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    "story_id": "mp-2026-08-06-027",
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    "headline": "The Reaction Diagram Hid an NP-Complete Question",
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    "dek": "Assigning real molecules to an abstract reaction network while preserving mass balance and allowed mechanisms is computationally hard, but pruning helps in practice.",
    "summary": "Assigning real molecules to an abstract reaction network while preserving mass balance and allowed mechanisms is computationally hard, but pruning helps in practice.",
    "body_text": "A theoretical chemistry preprint formalizes molecular realizability: whether the nodes of an abstract reaction network can be assigned known molecules while satisfying mass balance and specified reaction mechanisms. The authors prove the general decision problem NP-complete and present a backtracking-and-pruning algorithm for practical instances. The result concerns computational assignment under a defined database and rule set; it does not show that an assigned network will be kinetically viable in a laboratory.",
    "why_it_matters": "Assigning real molecules to an abstract reaction network while preserving mass balance and allowed mechanisms is computationally hard, but pruning helps in practice.",
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      "The result concerns computational assignment under a defined database and rule set; it does not show that an assigned network will be kinetically viable in a laboratory."
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    "tags": [
      "reaction networks",
      "complexity",
      "computational chemistry"
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  "sources": [
    {
      "source_id": "source-2026-08-06-016",
      "title": "arXiv preprint 2608.04635",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2608.04635",
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    "title": "The Reaction Diagram Hid an NP-Complete Question",
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