Kissing number in dimension 19
The largest known such that non-overlapping unit spheres can all touch one central unit sphere in : a lower bound on the kissing number .
- steps
- 2
- by AI
- 1
- since
- 2023
The line is the frontier over time. Filled dots are steps that moved it; muted dots are results that did not. Orange dots are catalog entries, results with AI in the loop. Hollow dots are candidates under review and never move the line. Grey dots along the bottom edge are results from before the quantity had a number, placed there because they have no value on this axis. Dots that would overlap are nudged sideways a few pixels. Hover a dot for its value and attribution.
About this frontier
The kissing number is known exactly in dimensions 1, 2, 3, 4, 8 and 24 and in no others. Dimension 19 is one of the open ones, and progress is a construction: exhibit more spheres than anyone has before. The upper bound stands at 24,417, so the true value is somewhere in a gap of more than twelve thousand.
Every step, newest first
| Date | Value | Who | Model | Status | Source |
|---|---|---|---|---|---|
| 11 Mar 2026 | best An explicit binary code of length 19 and minimum distance 5 inside the 5-punctured extended binary Golay code. Wikipedia's kissing-number table now carries this value. | GPT-5.4 Pro, with Ho | GPT-5.4 Pro | AI step unreviewed | entry |
| 2023 | Recorded from the 2026 paper, which states it improves this bound by 256. Date approximate; the original was not opened here. | Cohn and Li | – | historical | source ↗ |
A short history on purpose. The 2026 paper states that it improves the bound of Cohn and Li by 256, which fixes the immediately preceding value at 11,692; earlier rungs exist in the sphere-packing literature but were not read here, and this site does not list values it has not seen. Wikipedia's kissing-number table already carries the new value and cites the same paper.
Changelog1 change
- Curatoradded this entry