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  "slug": "bunkbed-flow-obstructions",
  "title": "A single positive point in the bunkbed window",
  "shortTitle": "Flow-polynomial bunkbed obstructions",
  "url": "https://evidencepress.org/releases/bunkbed-flow-obstructions/",
  "oneLine": "An algebraic transfer yields homogeneous counterexamples throughout a parameter window, except at the known Ising point.",
  "abstract": "A candidate Eulerian-flow transfer theorem yields full homogeneous random-cluster bunkbed counterexamples at every prescribed interior edge probability. Separate spectral regimes, exact sign certificates and a Jordan-mode calculation give U_p intersect [alpha,691/250] = {2}. The graph may depend on p and q. Alpha is not a record lower endpoint; the global parameter classification and integer q>=3 remain unresolved.",
  "datePublished": "2026-09-30",
  "dateModified": "2026-09-30",
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  "doi": "10.5281/zenodo.23063182",
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      "name": "A Single Positive Point in the Bunkbed Window",
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    "Anonymous"
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    "name": "Random-cluster bunkbed parameter question",
    "url": "https://arxiv.org/abs/2509.18788v1"
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    {
      "citation": "Ayyer, Linusson and Ravichandran (2025), The bunkbed problem and the random cluster model: parameter question and earlier counterexample interval.",
      "url": "https://arxiv.org/abs/2509.18788v1",
      "doi": "10.48550/arXiv.2509.18788"
    },
    {
      "citation": "Gladkov, Pak and Zimin (2025), The bunkbed conjecture is false: ordinary-graph disproof and construction antecedents.",
      "url": "https://doi.org/10.1073/pnas.2420725122",
      "doi": "10.1073/pnas.2420725122"
    },
    {
      "citation": "Hollom (2025), The bunkbed conjecture is not robust to generalisation: hypergraph antecedents.",
      "url": "https://doi.org/10.1016/j.ejc.2025.104188",
      "doi": "10.1016/j.ejc.2025.104188"
    },
    {
      "citation": "Dong (2015), On zero-free intervals of flow polynomials: the prior flow-polynomial setting.",
      "url": "https://arxiv.org/abs/1403.1916",
      "doi": "10.48550/arXiv.1403.1916"
    }
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