Heilbronn problem for convex regions, 14 points: lower bound on the minimum triangle area
Lower bound: the records, digit by digit
- Apr 2, 2026≈ 0.027835580+3.2×10−5%by Together AI
- Nov 2025≈ 0.027835571first 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. Heilbronn problem for convex regions, 14 points: lower bound on the minimum triangle area [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/einsteinarena-heilbronn-convex-n14/
Only the lower bound is tracked. The lower bound has moved once since 2025, on Apr 2, 2026.
The largest value, over 14 points in the plane, of the minimum area of the triangles they form divided by the area of their convex hull. A given placement is a lower bound; larger is better.
A single n (14); floating-point computation (gain of 9e-9 over the previous value). 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.
Linked announcement in the registry
Every step, as a table : Lower bound (2 points)
Largest known value: prior record (AlphaEvolve V2) and new-SOTA repository record (April 2026).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| Apr 2, 2026 | 0.0278355805 Current record | published | Together AI | github.com |
| Nov 2025 | 0.0278355715 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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