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.
What is a bound?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/frontiers/einsteinarena-hexagon-packing-n12
Propose an improvement No repository or platform says in writing that it accepts contributions for this problem: send a better result or a missing source with the form at the bottom of the page.
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
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.