{
  "schema_version": 1,
  "problem_number": "AIM-ALGEBRAIC_GEOMETRY-0035",
  "title": "A Rank-One Obstruction for Odd-Primary Wood Equivalences",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let p be odd, h=(p-1)p^(r-1)m with r>=1 and m>1, and H=C_(p^r) a subgroup of the height-h Morava stabilizer. For Honda Morava E-theory over F_(p^h), put A=E^(hH). We prove that no finite p-local spectrum F satisfies A smash F equivalent to E as A-modules. More generally, if A smash F is equivalent to a nonzero finite wedge of q copies of E, then q>=2. No parity condition on the cells is required. The proof combines Ravenel's classical strict-stabilizer H^1 calculation, cyclotomic valuations, Galois base change, and an elementary modular-representation flag bound. An abstract rank-two matrix example shows the flag bound is optimal as a group-theoretic statement, without asserting a topological realization. The result concerns external finite-spectrum Wood equivalences only. Internal A-module filtrations, optimal realizable multiplicities, and the m=1,r>1 cases are not resolved; the broad source question AIM-ALGEBRAIC_GEOMETRY-0035 remains partially solved. This is an unrefereed preprint with AI assistance disclosed in ordinary prose. Classical inputs are credited; independent review, formal verification and absolute priority are not claimed.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.AT",
    "math.RT"
  ],
  "keywords": [
    "Wood equivalence",
    "Morava E-theory",
    "strict stabilizer",
    "Galois descent",
    "modular representation",
    "AIM-ALGEBRAIC_GEOMETRY-0035"
  ],
  "manuscript_version_date": "2026-10-15",
  "publication_date": "2026-10-15",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-15",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-algebraic-geometry-0035/",
  "pdf_url": "https://eulersolve.org/papers/aim-algebraic-geometry-0035/paper.pdf?v=13da5e6f8ae6",
  "doi": "10.5281/zenodo.23384092",
  "zenodo_record_url": "https://zenodo.org/records/23384092",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete external rank-one obstruction at odd p and h=(p-1)p^(r-1)m with m>1. The equivalence must be A-linear; no cell-parity assumption. Internal A-module filtrations, m=1 with r>1, and the optimal attainable multiplicity remain open. This does not resolve the whole AIM source question. Classical inputs are credited. Self-audited, unrefereed and AI-assisted; no absolute novelty, independent review or formal verification claimed.",
  "files": {
    "paper.pdf": {
      "sha256": "13da5e6f8ae644879ba3dbc542b198fa44e2037eade626627fa44db4d0c42095"
    },
    "source.zip": {
      "sha256": "2292669c0b1adf28b53b181d9ba2c98f0a6d773c5141b3abfa67ab14c7861cb0"
    },
    "verification_report.md": {
      "sha256": "4e9e49fed5a0cd3777ff68ed487e31306555ca015632e35ec8359e3f91db6347"
    }
  },
  "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."
}