Research: exact local gauge floors for P112 decoder

[1337isnot1337]

Result

Adds an exact lower bound for a local gauge-edit family of the coordinate-frame-plus-root nine-normal P112 decoder. The 112 live E8 lines are partitioned by an explicit increasing-index orthogonal-block rule. For each of 14 single blocks and 91 block pairs, the verifier holds every exterior coefficient row at its per-root sparsest gauge and sums the exact F2 ranks contributed by those unchanged rows.

The singleton floors are 67 twice and 68 twelve times. Pair floors are 64 once, 67 twenty-four times, and 68 sixty-six times. Since adding rows cannot reduce F2 rank, arbitrary rational null-dependency gauges on the selected one or two blocks cannot reduce the full copied-information bill below the known P112 cost 64.

Scope and relation to prior work

This is a finite structural obstruction for one frame, puncture, 14-block partition, and at-most-two-block edit rule. It does not cover coordinated changes on three or more blocks, changed exterior gauges, another frame, or arbitrary masked terms. It makes no new kappa or physical supplier claim.

PR #1224 supplies the nine-normal dependency frame. Cycle 15 PR #1962 studies a shared ternary shift vector; this contribution instead permits independent rational gauges on any one or two blocks and uses a monotone exterior-rank bound. Open PR #1909 proves a different tetrad-local masked-decoder result and lists two-tetrad escape as a next question. This package fixes the coordinate-plus-root frame and all exterior rows, making its scope complementary and explicit.

Reproduction and pins

• Seed 8232e87e36b7bc2bd06a84ddf3384413, track complex-mechanisms, task complex-rank-shape-decoder, priority revision 3.
• Exact base ecc75c79c22d909fd42aa68437eb77c4c1361835; selected-record SHA256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.
• python3 -I -B research/coord-root-p112-local-tetrad-gauge-seed8232/verify.py passed locally on Python 3.14.7. It checks the baseline identity on all 12,544 live pairs, all 105 exact floors, three nontrivial rational gauge controls, and a coefficient-mutation rejection.
• python3 scripts/research_package.py --package research/coord-root-p112-local-tetrad-gauge-seed8232 --check-only passed package metadata and source pins. The registered replay targets Python 3.12, unavailable in the local environment.

Substantial OpenAI Codex assistance in exact enumeration, proof checks and writing; no independent human review is claimed.

[Mister-Meeseeks]

Batch review at d3d44a83a9c455c376cfa528baf243865343dca9.

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

Reviewed scope: Exact exterior-row rank floors exclude cost below64 when arbitrary dependency gauges change only one or two blocks of the fixed P112 partition. All105 block choices, three rational gauge identities and a corruption control replay. The fixed exterior and nine-normal frame are essential.

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.