{
  "abstract": "We extend the discrete complex complement quotient (DCCQ) framework from binary Bernoulli counts to multinomial count compositions. For m+1 categories, m is the number of independent probability degrees of freedom. Integer count vectors modulo common scaling determine rational points of the m-dimensional probability simplex. Building on standard simplex and log-ratio coordinate geometry, for m >= 2 we define the full multinomial DCCQ coordinate map and show that it is a real-analytic diffeomorphism The previously established binary baseline m=1 gives a critical-line coordinate, while the ternary case m=2 gives the full open critical strip; higher multinomial models retain m-2 additional real contrasts. We also give a one-versus-rest specialization, an exact integer-lattice realization of the ternary coordinate, and a hyperbolic representation of its log-ratio. No zero-location theorem or proof of the Riemann Hypothesis is claimed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17899",
  "author_total": 1,
  "authors": [
    {
      "name": "Y. Kenan Yılmaz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qt9nj301w42k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17899",
  "fulltext_url": null,
  "id": "7qt9nj301w42k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17899",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.17899",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qt9nj301w42k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17899",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17899"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Generalized DCCQ: From Binary Quotients to Multinomial Simplex Geometry and Critical-Strip Coordinates",
  "title_text": "Generalized DCCQ: From Binary Quotients to Multinomial Simplex Geometry and Critical-Strip Coordinates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/7qt9nj301w42k",
  "venue": "arXiv",
  "versions": []
}