math-033-disprove: Disprove The Hadwiger–Nelson Problem (Chromatic Number of the Plane)

[IndieMath:math-033:disprove] Disprove the The Hadwiger–Nelson Problem (Chromatic Number of the Plane) conjecture through an IndieMath AI research attempt. Canonical statement: In ZFC, the chromatic number of the Euclidean plane is 5. Contributions fund model usage and related compute for this direction.