{
  "abstract": "We conduct a systematic, machine-checked mathematical physics investigation of ten coupled frontier hypotheses governing enstrophy production, fractional hyperviscous regularity thresholds, dispersive second-harmonic-generation (SHG) regulators, and three-dimensional resonant-triad hypergraph depletion across the Katz–Pavlović dyadic hierarchy and toroidal Fourier lattices. Rather than restricting formalization to known textbook identities, we evaluate an open ten-hypothesis research programme in which six of the ten hypotheses (60.0%) are positively proved and four plausible conjectures (40.0%) are formally refuted or obstructed by explicit counterexamples, integrability deficits, and arithmetic parity theorems. All twelve theorems (eight positive theorems and four formal counterexample/obstruction theorems) are machine-checked in the Lean 4 theorem prover (ANSE.DyadicNavierStokesRegulator) with zero sorryAx axioms and verified via environment-level definitional equality against a frozen canonical specification (ANSE.DyadicNavierStokesRegulatorSpec), accompanied by an exact arbitrary-precision rational and integer combinatorial replication harness and a 20-record 5-tier Elenchus epistemic ledger.",
  "abstract_shown": true,
  "affiliations": [
    "SocrateAI Lab"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xavier Callens"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fe2k1ntxwcd0.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23458238",
  "fulltext_url": null,
  "id": "5fe2k1ntxwcd0",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23458238",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23458238/files/Dyadic_NavierStokes_Regulator_Elenchus_Paper.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fe2k1ntxwcd0.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:20:55Z",
      "native_id": "23458238",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23458238"
    }
  ],
  "subjects": [],
  "title": "Cutoff-Uniform Enstrophy Bounds, Fractional Riccati Integrability Thresholds, and Resonant-Triad Depletion in Dyadic and Toroidal Fluid Hierarchies: A Machine-Checked Investigation of Ten Frontier Hypotheses",
  "title_text": "Cutoff-Uniform Enstrophy Bounds, Fractional Riccati Integrability Thresholds, and Resonant-Triad Depletion in Dyadic and Toroidal Fluid Hierarchies: A Machine-Checked Investigation of Ten Frontier Hypotheses",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:55Z",
  "url": "https://research.draconitic.com/paper/5fe2k1ntxwcd0",
  "venue": "Zenodo",
  "versions": []
}