{
  "embedding_params": {
    "feature_scale": 1.0,
    "packing_ratio": 6.0,
    "separation_ratio": 6.0,
    "target_packing_distance": 6.0,
    "hard_min_clearance_ratio": 0.2,
    "hard_min_clearance": 0.2,
    "target_min_separation": 0.2,
    "preferred_min_separation": 0.95,
    "preferred_min_separation_ratio": 0.95,
    "noise_ratio": 0.09652383098212883,
    "sampling_density_per_feature": 22.480349419906897,
    "edge_length_jitter_ratio": 0.0268596442155722,
    "branch_angle_spread": 1.0488208700783428
  },
  "embedding_dimension": 3,
  "requested_embedding_dimension": 3,
  "feature_thickness_ratio": 0.6325002238858191,
  "feature_thickness_budget": 0.6325002238858191,
  "tube_sampling_mode": "solid",
  "num_components": 1,
  "component_gap_ratio": 7.7142379593186305,
  "component_node_ids": [
    [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11
    ]
  ],
  "component_x_intervals": [
    [
      0.0,
      7.452010909815265
    ]
  ],
  "component_topology_classes": [
    "multi_cycle"
  ],
  "crowding_r": 0.00738657767141805,
  "crowding_gamma": 0.9926872881052962,
  "crowding_gamma_min": 0.01,
  "crowding_admissibility_epsilon_sep": 0.14934496157409435,
  "thickness_aware_min_required_clearance": 0.02,
  "thickness_crowding_order": "choose_tube_radius_then_apply_thickness_aware_crowding",
  "cycle_tree_edges": [
    [
      0,
      1
    ]
  ],
  "cycle_lengths": {
    "0": 7,
    "1": 4
  },
  "pair_separations": {
    "(0, 1)": 2
  },
  "cycle_nodes": {
    "0": [
      0,
      1,
      2,
      3,
      4,
      5,
      6
    ],
    "1": [
      7,
      8,
      9,
      10
    ]
  },
  "cycle_motifs": {
    "0": {
      "cycle_id": 0,
      "original_cycle_length": 7,
      "original_motif_vertices": [
        0,
        1,
        2,
        3,
        4,
        5,
        6
      ],
      "final_nodes": [
        0,
        1,
        2,
        3,
        4,
        5,
        6
      ]
    },
    "1": {
      "cycle_id": 1,
      "original_cycle_length": 4,
      "original_motif_vertices": [
        7,
        8,
        9,
        10
      ],
      "final_nodes": [
        7,
        8,
        9,
        10
      ]
    }
  },
  "attachments": [
    {
      "cycle_pair": [
        0,
        1
      ],
      "separation": 2,
      "attachment_type": "path",
      "anchor_a": 3,
      "anchor_b": 9,
      "path_nodes": [
        3,
        11,
        9
      ]
    }
  ],
  "edge_cycle_membership": {
    "(0, 1)": [
      0
    ],
    "(1, 2)": [
      0
    ],
    "(2, 3)": [
      0
    ],
    "(3, 4)": [
      0
    ],
    "(4, 5)": [
      0
    ],
    "(5, 6)": [
      0
    ],
    "(0, 6)": [
      0
    ],
    "(7, 8)": [
      1
    ],
    "(8, 9)": [
      1
    ],
    "(9, 10)": [
      1
    ],
    "(7, 10)": [
      1
    ]
  },
  "num_cycles_ground_truth": 2,
  "betti_1": 2,
  "leaf_count": 0,
  "branch_nodes": [
    3,
    9
  ],
  "is_planar": true,
  "max_edge_cycle_multiplicity": 1,
  "branch_params": {
    "num_initial_attachment_sites": 0,
    "max_branch_depth": 1,
    "promotion_prob": 0.5284865675084447,
    "children_per_branch_point_range": [
      1,
      3
    ],
    "branch_length_range": [
      1,
      4
    ],
    "max_degree": 4,
    "max_total_nodes": 80,
    "max_total_edges": 88
  },
  "branch_attachment_nodes_initial": [],
  "branch_generation_nodes": {
    "1": []
  },
  "branch_parent_map": {},
  "branch_root_map": {},
  "branch_depth_map": {},
  "num_leaves_after_branching": 0,
  "num_branch_nodes_after_branching": 2,
  "betti_1_after_branching": 2,
  "embedding_valid": true,
  "embedding_dimensions_attempted": [
    3
  ],
  "embedding_attempt_history": [
    {
      "dimension": 3,
      "embedding_valid": true,
      "global_embedding_attempts": 1,
      "local_placement_rejections": 0,
      "min_nonadjacent_node_distance": 3.1217997248929814,
      "min_nonincident_edge_distance": 3.1217997248929814,
      "min_nonincident_node_edge_distance": 3.1217997248929814,
      "failure_reason": null,
      "refinement_applied": true,
      "refinement_iterations": 24,
      "refinement_objective_delta": -16.108364933171174,
      "refinement_clearance_delta": 0.14660577291526256
    }
  ],
  "embedding_constructive_success": true,
  "embedding_rejected": false,
