{
  "definition1": {
    "edge_formula": "|E| = |E_G^X|(T+1) + |pa_G(S)|T + d(T+1) + dT",
    "exhaustive_d4": {
      "acyclic": 26064,
      "constructions": 26064,
      "edge_count_formula_matches": 26064,
      "edge_families_exactly_as_defined": 26064,
      "node_count_formula_matches": 26064
    },
    "node_formula": "|V| = 2d(T+1) + T",
    "random_large": {
      "acyclic": 60,
      "constructions": 60,
      "edge_count_matches": 60,
      "max_edges": 360,
      "max_nodes": 245,
      "node_count_matches": 60
    }
  },
  "dsep_claims": {
    "Ts": [
      1,
      2,
      3
    ],
    "control_naive": {
      "agreement": 0.931087811819856,
      "mismatches": 98787,
      "tested": 1433520
    },
    "control_no_inheritance": {
      "lemma1_converse_failures_without_inheritance": 0,
      "tested": 477840
    },
    "d": 4,
    "lemma1": {
      "converse_failure_witnesses": 17712,
      "tested": 1433520,
      "violations": 0
    },
    "n_models": 8688,
    "n_triples_per_model": 55,
    "per_T": {
      "1": {
        "control_naive_Sdeleted_mismatches": 32929,
        "lemma1_converse_failures": 5904,
        "lemma1_tested": 477840,
        "lemma1_violations": 0,
        "theorem1_tested": 477840,
        "theorem1_violations": 0
      },
      "2": {
        "control_naive_Sdeleted_mismatches": 32929,
        "lemma1_converse_failures": 5904,
        "lemma1_tested": 477840,
        "lemma1_violations": 0,
        "theorem1_tested": 477840,
        "theorem1_violations": 0
      },
      "3": {
        "control_naive_Sdeleted_mismatches": 32929,
        "lemma1_converse_failures": 5904,
        "lemma1_tested": 477840,
        "lemma1_violations": 0,
        "theorem1_tested": 477840,
        "theorem1_violations": 0
      }
    },
    "theorem1": {
      "agreement": 1.0,
      "tested": 1433520,
      "violations": 0
    },
    "theorem1_implication1_T_invariance": {
      "Ts_compared": [
        1,
        2,
        3,
        4
      ],
      "models": 8688,
      "models_whose_dsep_set_changes_with_T": 0
    },
    "theorem1_implication2_degenerate": {
      "models_where_Gplus_equals_G_minus_S": 543,
      "models_with_no_selection_parents": 543
    }
  },
  "random_sweep": {
    "Ts": [
      1,
      2,
      3,
      5
    ],
    "control_naive_Sdeleted_mismatches": 2876,
    "ds": [
      5,
      6,
      7,
      8,
      9,
      10
    ],
    "dsep_relations_tested": 143811,
    "lemma1_converse_failures": 1586,
    "lemma1_violations": 0,
    "models_per_d": 40,
    "theorem1_violations": 0,
    "theorem2_adjacency_pairs": 6200,
    "theorem2_adjacency_violations": 0,
    "theorem2_orientation_violations": 0,
    "theorem2_oriented_edges": 779
  },
  "theorem2": {
    "adjacency_pairs_tested": 52128,
    "adjacency_violations": 0,
    "d": 4,
    "n_distinct_cpdags": 185,
    "n_models": 8688,
    "orientation_completeness_failures": 0,
    "orientation_soundness_violations": 0,
    "oriented_edges_tested": 2640,
    "oriented_edges_whose_head_is_in_an(S)": 0,
    "unoriented_edges_tested": 39030
  },
  "theorem2_control": {
    "checker_fired": 328,
    "corrupted_models_tested": 328
  },
  "theorem4": {
    "additional_oriented_edges_vs_single_domain": 172512,
    "adjacency_violations": 0,
    "configurations_with_strictly_more_orientations": 88176,
    "control_no_anS_expansion": {
      "configurations": 269328,
      "orientation_soundness_violations": 583356
    },
    "d": 4,
    "frac_strict_improvement": 0.327392621636072,
    "model_x_Iset_configurations": 269328,
    "monotonicity_violations": 0,
    "n_I_sets": 31,
    "n_models": 8688,
    "orientation_soundness_violations": 0,
    "total_oriented_edges_multi_domain": 254352
  }
}