{
  "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": 0.050228299882071795,
    "sampling_density_per_feature": 24.40417325499157,
    "edge_length_jitter_ratio": 0.015621821819194541,
    "branch_angle_spread": 0.8358004402470269
  },
  "embedding_dimension": 3,
  "requested_embedding_dimension": 3,
  "feature_thickness_ratio": 0.5942703420317723,
  "feature_thickness_budget": 0.5942703420317723,
  "tube_sampling_mode": "solid",
  "num_components": 1,
  "component_gap_ratio": 4.897890240503198,
  "component_node_ids": [
    [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8
    ]
  ],
  "component_x_intervals": [
    [
      0.0,
      3.0470052778913486
    ]
  ],
  "component_topology_classes": [
    "single_cycle"
  ],
  "crowding_r": 0.07567753583294921,
  "crowding_gamma": 0.9250792395253803,
  "crowding_gamma_min": 0.01,
  "crowding_admissibility_epsilon_sep": 0.18309228799366847,
  "thickness_aware_min_required_clearance": 0.02,
  "thickness_crowding_order": "choose_tube_radius_then_apply_thickness_aware_crowding",
  "cycle_tree_edges": [],
  "cycle_lengths": {
    "0": 5
  },
  "pair_separations": {},
  "cycle_nodes": {
    "0": [
      0,
      1,
      2,
      3,
      4
    ]
  },
  "cycle_motifs": {
    "0": {
      "cycle_id": 0,
      "original_cycle_length": 5,
      "original_motif_vertices": [
        0,
        1,
        2,
        3,
        4
      ],
      "final_nodes": [
        0,
        1,
        2,
        3,
        4
      ]
    }
  },
  "attachments": [],
  "edge_cycle_membership": {
    "(0, 1)": [
      0
    ],
    "(1, 2)": [
      0
    ],
    "(2, 3)": [
      0
    ],
    "(3, 4)": [
      0
    ],
    "(0, 4)": [
      0
    ]
  },
  "num_cycles_ground_truth": 1,
  "betti_1": 1,
  "leaf_count": 2,
  "branch_nodes": [
    0
  ],
  "is_planar": true,
  "max_edge_cycle_multiplicity": 1,
  "branch_params": {
    "num_initial_attachment_sites": 1,
    "max_branch_depth": 1,
    "promotion_prob": 0.2767038189447042,
    "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": [
    0
  ],
  "branch_generation_nodes": {
    "1": [
      5,
      6,
      7,
      8
    ]
  },
  "branch_parent_map": {
    "5": 0,
    "6": 5,
    "7": 0,
    "8": 7
  },
  "branch_root_map": {
    "5": 0,
    "6": 0,
    "7": 0,
    "8": 0
  },
  "branch_depth_map": {
    "5": 1,
    "6": 1,
    "7": 1,
    "8": 1
  },
  "num_leaves_after_branching": 2,
  "num_branch_nodes_after_branching": 1,
  "betti_1_after_branching": 1,
  "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": 2.5508568854238254,
      "min_nonincident_edge_distance": Infinity,
      "min_nonincident_node_edge_distance": 2.5508568854238254,
      "failure_reason": null,
      "refinement_applied": true,
      "refinement_iterations": 24,
      "refinement_objective_delta": -0.026733192335768652,
      "refinement_clearance_delta": 0.03758811147268748
    }
  ],
  "embedding_constructive_success": true,
  "embedding_rejected": false,
  "min_nonadjacent_node_distance": 2.5508568854238254,
  "min_nonincident_edge_distance": Infinity,
  "min_nonincident_node_edge_distance": 2.5508568854238254,
  "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": 0.5858453561118949,
    "objective_after": 0.5591121637761263,
    "objective_delta": -0.026733192335768652,
    "clearance_before": 2.513268773951138,
    "clearance_after": 2.5508568854238254,
    "clearance_delta": 0.03758811147268748,
    "accepted_steps": 24,
    "reason": "accepted"
  },
  "topology_class": "single_cycle",
  "sampled_topology_spec": {
    "topology_class": "single_cycle",
    "children_per_branch_point_range": [
      1,
