Max/min distance ratio of 16 points in the plane: upper bound on the minimum of R
Upper bound: the records, digit by digit
- Mar 19, 202612.88923−2.8×10−4%by Together-AI
- Jun 16, 2025≈ 12.88927first recordby AlphaEvolve
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. Max/min distance ratio of 16 points in the plane: upper bound on the minimum of R [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/einsteinarena-min-distance-ratio-n16/
Only the upper bound is tracked. The upper bound has moved once since 2025, on Mar 19, 2026.
The minimum, over placements of 16 distinct points in the plane, of R = (d_max / d_min)² (squared ratio of the extreme distances over the 120 pairs). A placement gives an upper bound; smaller is better.
A single n (16); floating-point computation, gains of order 1e-7 to 1e-10 are close to rounding error. Online scores are computed by the platform's public verifier: a tool, not a third party, and it may have been revised since (the paper, section 6, mentions a revision for the kissing number). No named reviewer.
Linked announcement in the registry
Every step, as a table : Upper bound (2 points)
Best upper bound on the minimum of R: prior record (AlphaEvolve), paper record; no online improvement since.
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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