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    "headline": "The Count Broke the Two-to-the-N Barrier",
    "slug": "the-count-broke-the-two-to-the-n-barrier",
    "dek": "A deterministic algorithm counted linear extensions of arbitrary partial orders in O*(1.89^n) time.",
    "summary": "A deterministic algorithm counted linear extensions of arbitrary partial orders in O*(1.89^n) time.",
    "body_text": "A linear extension orders every element of a partial order without violating its constraints. The new algorithm splits the problem by chain structure and, near an antichain, records only the first comparable element above each selected element before using a compressed dynamic program. Its O*(1.89^n) bound beats the long-standing 2^n general barrier and addresses a question posed in 2013. The result is theoretical, with a verification script supplied as an ancillary artifact.",
    "why_it_matters": "A deterministic algorithm counted linear extensions of arbitrary partial orders in O*(1.89^n) time.",
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      "The new algorithm splits the problem by chain structure and, near an antichain, records only the first comparable element above each selected element before using a compressed dynamic program."
    ],
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    "first_published_at": "2026-08-21T09:00:00.000-04:00",
    "modified_at": "2026-08-21T09:00:00.000-04:00",
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        "qualification": "The new algorithm splits the problem by chain structure and, near an antichain, records only the first comparable element above each selected element before using a compressed dynamic program."
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    "tags": [
      "algorithms",
      "partial orders",
      "exact counting"
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  "sources": [
    {
      "source_id": "source-2026-08-21-016",
      "title": "arXiv preprint 2608.19505",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2608.19505",
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      "published_at": "2026-08-18T20:00:00.000-04:00",
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    "name": "The Machine Press",
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    "description": "A daily newspaper for the age of artificial intelligence."
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  "cite_this_report": {
    "title": "The Count Broke the Two-to-the-N Barrier",
    "publisher": "The Machine Press",
    "published_at": "2026-08-21T09:00:00.000-04:00",
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