{
  "schema_version": 1,
  "problem_number": "OWR-1315-001",
  "title": "Projective Units and Witt Vanishing for Stable Module Categories",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let G be a finite group and let k be any field of odd positive characteristic. We prove that the symmetric and skew-symmetric Cartan homomorphisms from the Witt groups of projective kG-modules to those of all finite-dimensional kG-modules are isomorphisms. The proof constructs a projective symmetric form whose module Witt class is the trivial line. An explicit middle-layer calculation supplies this form for groups with normal cyclic Sylow subgroups; Dress's classical 2-local induction theorem then gives it for arbitrary G. Tensoring by a projective lift of the unit inverts both Cartan maps. Balmer's kernel-cokernel formulas consequently imply W^i(kG-stab)=0 for every integer i. No splitting-field hypothesis is required. The scope is the ordinary contragredient duality in odd positive characteristic, not characteristic-two variants, Grothendieck-Witt groups, support restrictions or endotrivial twists. This is an AI-assisted, self-audited, unrefereed preprint. No independent expert review, proof-assistant verification or absolute priority is claimed.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.KT",
    "math.RT"
  ],
  "keywords": [
    "Witt group",
    "stable module category",
    "Cartan homomorphism",
    "Dress induction",
    "projective unit",
    "OWR-1315-001"
  ],
  "manuscript_version_date": "2026-10-19",
  "publication_date": "2026-10-19",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-19",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-1315-001/",
  "pdf_url": "https://eulersolve.org/papers/owr-1315-001/paper.pdf?v=87e7c42bc77e",
  "doi": "10.5281/zenodo.23481009",
  "zenodo_record_url": "https://zenodo.org/records/23481009",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Ordinary Witt Cartan isomorphisms and stable Witt vanishing for every finite group over every field of odd positive characteristic, without a splitting-field hypothesis. Dress's classical induction theorem and Balmer's kernel-cokernel formulas are explicitly credited. Characteristic two, Grothendieck-Witt groups, supports and endotrivial twists are not covered. Finite diagnostic checks supplement the written general proof. AI-assisted, self-audited and unrefereed; novelty is unestablished and no independent review, formal certification, dataset-maintainer acceptance or absolute priority is claimed.",
  "files": {
    "paper.pdf": {
      "sha256": "87e7c42bc77ee37aee63e7fa0318d013cedc75ded85f4b2be17a0ef1f99720ce"
    },
    "source.zip": {
      "sha256": "812f5172542b1f6d12dfbea3cdc428240535027875006c530d46807d93379bb9"
    },
    "verification_report.md": {
      "sha256": "9a8817df5ae4e3a475f026c7abeb8b303e511e96b89adec7da2f87a304828045"
    }
  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}