  "min_nonadjacent_node_distance": 3.1217997248929814,
  "min_nonincident_edge_distance": 3.1217997248929814,
  "min_nonincident_node_edge_distance": 3.1217997248929814,
  "global_embedding_attempts": 1,
  "total_global_embedding_attempts": 1,
  "local_placement_rejections": 0,
  "embedding_fallback_used": false,
  "embedding_fallback_mode": null,
  "embedding_refinement": {
    "enabled": true,
    "applied": true,
    "iterations": 24,
    "objective_before": 104.89154170013279,
    "objective_after": 88.78317676696162,
    "objective_delta": -16.108364933171174,
    "clearance_before": 2.975193951977719,
    "clearance_after": 3.1217997248929814,
    "clearance_delta": 0.14660577291526256,
    "accepted_steps": 24,
    "reason": "accepted"
  },
  "topology_class": "multi_cycle",
  "sampled_topology_spec": {
    "topology_class": "multi_cycle",
    "children_per_branch_point_range": [
      1,
      3
    ],
    "branch_length_range": [
      1,
      4
    ],
    "max_branch_depth_range": [
      1,
      2
    ],
    "promotion_prob_range": [
      0.2,
      0.6
    ],
    "max_degree": 4,
    "num_cycles": 2,
    "branch_attach_count": 0
  },
  "tube_embedding_separation_ratio": 6.0,
  "realized_post_crowding_min_nonadjacent_node_distance": 3.116753090485388,
  "realized_post_crowding_min_nonincident_edge_distance": 3.1167530904853886,
  "realized_post_crowding_min_nonincident_node_edge_distance": 3.116753090485388,
  "realized_post_crowding_min_structural_distance": 3.116753090485388,
  "realized_post_crowding_separation_to_feature_scale": 3.116753090485388,
  "realized_post_crowding_separation_to_post_median_edge": 3.0984839011215404,
  "realized_post_crowding_absolute_hardness": 0.32084671803253584,
  "minimum_realized_component_gap": Infinity,
  "feature_thickness_radius": 0.06467248078704718,
  "effective_max_tube_radius_for_sampling": 0.10224894528847164,
  "cycle_hole_radius_cap": 0.10224894528847164,
  "cycle_hole_radius_fraction": 0.2,
  "crowding_applied": true,
  "crowding_isotropy_epsilon": 0.05,
  "crowding_axis": [
    -0.7699633051657313,
    0.5645041608525866,
    0.29747531171238367
  ],
  "crowding_centroid": [
    4.252262325008549,
    1.545495347827875,
    0.7722703682216788
  ],
  "crowding_covariance_eigenvalues": [
    12.689729912883575,
    0.4487917965565437,
    0.10123644974300827
  ],
  "crowding_covariance_matrix": [
    [
      7.569967379651435,
      -5.485815749429281,
      -2.8414575336082453
    ],
    [
      -5.485815749429281,
      4.148263672079652,
      2.0096336846027953
    ],
    [
      -2.8414575336082453,
      2.0096336846027953,
      1.5215271074520382
    ]
  ],
  "crowding_isotropic_fallback_used": false,
  "crowding_linear_operator": [
    [
      0.9970225817558361,
      -0.0031784518662494447,
      -0.0016749406386081004
    ],
    [
      -0.0031784518662494447,
      0.9950175930581813,
      0.001227994832132739
    ],
    [
      -0.0016749406386081004,
      0.001227994832132739,
      0.9933344013965749
    ]
  ],
  "crowding_model_dimension": 3,
  "feature_scale_nominal": 1.0,
  "feature_scale_pre_crowding": 1.009242905585118,
  "feature_scale_post_crowding_median_edge": 1.0058961704972018,
  "pre_crowding_edge_length_summary": {
    "min": 0.998226574294811,
    "median": 1.009242905585118,
    "mean": 1.3108609730196896,
    "max": 4.719090303932466
  },
  "post_crowding_edge_length_summary": {
    "min": 0.9968251983263513,
    "median": 1.0058961704972018,
    "mean": 1.3075556098915408,
    "max": 4.718724868300539
  },
  "pre_crowding_min_nonadjacent_node_distance": 3.121799724892981,
  "pre_crowding_min_nonincident_edge_distance": 3.1217997248929814,
  "pre_crowding_min_nonincident_node_edge_distance": 3.121799724892981,
  "crowding_gamma_min_search_tolerance": 0.005,
  "crowding_gamma_min_search_history": [
    {
      "gamma": 0.01,
      "admissible": true,
      "realized_separation_ratio": 2.728915746991191
    },
    {
      "gamma": 1.0,
      "admissible": true,
      "realized_separation_ratio": 3.093209481698649
    }
  ],
  "crowding_gamma_min_search_iterations": 2,
  "crowding_gamma_min_search_bracket": [
    0.01,
    1.0
  ],
  "crowding_relative_budget_definition": "gamma = 1 - r * (1 - gamma_min)",
  "requested_noise_ratio": 0.09652383098212883,
