{
  "schema_version": 1,
  "problem_number": "AIM-GEOMETRIC_GROUP_THEORY-0024",
  "title": "A Compact Cubulation of a Quadratic Free-by-Cyclic Group",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let phi be the automorphism of F(a,b,c) given by phi(a)=a, phi(b)=ab and phi(c)=bcb. We construct a compact nonpositively curved cube complex with fundamental group F(a,b,c) semidirect_phi Z. It has one vertex, seven edges, eight squares and two three-dimensional cubes. Its universal cover gives a free, proper, cocompact action on a three-dimensional CAT(0) cube complex. The construction uses an explicit four-vertex cyclic core and a cubical involution; all link and presentation calculations are supplied. This answers the literal ab formulation in frozen UnsolvedMath record AIM-GEOMETRIC_GROUP_THEORY-0024. It does not address the distinct aba formulation in the workshop report. AI-assisted, self-audited and unrefereed; no absolute-priority or proof-assistant certification claim.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "keywords": [
    "free-by-cyclic group",
    "CAT(0) cube complex",
    "cocompact cubulation",
    "local isometry",
    "nonpositive curvature",
    "AIM-GEOMETRIC_GROUP_THEORY-0024"
  ],
  "manuscript_version_date": "2026-10-18",
  "publication_date": "2026-10-18",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-18",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-geometric-group-theory-0024/",
  "pdf_url": "https://eulersolve.org/papers/aim-geometric-group-theory-0024/paper.pdf?v=a30c5e5705c7",
  "doi": "10.5281/zenodo.23446961",
  "zenodo_record_url": "https://zenodo.org/records/23446961",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "The proof treats the exact frozen mapping torus a->a, b->ab, c->bcb. The distinct b->aba workshop example is not resolved. The current live AIM page was not newly verified; the manuscript documents the frozen-source/workshop discrepancy. Minimal cubical dimension, virtual specialness and all fast mapping tori are not claimed. AI-assisted, self-audited and unrefereed; no independent review, proof-assistant certification or absolute-priority claim.",
  "files": {
    "paper.pdf": {
      "sha256": "a30c5e5705c7e52a948bf5140fc66021a5aa353e63cfb1273ffe8a0c309b9c15"
    },
    "source.zip": {
      "sha256": "f6df85c50259753b60fc50dd06eb5cf40ca12d2bcd3601a57638f4cd794dea52"
    },
    "verification_report.md": {
      "sha256": "886f22c8e4790825cdd8744fc864bd2ff82502b0a0fc2a1db9ad77208c138a52"
    }
  },
  "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."
}