{
  "abstract": "We investigate the reconstruction of primitive time shifts in Fibonacci dynamics modulo powers of three. Using the Fibonacci transfer matrix and three scalar observables, we characterize the time positions at which the true primitive shift is uniquely determined by a single observation.\n\nFor every integer k >= 2, we establish an explicit classification of these positions in terms of residue classes modulo 12. Each scalar observable admits exactly one quarter of the full period as uniquely identifying positions, and the three corresponding witness sets are pairwise disjoint.\n\nThe proof combines a complete base classification modulo 9, 3-adic lifting arguments, Fibonacci reflection identities, and explicit constructions of competing primitive shifts.\n\nThe theoretical results are accompanied by reproducible computational verification using Python and its standard library. The computational audits independently test the underlying identities and reconstruction properties over finite precision levels.\n\nThis work contributes an explicit classification of scalar reconstruction uniqueness in modular Fibonacci dynamics, complementing classical results on Fibonacci periods and linear recurrences modulo prime powers.",
  "abstract_shown": true,
  "affiliations": [
    "ORCID"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ivo Vajc",
      "orcid": "0009-0005-5145-6491"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8r4my52f0srmv.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23437165",
  "fulltext_url": null,
  "id": "8r4my52f0srmv",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23437165",
  "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/23437165/files/Theorem_58_1_Revised.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8r4my52f0srmv.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:21:19Z",
      "native_id": "23437165",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23437165"
    }
  ],
  "subjects": [],
  "title": "Universal Classification of Primitive Scalar Witnesses in Fibonacci Dynamics Modulo Powers of Three",
  "title_text": "Universal Classification of Primitive Scalar Witnesses in Fibonacci Dynamics Modulo Powers of Three",
  "type": "preprint",
  "updated_at": "2026-10-31T12:21:19Z",
  "url": "https://research.draconitic.com/paper/8r4my52f0srmv",
  "venue": "Zenodo",
  "versions": []
}