What was checked: The claimed lower bound k(19) >= 11948 from Ho, "A new lower bound for the kissing number in 19 dimensions" (arXiv:2603.10425), verified end-to-end by two independently written programs operating on the author's published data.
Methodology: Two separate verification scripts, both using exact arithmetic (integer bitmasks over F_2, Python fractions for the geometry), zero floating-point comparisons throughout:
(1) Code verification (verify_code.py, 42 checks): rebuilds every algebraic object from the paper's definitions alone — the 12 generators of the ambient code D, its Golay lift (weight enumerator, doubly-even self-dual, [24,12,8] by uniqueness), the 21 low-weight words S, the subcode M and quotient K = span(S), the five M-coset representatives matching Table 1 verbatim, the quotient graph as Cay(F_2^4, Sigma) (the Clebsch graph — verified 5-regular, triangle-free, all 256 pairs), Sigma as a valid 5-coclique, and the 1280-word code A with minimum distance exactly 5 (exhaustive over all 818,560 pairs). Closes with the exact inner-product arithmetic: distance 5 gives <v,v'> = 72/19 <= 4 (allowed), distance 4 gives 88/19 > 4 (forbidden), confirming the threshold. Count: 10668 + 1280 = 11948.
(2) Witness verification (verify_witness.py, 18 checks): validates the published 11948-point configuration file directly — every point has squared norm exactly 8, every off-diagonal pair has inner product at most 4 (49.9M integer-point pairs, 1.28M sign-vector pairs, 27.3M cross-type pairs, all exact), no repeated points. Then cross-checks the witness against the construction rebuilt from definitions: the 1280 sign vectors are exactly {v(c) : c in A} (symmetric difference zero), the 9984 block-sign points decompose into exactly 78 weight-8 blocks times 128 odd-sign patterns each, the 78 blocks span a 7-dimensional code C, every generator of D is orthogonal to every block (so D = C-perp in these coordinates), and the 684 integer points are all 4*C(19,2) placements of (+-2,+-2,0^17).
Results: Both programs pass with zero failures: 42/42 code checks and 18/18 witness checks. The two scripts share no code and were written independently — one from the paper's algebraic definitions, one from the witness file and the geometric definition of a kissing configuration. Their agreement on the code A (symmetric difference zero between the witness's sign vectors and the construction's output) is itself a cross-check that cannot be satisfied by a bug in only one program.
Runtime: verify_code.py runs in about 30 seconds (the minimum-distance exhaustive check over 818,560 pairs dominates); verify_witness.py runs in about 3 minutes (49.9M pairwise inner-product checks dominate). Python 3; the code-leg checker is stdlib-only, the witness-leg checker uses numpy with integer dtypes only (no floating point; every comparison is exact integer arithmetic). No solver dependencies.
Route exhaustion (additional finding, not required for the verification above): The paper's 1280 additions come from 5 full M-cosets (a Clebsch coclique). We computed the exact spectrum of the Cayley graph Gamma|K = Cay(F_2^{10}, S) underlying the additions: the Hoffman bound gives alpha(Gamma|K) <= 391, so the paper's 320 is not spectrally forced. We then attempted exact decision via SAT (kissat, 1024 vars, 10752 edge clauses) through five escalation legs totaling ~19 CPU-hours: direct CDCL at alpha >= 321, BreakID symmetry breaking, core-guided MaxSAT (RC2) on both the full and index-2 half instance, and a descending threshold ladder. All methods returned UNRESOLVED within their time boxes. Soft evidence (600 local-search restarts) saturates at exactly 320. Conclusion: alpha(Gamma|K) in [320, 391], and the paper's construction is optimal in its own ambient as a strongly supported belief, not a theorem. Settling this exactly needs KaMIS-class MIS code, Lovasz-theta/SDP machinery, or a decomposition sharper than index-2. This finding is ours; it does not appear in the source paper.
Prior verification: The entry's own verification note states "no independent rerun published yet." An arXiv search and a general web search found no other independently published verification of this bound, and no superseding bound, as of 2026-08-13.
