{
  "abstract": "In this paper, we establish a rigorous geometric framework that applies the formal architecture of finite-dimensional bi-Hamiltonian structures and Nambu-Poisson mechanics to macroeconomic growth theory. Moving beyond static empirical correlations, we deploy Ryuzo Sato's principle of simultaneous holotheticity to demonstrate that economic production functions emerge natively as stable, time-independent geometric leaves of integrable flows. We construct a unified, hierarchical taxonomy of three fundamental economic growth regimes that sequentially generalize one another: the classical, unconstrained Cobb-Douglas mode; the resource-limited S-shaped econsystem response; and the capacity-bounded \"overshoot-and-collapse\" regime. Furthermore, we push this paradigm into non-smooth territory by investigating the structural boundary crises that occur when aggregate economic trajectories encounter definitive resource carrying capacity ceilings. We show that these capacity limits induce a catastrophic rank-collapse of the compatible contravariant Poisson pencil.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01661",
  "author_total": 2,
  "authors": [
    {
      "name": "Sarah Finkle"
    },
    {
      "name": "Roman G. Smirnov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/394grk94gb35n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01661",
  "fulltext_url": null,
  "id": "394grk94gb35n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01661",
  "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.soc-ph"
    ],
    [
      "openalex",
      "2002|Economic Growth and Productivity"
    ]
  ],
  "openalex": "W7207728776",
  "pdf_url": "https://arxiv.org/pdf/2609.01661",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/394grk94gb35n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01661",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01661"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Simultaneous Holotheticity and Bi-Hamiltonian Structures in Economic Growth Theory",
  "title_text": "Simultaneous Holotheticity and Bi-Hamiltonian Structures in Economic Growth Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/394grk94gb35n",
  "venue": "arXiv",
  "versions": []
}