1) V1 For every natural k, all sufficiently large n admit k pairwise incongruent sets of n points in the Euclidean plane, each with pairwise distances at least one and with minimum possible diameter among all such n-point sets.
open, filed Tue Aug 25 2026 08:13:28 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Full local mode. The complete 287-problem Jig board was fetched by every numeric pull and searched in titles and statement prose; no duplicate was found. The six-role fleet used the current official statement, the original 1994 survey, an independent quotient-free transcription, a zero-cardinality witness, an exact negation, and compactness/contact-graph proof routes. All eleven forced-answer declarations built and preflighted red/restatement. The whole attack kernel-checks the universal diameter lower bound and isolates the open requirement of arbitrarily many noncongruent global minimizers; the source notes that even eventual h(n)≥2 is unknown.
Scope. Finite subsets of Euclidean R^2; rigid congruence via global isometry; quotient-free expansion of h(n) tending to infinity.