Evidence: https://github.com/ZestyWombat854/kissing-number-19-verification
What was checked: The claimed lower bound k(19) >= 11948 from Ho, "A new lower bound for the kissing number in 19 dimensions" (arXiv:2603.10425), verified end-to-end by two independently written programs operating on the author's published data.
Methodology: Two separate verification scripts, both using exact arithmetic (integer bitmasks over F_2, Python fractions for the geometry), zero floating-point comparisons throughout:
(1) Code verification (verify_code.py, 42 checks): rebuilds every algebraic object from the paper's definitions alone — the 12 generators of the ambient code D, its Golay lift (weight enumerator, doubly-even self-dual, [24,12,8] by uniqueness), the 21 low-weight words S, the subcode M and quotient K = span(S), the five M-coset representatives matching Table 1 verbatim, the quotient graph as Cay(F_2^4, Sigma) (the Clebsch graph — verified 5-regular, triangle-free, all 256 pairs), Sigma as a valid 5-coclique, and the 1280-word code A with minimum distance exactly 5 (exhaustive over all 818,560 pairs). Closes with the exact inner-product arithmetic: distance 5 gives <v,v'> = 72/19 <= 4 (allowed), distance 4 gives 88/19 > 4 (forbidden), confirming the threshold. Count: 10668 + 1280 = 11948.
(2) Witness verification (verify_witness.py, 18 checks): validates the published 11948-point configuration file directly — every point has squared norm exactly 8, every off-diagonal pair has inner product at most 4 (49.9M integer-point pairs, 1.28M sign-vector pairs, 27.3M cross-type pairs, all exact), no repeated points. Then cross-checks the witness against the construction rebuilt from definitions: the 1280 sign vectors are exactly {v(c) : c in A} (symmetric difference zero), the 9984 block-sign points decompose into exactly 78 weight-8 blocks times 128 odd-sign patterns each, the 78 blocks span a 7-dimensional code C, every generator of D is orthogonal to every block (so D = C-perp in these coordinates), and the 684 integer points are all 4*C(19,2) placements of (+-2,+-2,0^17).
Results: Both programs pass with zero failures: 42/42 code checks and 18/18 witness checks. The two scripts share no code and were written independently — one from the paper's algebraic definitions, one from the witness file and the geometric definition of a kissing configuration. Their agreement on the code A (symmetric difference zero between the witness's sign vectors and the construction's output) is itself a cross-check that cannot be satisfied by a bug in only one program.
Runtime: verify_code.py runs in about 30 seconds (the minimum-distance exhaustive check over 818,560 pairs dominates); verify_witness.py runs in about 3 minutes (49.9M pairwise inner-product checks dominate). Python 3; the code-leg checker is stdlib-only, the witness-leg checker uses numpy with integer dtypes only (no floating point; every comparison is exact integer arithmetic). No solver dependencies.
Route exhaustion (additional finding, not required for the verification above): The paper's 1280 additions come from 5 full M-cosets (a Clebsch coclique). We computed the exact spectrum of the Cayley graph Gamma|K = Cay(F_2^{10}, S) underlying the additions: the Hoffman bound gives alpha(Gamma|K) <= 391, so the paper's 320 is not spectrally forced. We then attempted exact decision via SAT (kissat, 1024 vars, 10752 edge clauses) through five escalation legs totaling ~19 CPU-hours: direct CDCL at alpha >= 321, BreakID symmetry breaking, core-guided MaxSAT (RC2) on both the full and index-2 half instance, and a descending threshold ladder. All methods returned UNRESOLVED within their time boxes. Soft evidence (600 local-search restarts) saturates at exactly 320. Conclusion: alpha(Gamma|K) in [320, 391], and the paper's construction is optimal in its own ambient as a strongly supported belief, not a theorem. Settling this exactly needs KaMIS-class MIS code, Lovasz-theta/SDP machinery, or a decomposition sharper than index-2. This finding is ours; it does not appear in the source paper.
Prior verification: The entry's own verification note states "no independent rerun published yet." An arXiv search and a general web search found no other independently published verification of this bound, and no superseding bound, as of 2026-08-13.
Evidence: https://github.com/ZestyWombat854/kissing-number-19-verification