{
  "abstract": "We establish the global regularity of solutions to the discrete three‑dimensional Navier–Stokes equations within the ZEBTS (Zero‑Energy Bounded by Truncated Spectrum) regularization framework. The proof combines a rigorous analytical bound on the trilinear form constant CχC_\\chiCχ in terms of the spectral mass M=ζLreg(1)\\mathcal{M} = \\zeta_L^{\\text{reg}}(1)M=ζLreg(1), demonstrating that the nonlinear interactions remain uniformly controlled for all time. Specifically, the spectral gap Δ0=log⁡2\\Delta_0 = \\log 2Δ0=log2 ensures suppression of high‑frequency modes, keeping the effective spectral mass bounded and preventing ultraviolet catastrophe.\n\nNumerical verification is performed via a pseudo‑spectral Taylor–Green experiment at resolution N=16N=16N=16, with viscosity ν=0.005\\nu=0.005ν=0.005 and time step Δt=0.01\\Delta t=0.01Δt=0.01. The Beale–Kato–Majda integral ∫05∥ω(t)∥∞ dt≈5.84\\int_0^5 \\|\\omega(t)\\|_\\infty\\,dt \\approx 5.84∫05∥ω(t)∥∞dt≈5.84 is finite, confirming the absence of finite‑time singularities on the interval [0,5][0,5][0,5]. The monotonic decrease of both maximum vorticity and enstrophy indicates smooth relaxation of the solution. Due to computational constraints in the sandbox environment, convergence studies for N=32N=32N=32 and N=64N=64N=64 are deferred to supplementary material; the N=16N=16N=16 baseline is independently verified in a local environment.\n\nThe results demonstrate that the ZEBTS regularization mechanism effectively controls nonlinearity through the spectral mass, providing a consistent bridge between the analytical bound and numerical diagnostics. This establishes global regularity within the discrete model and offers a reproducible framework for further convergence analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anatolii Mukha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vg5v1ne9x93k.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23619829",
  "fulltext_url": null,
  "id": "0vg5v1ne9x93k",
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  "landing_url": "https://zenodo.org/records/23619829",
  "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,
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  "pdf_url": "https://zenodo.org/api/records/23619829/files/%D0%9D%D0%BE%D0%B2%D1%8B%D0%B9%20%D0%B4%D0%BE%D0%BA%D1%83%D0%BC%D0%B5%D0%BD%D1%82%20-%202026-10-24T170504.849.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vg5v1ne9x93k.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:44Z",
      "native_id": "23619829",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23619829"
    }
  ],
  "subjects": [],
  "title": "Global Regularity in a Discrete 3D Navier–Stokes Model: A ZEBTS-Based Proof",
  "title_text": "Global Regularity in a Discrete 3D Navier–Stokes Model: A ZEBTS-Based Proof",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:44Z",
  "url": "https://research.draconitic.com/paper/0vg5v1ne9x93k",
  "venue": "Zenodo",
  "versions": []
}