      3
    ],
    "branch_length_range": [
      1,
      4
    ],
    "max_branch_depth_range": [
      1,
      1
    ],
    "promotion_prob_range": [
      0.2,
      0.6
    ],
    "max_degree": 4,
    "num_cycles": 1,
    "branch_attach_count": 1
  },
  "tube_embedding_separation_ratio": 6.0,
  "realized_post_crowding_min_nonadjacent_node_distance": 2.4131575938254217,
  "realized_post_crowding_min_nonincident_edge_distance": Infinity,
  "realized_post_crowding_min_nonincident_node_edge_distance": 2.4131575938254217,
  "realized_post_crowding_min_structural_distance": 2.4131575938254217,
  "realized_post_crowding_separation_to_feature_scale": 2.4131575938254217,
  "realized_post_crowding_separation_to_post_median_edge": 2.4734736124513623,
  "realized_post_crowding_absolute_hardness": 0.4143948172132285,
  "minimum_realized_component_gap": Infinity,
  "feature_thickness_radius": 0.08154614399683424,
  "effective_max_tube_radius_for_sampling": 0.1372206186800997,
  "cycle_hole_radius_cap": 0.1372206186800997,
  "cycle_hole_radius_fraction": 0.2,
  "crowding_applied": true,
  "crowding_isotropy_epsilon": 0.05,
  "crowding_axis": [
    -0.5444662276155947,
    -0.3365426907349534,
    0.7683069336527693
  ],
  "crowding_centroid": [
    1.7630630655565203,
    0.12412662241215393,
    -0.2618862729824085
  ],
  "crowding_covariance_eigenvalues": [
    1.1421000359696585,
    0.6519835244324793,
    0.07056085629893614
  ],
  "crowding_covariance_matrix": [
    [
      0.7970701057630902,
      0.0798565054978673,
      -0.20952826823485898
    ],
    [
      0.0798565054978673,
      0.22511317823326468,
      -0.34507830472349915
    ],
    [
      -0.20952826823485898,
      -0.34507830472349915,
      0.8424611327047182
    ]
  ],
  "crowding_isotropic_fallback_used": false,
  "crowding_linear_operator": [
    [
      0.9472890099613234,
      0.013728190150289865,
      -0.031340641081633494
    ],
    [
      0.013728190150289865,
      0.9335648384804023,
      -0.019372117394980282
    ],
    [
      -0.031340641081633494,
      -0.019372117394980282,
      0.969304630609035
    ]
  ],
  "crowding_model_dimension": 3,
  "feature_scale_nominal": 1.0,
  "feature_scale_pre_crowding": 1.0026477588029203,
  "feature_scale_post_crowding_median_edge": 0.9756148526014944,
  "pre_crowding_edge_length_summary": {
    "min": 0.9908406840621031,
    "median": 1.0026477588029203,
    "mean": 1.0040331472162463,
    "max": 1.0297341276578502
  },
  "post_crowding_edge_length_summary": {
    "min": 0.9207478708860007,
    "median": 0.9756148526014944,
    "mean": 0.9732635638969042,
    "max": 1.0208202993662965
  },
  "pre_crowding_min_nonadjacent_node_distance": 2.5508568854238254,
  "pre_crowding_min_nonincident_edge_distance": Infinity,
  "pre_crowding_min_nonincident_node_edge_distance": 2.5508568854238254,
  "crowding_gamma_min_search_tolerance": 0.005,
  "crowding_gamma_min_search_history": [
    {
      "gamma": 0.01,
      "admissible": true,
      "realized_separation_ratio": 1.326168071652709
    },
    {
      "gamma": 1.0,
      "admissible": true,
      "realized_separation_ratio": 2.5441206675306796
    }
  ],
  "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": 0.050228299882071795,
  "realized_noise_ratio": 0.050228299882071795,
  "max_admissible_noise_ratio_after_crowding": 0.3716775509719588,
  "requested_crowding_r": 0.07567753583294921,
  "realized_crowding_r": 0.07567753583294921,
  "staged_generation_order": "topology -> max-separation embedding -> admissible thickness -> thickness-constrained crowding -> clearance-capped noise -> sampling",
