An independent exact verification of an 11948-point kissing configuration in 19 dimensions

In 2026, B. S. Ho published a claimed new lower bound for the kissing number in 19
dimensions: at least 11948 unit balls can simultaneously touch a central unit ball
without overlapping (arXiv:2603.10425), improving the previous bound of Cohn and Li
by 256. The coordinates were released publicly.

This deposit contains an independent verification of that configuration. The checker
was written from the mathematical definition of a kissing configuration and does not
use, import, or execute the author's own verification scripts.

The verification is exact. Every coordinate in the published file is one of
0, +/-1, +/-2, or +/-sqrt(8/19), so all 11948 vectors have squared norm 8, and the
kissing condition |v_i - v_j|^2 >= 8 is equivalent to <v_i, v_j> <= 4. This reduces to
three integer tests: for the 10668 integer vectors, <v,w> <= 4; for integer-versus-sign
pairs, <v,s> <= 6; and for the 1280 sign vectors, <s,t> <= 9. All 71,371,378 pairs were
checked and none violate the condition. Each of the three bounds is attained exactly,
as expected of an extremal configuration. No binary floating-point value appears
anywhere on the proof path.

Four independent cross-checks agree: exact rational re-derivation of the three integer
thresholds; a bitwise popcount computation which independently recovers the binary code
parameters claimed in the paper (length 19, size 1280, minimum Hamming distance 5) from
the geometry alone; a direct squared-difference computation that forms no Gram matrix;
and a pure-Python resampling of integer-versus-sign pairs. The data file was pinned by
SHA-256 against the checksum published in the author's repository.

Scope. What is established is that the published configuration is valid, hence that the
kissing number in 19 dimensions is at least 11948. The verification depends on no cited
theorem, no numerical optimizer, and no rounded data. It does not establish that 11948
is optimal, and it makes no claim of novelty: the construction is entirely Ho's. The
contribution is an independent certificate of a claim that had not yet been refereed.