{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1293",
  "content_hash": null,
  "slug": "commuting-nilpotent-subspace-m5-f2-status-20260801",
  "type": "claim",
  "title": "Current checked status and unresolved remainder",
  "summary": "As of 2026-08-01, Britnell and Wildon classify commuting nilpotent similarity classes, while the maximum-dimensional linear-subspace orbit classification over F_2 remains unverified. The unresolved target is: Prove the maximum possible dimension and exhibit a subspace attaining it. Give one canonical representative of every GL5(F2)-orbit at the maximum dimension, with a complete orbit or stabilizer certificate.",
  "relevance": "Records the strongest checked neighboring result and the exact remainder that later work must settle.",
  "relevance_source": "recorded",
  "body": "A dated review on 2026-08-01 checked the structured sources below, exact-title and exact-parameter searches, nearby formulations, and the current TheoremDB corpus. Britnell and Wildon classify commuting nilpotent similarity classes, while the maximum-dimensional linear-subspace orbit classification over F_2 remains unverified.\n\nA complete resolution must satisfy: Prove the maximum possible dimension and exhibit a subspace attaining it. Give one canonical representative of every GL5(F2)-orbit at the maximum dimension, with a complete orbit or stabilizer certificate.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1001.0811",
      "locator": "Dataset references and 2026-08-01 exact-parameter status search."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1001.0811",
    "locator": "Dataset references and 2026-08-01 exact-parameter status search."
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1292",
      "title": "Complete the stated acceptance conditions",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "commuting-nilpotent-subspace-m5-f2",
      "title": "commuting nilpotent subspace m5 f2",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}