Optimality of the added-vector code in the 19-dimensional kissing construction

The manuscript proves the upper bound $|A|\le1280$ for every admissible subset of the fixed ambient code $D$. Together with Ho’s existing construction, this determines the exact maximum. The proof partitions $D$ into 256 cosets of a 16-word subspace whose induced forbidden-distance graph is the Clebsch graph; each coset contributes at most five words. This does not determine the unrestricted kissing number $k(19)$ or improve the known 11948-point configuration. Independent expert review is pending.

The manuscript proves the upper bound $|A|\le1280$ for every admissible subset of the fixed ambient code $D$. Together with Ho’s existing construction, this determines the exact maximum. The proof partitions $D$ into 256 cosets of a 16-word subspace whose induced forbidden-distance graph is the Clebsch graph; each coset contributes at most five words. This does not determine the unrestricted kissing number $k(19)$ or improve the known 11948-point configuration. Independent expert review is pending.

For the fixed ambient binary code $D$ in the manuscript, every subset $A$ with minimum Hamming distance at least $5$ has size at most 1280, and Ho's construction attains 1280; equivalently $\alpha_5(D)=1280$. The same certificate gives $\alpha_5(K)=320$ for the stated 1024-word subcode $K$. This does not bound the unrestricted kissing number $k(19)$.

The source's explicit code coordinates, five-word Clebsch-graph certificate, coset argument, and exact verifier are accepted only as source-authenticated evidence in this draft; MFN did not execute the verifier.