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  "story": {
    "story_id": "mp-2026-09-08-008",
    "source_story_id": "tmp-story-circle-packing-discovery-loop",
    "edition_id": "mp-2026-09-08-morning-0061",
    "edition_url": "https://themachinepress.com/edition/2026-09-08",
    "position": 8,
    "story_type": "dispatch",
    "section": "weird-machine",
    "editorial_classification": "editorial",
    "headline": "Twenty-Eight Dollars Bought Ten Circle-Packing Records",
    "slug": "twenty-eight-dollars-bought-ten-circle-packing-records",
    "dek": "An LLM-guided optimization loop improved ten accepted Packomania results in 15 iterations, with an independent verifier keeping only valid gains.",
    "summary": "An LLM-guided optimization loop improved ten accepted Packomania results in 15 iterations, with an independent verifier keeping only valid gains.",
    "body_text": "Discovery Loop starts with a simple solver, asks a language model to propose algorithmic changes, scores each candidate with an independent verifier and retains only improvements. Applied to a variable-radius circle-packing benchmark, the system improved the best known solutions for ten values of N between 101 and 114 by 2.4 to 5.4 percent. The run took 15 iterations and $27.72 in reported model cost, and the results were accepted by Packomania. This is a narrow optimization result, but it shows how inexpensive search can matter when claims are checked by a deterministic judge.",
    "why_it_matters": "An LLM-guided optimization loop improved ten accepted Packomania results in 15 iterations, with an independent verifier keeping only valid gains.",
    "limitations": [
      "Discovery Loop starts with a simple solver, asks a language model to propose algorithmic changes, scores each candidate with an independent verifier and retains only improvements."
    ],
    "importance": 8,
    "canonical_url": "https://themachinepress.com/story/mp-2026-09-08-008/twenty-eight-dollars-bought-ten-circle-packing-records",
    "json_url": "https://themachinepress.com/story/mp-2026-09-08-008.json",
    "first_published_at": "2026-09-08T09:00:00.000-04:00",
    "modified_at": "2026-09-08T09:00:00.000-04:00",
    "content_status": "new",
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    "carryover_reason": null,
    "key_claims": [
      {
        "claim_id": "claim-mp-2026-09-08-008-001",
        "text": "An LLM-guided optimization loop improved ten accepted Packomania results in 15 iterations, with an independent verifier keeping only valid gains.",
        "source_ids": [
          "source-2026-09-08-008"
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        "qualification": "Discovery Loop starts with a simple solver, asks a language model to propose algorithmic changes, scores each candidate with an independent verifier and retains only improvements."
      }
    ],
    "source_ids": [
      "source-2026-09-08-008"
    ],
    "tags": [
      "program evolution",
      "optimization",
      "circle packing"
    ],
    "image_url": "https://themachinepress.com/issues/2026-09-08/circle-packing-code-file.webp",
    "corrections": []
  },
  "sources": [
    {
      "source_id": "source-2026-09-08-008",
      "title": "arXiv preprint 2609.05093",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2609.05093",
      "canonical_url": "https://arxiv.org/abs/2609.05093",
      "source_type": "primary_research",
      "is_primary_source": true,
      "published_at": "2026-09-04T08:48:13.000-04:00",
      "accessed_at": "2026-09-08T08:20:00.000-04:00",
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  "corrections": [],
  "publisher": {
    "name": "The Machine Press",
    "url": "https://themachinepress.com",
    "description": "A daily newspaper for the age of artificial intelligence."
  },
  "cite_this_report": {
    "title": "Twenty-Eight Dollars Bought Ten Circle-Packing Records",
    "publisher": "The Machine Press",
    "published_at": "2026-09-08T09:00:00.000-04:00",
    "canonical_url": "https://themachinepress.com/story/mp-2026-09-08-008/twenty-eight-dollars-bought-ten-circle-packing-records"
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