{
  "abstract": "[Depreciated and replaced by V3] This pre-V3 paper is replaced by the corresponding V3 clean-room reconstruction: From Fold to Mathematics: An Exact, Parameter-Free and Machine-Closed Derivation of Mathematical Foundations from Smithian Fold Theory; From Fold to Physics: An Exact, Parameter-Free and Machine-Closed Reconstruction of Physical Science from Smithian Fold Theory. The V3 source platform is https://github.com/MettaMazza/ernos-labs-sft-platform. The original DOI, concept DOI, version number and files are preserved for transparent historical provenance; this record must not be presented or cited as current V3 work. One axiom. One operation. Zero free parameters. Three Clay Millennium problems — the Riemann hypothesis, the Yang–Mills mass gap, and Navier–Stokes regularity — share a hidden assumption: the continuum. This paper shows the assumption is the obstruction. With no continuum (the line replaced by the fold lattice, which has a smallest scale and no zero), each has a direct structural answer. RIEMANN: the critical line Re(s)=1/2 is the unique self-antipodal axis of the fold reflection x ↔ 1−x — the involution of the zeta functional equation — so the self-dual zeros are forced onto the half-One. YANG–MILLS: the spectrum is discrete with a positive least element (the floor 1/2^d), so a mass gap exists by construction and equals the floor. NAVIER–STOKES: the energy cascade is repeated halving that reaches the floor in finitely many folds and stops — no sub-floor scale, no blow-up. Each is the fold removing the continuum and reading off what remains (the fold-native structural answer/mechanism, not the continuum-formulation Clay proof). Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory",
  "abstract_shown": true,
  "affiliations": [
    "Ernos Labs"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Maria Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85567bczkghn7.bib",
  "cited_by": 7,
  "doi": "10.5281/zenodo.21026490",
  "fulltext_url": null,
  "id": "85567bczkghn7",
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  "landing_url": "https://doi.org/10.5281/zenodo.21026490",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3109|Advanced Mathematical Theories and Applications"
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  "openalex": "W7166583257",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-29",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/85567bczkghn7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:26:43Z",
      "native_id": "W7166583257",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.21026490"
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  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Advanced Mathematical Theories and Applications",
      "subfield": "statistical-nonlinear"
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  ],
  "title": "[Depreciated and replaced by V3] The Continuum Was the Bug: The Riemann Line, the Yang-Mills Mass Gap, and Navier-Stokes Regularity, Answered by Removing the Continuum",
  "title_text": "[Depreciated and replaced by V3] The Continuum Was the Bug: The Riemann Line, the Yang-Mills Mass Gap, and Navier-Stokes Regularity, Answered by Removing the Continuum",
  "type": "peer-reviewed",
  "updated_at": "2026-11-03T13:20:27Z",
  "url": "https://research.draconitic.com/paper/85567bczkghn7",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}