{
  "schema_version": 1,
  "problem_number": "AIM-OTHER-0001",
  "title": "Full Linear Homomesy Spaces for Rowmotion on Rooted Forests",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For every finite rooted forest with minimal roots, we compute the full spaces of linear order-ideal and antichain statistics that have zero average on every rowmotion orbit. The algorithm retains the orbit through the empty ideal and two affine hulls, each represented by at most n+1 vectors, instead of enumerating the orbits. A deletion lemma for Cartesian products yields scalar recursions for both zero-mesy dimensions and an exact rational basis algorithm using O(n^4) field operations, apart from integer gcd/lcm operations. The two full homomesy dimensions agree; the zero-mesy dimensions can differ by one. A known acyclic-toggle theorem transfers the ideal-indicator result to Coxeter toggle actions.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.CO"
  ],
  "keywords": [
    "rowmotion",
    "rooted forest",
    "homomesy",
    "zero-mesy",
    "affine hull",
    "order ideal",
    "exact algorithm",
    "AIM-OTHER-0001",
    "math.CO"
  ],
  "manuscript_version_date": "2026-09-29",
  "publication_date": "2026-09-29",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-09-29",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-other-0001/",
  "pdf_url": "https://eulersolve.org/papers/aim-other-0001/paper.pdf?v=fd5dc1a76776",
  "doi": "10.5281/zenodo.23032063",
  "zenodo_record_url": "https://zenodo.org/records/23032063",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Rooted forests only; known orbit mechanisms and Coxeter transfer credited; possible folklore, no absolute priority. Self-audited and unrefereed, with AI assistance; no independent peer review or absolute priority is claimed.",
  "files": {
    "paper.pdf": {
      "sha256": "fd5dc1a76776554562a960ea8d056b1580913d03af5525886915caa8d1e91d66"
    },
    "source.zip": {
      "sha256": "9d8fa0d7270b2235250eb6a1f20b9fd0c9edcf35583cb3c326c12de6fd82718f"
    },
    "verification_report.md": {
      "sha256": "1ba0eaddd6b4af28bb01469a096aae31f16053109a258dfe67d66a27fec3110a"
    }
  },
  "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."
}