Scoped negative result: algebraic P111 bit pairing-cost floor of 63

[VibeCodyH]

Scoped negative result; no new kappa. This proves that the shipped 111-port E8 bit unit has minimum total pairing rank 63 within its fixed label-decoder class, even with arbitrarily many asymmetric scalar totals. The existing nine rank-seven star totals attain the bound.

The proof replaces a solver exclusion with a basis-counting argument for nine terms and two small matrix obstructions for ten terms. Other term counts are excluded by rank or minimum term cost. It independently corroborates #620's reported floor while binding the theorem directly to #545's shipped coordinates.

The source binding catches a concrete numbering discrepancy: the same nine indices select different roots in the #493 supplier and the #595 geometry utility. They have 36 and 44 discounted ordered pairs, respectively. The verifier rejects the alternative ordering and checks the actual supplier's matrix witness.

Reproduce from the repository root, using Python 3.10+ and the standard library:

python3 -B research/e8-p111-pairing-floor/verify.py

Expected: PASS_P111_PAIRING_FLOOR: cost 63; 511 exact supports; 261121 support pairs; 12 negative controls.

Validation:

• Exact geometry, all 511 supports, all 81 hyperplane pairings, all 29 relevant count budgets, and an attaining cost-63 factorization pass.
• An optional separate SymPy implementation agrees on all supports and pairings using stored parent coordinates, and exhausts 672 small-domain basis factorizations.
• A relocated minimal-input replay passes on CPython 3.14.8, including isolated optimized mode. Regenerated receipt bytes match. Altered source bytes and a tampered result receipt fail.
• The repository's selected-record/source-integrity check and staged whitespace check pass. The unchanged expensive repository-wide and selected cold-replay suites were not run. No remote CI or formal multiplication-proof claim is made.

The finite theorem fixes both the decoder matrix and the label space of each individual factor. Other fitting matrices, factors outside that space, different punctures and vector-valued totals remain outside scope. The physical copy interpretation separately inherits #446's tree/drop and additive-charging premises. No supplier, selected frontier or upstream/ file changes.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. OS-random assignment seed 45, structural decoder track. Main remains at that base; final metadata covered 567 open PRs through #748. #631, #669, #703, #717, #726 and #747 have distinct scopes, recorded with source pins. No pinned coordination issue exists, so the claim is local.

Credit: Joel Pulikkan / GamingPuzzled (#620); DreamingOfClouds (#545, #446, #595); eumemic (#493, #555); and Dylan Crow / utcorvusvolat-dotcom (#370). Prepared by Cody Harris (@VibeCodyH) with substantial OpenAI Codex assistance in proof development, implementation, verification and writing. Apache-2.0. Detailed scope and attribution are in the package.

[Mister-Meeseeks]

100-PR batch review at 287758702129e6cbca187356b92b311e8a1c843d.

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

Reviewed scope: Independent P111 label-factorization floor 63 and source-order reconciliation; fixed label/decoder class only.

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.