{
  "abstract": "We study filter-Laver forcing on omegaxomega with successor sets containing final quadrants. The observation retaining the minimum coordinate and orientation is a complete projection. Its finite nontrivial hidden-label quotients are Cohen, whereas the full offset quotient has Boolean density equal to the ground-model dominating number dV . For the associated grid-meager ideal I_box, we prove cov(I_box) = add(M) for the usual meager ideal M, and obtain further cardinal bounds. We also analyze threshold games, oracle degrees and the distinction between positive and filter-large certificate sets: recurrent filter-large acceptance admits refinements whose every branch succeeds. As an arithmetic application, we prove Wilfs inequality c \\leq 13e for numerical semigroups with thirteen elements below the conductor c, where eis the embedding dimension. A complete arithmetic proof, including a bounded exact computation, is given in the appendix. Its terminating certificate procedures supply a computable quadrant tree and uniform refinements for every forcing condition. Finite support kernels describe persistence of the registered proofs; arithmetic absoluteness explains precisely why forcing organizes these certificates without replacing their arithmetic justification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32078",
  "author_total": 1,
  "authors": [
    {
      "name": "Michel Gaspar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rtg21n19ctfa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32078",
  "fulltext_url": null,
  "id": "8rtg21n19ctfa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32078",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214718099",
  "pdf_url": "https://arxiv.org/pdf/2609.32078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rtg21n19ctfa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Oracle-Tree Forcing and Wilfs Inequality for Thirteen Left Elements",
  "title_text": "Oracle-Tree Forcing and Wilfs Inequality for Thirteen Left Elements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8rtg21n19ctfa",
  "venue": "arXiv",
  "versions": []
}