{
  "abstract": "This record presents Version 2.0 of the deterministic cascade framework, providing a formalized combinatorial model for composite number generation and prime void preservation across short quadratic intervals I_n = (n^2, (n+1)^2).\n\nKey Updates & Formal Results in Version 2.0:\n\nZero-Redundancy Multiplier Partitioning: Implements an exact canonical factor decomposition C = p \\cdot m subject to \\min(\\mathbb{P}(m)) \\ge p, eliminating composite coordinate overlap and bypassing traditional inclusion-exclusion parity barriers.\n\nThe X/3 Late-Born Cutoff Invariance: Demonstrates that for X = (n+1)^2, primes strictly exceeding X/3 cannot instantiate odd composite branches below X (as 3p > X), proving that target quadratic intervals lie entirely within an inactive generator zone and restricting active generators strictly to p \\le n.\n\nMultiplier Horizon Sparsity & Collision Dynamics: Details branch step dilation (2p > \\sqrt{8n}) for upper generators (\\sqrt{2n} < p \\le n), forcing active multiplier sets \\mathcal{M}(p, n) into singleton or empty states under canonical filtering.\n\nEmpirical Validation (n \\in [9, 200]): Provides exact computational data confirming that composite saturation remains structurally capped (\\le 83.5\\%) while prime voids scale monotonically from N_{\\text{void}} = 3 up to 33.\n\nAnalytical Research Target: Outlines the remaining objective to establish an unconditional proof of Legendre's Conjecture by bounding prime gap variance via exponential phase sums.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Naresh Sharma"
    },
    {
      "name": "Naresh Sharma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/egx6n0cz9aa63.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23419683",
  "fulltext_url": null,
  "id": "egx6n0cz9aa63",
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  "landing_url": "https://zenodo.org/records/23419683",
  "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/",
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  "pdf_url": "https://zenodo.org/api/records/23419683/files/Untitled%20document%20(3).pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/egx6n0cz9aa63.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "23419683",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23419683"
    }
  ],
  "subjects": [],
  "title": "A Deterministic Cascade Framework: Generator Partitioning, Upper-Zone Dynamics, and Prime Void Persistence in Quadratic Intervals",
  "title_text": "A Deterministic Cascade Framework: Generator Partitioning, Upper-Zone Dynamics, and Prime Void Persistence in Quadratic Intervals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:39Z",
  "url": "https://research.draconitic.com/paper/egx6n0cz9aa63",
  "venue": "Zenodo",
  "versions": []
}