{
  "taskid": "08cac496dfa93874dd7d16893038da16b0d2dbc92f844d09512ca0cc78c03b46i0",
  "node": "t55",
  "claimid": "4dd439fff2558f60c630269bc9f0c5c77e00f4a1abd5e6a6c4c87dee1d2de753i0",
  "result": {
    "type": "triage",
    "conjecture": 55,
    "judgment": {
      "well_defined": true,
      "finitely_refutable": false,
      "finitely_refutable_reason": "The conjecture is an infinitary/asymptotic assertion (over all large parameters or an infinite family); a finite computation or finite counterexample cannot refute it.",
      "known_conflict": "none",
      "difficulty": 2,
      "importance": 2
    },
    "route": "literature",
    "note": "Transitive subtournament and order well defined; ceil(log2 n) + O(1) is a definite shape. Known status (corrected): the lower bound side is classical and proven - every n-vertex tournament contains a transitive subtournament of order >= log2 n + 1 (Erdos-Moser 1964). The upper bound side is only partially pinned: random tournaments / known constructions admit no transitive subtournament of order > (2 + o(1)) log2 n, and the matching first-moment heuristic sits at ~2 log2 n + 1 - this bounds the guaranteed order from above but does NOT establish tightness at log2 n. Hence the exact multiplicative constant lies in [1,2] and remains OPEN; the conjecture's 'and this order is optimal' clause is NOT settled. No known conflict with the literature is recorded: the ~2 log2 n upper bound is compatible with, and weaker than, the conjectured tightness - so this is recorded as current open status, not as a settled result and not as a conflict. Not finitely refutable: the O(1) constant is unspecified, so no finite counterexample can pin it down. Route literature: match against the classical log2 n lower bound (Erdos-Moser 1964) and the ~2 log2 n upper-bound constructions.",
    "hash": "2f273da81c33381ef6c9d9d9bc2e7206bcbf149d803279d95b1f7c38f1ad7032"
  },
  "hash": "f63be11c1d077cea6ac26f69a489dd44aa4bdf29cc4932cceaa91fbfe7fb317b",
  "childids": []
}