{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R622",
  "content_hash": null,
  "slug": "qafp-attempt-trivial-automorphism-preprint",
  "type": "attempt",
  "title": "The 2017 triviality claim was withdrawn after a computational error",
  "summary": "The arXiv record says a crucial mistake was found, so this fixture retains the peer-reviewed order-two bound and the involution case.",
  "relevance": "For A binary q-analog of the Fano plane, record qafp-attempt-trivial-automorphism-preprint (“The 2017 triviality claim was withdrawn after a computational error”) documents a concrete method, search boundary, or failed route. The record states: The arXiv record says a crucial mistake was found, so this fixture retains the peer-reviewed order-two bound and the involution case.",
  "relevance_source": "recorded",
  "body": "A 2017 arXiv preprint by Bamberg, Ihringer, Lansdown, and Royle claimed that every binary q-Fano plane has trivial automorphism group. Its current arXiv record marks the paper withdrawn and states that a crucial mistake was found in the computations. No conclusion from that computation is used here.\n\nLater peer-reviewed work in 2022 states the established conclusion as at most one nonidentity automorphism. Kurz's 2025 survey repeats the alternative that the group is trivial or has order two. This dataset therefore keeps the peer-reviewed order-two bound and preserves the withdrawn preprint as a negative research trace.",
  "status": "failed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the possible automorphism groups of a binary q-Fano plane",
    "bounds": {
      "field_order": {
        "min": 2,
        "max": 2
      },
      "ambient_dimension": {
        "min": 7,
        "max": 7
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1709.05145v2",
      "locator": "Bamberg, Ihringer, Lansdown, and Royle, The binary q-analogue of the Fano plane has a trivial automorphism group, arXiv:1709.05145v2, withdrawn; the arXiv record states that a crucial mistake was found in the computations"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1709.05145v2",
    "locator": "Bamberg, Ihringer, Lansdown, and Royle, The binary q-analogue of the Fano plane has a trivial automorphism group, arXiv:1709.05145v2, withdrawn; the arXiv record states that a crucial mistake was found in the computations"
  },
  "models": [],
  "relations": [
    {
      "slug": "R626",
      "title": "Any solution has at most one nonidentity automorphism and tightly fixed intersections",
      "object_type": "claim",
      "relation": "qualifies",
      "direction": "outgoing"
    },
    {
      "slug": "q-analog-fano-plane",
      "title": "q analog fano plane",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}