{
  "schema_version": 1,
  "problem_number": "OWR-14299097-016",
  "title": "A Quotient Obstruction to Strict Character Exponents in Almost Quasisimple Groups",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "A workshop problem asks for an exponent 0 <= alpha(g) < 1 such that |chi(g)| <= chi(1)^alpha(g) for every irreducible complex character of a finite almost quasisimple group and every noncentral element g. The unrestricted formulation has an elementary quotient obstruction. The almost simple group PGammaL_3(4) has quotient S_3 by PSL_3(4). Inflating the irreducible degree-two character of this quotient gives value 2 at a noncentral transvection, so no exponent below 1 exists. More generally, if H is the inverse image of the simple socle in G/Z(G) and E=H', the required exponents exist at all noncentral elements exactly when G/E is abelian. In that case we give the explicit, deliberately weak exponent 1-16/(ord(g)^2 |G| log |G|). This is a correction to the all-character formulation, not an improvement on optimal character bounds for quasisimple groups. The construction uses classical methods; novelty and priority are not certified. This is an unrefereed preprint, with AI assistance disclosed in the text.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "keywords": [
    "OWR-14299097-016",
    "math.RT",
    "math.GR"
  ],
  "manuscript_version_date": "2026-10-21",
  "publication_date": "2026-10-23",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-23",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-14299097-016/",
  "pdf_url": "https://eulersolve.org/papers/owr-14299097-016/paper.pdf?v=d1a77c2d4dc6",
  "doi": "10.5281/zenodo.23585977",
  "zenodo_record_url": "https://zenodo.org/records/23585977",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "The unrestricted all-character existence assertion in Problem 1 is false: PGammaL_3(4)/PSL_3(4) is S_3, whose inflated degree-two irreducible character equals two at the noncentral transvection [I+E_12]. No alpha<1 works. For an almost quasisimple G, with E the derived subgroup of the preimage of its simple socle, existence at every noncentral element is equivalent to G/E being abelian. An elementary weak exponent is proved in that repaired setting. Optimal faithful-character bounds and the quoted quasisimple theorems are not resolved or contradicted. This is a self-audited, AI-assisted, unrefereed preprint. No independent certification, formal proof verification or absolute-priority claim is made.",
  "files": {
    "paper.pdf": {
      "sha256": "d1a77c2d4dc6fdc2cce1c7089bf010bbe12c769823619a6bbd6d6a144ddade45"
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    "source.zip": {
      "sha256": "1de2e13d98d3e73a4aad30b401304bc55dc074148adccbc3ba59fe6c2eaf01ee"
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    "verification_report.md": {
      "sha256": "0cef6f893ecbd42a9eea9e91c9278132bc6390b76d2a2ab679d73d9692f922df"
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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."
}