{
  "abstract": "This work investigates the clock not as an instrument, but as a mathematical object. The foundation is the main theory p ≡ 1 (mod q). This theory has two forms. The theoretical form (q + 1 = p) is one round and m = 1. The actual form (2q + 1 = p) is two rounds and m = 2.\n\nThe actual form is the core. Two rounds create a double cycle: for the clock this is day and night (25 ≡ 1 mod 12), for the week it is two moments within one week (15 ≡ 1 mod 7). So m = 2 does not mean you have two separate units, but that you have one unit with two different moments. This pattern repeats itself in the month (30 = 2 × 15) and the year (12 = 2 × 6). This is how a spiral emerges: you keep returning to position 1, but at a higher level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Bilal el issaoui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wpgcr9as350s.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23485100",
  "fulltext_url": null,
  "id": "2wpgcr9as350s",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23485100",
  "language": "eng",
  "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/23485100/files/The-Clock%20as%20a%20Mathematical%20Object.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wpgcr9as350s.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:20:50Z",
      "native_id": "23485100",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23485100"
    }
  ],
  "subjects": [],
  "title": "Architectural Framework for a Positional Clock System",
  "title_text": "Architectural Framework for a Positional Clock System",
  "type": "preprint",
  "updated_at": "2026-11-02T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2wpgcr9as350s",
  "venue": "Zenodo",
  "versions": []
}