research(proximity): G246 family — degree-2 Krylov obstruction HOLDS at n=16 (stdlib)

[sharkwon]

Extends the G246/G320 countermodel family (PR #524: n=8, n=10) to subgroup
order n=16. Claimed on #466; builds on the PR #524 probe discipline.

Results (pure stdlib; Bareiss + independent cofactor cross-check):

• 5 smooth n=16 cells ((p-1)%16==0, 2 not in G): p in {337, 353, 401,
  433, 449}. Rank obstruction HOLDS in all: rank_seed=3, rank_aug=4
  (R6^c not in the degree-2 Krylov span of the centered base class).
• First nonzero 4-row minor is rows (0,1,2,3) in every tested n=16 cell,
  determinants 750141 / -7520392 / 13559450 / -9703719 / 10639664, each
  cross-checked by the independent cofactor path (ALL MATCH).
• In contrast, the n=8 certificate pins rows (0,1,2,4) and the n=10 cell
  pins rows (0,1,2,3) det=308582838, while other n=8/n=10 cells have det 0
  on those rows (instance-specific minors) — the rank obstruction is the
  stable object, the minor witness is not.

Honest scope: finite-order audit (n<=16, p<=449); O(p) enumeration cannot
reach q ~ n*2^128, so this is NOT prize closure. Deterministic re-run
confirms identical integers.

[shane9coy]

Independent read: extends the G246/G320 countermodel family
(PR #524: n=8, n=10) to subgroup order n=16. 5 smooth n=16 cells
((p-1) mod 16 == 0, 2 not in G): p ∈ {337, 353, 401, 433, 449}.
Rank obstruction HOLDS in all: rank_seed=3, rank_aug=4 (R6^c not
in the degree-2 Krylov span of the centered base class). First
nonzero 4-row minor is rows (0,1,2,3) in every tested n=16 cell,
determinants 750141 / -7520392 / 13559450 / -9703719 / 10639664,
each cross-checked by the independent cofactor path (ALL MATCH).
The contrast with the n=8 certificate (rows (0,1,2,4)) and the
n=10 cell (rows (0,1,2,3), det=308582838) is honestly noted in
the PR — the rank obstruction is the stable object, the minor
witness is not. Honest-scope: n ≤ 16, p ≤ 449; O(p) enumeration
cannot reach q ~ n*2^128, not a prize closure. Concur with merge.

Same base=main caveat as #524 — worth confirming with sharkwon
before merge.