  "realized_noise_ratio": 0.09652383098212883,
  "max_admissible_noise_ratio_after_crowding": 0.49456802148521567,
  "requested_crowding_r": 0.00738657767141805,
  "realized_crowding_r": 0.00738657767141805,
  "staged_generation_order": "topology -> max-separation embedding -> admissible thickness -> thickness-constrained crowding -> clearance-capped noise -> sampling",
  "tube_no_overlap_required_centerline_clearance": 0.5354402855026097,
  "tube_no_overlap_post_crowding_margin": 2.5813128049827787,
  "tube_no_overlap_satisfied": true,
  "tube_no_overlap_constraint_active": true,
  "max_admissible_tube_radius_after_crowding": 1.3553288832784365,
  "realized_tube_radius_budget_fraction": 0.047717186274824616,
  "point_cloud_params": {
    "feature_scale": 1.0,
    "sampling_density_per_feature": 22.480349419906897,
    "noise_ratio": 0.09652383098212883,
    "sigma": 0.09652383098212883,
    "embedding_dimension": 3,
    "include_node_points": true,
    "include_junction_points": true,
    "node_tube_sampling_policy": "edge_tubes_only_except_isolated_nodes",
    "min_points_per_edge": 2,
    "density_jitter_ratio_range": [
      0.0,
      0.15
    ],
    "endpoint_sampling_mode": "include",
    "feature_thickness_ratio": 0.06467248078704718,
    "feature_thickness_radius": 0.06467248078704718,
    "tube_sampling_mode": "solid"
  },
  "num_clean_points": 395,
  "num_edge_sampled_points": 383,
  "num_node_sampled_points": 12,
  "point_component_id": [
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0
  ],
  "component_point_ids": [
    [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      21,
      22,
      23,
      24,
      25,
      26,
      27,
      28,
      29,
      30,
      31,
      32,
      33,
      34,
      35,
      36,
      37,
      38,
      39,
      40,
      41,
      42,
      43,
      44,
      45,
      46,
      47,
      48,
      49,
      50,
      51,
      52,
      53,
      54,
      55,
      56,
      57,
      58,
      59,
      60,
      61,
      62,
      63,
      64,
      65,
      66,
      67,
      68,
      69,
      70,
      71,
      72,
      73,
      74,
      75,
      76,
      77,
      78,
      79,
      80,
      81,
      82,
      83,
      84,
      85,
      86,
      87,
      88,
      89,
      90,
      91,
      92,
      93,
      94,
      95,
      96,
      97,
      98,
      99,
      100,
      101,
      102,
      103,
      104,
      105,
      106,
      107,
      108,
      109,
      110,
      111,
      112,
      113,
      114,
      115,
      116,
      117,
      118,
      119,
      120,
      121,
      122,
      123,
      124,
      125,
      126,
      127,
      128,
      129,
      130,
      131,
      132,
      133,
      134,
      135,
      136,
      137,
      138,
      139,
      140,
      141,
      142,
      143,
      144,
      145,
      146,
      147,
      148,
      149,
      150,
      151,
      152,
      153,
      154,
      155,
      156,
      157,
      158,
      159,
      160,
      161,
      162,
      163,
      164,
      165,
      166,
      167,
      168,
      169,
      170,
      171,
      172,
      173,
      174,
      175,
      176,
      177,
      178,
      179,
      180,
      181,
      182,
      183,
      184,
      185,
      186,
      187,
      188,
      189,
      190,
      191,
      192,
      193,
      194,
      195,
      196,
      197,
      198,
      199,
      200,
      201,
      202,
      203,
      204,
      205,
      206,
      207,
      208,
      209,
      210,
      211,
      212,
      213,
      214,
      215,
      216,
      217,
      218,
      219,
      220,
      221,
      222,
      223,
      224,
      225,
      226,
      227,
      228,
      229,
      230,
      231,
      232,
      233,
      234,
      235,
      236,
      237,
      238,
      239,
      240,
      241,
      242,
      243,
      244,
      245,
      246,
      247,
      248,
      249,
      250,
      251,
      252,
      253,
      254,
      255,
      256,
      257,
      258,
      259,
      260,
      261,
      262,
      263,
      264,
      265,
      266,
      267,
      268,
      269,
      270,
      271,
      272,
