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Construct an exact rank-32 P112 query interface by repairing 24 ports - #3370
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Mister-Meeseeks merged 1 commit intoOct 18, 2026
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PR3356's thirteen full eight-frames leave four residual pairs, giving seventeen even groups and a rank-34 scalar fit. Replacing two of those frames plus the residual pairs with two six-groups and three four-groups reduces the total to sixteen groups and 32 scalar queries. Eleven original full frames remain unchanged.
A sixteen-plane nonorthogonality clique forces I32, so the new matching's minimum fitting rank is 32 over every field, or 32d for uniform d-dimensional payloads with arbitrary directed free blocks. This also shows why maximizing full eight-frame count is not the same objective as minimizing query groups.
Finite construction; no new κ. The complete-plane one-total tariff remains 224 (
22 rank-8 + 4 rank-6 + 6 rank-4). Source access, frames, restoration, hosting, precision and a full native supplier remain separate obligations. No minimum across all matchings or fourteen-frame impossibility is claimed.Base:
6f100d4bb5083f8c35d96fd95a539811c62f245c. Package:research/paired-plane-frame-repair/. The selected payload is hash-bound; PR3356's exact certificate is retained froma91a44a049cd6114d0edaea714914b64f90c601d, so replay needs no pending Git object.All three
PASS_FRAME_REPAIR_*markers andPASS_REGISTERED_RESEARCH_PACKAGEpass locally. Evidence includes the entire ordered mask (11,392 forced entries), the forced I32, independently implemented explicit-vector geometry and dense three-field ranks, all 224 source/dirty-target columns of the algebraic query program, full-plane tariff and meaningful mutation controls. Registered Python 3.12, optimized read-only Git-free Python 3.14 and committed-byte/source-history checks pass. The optional solver replay reproduced the exact groups in 79 bounded instances; negative solver reports and timed-out pilots are not impossibility proofs.Main, open PRs, issues and claims were refreshed. A near-simultaneous full-partition claim is distinct from this completed local repair; fourteen-frame packing remains open. Canonical claim.
Credit Nick Petalas/PR3356, Matarener/Mark/PR3335, ywz65, thakrarsagar, Cinna Davis, Adam Gall, ctoth, Philippe Van Velzen, Jeremy Diviney and the selected E8/P112 lineage. Tekalign, with substantial OpenAI Codex assistance. Apache-2.0. Independent mathematical review remains open.