Kissing Number in 19 Dimensions
The kissing number in 19 dimensions is at least 11948, improving the Cohn-Li bound by 256, via a binary code of length 19 and minimum distance 5 fed through the Cohn-Li odd-sign construction.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Sphere packings
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-03-11
- Model
- GPT-5.4 Pro
- Vendor
- OpenAI
- Collaborators
- Boon Suan Ho
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
A record lower bound; the kissing number in dimension 19 remains unknown.
What the AI did
"GPT-5.4 Pro was used in the discovery of the construction and in revising the exposition." The verifying computation is a finite check with public scripts and explicit coordinates for the 11948-point configuration.
Verification
A finite certificate with public code and coordinates; no independent rerun published yet.