Exclude five-term triple savings in rank-57 P112 triad fits

[flyingviper]

Change and mathematical scope

Replacing any three gauge-adapted canonical terms by at most five arbitrary rational rank-one terms cannot lower their complete physical-group invoice. A groupwise conjugacy transfers this result to every rank-57 fit on the fixed PR2757 triad mask, preserving each term's cost. Disjoint replacements retain the 334 baseline. Larger or overlapping replacements and higher-rank fits remain open. The 296 target and selected multiplication bound are unchanged.

The certificate regenerates all 325 rank-three and 940 rank-four eight-element matroids, including loops and parallels, and all 9,377 marked support classes. Fields, Ingleton exclusions, universal merges and selective transfers leave 135 classes. Complete pricing covers all 29,260 literal target triples and every order: 6,075 envelope minima and 27,304 actual class/table jobs. A separate annihilator-based implementation agrees on every minimum. The four-term foundation and inherited seven-point inputs are explicitly replayed.

Task and overlap

Only research/p112-triad-matroid-boundary/ is added. Base: canonical main 20ecf28, priority revision 6. TASK.json records the changed scope from coverage-law-change to the donor-assigned rational-decoder cost296 goal. The addition is a complete five-term triple boundary and its transfer to all minimum-rank triad fits.

Nick Petalas' #3505, #3513, #3527 and #3538 retain credit. PR3538's pending proof bytes are retained at e63a763, so scientific replay needs no foreign Git objects. The gauge starts from flyingviper's #2757 normal form and retains its predecessor lineage. The open-PR overlap pass was refreshed; Discussions returned persistent HTTP406, so that coverage remains a stated gap.

Validation

The complete registered replay passed in 627.72 seconds. A fresh committed Git-free export passed all five commands in 596.61 seconds with every extracted file unchanged. Both cost implementations agree; 332 arithmetic/geometry mutations are rejected. Source-pin, metadata, committed-byte and source-history checks passed. Separate AI-agent adversarial review found no blocker. Only the validation record changed after scientific replay.

git-independent scientific replay is documented in VALIDATION.md. From the repository root:

python3.12 -Werror -B scripts/research_package.py --package research/p112-triad-matroid-boundary
python3.12 -Werror -B scripts/check_research_commit.py --package research/p112-triad-matroid-boundary --check-source-history

These are scoped exact computations and written arguments, not independent human or formal-kernel review. Native execution and complete supplier obligations remain open.

Credit

Prepared by flyingviper with substantial OpenAI Codex assistance, including separate mathematical and implementation checks. Exact predecessor bindings and attribution are in SOURCES.json. New work is Apache-2.0.

Open next questions

README.md and TASK.json record the next tests: an exact six-or-more-term triple or larger joint block with complete physical pricing, or a rank-at-least58 fitting matrix or changed cover. No cheaper witness or complete native consumer is supplied. Reaching 296 from 334 requires 38 compatible saved charges.