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    "story_id": "mp-2026-11-03-006",
    "source_story_id": "tmp-story-zebra-exact-cover",
    "edition_id": "mp-2026-11-03-morning-0116",
    "edition_url": "https://themachinepress.com/edition/2026-11-03",
    "position": 6,
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    "section": "research",
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    "headline": "The Language Model Writes the Puzzle. The Solver Proves It.",
    "slug": "the-language-model-writes-the-puzzle-the-solver-proves-it",
    "dek": "A neuro-symbolic system translates Zebra puzzles into exact-cover tool calls, then uses solver feedback to repair incomplete or contradictory encodings.",
    "summary": "A neuro-symbolic system translates Zebra puzzles into exact-cover tool calls, then uses solver feedback to repair incomplete or contradictory encodings.",
    "body_text": "Language models can parse natural clues but do not inherit the soundness and completeness of a symbolic solver. This framework asks a model to convert entities and constraints from a Zebra-style puzzle into structured calls that build an exact-cover instance. The solver computes the answer and returns feedback when the encoding is invalid, underconstrained or overconstrained; the system can then revise the translation, using the puzzle's promised uniqueness as an additional signal. Across multiple model sizes, post-training methods and families, the authors report consistent gains over chain-of-thought prompting and tested neuro-symbolic baselines. The guarantee applies to the exact-cover solution after a correct encoding, not to every semantic interpretation produced by the model.",
    "why_it_matters": "A neuro-symbolic system translates Zebra puzzles into exact-cover tool calls, then uses solver feedback to repair incomplete or contradictory encodings.",
    "limitations": [
      "Language models can parse natural clues but do not inherit the soundness and completeness of a symbolic solver.",
      "The guarantee applies to the exact-cover solution after a correct encoding, not to every semantic interpretation produced by the model."
    ],
    "importance": 8,
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    "first_published_at": "2026-11-03T09:00:00.000-05:00",
    "modified_at": "2026-11-03T09:00:00.000-05:00",
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        "text": "A neuro-symbolic system translates Zebra puzzles into exact-cover tool calls, then uses solver feedback to repair incomplete or contradictory encodings.",
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        "qualification": "Language models can parse natural clues but do not inherit the soundness and completeness of a symbolic solver."
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    "source_ids": [
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    "tags": [
      "neuro-symbolic AI",
      "logic",
      "exact cover",
      "tool use"
    ],
    "image_url": null,
    "corrections": []
  },
  "sources": [
    {
      "source_id": "source-2026-11-03-006",
      "title": "arXiv preprint 2611.03641, original v1",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2611.03641v1",
      "canonical_url": "https://arxiv.org/abs/2611.03641v1",
      "source_type": "primary_research",
      "is_primary_source": true,
      "published_at": "2026-11-02T13:58:21.000-05:00",
      "accessed_at": "2026-11-03T08:18:17.000-05:00",
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  "publisher": {
    "name": "The Machine Press",
    "url": "https://themachinepress.com",
    "description": "A daily newspaper for the age of artificial intelligence."
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  "cite_this_report": {
    "title": "The Language Model Writes the Puzzle. The Solver Proves It.",
    "publisher": "The Machine Press",
    "published_at": "2026-11-03T09:00:00.000-05:00",
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