SCOPE: Certified Theorem Proving with a Language Model as the Policy Planner

arXiv:2610.08319v1 Announce Type: new Abstract: In proof assistants such as Lean, a generated proof must pass machine compilation checks, so evaluation needs no human scoring. Direct generation fails on multi-step numeric propositions: a proof is valid only if every content integer is correct, so the pass rate is bounded by the k-th power of the per-integer accuracy. Controlled corruption across 2,617 reference proofs confirms this power law. SCOPE (State-Conditioned Operator Planning and Execution) enforces the natural division of labor: the model plans over an operator vocabulary, a symbolic

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