{
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  "slug": "gk-shared-phosphatase-connectedness",
  "title": "Path connectedness of multistationarity in a two-layer phosphorylation cascade with a shared phosphatase",
  "shortTitle": "One connected region for biochemical multistationarity",
  "url": "https://evidencepress.org/releases/gk-shared-phosphatase-connectedness/",
  "oneLine": "An exact overlapping fibre joins two auxiliary regions in the full space of reaction rates and conserved totals.",
  "abstract": "This unrefereed candidate gives a written proof that the full positive sixteen-dimensional multistationarity region of a two-layer phosphorylation cascade with a shared phosphatase is path connected. Two negative-critical auxiliary components have overlapping physical images, certified by exact rational equilibria. A zero-to-negative coordinate ray includes degenerate multistationary parameters. The claim contradicts Conjecture 4.3 of Kaihnsa and Wang, version 1, and does not concern equilibrium stability or fixed-rate slices.",
  "datePublished": "2026-09-20",
  "dateModified": "2026-09-20",
  "version": "0.1.0-candidate",
  "doi": "10.5281/zenodo.22858244",
  "doiUrl": "https://doi.org/10.5281/zenodo.22858244",
  "conceptDoi": "10.5281/zenodo.22858243",
  "pdfUrl": "https://github.com/ipitchford/gk-shared-phosphatase-connectedness/releases/download/v0.1.0-candidate/gk-shared-phosphatase-connectedness-v0.1.0-candidate.pdf",
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  "repoUrl": "https://github.com/ipitchford/gk-shared-phosphatase-connectedness",
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      "name": "Audio briefing",
      "description": "AI-generated communication, not additional mathematical evidence."
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  "authors": [
    "Anonymous"
  ],
  "license": "CC0-1.0",
  "status": "unrefereed-candidate",
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    "independentlyReproduced": false,
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      "note": "Two algebraic encodings with shared SymPy dependency; ordinary and optimized modes and three semantic negative controls. Global topology is a written proof.",
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      "note": "Internal model reports and supplied evidence do not establish this external assurance dimension."
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    },
    {
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      "label": "Editorial peer review",
      "question": "Has a journal or venue run peer review to a decision?",
      "state": "not-assessed",
      "note": "Internal model reports and supplied evidence do not establish this external assurance dimension."
    },
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      "dimension": "dataEnvironmentReproducibility",
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      "question": "Are data and computational environment pinned well enough to rebuild?",
      "state": "partial",
      "evidenceUrl": "https://github.com/ipitchford/gk-shared-phosphatase-connectedness/blob/v0.1.0-candidate/README.md",
      "note": "Pinned SymPy/mpmath requirements and Linux CI; PDF build is not hermetic."
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    "humanRole": "Research direction, supplied reviews and explicit publication authority; scholarly creator Anonymous.",
    "disclosure": "Supplied anonymous review and internal model reports do not establish authenticated unaffiliated validation."
  },
  "attributionBoundary": null,
  "problem": {
    "name": "Kaihnsa–Wang Conjecture 4.3, version 1",
    "url": "https://arxiv.org/abs/2607.25456v1"
  },
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  "metadataProvenance": "Source repairs and internal assessment are distinct from subsequent operational publication and public readback.",
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  "keywords": [
    "multistationarity",
    "phosphorylation cascade",
    "shared phosphatase",
    "path connectedness",
    "exact certificate"
  ],
  "keyResults": [
    "Path connectedness of the full positive rates-and-totals multistationarity region.",
    "Exact rational fibre meeting both negative auxiliary components.",
    "Physical image overlap contains a nonempty open subset.",
    "Explicit zero-to-negative attachment includes degenerate multistationary parameters."
  ],
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  "evidencePackage": "Written global proof; exact rational overlap certificate; two public algebraic checkers; normal and optimized producer replay with semantic negative controls; internal editorial reports and file manifest.",
  "openProblems": [
    "Classify connectivity of fixed-rate or fixed-total multistationarity slices.",
    "Determine the topology of regions with multiple stable equilibria.",
    "Investigate when auxiliary component images overlap in larger cascades."
  ],
  "mathObjects": [],
  "relatedWorks": [
    {
      "citation": "Kaihnsa and Wang (2026), Disconnectivity in Multistationarity Regions of Cascade of Goldbeter–Koshland Loops: exact target, version 1.",
      "url": "https://arxiv.org/abs/2607.25456v1",
      "doi": "10.48550/arXiv.2607.25456"
    },
    {
      "citation": "Conradi, Feliu, Mincheva and Wiuf (2017), Identifying parameter regions for multistationarity: primary degree criterion.",
      "url": "https://doi.org/10.1371/journal.pcbi.1005751",
      "doi": "10.1371/journal.pcbi.1005751"
    },
    {
      "citation": "Telek and Feliu (2023), Topological descriptors of the parameter region of multistationarity: Deciding upon connectivity.",
      "url": "https://doi.org/10.1371/journal.pcbi.1010970",
      "doi": "10.1371/journal.pcbi.1010970"
    },
    {
      "citation": "Feliu and Wiuf (2012), Enzyme-sharing as a cause of multi-stationarity in signalling systems: motif (k) and elimination antecedent.",
      "url": "https://doi.org/10.1098/rsif.2011.0662",
      "doi": "10.1098/rsif.2011.0662"
    }
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        "Multiple equilibria do not imply multiple stable equilibria.",
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