{
  "id": "oai:papers.qnfo.org:universe-category-functor",
  "slug": "universe-category-functor",
  "title": "The Universe Category: A Single Functor Encoding Quantization, Stability, and Factorization",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "This paper proposes a single categorical object — a functor from the divisibility category of the positive integers to the category of smooth compact manifolds — and investigates whether its image simultaneously encodes three structures that have historically been treated as separate: quantization (integer-valued topological invariants), stability (ultrametric hierarchy), and prime factorization (homology rank). The functor F: P → M sends an integer n to the product of spheres ∏_p mid rad(n) S^p-1, where rad(n) is the square-free kernel. By the Künneth formula the total homology rank of the image is 2^ω(n), where ω(n) is the number of distinct prime factors. We verify this property computationally for all n ≤ 100,000 and verify the associated prime-power criterion: n is a prime power if and only if the homology rank of its image is exactly 2. The synthesis claim — that quantization, stability, and factorization are three faces of one categorical structure — is stated as a pre-registered conjecture with explicit disconfirmation conditions. Consistent with the evidential-weight standards applied throughout this research program, all structural correspondences identified here are labeled [RETRODICTION — not evidence]: post-hoc syntheses carrying zero independent evidential weight until novel predictions accrue.",
  "abstract_markdown": "This paper proposes a single categorical object — a functor from the divisibility category of the positive integers to the category of smooth compact manifolds — and investigates whether its image simultaneously encodes three structures that have historically been treated as separate: quantization (integer-valued topological invariants), stability (ultrametric hierarchy), and prime factorization (homology rank). The functor $F: \\mathcal{P} \\to \\mathcal{M}$ sends an integer $n$ to the product of spheres $\\prod_{p \\mid \\mathrm{rad}(n)} S^{p-1}$, where $\\mathrm{rad}(n)$ is the square-free kernel. By the Künneth formula the total homology rank of the image is $2^{\\omega(n)}$, where $\\omega(n)$ is the number of distinct prime factors. We verify this property computationally for all $n \\leq 100{,}000$ and verify the associated prime-power criterion: $n$ is a prime power if and only if the homology rank of its image is exactly 2. The synthesis claim — that quantization, stability, and factorization are three faces of one categorical structure — is stated as a pre-registered conjecture with explicit disconfirmation conditions. Consistent with the evidential-weight standards applied throughout this research program, all structural correspondences identified here are labeled [RETRODICTION — not evidence]: post-hoc syntheses carrying zero independent evidential weight until novel predictions accrue.",
  "date": "2026-08-01",
  "first_published": "2026-08-01",
  "last_revised": "2026-08-01T00:00:00Z",
  "modified": "2026-08-01T00:00:00Z",
  "version": "0.2.0",
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  "language": "en",
  "keywords": [
    "category theory",
    "Morse theory",
    "ultrametric geometry",
    "prime factorization",
    "topological invariants",
    "consilience",
    "structural realism",
    "philosophy of mathematics",
    "foundations of quantum mechanics"
  ],
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  "doi": null,
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  "url": "https://papers.qnfo.org/papers/universe-category-functor",
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  "sha256": "03795a360525ff52359981578ba0ac57043852b0f68677f820c5b1da0d6092c7",
  "version_url": "https://papers.qnfo.org/papers/universe-category-functor/v/0.2.0",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "The Universe Category: A Single Functor Encoding Quantization, Stability, and Factorization"
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        "subject": "Morse theory"
      },
      {
        "subject": "ultrametric geometry"
      },
      {
        "subject": "prime factorization"
      },
      {
        "subject": "topological invariants"
      },
      {
        "subject": "consilience"
      },
      {
        "subject": "structural realism"
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      {
        "subject": "philosophy of mathematics"
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        "subject": "foundations of quantum mechanics"
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