Optimality of the added-vector code in the 19-dimensional kissing construction
resolvedconfidence 70%
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Let \(D\subseteq\mathbb F_2^{19}\) be the fixed 4096-word ambient binary linear code used in Ho’s 19-dimensional improvement of the Cohn–Li kissing construction. Is every subset \(A\subseteq D\) with minimum Hamming distance at least \(5\) of size at most \(1280\)? No linearity assumption is imposed on \(A\).
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
ChatGPT (OpenAI, model version unstated)
The manuscript's Section 5: "ChatGPT (OpenAI) was used for literature search, the optimization-based search for the five-word certificate, development and checking of the proof, preparation of the verification program, and drafting and translation of the manuscript. The mathematical argument and the exact verification data are given explicitly; a language-model output or a numerical solver status is not used as a substitute for proof." Certificate found and proof developed with the model under the author's direction: co-developed.
Site-confirmed: the author's exact verifier (anc/verify_golay_1280_optimality.py, Python standard library, exact arithmetic) was replayed here on 6 September 2026 from a clone of cheptil/kissing-number-19-dimensions at 0a90b8e and passed every check: the five generator identities and rank certificate, the weight distribution of the 16-word subspace, the exact Fourier dual certificate, the independence number 5 of the 16-vertex certificate graph by exact subset DP, the 256 cosets giving 1280, and the explicit matching constructions with minimum distances 6 and 5. The manuscript's Section 5 discloses ChatGPT's role. No independent expert statement; the tier records a replayed certificate, not a referee.
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.
Known method families
computation (source-reported)
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.