AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-26
A frame-indifferent rank-one convex function in three dimensions which is not quasiconvex
The authors construct a function W on 3×3 matrices that is frame-indifferent and rank-one convex but not quasiconvex. Near the rotation group SO(3), W is an explicit degree-four polynomial in the strain F^TF − Id, and quasiconvexity fails at F = Id through a third-order mechanism. The work was carried out with the assistance of the AI model Claude Opus 5.5, and the main proofs were formally verified in Lean 4.