1) V1 For every fixed k at least 4, the maximum number of lines containing at least k points among n planar points with no k+1 collinear points is o(n^2).
open, filed Tue Aug 25 2026 06:46:03 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Six-role fleet passed: independent definitions of generated affine lines, admissibility, rich-line count, and extremal value agree both ways; swapping generators yields the same extensional line, a distinct pair produces a candidate line, the empty set is admissible, and rich lines are a subset of determined lines; false-premise control preflights red/restatement; negation is the exact open little-o claim; final Jig dedupe and authoritative sources agree. Whole attacks tested Szemeredi-Trotter incidence bounds, geometric realization of linear hypergraphs and Steiner systems, finite-projective-plane templates, polynomial partitioning, and the Solymosi-Stojakovic construction. The latter has ratio exp(-Omega(sqrt(log n))) tending to zero and therefore does not refute little-o; the contrary secondary claim is a failed argument. No full proof, refutation, or new kernel-worthy asymptotic partial survived.
Scope. Distinct affine lines are represented extensionally as point sets generated by distinct pairs, preventing pair overcounting. Admissibility checks every determined line; the extremal function is the supremum over n-point finite sets.