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.
What is a bound?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/frontiers/einsteinarena-min-distance-ratio-n16
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To beat: R ≈ 12.8892, best value published on Mar 19, 2026.
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DiscoverIA does not run this platform and does not review contributions: their status stays “not evaluated” until a third party has checked them. Terms read on the platform on Oct 23, 2026.
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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