{
  "abstract": "We present a revised twelve-axiom formulation of the Chrysene Formalism that rigorously separates its molecular, tensorial, noncommutative, spectral, and physical layers. The molecular reduct is restricted to a finite four-ring polyhex comparison class whose canonical reference point group is conjugate in O(3) to the standard C2h realization and whose two primary attachment directions are intrinsically inequivalent. The 3,6,9,12 <-> 2,5,8,11 dual cipher is realized as a uniform one-step perimeter displacement. A local structural tensor Psi-C generates a Z3-indexed tensor network. Its quasi-local observable algebra and lattice-translation action produce the crossed-product sequence algebra A-C = Q-C semidirect product Z3, whose noncommutativity follows from translation of localized operations rather than from geometric orthogonality. The dual cipher defines a second structural tensor, a native Z2 x Z2 four-state alphabet, and a commutant representation of the primary sequence algebra. The sequence algebra is equipped with the spectral triple (A-C-circ, H-omega, D-C). An explicit faithful tracial representation and finite-filtration Dirac operator give bounded commutators and compact resolvent on the infinite Z3 architecture without compactifying the lattice or requiring translation invariance of D-C. Physical transfer, polarization response, and admissibility geometry are introduced as distinct subsequent structures. An exhaustive enumeration of the seven free four-cell polyhexes selects a unique canonical carbon framework with the required C2h point-group type, and its graph is independently identified with chrysene. An explicit extension of the standard numbered chrysene reference node satisfies all twelve axioms, proving non-vacuity. Consequently, every full model has canonical carbon-framework reduct polyhex-congruent to chrysene, while the standard 3,6,9,12 <-> 2,5,8,11 locant frame is retained on the reference and standard-locant realization class rather than derived uniquely from the axioms. The Ny = Nx + 2 relation, a structurally induced GF(4) field law, directional transfer and optical anisotropy, spectral--path metric reconstruction, real spectral structure, spectral dimension, higher-algebraic braiding, emergent assembly chirality, and dynamical scission remain theorem-level problems.",
  "abstract_shown": true,
  "affiliations": [
    "Annals of the Chrysene Formalism San Francisco , California , USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Charles D. Schaper",
      "orcid": "0000-0001-6156-8511"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1n05fhptdnvqz.bib",
  "cited_by": 14,
  "doi": "10.68366/5jctze12",
  "fulltext_url": null,
  "id": "1n05fhptdnvqz",
  "issns": [
    "3144-2021"
  ],
  "landing_url": "https://doi.org/10.68366/5jctze12",
  "language": "en",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214955900",
  "pdf_url": "https://chrysene.com/index.php/acf/article/download/40/80",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1n05fhptdnvqz.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W7214955900",
      "source": "openalex",
      "url": "https://doi.org/10.68366/5jctze12"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Advanced Operator Algebra Research",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The Chrysene Formalism Revisited: A Twelve-Axiom Foundation for Molecular Characterization, Tensorial Noncommutative Geometry, and Operator Response",
  "title_text": "The Chrysene Formalism Revisited: A Twelve-Axiom Foundation for Molecular Characterization, Tensorial Noncommutative Geometry, and Operator Response",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:21:00Z",
  "url": "https://research.draconitic.com/paper/1n05fhptdnvqz",
  "venue": "Annals of the Chrysene Formalism",
  "versions": []
}