  "tube_no_overlap_required_centerline_clearance": 0.3840054875219557,
  "tube_no_overlap_post_crowding_margin": 2.029152106303466,
  "tube_no_overlap_satisfied": true,
  "tube_no_overlap_constraint_active": true,
  "max_admissible_tube_radius_after_crowding": 1.0961221971485673,
  "realized_tube_radius_budget_fraction": 0.07439512146452916,
  "point_cloud_params": {
    "feature_scale": 1.0,
    "sampling_density_per_feature": 24.40417325499157,
    "noise_ratio": 0.050228299882071795,
    "sigma": 0.050228299882071795,
    "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": 0.08154614399683424,
    "feature_thickness_radius": 0.08154614399683424,
    "tube_sampling_mode": "solid"
  },
  "num_clean_points": 238,
  "num_edge_sampled_points": 229,
  "num_node_sampled_points": 9,
  "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
  ],
  "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
    ]
  ],
  "nearest_feature_changed_rate": 0.14705882352941177,
  "nonincident_feature_confusion_rate": 0.07983193277310924,
  "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": 238,
  "num_nearest_feature_changes": 35,
  "num_nonincident_feature_confusions": 19,
  "num_cross_component_confusions": 0,
  "sample_id": 4,
  "difficulty": "full",
  "difficulty_coordinate": {
    "noise_ratio": 0.050228299882071795,
    "crowding_r": 0.07567753583294921,
    "sampling_density_per_feature": 24.40417325499157,
    "feature_thickness_ratio": 0.5942703420317723,
    "num_components": 1,
    "requested_embedding_dimension": 3
  },
  "realized_geometry": {
    "realized_separation_to_feature_scale": 2.4131575938254217,
    "realized_absolute_hardness": 0.4143948172132285,
    "crowding_gamma": 0.9250792395253803,
    "crowding_gamma_min": 0.01,
    "feature_thickness_radius": 0.08154614399683424,
    "feature_thickness_budget": 0.5942703420317723,
    "effective_max_tube_radius_for_sampling": 0.1372206186800997,
    "max_admissible_tube_radius_before_crowding": 0.1372206186800997,
    "cycle_hole_radius_cap": 0.1372206186800997,
    "cycle_hole_radius_fraction": 0.2,
    "requested_noise_ratio": 0.050228299882071795,
    "realized_noise_ratio": 0.050228299882071795,
    "max_admissible_noise_ratio_after_crowding": 0.3716775509719588,
    "requested_crowding_r": 0.07567753583294921,
    "realized_crowding_r": 0.07567753583294921,
    "thickness_aware_min_required_clearance": 0.18309228799366847,
    "thickness_clearance_noise_margin": 0.20091319952828718,
    "minimum_realized_component_gap": Infinity
  },
  "graph_summary": {
    "num_nodes": 9,
    "num_edges": 9,
    "num_components": 1,
    "num_clean_points": 238,
    "topology_classes": [
      "single_cycle"
    ]
  },
  "seed_bundle": {
    "point_cloud_seed": 416755125,
    "component_seed_bundles": [
      {
        "topology_seed": 629068594,
        "branch_seed": 169455032,
        "embedding_seed": 292758219,
        "topology_class": "single_cycle"
      }
    ]
  },
  "scheduled_normalized_axes": {
    "noise_ratio": 0.1679349993448433,
    "crowding_r": 0.1261292263882487,
    "sampling_density_per_feature": 0.02771287186085737,
    "feature_thickness_ratio": 0.26230971278504067
  },
  "scheduled_vector_magnitude": 0.16858613113361182,
  "scheduled_sample_rank": 4,
  "actual_normalized_axes": {
    "noise_ratio": 0.1679349993448433,
    "crowding_r": 0.1261292263882487,
    "sampling_density_per_feature": 0.02771287186085737,
    "feature_thickness_ratio": 0.26230971278504067
  },
  "actual_difficulty_coordinate": [
    0.050228299882071795,
    0.07567753583294921,
    24.40417325499157,
    0.5942703420317723
  ],
  "difficulty_relaxation_factor": 1.0
}