{
  "abstract": "Wetterich showed that certain 1+1D probabilistic cellular automata are equivalent to fermionic QFTs and posed the 3D construction as an open problem. We construct one: a layered automaton (\"coincube\") whose conversion blocks form the real quaternion representation of Cl(0,3), controlled by binary environment fields whose streaming outruns the carrier (\"fresh tape\") -- no bit is consulted twice, and the single-particle ensemble propagator equals the annealed Bloch operator at every time. Exact results: the step operator is unitary for an explicit complex structure; the local Grassmann action is extracted mechanically; the single-carrier excitation is a Weyl fermion with an isotropic leading cone (slope ratios 1 within errors, factorized transport excluded by >=10 error bars); at finite momentum the node carries a parity-odd anisotropy c(q)kx ky kz/|k|, cancelled on the Dirac branch whose gap is 2 arctan[qm/(1-qm)], while off-resonant spectators stay massless; media-mediated interaction obeys Ug = (1-2gq^2) U. Obstructions: ballistic transport admits only finite velocity sets; Abelian sign gauges leave the factorized surface; no protected 2-component node survives an exhaustive search. Finally, a dichotomy for the quaternionic event class: an isotropic cone forces overdamping -- Q = w_0/Gamma <= pi/(2 ln 2) at all densities, 0.66 at working density -- while in-state unitarity forces factorized transport. Postselected two-boundary amplitudes evade this, exactly unitary at all times under the fresh tape, with induced weight positivity open: the relativistic object here is an amplitude whose probabilistic reading is unsettled.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14749",
  "author_total": 1,
  "authors": [
    {
      "name": "Piotr Stanisław Topa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a827qdm333hd4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14749",
  "fulltext_url": null,
  "id": "a827qdm333hd4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14749",
  "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",
      "hep-lat"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1703|Cellular Automata and Applications"
    ]
  ],
  "openalex": "W7213244304",
  "pdf_url": "https://arxiv.org/pdf/2609.14749",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a827qdm333hd4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14749",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14749"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fermionic quantum field theories as probabilistic cellular automata in three dimensions",
  "title_text": "Fermionic quantum field theories as probabilistic cellular automata in three dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/a827qdm333hd4",
  "venue": "arXiv",
  "versions": []
}