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Incomplete Proofs Kept Their Verified Pieces

ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.

Published Updated Story ID: mp-2026-08-30-014
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Summary

ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.

Neural models propose decompositions, repairs and schema combinations while Lean verifies each transition. Within a problem, the system evolves partial AND-OR proof graphs; across problems, verified subgraphs enter a persistent schema library with unresolved premises exposed as new goals. The authors report the highest average solve rate among evaluated systems on three competition-level Lean benchmarks. Formal verification preserves soundness of accepted steps, not the usefulness of every proposal.

Why it matters

ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.

Limits and context

  • Formal verification preserves soundness of accepted steps, not the usefulness of every proposal.

Key claims

  1. ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.

    Qualification: Formal verification preserves soundness of accepted steps, not the usefulness of every proposal.

    Evidence: source-2026-08-30-014

Sources

  1. arXiv preprint 2608.26334arXiv · primary research

Corrections

No corrections have been recorded for this story.