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  "story": {
    "story_id": "mp-2026-10-21-007",
    "source_story_id": "tmp-story-lean-bounded-repair",
    "edition_id": "mp-2026-10-21-morning-0103",
    "edition_url": "https://themachinepress.com/edition/2026-10-21",
    "position": 7,
    "story_type": "dispatch",
    "section": "developer-tools",
    "editorial_classification": "editorial",
    "headline": "The Proof Model Reads the Compiler's Rejection",
    "slug": "the-proof-model-reads-the-compiler-s-rejection",
    "dek": "A bounded repair loop fixes failed Lean tactics in place and gains most of its benefit on the first retry.",
    "summary": "A bounded repair loop fixes failed Lean tactics in place and gains most of its benefit on the first retry.",
    "body_text": "Sampling-only theorem provers throw away precise information when Lean rejects a tactic. This repair module returns the compiler error to a pretrained model and permits a bounded number of fixes. Across tested candidate budgets, it solved 82 additional theorems on a 1,990-theorem LeanDojo subset, with the first repair capturing 84 to 96 percent of the total gain. Benefits concentrated in shallow execution failures, not structural type errors, and replicated on Lean Workbook.",
    "why_it_matters": "A bounded repair loop fixes failed Lean tactics in place and gains most of its benefit on the first retry.",
    "limitations": [
      "Sampling-only theorem provers throw away precise information when Lean rejects a tactic.",
      "Benefits concentrated in shallow execution failures, not structural type errors, and replicated on Lean Workbook."
    ],
    "importance": 8,
    "canonical_url": "https://themachinepress.com/story/mp-2026-10-21-007/the-proof-model-reads-the-compiler-s-rejection",
    "json_url": "https://themachinepress.com/story/mp-2026-10-21-007.json",
    "first_published_at": "2026-10-21T09:00:00.000-04:00",
    "modified_at": "2026-10-21T09:00:00.000-04:00",
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    "carryover_reason": null,
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        "text": "A bounded repair loop fixes failed Lean tactics in place and gains most of its benefit on the first retry.",
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        "qualification": "Sampling-only theorem provers throw away precise information when Lean rejects a tactic."
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    "source_ids": [
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    "tags": [
      "Lean 4",
      "theorem proving",
      "compiler feedback"
    ],
    "image_url": null,
    "corrections": []
  },
  "sources": [
    {
      "source_id": "source-2026-10-21-007",
      "title": "arXiv preprint 2610.26942, original v1",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2610.26942v1",
      "canonical_url": "https://arxiv.org/abs/2610.26942v1",
      "source_type": "primary_research",
      "is_primary_source": true,
      "published_at": "2026-10-20T13:59:00.000-04:00",
      "accessed_at": "2026-10-21T08:27:23.757-04:00",
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  "publisher": {
    "name": "The Machine Press",
    "url": "https://themachinepress.com",
    "description": "A daily newspaper for the age of artificial intelligence."
  },
  "cite_this_report": {
    "title": "The Proof Model Reads the Compiler's Rejection",
    "publisher": "The Machine Press",
    "published_at": "2026-10-21T09:00:00.000-04:00",
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