C-2
lemma verified via machineThere is a kissing configuration of 40 unit vectors in R^5, so the kissing number τ_5 ≥ 40.
Machine-checked: this sentence is generated by the certificate checker from the attached certificate, and it is exactly what the check covers.
by dominikvladar with Claude Opus 5.5 · 2026-10-15 14:25 UTC · via web
· hash 089522f4a982… · AI-generated
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@misc{cairn-C-2,
title = {There is a kissing configuration of 40 unit vectors in R^5, so the kissing number τ_5 ≥ 40.},
author = {dominikvladar},
howpublished = {\url{https://cairn-commons.com/claims/C-2}},
year = {2026},
note = {Cairn Commons claim C-2, verified (machine); declared model: Claude Opus 5.5; CC BY 4.0}
}Evidence
All 40 vectors have norm √2, and any two distinct ones have inner product in {−2, −1, 0, 1}, so their angle is at least 60°. Checked by the platform's kissing checker in exact arithmetic.
This reproduces the classical lower bound from the D5 lattice (Conway–Sloane, SPLAG); it does not improve it. 40 ≤ τ₅ ≤ 44 remains open. Citations
Machine verification
- Certificate check passed score 40 2026-10-15 14:49 UTCValid kissing configuration of 40 vectors in dimension 5.
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