{
  "abstract": "We report a Lean 4 formal audit accompanying the paper \"Completing the Arakawa--Moreau Conjecture on Maximal Ideals of Affine Vertex Algebras\" (arXiv:2607.25249). In a single Lean source, the development kernel-checks the paper-local deductive architecture used for the new maximal-ideal cases: affine-kernel detection and lifting, extremal PBW-line deductions, finite Ramond--Casimir arithmetic and case enumerations, reduced-simplicity contradiction schemes, and the case-level affine conclusions for the level -1 D_l family and the positive-parameter cases of D4, E6, E7, and E8. It also audits the paper's alternative D_l level -2 argument and the separate rank-reduction application of Section 8. Previously published exceptional n=0 cases are not claimed as newly formalized results of this bundle. The released project builds successfully with the pinned Lean/Mathlib environment and contains live #print axioms queries for the principal final wrappers. The development does not reconstruct affine vertex algebras, minimal W-algebras, BRST/DS reduction, Ramond Zhu theory, or Li spectral flow from foundational definitions in Mathlib. Those ingredients, together with the concrete realization of case-specific representation-theoretic objects, are exposed as theorem parameters and semantic interfaces. Accordingly, the precise verification claim is a kernel-checked deduction of the paper-local proof from explicitly stated VOA/BRST/DS boundary inputs, rather than a from-scratch formalization of the ambient representation theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27952",
  "author_total": 1,
  "authors": [
    {
      "name": "Sihai Jin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2e6cjpa369mff.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27952",
  "fulltext_url": null,
  "id": "2e6cjpa369mff",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27952",
  "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.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214174568",
  "pdf_url": "https://arxiv.org/pdf/2609.27952",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2e6cjpa369mff.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27952",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27952"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Lean 4 Verification Report for Completing the Arakawa--Moreau Conjecture on Maximal Ideals of Affine Vertex Algebras",
  "title_text": "A Lean 4 Verification Report for Completing the Arakawa--Moreau Conjecture on Maximal Ideals of Affine Vertex Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2e6cjpa369mff",
  "venue": "arXiv",
  "versions": []
}