Repository navigation
Add exact shared correction basis across P112 frames - #2308
Merged
Mister-Meeseeks merged 1 commit intoOct 15, 2026
Merged
Mister-Meeseeks merged 1 commit into
Mister-Meeseeks merged 1 commit into
Conversation
This was referenced Oct 15, 2026
Mister-Meeseeks
pushed a commit
that referenced
this pull request
Oct 15, 2026
Audits the complete-charge handoff of PR #2308's named P112 frame pair. The two frames share four ports (union 12) and their rational common-basis identity checks. The displayed cross-block factors cost 40 separate support-pairing COPY units and leave 32 forbidden cross-frame entries (a scalar counterexample moves dirty target 11 to 23/2), and rescaling changes coefficient-parity rank without changing the support bill. The forced 12-by-64 additive correction rectangle has rank 12 (a minor of twice it has determinant 2048), so any complete additive scalar correction that keeps G/2 needs at least 12 COPY units, while the frozen-profile 5% screen allows at most 8; the favorable 12-unit moment is 1.000428993633190. Not an optimum or a bound on redesigned decoders; no supplier or kappa change. Adds research/p112-shared-correction-cost-audit/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Result
This adds an exact local mechanism for sharing the rank-8 correction basis between two distinct orthogonal frames in the selected P112 plane-upgrade model. It follows the pair-sharing question raised by philippeVV's single-frame probe in Discussion #2278.
The pinned selected 112 q labels are mapped bijectively to P112 by checking their complete binary pairing and all eight deleted-frame signatures. The verifier then enumerates all 1,260 P112 frames, all 135 common directions, and all 1,539,720 same-direction frame pairs (20,160 frame-direction correction blocks). For every fixed direction, every block factors exactly through one rational rank-8 basis. The common denominator is 2; writing the basis as
M0/2gives integer coefficient matrices whose combined F2 row span has rank 4. The certificate's explicit witness pair has F2 coefficient rank 1.Under the pinned matrix-coefficient price model, charging one shared correction at +8 gives an exact selected-profile relaxation of 0.999388703606489 at the conservative 5% target. The one-frame +8 case (1.000367800102208) and the two-frame unshared +16 case (1.000490187164172) fail that screen.
Scope
This is a shared correction mechanism and favorable local moment screen, not a completed multiplication supplier, conditional bound, or new κ. The denominator-2 basis requires precision accounting. Source access, copies, legal frame schedule, hosting, transitions, restoration, all-size realization, and the matching bit-side construction remain unpriced or unbuilt.
The current P104 pooled correction-space result in Discussion #2245 / PR #2251 concerns a different trace, target matrices and timing model. This package works on selected P112 same-direction frame pairs. It also differs from PR #1825's paired plane decoder, Discussion #2126's 56 shared matched planes, the tri-plane work in Discussion #2024 / PR #2041, and the five-dimensional cover claim in Discussion #2292.
Reproduce
The exact verifier passes on local Python 3.14.7; package metadata and source pins pass the repository check. Registered CI replay is configured for Python 3.12.
Source, predecessor, base-commit and selected-record pins, exhaustive domain, exact arithmetic, positive controls, and two meaningful negative controls are in
research/cycle47-shared-frame-correction/.Prepared by Cinna Davis with substantial OpenAI Codex assistance. The #2278 single-frame probe and cited predecessor work remain attributed in the package. No independent human review is claimed.