{
  "abstract": "Higher-dimensional theories distinguish the dimensionality of a microscopic description from the number of directions accessible to a physical observer. Relating these notions requires not only dimensional reduction, but also a consistent preservation of operational independence across different levels of description. We establish sufficient conditions under which a compositional operational rank is preserved first as the dimension of a smooth integral leaf and then as an observable Fisher-information rank. The key requirement is closure-faithfulness: the smooth realization must preserve the dependency relations of the operational closure, rather than merely its total rank. Together with real representability, constant rank, involutivity, and observer/scale compatibility, this yields a local integral leaf whose dimension equals the operational rank. A further primary-identification condition is required at the measurement level. If an independently specified observer image coincides locally with the primary integral distribution and the admissible protocols provide local resolution, finite labeled-mixture closure, and locally constant outcome support, then the same rank can be realized by a finite composite Fisher-information protocol. The construction holds for arbitrary finite rank. At r = 4 it provides a conditional operational criterion for dimensional reduction in higher-dimensional theories: a viable reduction must preserve the relevant operational dependency structure, not merely produce four effective coordinates. Quantum-hardware negative controls further show that the same restricted Fisher rank can conceal different larger ranks under a broader pre-specified measurement protocol. The framework therefore constrains the operational outcome of dimensional reduction without imposing a universal four-dimensional bound on microscopic state spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35764",
  "author_total": 2,
  "authors": [
    {
      "name": "Nikolay D. Tulupov"
    },
    {
      "name": "Alexander M. Tishin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqxbhavc7ryy6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35764",
  "fulltext_url": null,
  "id": "aqxbhavc7ryy6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35764",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7223998527",
  "pdf_url": "https://arxiv.org/pdf/2610.35764",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqxbhavc7ryy6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35764",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35764"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Compositional Operational Rank, Smooth Realizability, and Dimensional Reduction",
  "title_text": "Compositional Operational Rank, Smooth Realizability, and Dimensional Reduction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/aqxbhavc7ryy6",
  "venue": "arXiv",
  "versions": []
}