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  "problem_id": "vibemathed:target-free-clique-conjecture",
  "title": "The Target-Free Clique Conjecture for Threshold-Linear Networks",
  "canonical_statement": "The target-free clique conjecture asserts that the supports of stable fixed points of a nondegenerate combinatorial threshold-linear network are exactly its target-free cliques, the bidirected cliques no outside vertex receives an edge from every member of. An explicit six-neuron counterexample refutes it.",
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      "status": "resolved",
      "occurred_at": "2026-07-23T00:00:00.000Z",
      "title": "arXiv:2607.21396 - A six-neuron counterexample to the target-free clique conjecture",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "attempted_at": "2026-07-23T00:00:00.000Z",
      "human_collaborators": [
        "Jesse Geneson"
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      "note": "The counterexample is a single fixed six-vertex graph with an explicit parameter regime, so the refutation reduces to a finite determinant and clique computation set out in the paper. Single-author arXiv preprint, not yet peer-reviewed.",
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    "VibeMath has not independently verified the mathematical claim.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
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