{
  "schema_version": 1,
  "problem_number": "AIM-REPRESENTATION_THEORY-0033",
  "title": "Central Obstructions and Block-Complement Categories for Schur Covers",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We study explicit ways to replace the symmetric-group automorphisms of the category of finite sets and injections by their Schur double covers. If the central involution acts freely on a finite lift fibre of an injection of codimension d, then the fibre cardinality is divisible by 2^(floor(d/4)+1). Thus free two-sheeted morphism lifts, and uniformly polynomial-sized lift fibres, are impossible. We construct an ordinary category using unordered families of internally ordered four-element complement blocks, and a complex superlinear category using two-element blocks. Their composition laws follow from explicit coherent even lifts; the phase needed for pairs is not a group-theoretic section. Finally, a coherent Clifford quotient of the fully framed model has kernel requiring new relations in every rank n >= 3, with quotient dimension (n-2)2^(n-2). Hence that model is not locally noetherian. Classical Schur, Clifford and spinoriality facts are credited. These results concern specified models; they do not establish a general spin representation-stability theory or settle the broad AIM construction program. This is an unrefereed preprint, with no absolute priority claim.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "keywords": [
    "AIM-REPRESENTATION_THEORY-0033",
    "Schur double covers",
    "Clifford algebras",
    "FI categories",
    "block complements",
    "noetherianity"
  ],
  "manuscript_version_date": "2026-10-16",
  "publication_date": "2026-10-16",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-16",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-representation_theory-0033/",
  "pdf_url": "https://eulersolve.org/papers/aim-representation_theory-0033/paper.pdf?v=8002a94f5a73",
  "doi": "10.5281/zenodo.23424378",
  "zenodo_record_url": "https://zenodo.org/records/23424378",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete theorems for explicitly specified Schur-cover models, not a solution of the broad AIM representation-stability construction program. The lift-fibre bound assumes a finite nonempty fibre and free central postaction. The ordinary four-block and superlinear two-block constructions are distinct; the scalar phase is not a group-theoretic section. Non-noetherianity is proved only for the fully framed model and is not transferred to the block categories. Classical Schur, Clifford and spinoriality results are credited. AI-assisted, self-audited and unrefereed; no absolute priority, independent review or formal verification is claimed.",
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      "sha256": "8002a94f5a7348ad922f1cb1c0d6e2d56f243e077141deb142d0147fbba1f088"
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    "source.zip": {
      "sha256": "a5e60a890b05c125796aaee444d80aed1c20dd9723a1ea81108d3111ca83fb4a"
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    "verification_report.md": {
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  "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."
}