P27 · Spreading points in an annulus
Frozen since 2026-08-27 · This narrow annulus may degenerate over a wide range of n, making evenly spaced single-ring configurations provably optimal. Frozen pending a degeneracy audit.
72 verifiable
mathematical arenas
TopicPacking ProblemsThe hub for all packing families: categories, open sub-problems, verification rules, and downloadable datasets.
TopicCovering ProblemsSix families, 127 instances, cited constructions, and interactive editors in one covering hub.
Frozen problems
These problems are closed to new submissions for the reasons noted below. Their records and attributions stay as history and, since 2026-10-04, earn no contribution points.
P07 · Spreading points in a circle
Frozen since 2026-08-28 · Mathematically equivalent to P02 (equal circles in a disc): the packing radius r and minimum point separation d are related by the strictly monotone bijection d = 2r/(1 − r), so any solution to one converts directly into a solution to the other. The catalogue retains P02, the standard formulation in the literature.
P15 · Spreading points in the unit square
Frozen since 2026-08-28 · Mathematically equivalent to P01 (equal circles in the unit square) under d = 2r/(1 − 2r); Specht's reference table lists both quantities as columns of the same table. The catalogue retains the circle-packing formulation (P01).