[1337isnot1337]

Result

Adds a scoped, exact negative result for one symmetric ten-term P112 decoder. The pinned witness from PR1633 has support-rank invoice (8,8,8,8,8,8,8,8,9,9), total 82. The verifier exhausts every rational Householder gauge O_s=I-2ss^T/(s^Ts) for nonzero ternary normal s in {-1,0,1}^10, modulo sign: 29,524 candidates. All ten terms remain active, every exact P112 identity is preserved by the checked orthogonal numerator, and the candidates produce nine support-rank histograms, all using only ranks 8 and 9. The minimum invoice remains 82.

Cost screen and limits

Substituting the best ten-term support profile for the selected eight rank-8 centre children changes the centre mass from 64 to 82. Even with all coefficient, frame, precision, hosting, storage and restoration overhead waived, the exact selected-profile ceiling is in [0.000834274164361244, 0.000834274164361245], below the selected fixed-word ceiling 0.001690054109089 and its 5% target 0.00177455681454345. This closes only the searched Householder orbit of the one pinned symmetric witness. It is not a lower bound for all ten-term, asymmetric or other-support decoders; no supplier adoption or new kappa is claimed.

Reproduction

python3 -B research/p112-householder-gauge-seed06ace/verify.py
python3 scripts/research_package.py --package research/p112-householder-gauge-seed06ace --check-only

The direct verifier and package metadata/source-pin check pass locally under Python 3.14.7. The registered replay targets Python 3.12, unavailable locally; that replay remains for CI/reviewer confirmation.

Pins and credit

Seed 06ace58bfc2b63b47b02129f729e35d4; track complex-mechanisms; task complex-rank-shape-decoder; priority revision 3. Exact base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. The selected review, source manifest, assembly certificate, and ceiling implementation are pinned in SOURCES.json.

The witness is from Hanson Sun's open PR1633 at head 652264fa1f70820139b2730363a0056b7fadc689; its exact result artifact is pinned in WITNESS.json and SOURCES.json. The bounded claim and handoff are in Discussion #1622 comment 18925227. PR1224, PR1077 and PR968 are credited in the README. Substantial OpenAI Codex assistance is disclosed.

[Mister-Meeseeks]

Batch review at 0d33d6020aa50d383067510df78dcc0515bba4f4.

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

Reviewed scope: Complete29524 ternary Householder-gauge census on pinned1633 witness retains minimum support bill82; nine histograms and exact orthogonality/identity checks pass. Five controls and directed moment screen reject the entire stated finite orbit even before extra costs. Other witnesses, asymmetric factors and unrestricted coefficients are not excluded.

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.