{
  "schema_version": 1,
  "problem_number": "AIM-GEOMETRIC_GROUP_THEORY-0126",
  "title": "An Explicit Generating Pair for Radu's Simple Tree Lattice",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We give an explicit generating pair for the torsion-free infinite simple group in Corollary IV(ii) of Radu's paper on lattices in products of trees. The pair is x1*x3 and x1*y3. A short group calculation using only the first five displayed equations recovers every original generator. Thus this specific group has minimum generator number two. We also give a two-generator presentation with seven defining equations. This excludes one concrete candidate for a finitely presented simple group that is not two-generated; the general existence question remains unresolved. Simplicity and geometric structure are credited to Radu. The preprint is unrefereed and AI-assisted; no absolute priority, independent review or formal verification is claimed.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.GR"
  ],
  "keywords": [
    "simple groups",
    "generator rank",
    "lattices in products of trees",
    "explicit presentations",
    "combinatorial group theory",
    "AIM-GEOMETRIC_GROUP_THEORY-0126"
  ],
  "manuscript_version_date": "2026-10-14",
  "publication_date": "2026-10-14",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-14",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-geometric-group-theory-0126/",
  "pdf_url": "https://eulersolve.org/papers/aim-geometric-group-theory-0126/paper.pdf?v=638a3bbc5b0a",
  "doi": "10.5281/zenodo.23364044",
  "zenodo_record_url": "https://zenodo.org/records/23364044",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete proof of two-generation for the single group in Radu Corollary IV(ii), with an explicit equivalent presentation. The general AIM existence problem is not resolved. No new simplicity construction, minimal relation count, certified novelty, independent review or formal verification is claimed.",
  "files": {
    "paper.pdf": {
      "sha256": "638a3bbc5b0a46a91d68596ef7d3deea3438357d4416129b8dc88c5252e82424"
    },
    "source.zip": {
      "sha256": "dfd6bec35134f42a2aba04495e629eb48ec1a32402f1de1c1f55e595d7299293"
    },
    "verification_report.md": {
      "sha256": "76fba340c6274e0ec24e91fddf06e5cfe064f171b417694d78857732d7028ca4"
    }
  },
  "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."
}