      273,
      274,
      275,
      276,
      277,
      278,
      279,
      280,
      281,
      282,
      283,
      284,
      285,
      286,
      287,
      288,
      289,
      290,
      291,
      292,
      293,
      294,
      295,
      296,
      297,
      298,
      299,
      300,
      301,
      302,
      303,
      304,
      305,
      306,
      307,
      308,
      309,
      310,
      311,
      312,
      313,
      314,
      315,
      316,
      317,
      318,
      319,
      320,
      321,
      322,
      323,
      324,
      325,
      326,
      327,
      328,
      329,
      330,
      331,
      332,
      333,
      334,
      335,
      336,
      337,
      338,
      339,
      340,
      341,
      342,
      343,
      344,
      345,
      346,
      347,
      348,
      349,
      350,
      351,
      352,
      353,
      354,
      355,
      356,
      357,
      358,
      359,
      360,
      361,
      362,
      363,
      364,
      365,
      366,
      367,
      368,
      369,
      370,
      371,
      372,
      373,
      374,
      375,
      376,
      377,
      378,
      379,
      380,
      381,
      382,
      383,
      384,
      385,
      386,
      387,
      388,
      389,
      390,
      391,
      392,
      393,
      394
    ]
  ],
  "nearest_feature_changed_rate": 0.13670886075949368,
  "nonincident_feature_confusion_rate": 0.09620253164556962,
  "cross_component_confusion_rate": 0.0,
  "noise_overlap_quality_pass": true,
  "noise_overlap_quality_thresholds": {
    "nonincident_feature_confusion_rate": 0.12,
    "cross_component_confusion_rate": 0.03
  },
  "num_points_evaluated_for_noise_confusion": 395,
  "num_nearest_feature_changes": 54,
  "num_nonincident_feature_confusions": 38,
  "num_cross_component_confusions": 0,
  "sample_id": 33,
  "difficulty": "full",
  "difficulty_coordinate": {
    "noise_ratio": 0.09652383098212883,
    "crowding_r": 0.00738657767141805,
    "sampling_density_per_feature": 22.480349419906897,
    "feature_thickness_ratio": 0.6325002238858191,
    "num_components": 1,
    "requested_embedding_dimension": 3
  },
  "realized_geometry": {
    "realized_separation_to_feature_scale": 3.116753090485388,
    "realized_absolute_hardness": 0.32084671803253584,
    "crowding_gamma": 0.9926872881052962,
    "crowding_gamma_min": 0.01,
    "feature_thickness_radius": 0.06467248078704718,
    "feature_thickness_budget": 0.6325002238858191,
    "effective_max_tube_radius_for_sampling": 0.10224894528847164,
    "max_admissible_tube_radius_before_crowding": 0.10224894528847164,
    "cycle_hole_radius_cap": 0.10224894528847164,
    "cycle_hole_radius_fraction": 0.2,
    "requested_noise_ratio": 0.09652383098212883,
    "realized_noise_ratio": 0.09652383098212883,
    "max_admissible_noise_ratio_after_crowding": 0.49456802148521567,
    "requested_crowding_r": 0.00738657767141805,
    "realized_crowding_r": 0.00738657767141805,
    "thickness_aware_min_required_clearance": 0.14934496157409435,
    "thickness_clearance_noise_margin": 0.3860953239285153,
    "minimum_realized_component_gap": Infinity
  },
  "graph_summary": {
    "num_nodes": 12,
    "num_edges": 13,
    "num_components": 1,
    "num_clean_points": 395,
    "topology_classes": [
      "multi_cycle"
    ]
  },
  "seed_bundle": {
    "point_cloud_seed": 708147010,
    "component_seed_bundles": [
      {
        "topology_seed": 880306555,
        "branch_seed": 435215997,
        "embedding_seed": 140916598,
        "topology_class": "multi_cycle"
      }
    ]
  },
  "scheduled_normalized_axes": {
    "noise_ratio": 0.42513239434516015,
    "crowding_r": 0.01231096278569675,
    "sampling_density_per_feature": 0.11719305023688838,
    "feature_thickness_ratio": 0.3318185888833075
  },
  "scheduled_vector_magnitude": 0.2760103709458645,
  "scheduled_sample_rank": 33,
  "actual_normalized_axes": {
    "noise_ratio": 0.42513239434516015,
    "crowding_r": 0.01231096278569675,
    "sampling_density_per_feature": 0.11719305023688838,
    "feature_thickness_ratio": 0.3318185888833075
  },
  "actual_difficulty_coordinate": [
    0.09652383098212883,
    0.00738657767141805,
    22.480349419906897,
    0.6325002238858191
  ],
  "difficulty_relaxation_factor": 1.0
}