{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R922",
  "content_hash": null,
  "slug": "abelian-square-free-uniform-morphism-minimum-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-31. An 85-uniform abelian-square-free endomorphism is known and was shown minimal inside its cyclic-symmetry form; the checked sources do not identify the unrestricted least modulus. Give an \\(L\\)-uniform morphism with a complete finite-test or direct proof that it preserves abelian-square-freeness, and prove that no such morphism exists for any smaller modulus.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-07-31. An 85-uniform abelian-square-free endomorphism is known and was shown minimal inside its cyclic-symmetry form; the checked sources do not identify the unrestricted least modulus.\n\nA complete resolution must satisfy this condition: Give an \\(L\\)-uniform morphism with a complete finite-test or direct proof that it preserves abelian-square-freeness, and prove that no such morphism exists for any smaller modulus.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1007/3-540-55719-9_62",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/3-540-55719-9_62",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "relations": [
    {
      "slug": "R921",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "abelian-square-free-uniform-morphism-minimum",
      "title": "abelian square free uniform morphism minimum",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}