{
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  "problem_id": "vibemathed:prim-dijkstra-manhattan-complexity",
  "title": "Complexity of Terminal-Only Manhattan Prim-Dijkstra Routing",
  "canonical_statement": "Prim-Dijkstra routing interpolates between a minimum spanning tree and a shortest-path tree, and has been used and improved in VLSI physical design since the early 1990s, but the complexity of the terminal-only Manhattan decision problem was never settled. It is weakly NP-complete. A continuous cost-radius tradeoff with a balanced $(2,2)$ guarantee accompanies the classification.",
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      "type": "proved",
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      "occurred_at": "2026-07-18T00:00:00.000Z",
      "title": "arXiv:2607.17005 - Provably Good Prim-Dijkstra Revisited: New Theory and a Practical Algorithm for a Classical VLSI Routing Problem with LLMs",
      "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": "2026-07-18T00:00:00.000Z",
      "human_collaborators": [
        "Keren Zhu"
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      "outcome": "The paper is a designed experiment rather than an incidental use. One model was run under five deliberately incompatible research conditions that differed in premise and information boundary: construct and adversarially audit an NP-completeness proof from the problem definition alone; pursue a polynomial-time exact algorithm blind, without literature or the option of retreating to a hardness claim; pursue the same informed; assume hardness and seek a bicriteria guarantee; and synthesize the record into a solver against an evaluator frozen beforehand. The hardness track produced the NP-completeness proof. The two exact tracks converged on the same architecture and produced counterexamples rather than a proof, which the author treats as a control.",
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      "label": "arXiv:2607.17005 - Provably Good Prim-Dijkstra Revisited: New Theory and a Practical Algorithm for a Classical VLSI Routing Problem with LLMs",
      "url": "https://arxiv.org/abs/2607.17005",
      "kind": "primary-mathematical-source",
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      "label": "VibeMathed: Complexity of Terminal-Only Manhattan Prim-Dijkstra Routing",
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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}