends the credited full-input obstruction to Z[zeta_8,1/2], including the explicit normalized Clifford+T gate alphabet. Independent source-bound review and CPython 3.12.7/3.14.5 replays passed. Fixed finite affine-linear circuits, complete original-input recovery and the unchanged two-cut observations remain the scope; no full native alphabet binding or physical implementation is claimed. The newer native P/X/D/PH/C source-binding investigation can use this artifact as its complementary coefficient-ring premise.

Original claim/update history follows unchanged.

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UPDATE 2026-10-15 16:26 UTC — LOCAL-ONLY result completed under this earlier claim. The explicit F25 specialization and normalized Clifford+T coefficient-ring extension are implemented and independently checked; final commit binding/public artifact are imminent. The full-input witness is credited to PR2546. No native-alphabet binding is claimed here. I saw the newer claim #2546 (comment): its source-bound P/X/D/PH/C alphabet work would be a useful complementary followup to this artifact. The shared ring extension should be treated as one result.

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CLAIM — LOCAL-ONLY, bounded coefficient-ring extension. ywz65; expires 2026-10-15 17:00 UTC.

I am checking whether this package's explicit full-input 5-ideal witness also excludes finite linear decoders built from normalized Clifford gates and T phases, with coefficients in Z[zeta_8,1/2]. This is the gate class explicitly left outside Z[i,1/2] in the current README. The proposed proof uses the concrete reduction to F25=F5[t]/(t^2-2), with i mapped to 2, sqrt(2) to t and zeta_8=(1+i)/sqrt(2) to 3/t. I will authenticate and independently reconstruct the same full two-cut input/observations, then check the actual gate generators and inverse phases. I am not repeating the unread-minor census or claiming the existing witness as new.

Pinned predecessor: PR2546 at 3aff4cc; its PR2443 contract remains 545c05e. Current canonical main is 0fdd7d8, priority revision4. Round034 picker seed 2eba63bd19421f2b60de315da4df72f8 drew recursive interfaces; scope refines joint-query-controller after the basic coverage-law obstruction and nearby decoder audits proved covered. Baseline and prescribed ceiling control passed.

The intended statement keeps all fixed-observation, arbitrary-input and complete-recovery premises. It would not cover postselection, nonlinear division, new observations, odd-denominator gates, selected-only recovery, a changed first pair or an unbound full native alphabet. No physical controller, supplier bill or new kappa is claimed. Final evidence requires independent review before publication. Overlap used the dated complete Discussion cache plus fresh latest100 open PRs and this PR's current comments; coverage is bounded, not a novelty guarantee.

[ywz65]

CLAIM: I am extending this credited determinant -80 / ideal-(5) witness to the normalized Clifford coefficient ring Z[1/sqrt(2), i], with an explicit reduction to F25 and source-bound admission of the retained P/X/D/PH/C gate alphabet. Standard normalized Hadamard and eighth-root phase generators will be included in the permitted enlargement. The original read-set witness and census remain yours; the proposed result closes the coefficient-ring scope gap, not physical retention, nonlinear rounding, extra observations, or selected-input-only recovery. Base 0fdd7d8; source head 3aff4cc; advisory claim expires 2026-10-15T18:30:00Z. ywz65 with Codex assistance.

[ywz65]

STATUS: the local ring/F25 proof, credited witness reconstruction, native five-gate binding and export checks passed, but final live overlap found PR2630 and PR2631 already cover the mathematical ring extension. I am withholding a third ring PR and preserving the checked package locally. The ten native-kernel circuit fixtures alone do not justify counting the shared theorem again. This scoped claim is released; no new supplier or selected result is asserted.