{
  "abstract": "The millennium-old regularity problem of the three-dimensional incompressible Navier\n\nStokes (N-S) equations has long been trapped in the quagmire of weak solutions and energy\n\nestimates within Euclidean continuous spaces, where the core bottleneck lies in finite-time\n\nsingularity blow-up caused by vortex stretching. This paper proposes a novel Geometric\n\nTranslator Framework, completely bypassing traditional potential-field analysis. By rig\n\norously mapping material derivatives to the Frenet-Serret moving frame (ˆ t, ˆn, ˆ b) on Rieman\n\nnian manifolds, we geometrically re-express nonlinear convection, pressure gradients, and\n\nviscous dissipation as intrinsic curvature evolutions, centripetal reactions, and curvature\n\ngradient diffusions. Furthermore, by introducing the S-cutoff Planck grid minimum\n\nscale (bmin > 0) to lock out infinite curvature compression, combined with time-decaying\n\nkernel convolution envelope integrals, we establish the global boundedness of velocity gra\n\ndients. In addition, addressing the challenging §1b geometric inverse problem from the\n\nTheoPhysEval benchmark—where mainstream AI agents previously failed—our model suc\n\ncessfully reconstructs the underlying dynamics into an autonomous fractional-delay differ\n\nential equation on Riemannian manifolds. This paper completes a fully constructive proof\n\n(Q.E.D.) for both the global smoothness of the 3D N-S equations and complex trajectory\n\ninverse modeling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "HUA JIAN QI"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/954c34bccs5e6.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23477900",
  "fulltext_url": null,
  "id": "954c34bccs5e6",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23477900",
  "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/23477900/files/Geometric%20Translator%20and%20S-Cutoff%20Manifold.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/954c34bccs5e6.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:02Z",
      "native_id": "23477900",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23477900"
    }
  ],
  "subjects": [],
  "title": "Geometric Translator and S-Cutoff Manifold Regularization: A Purely Geometric Unified Proof of Global Smoothness for the 3D Navier-Stokes Equations and Complex Trajectory Inverse Problems",
  "title_text": "Geometric Translator and S-Cutoff Manifold Regularization: A Purely Geometric Unified Proof of Global Smoothness for the 3D Navier-Stokes Equations and Complex Trajectory Inverse Problems",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:02Z",
  "url": "https://research.draconitic.com/paper/954c34bccs5e6",
  "venue": "Zenodo",
  "versions": []
}