Spherical codes and designs

Placeholder. This problem is here so the problem panel can be tried out. Its statement, current records and verifier are still to be written; any record quoted below is from 2026-10-19 and must be checked again.

Problem

Find point sets on the sphere: kissing configurations, where no two points are closer than 60 degrees, and spherical t-designs with as few points as possible. A configuration is an exact certificate: the verifier checks every inner product in rational arithmetic. Upper bounds come from the Delsarte and Cohn–Elkies linear programs. As of 2026-10-19 the kissing number in dimension 11 is at least 593 (AlphaEvolve, 2025).