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AI systems are making rapid progress in mathematics, but this progress is hard to measure. Benchmarks of solved problems saturate, and in benchmarks of open problems each problem can be resolved for the first time only once. We present SqueezeBench, a benchmark that is resilient to saturation: a success raises the bar...
The smallest known counterexample to the Bernhart-Kainen dispersability conjecture is identified, a $16-vertex graph that enumeration found as raw data, and the agent found an explicit algebraic construction.
The tool lrat-catcher is proposed, which turns a certificate into a Lean theorem, which checks the certificate as a stream while the solver is still running, and supports cube-and-conquer and formulas derived by preprocessing, to still form Lean proofs of the original formula.
This work introduces a framework that addresses both verification levels in the Lean theorem prover, and can be used to prove formulation-level properties, such as equivalence, equisatisfiability, and the correctness of symmetry-breaking constraints, parametrically for entire problem families.
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