{
  "abstract": "In spectral geometry and operator-algebraic models of the Riemann zeta function—such as Ray-Singer determinants and Bost-Connes systems—the multiplicative monoid of positive integers is introduced as an external algebraic input. Here, on the compact normal collar orbifold C_{ell_p} = S^1_{2 ell_p}/Z_2 ~ [0, ell_p] supporting the ultraviolet boundary layer of a Z_2-symmetric hypersurface, we prove that smooth metric-scaling endomorphisms preserving the interface and boundary stratum form a commutative covering monoid End_scale(C_{ell_p}) ~ (N_{>0}, x) under composition. By geometric pullback, these endomorphisms generate the complete fluctuating eigenbasis of the self-adjoint Neumann Laplacian Delta_perp = -d^2/dy^2 from a single fundamental mode. The Galois correspondence of covering spaces and the Jordan-Holder theorem identify geometrically irreducible coverings with simple deck transformation groups Deck(Phi_p) ~ Z/pZ of prime degree, causing the normalized Mellin-Haar transform of the collar heat kernel A_perp(tau) = exp(-tau ell_p^2 Delta_perp / pi) to factorize unconditionally into the Euler product of zeta(s) for Re(s) > 1. In the meromorphically continued connected impedance Z_int(s) = -zeta'(s)/zeta(s), composite coverings with coprime factors possess decomposable direct-product deck groups Deck(Phi_{ab}) ~ Deck(Phi_a) x Deck(Phi_b) whose cumulants cancel identically, isolating prime-power coverings without invoking Mobius inversion. Poisson modular inversion of the Schwinger proper-time integral recovers the completed xi-function xi(s) = xi(1-s) and yields the Hadamard constant B = xi'(0)/xi(0) = -1 + (1/2) ln(4 pi) - gamma/2 directly from three collar invariants: vacuum-pole subtraction, Gaussian symplectic volume, and scale-drift entropy. This self-contained construction derives the Euler product from collar topology without claiming a proof of the Riemann hypothesis, and admits an optional braneworld realization as reactive interaction mass.\n\nKeywords: collar orbifold; scale covering monoid; simple deck transformation groups; non-local heat kernel; Poisson summation; Hadamard constant ; Riemann xi-function; connected boundary impedance; interaction mass; net-zero entropy.",
  "abstract_shown": true,
  "affiliations": [
    "XYLONIX PTE. LTD."
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jinhyuk Fred Chung",
      "orcid": "0000-0001-8766-7446"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67wwt167j20hd.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23669939",
  "fulltext_url": null,
  "id": "67wwt167j20hd",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23669939",
  "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/23669939/files/P6%20phys%20origin%20primes%20Rev1.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67wwt167j20hd.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:20:49Z",
      "native_id": "23669939",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23669939"
    }
  ],
  "subjects": [],
  "title": "The Arithmetic of Spacetime: Collar Covering Monoids, Heat-Kernel Modularity, and the Geometric Origin of Prime Numbers",
  "title_text": "The Arithmetic of Spacetime: Collar Covering Monoids, Heat-Kernel Modularity, and the Geometric Origin of Prime Numbers",
  "type": "preprint",
  "updated_at": "2026-11-09T12:20:49Z",
  "url": "https://research.draconitic.com/paper/67wwt167j20hd",
  "venue": "Zenodo",
  "versions": []
}