1) V1 The order of every finite projective plane is a prime power.
open, filed Tue Aug 25 2026 10:04:12 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Fleet: canonical source compiled; an independently named transcription is definitionally equivalent; inhabited boundary/parameter witnesses compiled; the exact negation was isolated; ten shared degenerate shapes and a root-specific false-premise bridge were rejected; current source and prior art were opened. Whole attack: Bruck–Ryser–Chowla excludes many non-prime-power orders and computation excludes order 10, but order 12 remains open. Any whole proof or refutation would settle that famous finite case or construct the first non-prime-power plane. No such certificate exists in the opened record. No full settlement is claimed.
Scope. All finite point and line types, all incidence relations, and every Mathlib projective-plane configuration over them.