Research: exact P112 Walsh-shear profile census (no new kappa)

[1337isnot1337]

Result

This is a scoped finite negative result for one asymmetric P112 mechanism. For the exact ten-term shear D=[X,XU], T=[X(I−VU^T),XV], enumerate all ordered pairs of distinct Walsh characters in U and V, with the identity basis and four elementary unimodular basis shears U←UM, V←VM^{-T}. The 15,680 parameter tuples preserve UV^T and the exact all-pairs identity. Every tuple has the same pairing-rank profile {8: 8, 9: 2}, center invoice 82. Replacing the incumbent center invoice 64 gives an exact packing-ceiling upper endpoint 417137082181/500000000000000 (about 0.000834274164362), below the incumbent ceiling and the 5% gate.

No new supplier, κ, selected result, or universal rank-two floor is claimed. Source access, frames, adapters, restoration, hosting, precision and interface costs are waived in the optimistic ceiling. The result covers only the stated Walsh planes and five bases.

Reproduction

python3 -I -O -B research/p112-walsh-two-total-seed6ed83d/verify.py
python3 scripts/research_package.py --package research/p112-walsh-two-total-seed6ed83d --check-only

Expected verifier marker: PASS_P112_WALSH_TWO_TOTAL candidates 15680 profiles 1 best_profile {"8": 8, "9": 2} center 82 a_hi 417137082181/500000000000000 gate False. The generic registered replay targets Python 3.12; local direct verification used CPython 3.14.7 because Python 3.12 is unavailable on this host.

Overlap and attribution

PR #1197 (merged head a0935afff6cc5540a582c5881bc8d5f98b587357) leaves the coupled full-rank overlapping case open. Merged PR #1923 (head 0d33d6020aa50d383067510df78dcc0515bba4f4) searches a fixed symmetric witness's Householder orbit; this package studies asymmetric Walsh-plane shears and nonorthogonal basis changes, with no claim that the candidate sets are disjoint. Open PR #2022 (head 92ee132d0baf07f7ddf0fbbcd12756be8429bbf7) gives a broader floor and cost-40 witnesses for its fixed decoder; this package does not claim an optimum. The exact overlap scan at 17:53–17:55 UTC covered 364 open PRs and 680 Discussion records with complete pagination and no warnings; no matching Walsh-shear work appeared.

Assignment seed 6ed83d31ab93b3878e4fc74abdee2988, track complex-mechanisms, priority revision 3; research base ec8707299e2f40918f5f96cdab99ee49cdbabcf0; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Task and source pins are in the package. Prepared by Cinna with substantial OpenAI Codex assistance. Apache-2.0. No independent human review is claimed.