Research: repair the mutual-zero neighborhood classification

[thakrarsagar]

PR #2890 Lemma C5's nonparallel-center branch predicts an edgeless mutual-zero neighborhood, but the rational factors P=[(1,1,0),(1,0,1),(0,1,1)], Q=[(1,1,-1),(1,-1,1),(-1,1,1)] give M=2I3: the nonparallel center has two adjacent neighbors. All canonical ties have cardinality two.

research/fstar-mutual-zero-neighborhood/ preserves the exact predecessor statement and proves the correct arbitrary-field classification: every mutual-zero neighborhood of a rank-at-most-three matrix with nonzero diagonal is a disjoint union of complete bipartite components and isolates. The proof reduces the principal neighborhood matrix to rank two and groups reciprocal column/kernel directions. The intended no-odd-wheel conclusion remains valid. The original normalization q_t=e1,p_t=e2 would force the center diagonal to zero; a valid dual coordinate change instead preserves it.

Validation: registered CPython 3.12.15 normal and isolated/optimized/warnings-as-errors replay; exact minimal three-row and twelve-row all-even fixtures; independent literal graph/component checks; a neighborhood with multiple bipartite components and an isolate; all 728 bounded F₂ type configurations; diagonal, one-way-zero, dual-coordinate and source-corruption controls; metadata, source bytes, publication history and whitespace checks. Two separate same-session agents audited the proof/package; no human acceptance or formal kernel check is implied.

Attribution: Aaron Wang/navinor's source at 08a44355403604c346f8d907811edce992382cc4 is retained unchanged, with original blob/SHA in SOURCES.json. New proof and controls by Sagar Thakrar with substantial OpenAI Codex assistance. Canonical claim/handoff, following the released source handoff.

Limits: the predecessor engine was inspected, not rerun; no changed census or comprehensive downstream audit is claimed. The twelve-row example has a full box twelve, so it is not an F-star counterexample. No supplier admission, selected-frontier change or κ improvement. Fork synced; contribution rebased on current canonical main.