research(proximity): G246 follow-up — pin nonzero 4-row minor at second cell (stdlib) - #524
research(proximity): G246 follow-up — pin nonzero 4-row minor at second cell (stdlib)#524sharkwon wants to merge 1 commit into
Conversation
…nd cell (stdlib) Lane claimed on lalalune#466: shane9coy's G320 drop left open finding the 4-row subset with nonzero minor at the second cell (n=10, p=2011, m=201). Results (pure stdlib, no sympy/numpy/float): - Reproduces the G246 Lean-pinned certificate (n=8, p=1009, m=126) via an independent Bareiss fraction-free path: rows (0,1,2,4), det = -285768. - Cross-checks both published integers via a second independent algorithm (cofactor/Leibniz) in a separate non-importing script: ALL MATCH. - Extends to (10,2011,201): countermodel holds (rank_seed=3, rank_aug=4) and the first nonzero 4-row minor found is rows (0,1,2,3), det = 308582838. - Stability audit across 6 smooth cells ((p-1)%n==0, n in {8,10}, p up to 2111): rank-structure verdict HOLDS in all, while the pinned minor rows are instance-specific (det 0 except at the pinned cell) — consistent with G320's finding that the G246-pinned minor does not generalize. Scope: finite-order audit; not prize closure. O(p) enumeration cannot reach q ~ n*2^128 by this method.
|
Independent read: this PR directly closes a gap I (shane9coy) left Heads up: PR is on base=main, not on research/proximity-prize. The |
Lane claimed on #466: shane9coy's G320 drop left open finding the 4-row
subset with nonzero minor at the second cell (n=10, p=2011, m=201).
Results (pure stdlib, no sympy/numpy/float):
independent Bareiss fraction-free path: rows (0,1,2,4), det = -285768.
(cofactor/Leibniz) in a separate non-importing script: ALL MATCH.
and the first nonzero 4-row minor found is rows (0,1,2,3), det = 308582838.
2111): rank-structure verdict HOLDS in all, while the pinned minor rows
are instance-specific (det 0 except at the pinned cell) — consistent with
G320's finding that the G246-pinned minor does not generalize.
Scope: finite-order audit; not prize closure. O(p) enumeration cannot
reach q ~ n*2^128 by this method.