Source authenticated

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.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 6, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: site-confirmed. Publication: preprint. AI contribution: ai-co-developed. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Optimality of the added-vector code in the 19-dimensional kissing construction · Ho's 1280-word code is optimal

Confidence: Not scored

Registry verification: site confirmed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

ChatGPT (OpenAI, model version unstated)
model · ai model contributor · OpenAI

Alexey M. Kolosov
human · human collaborator

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

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

specialist registry · passed

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.

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

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

kissing-number-19-dimensions

witness · pending

other link supplied by the VibeMathed registry.

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Optimality of the added-vector code in the 19-dimensional kissing construction evidence for this event

This event attributed to ChatGPT (OpenAI, model version unstated)

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

VibeMathed record: Optimality of the added-vector code in the 19-dimensional kissing construction evidence for this event

kissing-number-19-dimensions evidence for this event

This event attributed to Alexey M. Kolosov

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