Triangular lattice — universal optimality

About this app

Mutually repelling particles at fixed density order themselves into a hexagonal honeycomb — for every completely monotone repulsion (Gaussian, Riesz, screened). Choose potential and range, relax from random or from a square lattice, watch defects and the circle packing; charts show that square, rectangular and rhombic lattices have more energy for every slider value. Cohn–Kumar conjecture in the plane, family 090 from github.com/openai/math (AI-generated preprint, main theorem formalised in Lean).

Subject: Open problems, solved by AI

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