Research: sixteen-array transcript floor survives QQ16 selected shears

[jgilfoil]

An invertible A-to-T shear between QQ16's complete F0 and B1 calls still leaves a quantified information deficit. With the retained local maps and ordinary tail, an additional rational-linear record of total rank d leaves at least ceil(77N/5)-d dimensions of original joint A/T input invisible. One dense eight-coordinate query leaves at least ceil(37N/5); fifteen uniform scalar owner arrays are insufficient, so sixteen are necessary. Sufficiency is open. The necessary unrestricted total rank is ceil(77N/5), not 16N.

Only research/qq16-shear-transcript-floor/ is added. The package contains the ordered proof, exact source pins, a separate fourth-moment implementation, noncommuting rational fixtures, the retained logical tail, and read-only replay with corruption controls.

Scope and overlap

The decoder gets all post-B1 selected cuts, later homogeneous selected-only controls, five forward histories and completed-X descendants. Pre-B1 selected transients must be counted in d; the former-Y endpoint is excluded. Record-driven paired updates vanish when the record is zero. The ordinary fields and retained local maps stay fixed.

Concurrent #2368 (e5d4d78dcfdd55d323fcbc60df477b9f25c7abff) independently proves the overlapping B0-read obstruction using the second moment, and also permits invertible pairings. Its written proof was read during publication; its kernel is equivalent on that restriction. This contribution adds the arbitrary rank-d record bound, the stronger fourth-moment deficit and sixteen-array floor, and a separate exact text-source moment checker. No first-closure claim. The original package was committed locally at 06:08 UTC before reading #2368.

#2189 supplies the credited fourth moment and rank bound 117N/5; that numerical result is reused, not claimed as new. #2326 supplied the dense-query handoff. #2354 concerns the coordinate threshold of its specified common-axis family, while #2346 excludes early selected intervention and has a different final-only contract.

Validation

Linux x86_64, CPython 3.12.3, standard library:

python3 -I -B scripts/research_package.py --package research/qq16-shear-transcript-floor

Registered normal and optimized replay passed in the publication checkout: 18 mathematical/schedule failure controls and five integration tests, including Git-free read-only relocation, source drift, receipt type corruption and overwrite refusal. Checks include 336 owner routes, six 9,216-product tables, exact moments 24,28,109/3,1823/36, the spectral certificate, full-input fixture kernels and the 17-event tail. Patch application, metadata/source pins and whitespace checks pass. Separate agent reviews found no substantive blocker; no human or hosted-CI pass is claimed.

Hosted workflows currently report action_required; the registered-package run awaits maintainer approval before execution.

The theorem uses the written rank argument; finite fixtures do not replace it. Compressed packets, native field types/words and full supplier cold replay were not run. The selected-baseline orientation command was attempted in the initial bounded export and could not verify its complete inventory; no baseline pass is claimed. No native tariff, supplier admission or new κ is claimed.

Base and publication refresh: canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Refreshed overlap covered 584 open PRs including drafts and 1,112 Discussion records with complete pagination and no warnings. Details and exact heads are in TASK.json.

Canonical finding and handoff.

Credit Ali Romman, commdata2338, @starship-s, Adam Gall, CubeJerry, Cinna Davis, Nick Petalas, Ross Richardson, Charles Bethin, Brody Arbon and the retained construction lineage in the README/NOTICE references. Prepared for Jason (@jgilfoil) with substantial OpenAI Codex assistance in derivation, implementation, checking and writing. New work Apache-2.0.