Research / Aug 19, 2026

First open case of the big-line-big-clique conjecture

Must every sufficiently large finite point set contain four collinear points or six pairwise visible points?

Model / AI: GPT-5.6 Sol Pro

self-reported (first open case)

Aug 19, 2026

Explicit (4,6) threshold

Model / AI: GPT-5.6 Sol Pro

self-reported (first open case)

Édouard Bonnet reports that after an initial failed attempt and further prompting, GPT-5.6 Sol Pro produced a detailed proof. The paper proves that 10^11055931 points force four collinear points or a six-vertex visibility clique.

Source read 2026-09-08. Read the abstract and AI-use disclosure in arXiv v1. The proof was not independently checked.

Paper — Paper