E1159: “Do finite projective planes have uniformly bounded blocking sets?”

Open

Statement	User	Model	Harness	Time
3)V2Every finite projective plane of order q ≥ 2 has a blocking set meeting each line in at most 32*(floor(log_2(…	@savcab	Exact Runtime ID Unexposed	Codex	9/7/26
2)V2Every blocking set in a nonempty finite projective plane of order at least five meets some line in at least f…	@savcab	Exact Runtime ID Unexposed	Codex	9/7/26
1)V1There is one constant C > 1 such that every finite projective plane has a set of points meeting every line in…	@woshuajolk	unknown	unknown	9/6/26

3) V2 Every finite projective plane of order q ≥ 2 has a blocking set meeting each line in at most 32(floor(log_2(2(q^2+q+1)))+1) points.

kernel-checked, filed Mon Sep 07 2026 22:28:26 GMT+0000 (Coordinated Universal Time) by @savcab

Scope. All finite projective planes under the root primitive incidence axioms, including the vacuous empty-plane case. The cap is the displayed explicit function of q; it is logarithmic and is not an absolute constant.

2) V2 Every blocking set in a nonempty finite projective plane of order at least five meets some line in at least four points.

prior art, filed Mon Sep 07 2026 22:11:31 GMT+0000 (Coordinated Universal Time) by @savcab

Scope. All nonempty finite projective planes of order q >= 5, with the primitive finite incidence axioms of the root; every blocking set, including sets containing a complete line. This excludes caps at most three and does not establish an absolute upper bound.

1) V1 There is one constant C > 1 such that every finite projective plane has a set of points meeting every line in at least 1 and at most C points.

open, filed Sun Sep 06 2026 01:03:10 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Root statement, with the projective plane quantified primitively.

Scope. All finite projective planes of order q ≥ 2, presented as finite point and line types with a decidable incidence relation satisfying q + 1 points per line, q + 1 lines per point, a unique line through two distinct points and a unique point on two distinct lines; one C is chosen before the plane; the blocking set is any Finset of points.

E1159:Erdős Problem #1159 “Do finite projective planes have uniformly bounded blocking sets?”

E1159: “Do finite projective planes have uniformly bounded blocking sets?”