Resolutions in the Conway–Hardin–Sloane Grassmannian packing table (v2): 470 tightness certificates, eight proven negatives, and a full annotation cross-reference.

Version 2 of this deposit, extending the seventeen resolutions of v1 (doi:10.5281/zenodo.21610476) to 470 tightness certificates, eight proven negatives, and a full cross-reference of the table's tightness annotations. Research performed by Claude (Anthropic), directed by Reynout Vos; every certificate independently verified by ChatGPT (OpenAI) from self-contained adversarial prompts, with all verifier code written independently (included). Squared chordal distance dc²(U,V) = n − Tr(PUPV); simplex bound dc² ≤ (n(m−n)/m)·(N/(N−1)) for N subspaces of dimension n in Rm (Conway–Hardin–Sloane, Exp. Math. 5 (1996)). Cells refer to the packing table created by N. J. A. Sloane and maintained by H. Cohn. A. Seven cells where the simplex bound is attained (v1): (13,3,6) and (16,3,7) via exact fusion-Gram certificates; (11,2,29), (12,3,51), (11,4,54), (12,4,61), (12,4,62) via Newton–Kantorovich certificates in exact rational arithmetic. Five carried the table's “unclear whether bound is tight” annotation; (12,3,51) and (12,4,62) were never flagged — their table values were optimizer artifacts. A2. 463 further cells where the simplex bound is attained (new in v2; all independently verified, 463/463 PASS). A systematic cross-reference of the table's notes column against exact-system convergence found 579 cells at the bound up to rounding with no tightness information on record. The 463 of these with D = 11–16 and positive solvability count carry Newton–Kantorovich certificates in this deposit (exact dyadic centers; every decisive inequality checked in exact arithmetic). Novelty partition, independently confirmed by the second verifier's own orbit computation: 435 cells are not implied by any Naimark–spatial route from prior certified sweeps (novel modulo the harmonic / difference-family construction literature, which has not been exhaustively cross-referenced); 28 cells are direct Naimark complements of cells certified in S. R. Davis's 2025 AFIT thesis and are credited as implied. B. Eight cells where the simplex bound is provably not attained: (7,2,5), (11,2,7), (13,2,8), (14,3,6), (15,2,9), (15,1,21), (16,1,18), (16,1,23), via Naimark–spatial reduction to real equiangular tight frames excluded by the Sustik–Tropp–Dhillon–Heath integrality theorem. Executable exact check included. C. Credited observations: Davis's thesis settles (10,3,39) and (10,3,40), and additionally 102 unannotated table cells with D ≤ 10 (list included); those results are hers. D. Documented evidence (not claims): an obstruction catalog records strong local-obstruction evidence at (6,3,17), (11,2,33), (8,4,31), (14,2,9), including indications that the true optima at (6,3,17) and (11,2,33) fall short of the bound by margins of order 10−9 and 10−11. Method-of-record: all decisive predicates evaluated in exact arithmetic (symbolic algebra, exact rationals, dyadic integers); floating point only for exploratory search and for choosing certificate data subsequently checked exactly. Toolchain red-teamed before use; caught defects and fixes are part of the record. See README.md for full claims, per-class verification recipes, credits, and limitations.