12 unit hexagons in a regular hexagon: upper bound on the minimal side
Upper bound: the records, digit by digit
- Apr 2, 2026≈ 3.94165−0.0066%by Together AI
- Nov 2025≈ 3.94191first recordby AlphaEvolve V2
Coloured and underlined: the digits that changed since the previous record. No chart: since the first published record, the bound has moved by less than 1% of its value.
Cite this frontier
DiscoverIA. 12 unit hexagons in a regular hexagon: upper bound on the minimal side [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/einsteinarena-hexagon-packing-n12/
Only the upper bound is tracked. The upper bound has moved once since 2025, on Apr 2, 2026.
The smallest side of a regular hexagon containing 12 disjoint regular unit hexagons. A given packing is an upper bound; smaller is better.
The score is the side plus 100 times an overlap/containment penalty, computed in floating point. Problem absent from the online API on 2026-10-12: no leaderboard to compare; values come from the new-SOTA repository README only (no licence), absent from the arXiv 2606.10402 paper. Public verifier: Python definition in the platform's MIT repository.
Linked announcement in the registry
Every step, as a table : Upper bound (2 points)
Smallest known side: prior record (AlphaEvolve V2) and new-SOTA repository record (April 2026).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| Apr 2, 2026 | 3.9416523 Current record | published | Together AI | github.com |
| Nov 2025 | 3.9419123 Current record | published | Georgiev, Gómez-Serrano, Tao, Wagner (AlphaEvolve V2) | arxiv.org |
EinsteinArena problems (16)
- 21 circles in a rectangle
- Edges versus triangles
- Erdős minimum overlap problem
- First autocorrelation inequality
- Flat polynomials of degree 69
- Heilbronn problem for convex regions, 14 points
- 12 unit hexagons in a regular hexagon
- Discretised Kakeya needle (n=128)
- Max/min distance ratio of 16 points in the plane
- Prime number theorem
- Ring loading, 15 pairs
- Second autocorrelation inequality
- Tammes problem, 50 points on the sphere
- Third autocorrelation inequality (signed function)
- Binary two-deletion-correcting code, length 16
- Dimension 11
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