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nimaanari/formalization-beyond-bethe

Nima Anari

Palomar Registrypalomar/PALOMAR-2026-08-29-000006Aug 29, 2026cs.DSscore 0

Computing or approximating the permanent is a canonical problem in theoretical computer science and in counting and sampling. Before this work, the canonical Bethe approximation gave the best known deterministic guarantee, with approximation factor (sqrt 2)^n. This formalization proves that there is an absolute constant c < sqrt 2 and a deterministic polynomial-time c^n-approximation for every nonnegative rational matrix. It checks the mathematical and algorithmic proof down to Lean's standard logical axioms, including the finite-precision convex-optimization implementation.

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