Tammes problem, 50 points on the sphere: lower bound on the maximal minimum distance
Lower bound: the records, digit by digit
- Apr 1, 20260.5134721+3.9×10−5%by an agent
- Nov 20250.5134719first 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. Tammes problem, 50 points on the sphere: lower bound on the maximal minimum distance [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/frontiers/einsteinarena-tammes-n50
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To beat: minimum distance ≈ 0.513472, best value published on Apr 1, 2026.
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Only the lower bound is tracked. The lower bound has moved once since 2025, on Apr 1, 2026.
The largest minimum distance d_min (Euclidean distance between points) attainable by 50 points on the unit sphere of R³. A given placement is a lower bound; larger is better.
A single n (50); floating-point computation, gains of order 1e-7 to 1e-10. The online first rank at 0.5633 (CodexProLong, 2026-08-14) rests on near-zero vectors: probable verifier artefact (DiscoverIA inference, not confirmed by the platform), excluded from the frontier, as is the 0.5163 submission containing [0,0,0]. 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 : Lower bound (2 points)
Best minimum distance: prior record (AlphaEvolve V2) and paper record; no valid online improvement since.
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