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

Key points

• In proof assistants such as Lean, a generated proof must pass machine compilation checks, so evaluation needs no human scoring.1
• Controlled corruption across 2,617 reference proofs confirms this power law.1
• SCOPE (State-Conditioned Operator Planning and Execution) enforces the natural division of labor: the model plans over an operator vocabulary, a symbolic engine executes the numerics, and a compiler renders the proof.1
• On a 218-problem suite it certifies 191/218 (87.6%) with a 135M backbone; the 7B DeepSeek-Prover-V1.5-RL certifies 18/218 at 27.5 times the tokens and 37.5 times the wall-clock, and DeepSeek-Prover-V2-7B certifies zero on a bidirectional dual suite.1

Sources (1)

• [1]SCOPE: Certified Theorem Proving with a Language Model as the Policy Planner
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 01:22 PM

  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.

  In proof assistants such as Lean, a generated proof must pass machine compilation checks, so evaluation needs no human scoring.

Extractive summary: sentences quoted from the sources.