{
  "abstract": "Local kinetic exponents and next-generation radii diagnose infinitesimal invasion, but they need not determine whether a nonlinear organized state is accessible. Motivated by the kinetic component of Gate~7 in a twelve-gate nonequilibrium framework, we study cooperative networks whose productive linearization contains no closed cycle. We prove that an acyclic productive Jacobian has $R=0$ and $λ_{\\rm kin}=-\\min_i d_i<0$ for every drive, while a nonlinear return path can create a stable finite-amplitude branch through a saddle-node. In a canonical catalyst--assembly model, the saddle's stable manifold---not a threshold in either concentration---is the deterministic establishment boundary, so equal-abundance seeds of different composition can have opposite outcomes. At finite copy number, establishment becomes a committor and first-passage problem. For a benchmark protocol with $Γ=2$, $Ω=16$, $η=0.02$, and horizon $T=1000$, density-Hill and pair-count generators give first-entrance probabilities $0.633$ and $0.339$; their interpolated half-success drives are $1.900$ and $2.148$, an approximately $13.1\\%$ shift. The associated constant-source deterministic system retains a stable low state, so these transitions are fluctuation- and discrete-arrival-enabled. The finite-amplitude regime is not confined to exact acyclicity: a weak linear return leaves a finite interval with $0<R<1$, $λ_{\\rm kin}<0$, and bistability. A general cooperative-return criterion separates the superlinear local condition from the global return-profile structure required for a fold. The resulting hierarchy of branch existence, basin accessibility, and finite-time stochastic establishment replaces a single onset threshold by a protocol-dependent kinetic criterion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05458",
  "author_total": 2,
  "authors": [
    {
      "name": "Ferran Martínez-Reyes"
    },
    {
      "name": "Slava G. Turyshev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ada6pd4grfez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05458",
  "fulltext_url": null,
  "id": "4ada6pd4grfez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05458",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.gen-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05458",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ada6pd4grfez.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05458",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05458"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.gen-ph",
      "subfield": "general"
    }
  ],
  "title": "Finite-amplitude establishment beyond local invasion in cooperative chemical networks",
  "title_text": "Finite-amplitude establishment beyond local invasion in cooperative chemical networks",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:18Z",
  "url": "https://research.draconitic.com/paper/4ada6pd4grfez",
  "venue": "arXiv",
  "versions": []
}