{
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "configs_scanned": 416,
  "configs_with_definition_holes": 10,
  "definition_hole_entries": 65,
  "entries": [
    {
      "config": "lean/ComparatorChallenges/Brenier.json",
      "challenge_module": "ComparatorChallenges.Brenier",
      "solution_module": "OAI.Analysis.Brenier.Stability",
      "definition_names": [
        "OAI.Problem358.E",
        "OAI.Problem358.uniformMeasure",
        "OAI.Problem358.IsSupported",
        "OAI.Problem358.IsCoupling",
        "OAI.Problem358.quadraticPlanCost",
        "OAI.Problem358.wasserstein2",
        "OAI.Problem358.graphPlan",
        "OAI.Problem358.IsQuadraticOptimalMap",
        "OAI.Problem358.IsUniqueQuadraticOptimalMap",
        "OAI.Problem358.mapL2Dist",
        "OAI.Problem358.cube",
        "OAI.Problem358.HasExactlyThreeAtoms"
      ],
      "theorem_names": [
        "OAI.Problem358.one_third_stability",
        "OAI.Problem358.one_third_exponent_is_sharp"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/DefocusingNLS.json",
      "challenge_module": "ComparatorChallenges.DefocusingNLS",
      "solution_module": "OAI.MathematicalPhysics.DefocusingNLS.MainTheorems",
      "definition_names": [
        "OAI.DefocusingNLS.sobolevProduct",
        "OAI.DefocusingNLS.schrodingerFlow",
        "OAI.DefocusingNLS.sobolevOddPower"
      ],
      "theorem_names": [
        "OAI.DefocusingNLS.stable_blowup",
        "OAI.DefocusingNLS.gaussian_blowup",
        "OAI.DefocusingNLS.gaussian_not_almost_sure_global"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/ElementaryPositivity.json",
      "challenge_module": "ComparatorChallenges.ElementaryPositivity",
      "solution_module": "OAI.Combinatorics.Chromatic.Main",
      "definition_names": [
        "OAI.elementaryPositivityWitness"
      ],
      "theorem_names": [],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/EuclideanFiveColor.json",
      "challenge_module": "ComparatorChallenges.EuclideanFiveColor",
      "solution_module": "OAI.Geometry.PlaneColoring.Five",
      "definition_names": [
        "OAI.EuclideanFiveColor.ProperColoring"
      ],
      "theorem_names": [
        "OAI.EuclideanFiveColor.no_proper_five_coloring"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/KServer.json",
      "challenge_module": "ComparatorChallenges.KServer",
      "solution_module": "OAI.Combinatorics.KServer.Main",
      "definition_names": [
        "OAI.KServer.Configuration",
        "OAI.KServer.LabelDistribution",
        "OAI.KServer.Policy",
        "OAI.KServer.serve",
        "OAI.KServer.serviceCost",
        "OAI.KServer.pathProbability",
        "OAI.KServer.expectedCost",
        "OAI.KServer.optimalCost",
        "OAI.KServer.MainStatement"
      ],
      "theorem_names": [
        "OAI.KServer.main_theorem"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/LogspaceEquality.json",
      "challenge_module": "ComparatorChallenges.LogspaceEquality",
      "solution_module": "OAI.Computability.Logspace.Equality",
      "definition_names": [
        "OAI.ExactDerandomization.Word",
        "OAI.ExactDerandomization.Language",
        "OAI.ExactDerandomization.CoinTape",
        "OAI.ExactDerandomization.Direction.move",
        "OAI.ExactDerandomization.Direction.moveInput",
        "OAI.ExactDerandomization.readInput",
        "OAI.ExactDerandomization.Machine.initial",
        "OAI.ExactDerandomization.Machine.step",
        "OAI.ExactDerandomization.Machine.run",
        "OAI.ExactDerandomization.Machine.spaceThrough",
        "OAI.ExactDerandomization.Machine.LogSpace",
        "OAI.ExactDerandomization.Machine.Deterministic",
        "OAI.ExactDerandomization.Machine.HaltsBy",
        "OAI.ExactDerandomization.Machine.Decides",
        "OAI.ExactDerandomization.Machine.extendCoins",
        "OAI.ExactDerandomization.Machine.acceptanceProbability",
        "OAI.ExactDerandomization.polynomialClock",
        "OAI.ExactDerandomization.L",
        "OAI.ExactDerandomization.RL",
        "OAI.ExactDerandomization.BPL"
      ],
      "theorem_names": [
        "OAI.ExactDerandomization.exact_logarithmic_space_derandomization"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/Naimark.json",
      "challenge_module": "ComparatorChallenges.Naimark",
      "solution_module": "OAI.Analysis.Naimark.Tracial",
      "definition_names": [
        "OAI.NaimarkZFC.IsSimpleCStar",
        "OAI.NaimarkZFC.IsState",
        "OAI.NaimarkZFC.IsFaithfulTracialState",
        "OAI.NaimarkZFC.IsIrreducible",
        "OAI.NaimarkZFC.UnitarilyEquivalent",
        "OAI.NaimarkZFC.HasUniqueIrreducibleRepresentation",
        "OAI.NaimarkZFC.IsIsomorphicToCompacts"
      ],
      "theorem_names": [
        "OAI.NaimarkZFC.main"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/OccupiedOverlap.json",
      "challenge_module": "ComparatorChallenges.OccupiedOverlap",
      "solution_module": "OAI.RepresentationTheory.RowColumn.Occupied",
      "definition_names": [
        "OAI.CubeShuffle.UnitaryFinite.IsUnitary",
        "OAI.CubeShuffle.Specht.hilbertSpace",
        "OAI.CubeShuffle.Specht.unitaryRepresentation",
        "OAI.CubeShuffle.Specht.relabelledUnitary",
        "OAI.RowColumn.OccupiedOverlapEndpoint"
      ],
      "theorem_names": [
        "OAI.RowColumn.occupied_overlap_endpoint",
        "OAI.RowColumn.occupied_overlap"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/Rokhlin.json",
      "challenge_module": "ComparatorChallenges.Rokhlin",
      "solution_module": "OAI.Dynamics.MultipleMixing.Main",
      "definition_names": [
        "OAI.Rokhlin.timeMap",
        "OAI.Rokhlin.IsMixing",
        "OAI.Rokhlin.layoutTime",
        "OAI.Rokhlin.MixingOfOrder"
      ],
      "theorem_names": [
        "OAI.Rokhlin.mixing_all_finite_orders"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    },
    {
      "config": "lean/ComparatorChallenges/SpinAngle.json",
      "challenge_module": "ComparatorChallenges.SpinAngle",
      "solution_module": "OAI.RepresentationTheory.SpinAngle.TypeAngle",
      "definition_names": [
        "OAI.SpinAngle.TypeAngle.row",
        "OAI.SpinAngle.TypeAngle.column",
        "OAI.SpinAngle.TypeAngle.phi"
      ],
      "theorem_names": [
        "OAI.SpinAngle.TypeAngle.one_sided_type_angle"
      ],
      "semantic_review_status": "pending",
      "kernel_check_status": "not_run"
    }
  ],
  "primary_documentation": "https://github.com/leanprover/comparator",
  "interpretation": "Static declared definition holes are review obligations, not detected errors. Checker acceptance verifies specified structural/type/axiom conditions; intended mathematical meaning needs additional oversight. No kernel or semantic audit performed here."
}