Research: prove the eleven-line anchor-box floor seven

[thakrarsagar]

Eleven rational lines with three totals, nonzero diagonal pairings and nonempty canonical tied sets now admit an anchor box of at least seven. The new analytic matrix theorem works over any field: a rank-at-most-three eleven-by-eleven matrix with nonzero diagonal contains an ordered nonzero four-block. Its seven-row complement supplies a triple, and the retained asymmetric labels give the box witness.

The proof first obtains a half-size ordered block in rank two, then excludes repeated projective factor directions in an alleged eleven-row obstruction. The remaining zero lines would each contain at least four of eleven distinct points, requiring at least 66 distinct point pairs where only 55 exist. PROOF.md includes the needed seven-row lemma from PR #3420, so the analytic argument is self-contained.

The focused package is research/fstar-eleven-line-floor/. It includes the proof, exact constructor, finite semantic controls, source pins and open next question. The (4,4,3) duplication of Aaron Wang's PR #2978 core has box exactly eight; it is a positive control, not a sharpness example for seven.

Validation: registered CPython 3.12.15 normal and isolated/optimized/warnings-as-errors replay; exact source bytes, metadata/pins, publication source history and whitespace checks. The executable controls do not replace the analytic proof or constitute an exhaustive matrix census. Same-session agents audited the proof and package; this is not independent human acceptance or formal proof checking.

Attribution: DreamingOfClouds's PR #1590/#2111 F-star/certificate definitions, Aaron Wang/navinor's PR #2914/#2978/#3031 directed-box/SG/core lineage, and the PR #3409/#3420 two-block and seven-row lemmas are retained. The oracle is exported unchanged from corrected PR #3393 at 8e1e574fa68465dc0ec69d07852266b9597f9597, through PR #3420 head e2d39da9c7109f361d6cff677cf9f8eba51f3dd6. SOURCES.json records exact lineage and assistance disclosures.

Coordination: canonical claim and handoff. This starts from refreshed canonical main and preserves the selected frontier.

Limits: nonempty ties remain an explicit hypothesis. Sharpness at seven, the next twelve-line floor-eight threshold, general F-star and physical supplier admission remain open. κ is unchanged.