Research: exact P112 shared-gauge decoder census

[1337isnot1337]

Result

Adds a source-pinned exact census for one correlated coefficient-gauge family on the coordinate-frame-plus-root P112 decoder. The verifier exhausts all 6,561 w in {-1,0,1}^8 shifts and finds costs 64 (2 assignments, each with an inactive term), 72 (3 active nine-term assignments), and 73 (6,556 active assignments). The exact active minimum is 72, above the known P112 comparator of 64. It verifies the five cost-at-most-72 identities on all 112^2 live pairs and rejects a one-coefficient mutation.

Scope

This is a finite obstruction for one frame, puncture, shared-shift rule, and ternary box. It does not bound independent per-root gauges, other frames, or shifts outside the box. It reports no new kappa, implementation circuit, or selected-record change. The package distinguishes this correlated family from PR #1224's per-root ratio-class search and records adjacent open work.

Reproduction and pins

• Assignment: seed 655425ccd826280b13917975e2854d16, complex-mechanisms, task complex-rank-shape-decoder, priority revision 3.
• Exact base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected-record SHA256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• Local exact command passed on Python 3.14.7: python3 -I -B research/coord-root-p112-global-gauge-seed655425/verify.py.
• python3 scripts/research_package.py --package research/coord-root-p112-global-gauge-seed655425 --check-only passed source and package metadata checks. The registered replay targets Python 3.12; Python 3.12 is not installed in the local environment.

Substantial OpenAI Codex assistance in exact search, verification, and prose; no independent human review is claimed.

[Mister-Meeseeks]

Batch review at bcb7c7ddee555526b42638b70b01b2489bb69c24.

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

Reviewed scope: Complete6561 ternary shared-gauge assignments on the pinned P112 nine-normal frame yield active minimum72; both cost64 assignments have an empty term. Exact low-cost identities and mutation checks cover that correlated finite box only, not independent per-root gauges or unrestricted coefficients.

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.