Prove threshold-preserving dominance for class-C campaigns

[krzysztofwojt]

The class-C campaign needs a sound implication from a larger flat configuration to a smaller listed cover, at the same target threshold. This package proves that implication and supplies exact, threshold-aware row certificates.

For nested flats, the covered labels grow, the residual label rank cannot increase, and H(smaller) ⊆ H(larger). A uniform span pass therefore transfers without weakening its threshold. Conditional on the inherited listed-cover premise:

• 6554@T7 and 5555@T8 suffice for the 16 table-coverable HARD rows; row 37 remains unresolved.
• 6554@T6 and 5555@T8 suffice for all 64 table-coverable rows.
• T8 for both does not imply the required result for HARD rows 7, 8 and 13.

The audit also found that the initial PR #3315 head c4fe4244b52bb9111b9117aba066229316fc58ab's named literal triple covers only 55 of those 64 rows, missing 4,5,6,17,20,28,33,66,69. The literal minimum is four for all rows and three for the HARD subset; dimension closure gives two. All five original #2954 coverage totals are recovered, retaining their original credit.

After my advance claim, the predecessor author adopted dimension closure at 240e7f68c6be0cd7193abdd1d686ec5b90ab5355, credited the observation and explicitly left the same-target lemma open. This PR supplies that missing implication and its bounded replay; it does not characterize the amended checker as still using literal incidence.

Evidence

python3.12 -B scripts/research_package.py --package research/class-c-dominance-campaign
python3.12 -B scripts/check_research_commit.py --package research/class-c-dominance-campaign

Both pass at c5ae026dd7e482aabcb4c2f97e8a72bbcb762297. The primary sorted-dimension implementation and a separately written injective-role matcher agree on all 169 ordered configuration comparisons and the complete incidence object. Both independently enumerate minimum covers. Four rejecting certificate mutants cover threshold weakening, false dominance, invented cover and budget overflow. Normal and optimized direct replay pass.

All ten package files match the committed bytes. The official export integrity check and both optimized scripts also pass from the final committed, read-only, Git-free export. Environment: CPython 3.12 on macOS, standard library only, each direct check under one second. Internal AI review found no scoped blocker; no independent human or proof-kernel review is claimed. Hosted CI is separate.

Started at canonical main 463113d675af7410ac91d53a4fed51ec6494eb9a and rebased onto refreshed main b0186c6b75280913969f101c169fe3fb07afd137; priority revision 6 and the selected record are unchanged. Final overlap refresh covered 248 open PRs and 2,170 Discussion records with complete pagination and no warnings. Arbitrary diffs and unpublished work are outside coverage.

Scope and credit

No geometric span pass, new row exclusion, RRC validation, complete configuration-list reconstruction, CPU-hour saving, supplier, new kappa or selected-frontier change. The original cover assertions, g bounds and Lemma B remain inherited. No large census, selected cold replay, Lean or Docker was run. Only one new opt-in research package changes.

Credit DreamingOfClouds' pinned help package 1b25759bff5486293a9083ebbe0097b5f6642e08, original totals and retained #2816/#2826/#2862 lineage; muatfannajm-dot / #3315's table audit and handoff; Tekalign / #2975/#3000's separate accelerations. Krzysztof Wojt, with substantial OpenAI Codex assistance including Luna supporting checks. Apache-2.0. Exact sources, proof, limitations and Open next questions are in the package.