{
  "abstract": "The Golden Orbit\n\nReversible Golden Scaling, Algebraic Orbits, and Coherence in a Graded Multilinear Algebra\n\nC. J. Tully\n\nIndependent Researcher and Engineer\n\nORCID: 0009-0007-5661-7332\n\nOctober 2026\n\nAbstract\n\nWe study the discrete dynamics generated by repeated application of a reversible golden-scaling transformation on a graded multilinear algebra. Let K = ℚ(√5) and let\n\nφ = (1 + √5)/2\n\nbe the fundamental positive unit of the golden field. For an integer-graded algebra\n\nL = ⊕_{k ∈ ℤ} L_k,\n\nthe golden-scaling operator S_φ is defined on homogeneous elements by S_φ(x_k) = φ^k x_k. Under the assumption that the multilinear operation is homogeneous of degree zero, S_φ is an invertible algebra automorphism. We define the bilateral golden orbit\n\nO_φ(x) = { S_φ^n(x) : n ∈ ℤ }\n\nand derive its explicit componentwise form. The orbit is algebraically reversible. Bounded bilateral orbits occur only for states supported in degree zero. Any coherence predicate that is invariant under a single application of S_φ remains constant along the entire orbit. These results separate algebraic symmetry, coherence preservation, and metric stability for the iterated golden scaling introduced in earlier work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Chloe Tully",
      "orcid": "0009-0007-5661-7332"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sjfjcxat40tk.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23407270",
  "fulltext_url": null,
  "id": "0sjfjcxat40tk",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23407270",
  "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": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sjfjcxat40tk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:23Z",
      "native_id": "23407270",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23407270"
    }
  ],
  "subjects": [],
  "title": "The Golden Orbit Reversible Golden Scaling, Algebraic Orbits, and Coherence in a Graded Multilinear Algebra",
  "title_text": "The Golden Orbit Reversible Golden Scaling, Algebraic Orbits, and Coherence in a Graded Multilinear Algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:21Z",
  "url": "https://research.draconitic.com/paper/0sjfjcxat40tk",
  "venue": "Zenodo",
  "versions": []
}