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    "headline": "Incomplete Proofs Kept Their Verified Pieces",
    "slug": "incomplete-proofs-kept-their-verified-pieces",
    "dek": "ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.",
    "summary": "ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.",
    "body_text": "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.",
    "limitations": [
      "Formal verification preserves soundness of accepted steps, not the usefulness of every proposal."
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    "modified_at": "2026-08-30T09:00:00.000-04:00",
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        "text": "ProofEvolve stores kernel-checked partial proof graphs so unfinished work can contribute to later theorems.",
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        "qualification": "Formal verification preserves soundness of accepted steps, not the usefulness of every proposal."
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    "tags": [
      "theorem proving",
      "Lean",
      "neuro-symbolic AI"
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  "sources": [
    {
      "source_id": "source-2026-08-30-014",
      "title": "arXiv preprint 2608.26334",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2608.26334",
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      "published_at": "2026-08-26T15:15:27.000-04:00",
      "accessed_at": "2026-08-30T08:23:14.000-04:00",
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    "description": "A daily newspaper for the age of artificial intelligence."
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  "cite_this_report": {
    "title": "Incomplete Proofs Kept Their Verified Pieces",
    "publisher": "The Machine Press",
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