{
  "schema_version": 1,
  "problem_number": "AIM-OTHER-0011",
  "title": "Corner Itineraries and Resonance of ASM Superpromotion",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We construct an explicit binary-word factor of Striker-Williams superpromotion on alternating sign matrices of order n. The membership indicator of a specified corner of the ASM poset returns after 3n-2 steps. Its itinerary of that length therefore intertwines superpromotion with cyclic rotation. For n >= 3, rotation on the image has effective order exactly 3n-2; the n = 2 exception has effective order 2. The proof combines a face-stratum bijection with time-shift recombination on the tetrahedral poset and does not enumerate full orbits. Evaluation takes O(n^4) elementary toggle tests. This is a dynamical itinerary factor, not a static noncrossing model or the proposed order-polytope projection.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.CO"
  ],
  "keywords": [
    "alternating sign matrices",
    "superpromotion",
    "resonance",
    "poset toggles",
    "binary words",
    "AIM-OTHER-0011"
  ],
  "manuscript_version_date": "2026-10-05",
  "publication_date": "2026-10-05",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-05",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-other-0011/",
  "pdf_url": "https://eulersolve.org/papers/aim-other-0011/paper.pdf?v=94dbc7d4f0ad",
  "doi": "10.5281/zenodo.23160691",
  "zenodo_record_url": "https://zenodo.org/records/23160691",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete proof of the dynamical corner-factor theorem for ASM superpromotion, associated with AIM Problem 2.7 and UnsolvedMath AIM-OTHER-0011. No static noncrossing model, independent characterization of all image words, order-polytope projection or full-action periodicity is claimed. The whole source record is not counted as closed. The ASM poset, superpromotion, empty/full-ideal orbit and general resonance framework are credited prior work. The arbitrary-n proof is separate from finite exact regression evidence. Novelty and absolute priority remain undetermined after a bounded primary-source search. AI-assisted, self-audited and unrefereed; no independent review or proof-assistant formalization is claimed.",
  "files": {
    "paper.pdf": {
      "sha256": "94dbc7d4f0ad9a42a0a7429fb9cbec7bd9746cbd4a66de53c9bd7de704f6cdd0"
    },
    "source.zip": {
      "sha256": "ca67317cd6f61e2a72d1eb778323d548f93098f7b1c86556fb6344b4d140c23e"
    },
    "verification_report.md": {
      "sha256": "7275a0bc1235076ada693b6a91a2366b7b926d9e3612d19888872c216bbd7149"
    }
  },
  "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."
}