{
  "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": 0.05309916701865869,
    "sampling_density_per_feature": 21.57048393202728,
    "edge_length_jitter_ratio": 0.025622902826060046,
    "branch_angle_spread": 1.0673829358121245
  },
  "embedding_dimension": 3,
  "requested_embedding_dimension": 3,
  "feature_thickness_ratio": 0.6899001961560889,
  "feature_thickness_budget": 0.6899001961560889,
  "tube_sampling_mode": "solid",
  "num_components": 1,
  "component_gap_ratio": 7.247911558104713,
  "component_node_ids": [
    [
      0,
      1,
      2
    ]
  ],
  "component_x_intervals": [
    [
      0.0,
      1.7827077605944925
    ]
  ],
  "component_topology_classes": [
    "tree"
  ],
  "crowding_r": 0.08783090342742239,
  "crowding_gamma": 0.9130474056068518,
  "crowding_gamma_min": 0.01,
  "crowding_admissibility_epsilon_sep": 1.3998003923121778,
  "thickness_aware_min_required_clearance": 0.02,
  "thickness_crowding_order": "choose_tube_radius_then_apply_thickness_aware_crowding",
  "cycle_tree_edges": [],
  "cycle_lengths": {},
  "pair_separations": {},
  "cycle_nodes": {},
  "cycle_motifs": {},
  "attachments": [],
  "edge_cycle_membership": {},
  "num_cycles_ground_truth": 0,
  "betti_1": 0,
  "leaf_count": 2,
  "branch_nodes": [],
  "is_planar": true,
  "max_edge_cycle_multiplicity": 0,
  "branch_params": {
    "num_initial_attachment_sites": 3,
    "max_branch_depth": 1,
    "promotion_prob": 0.5309540524418592,
    "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": [
      1,
      2
    ]
  },
  "branch_parent_map": {
    "1": 0,
    "2": 1
  },
  "branch_root_map": {
    "1": 0,
    "2": 0
  },
  "branch_depth_map": {
    "1": 1,
    "2": 1
  },
  "num_leaves_after_branching": 2,
  "num_branch_nodes_after_branching": 0,
  "betti_1_after_branching": 0,
  "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": Infinity,
      "min_nonincident_edge_distance": Infinity,
      "min_nonincident_node_edge_distance": Infinity,
      "failure_reason": null,
      "refinement_applied": false,
      "refinement_iterations": 12,
      "refinement_objective_delta": 0.0,
      "refinement_clearance_delta": NaN
    }
  ],
  "embedding_constructive_success": true,
  "embedding_rejected": false,
  "min_nonadjacent_node_distance": Infinity,
  "min_nonincident_edge_distance": Infinity,
  "min_nonincident_node_edge_distance": Infinity,
  "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": false,
    "iterations": 12,
    "objective_before": 1.8281863995509326e-05,
    "objective_after": 1.8281863995509326e-05,
    "objective_delta": 0.0,
    "clearance_before": Infinity,
    "clearance_after": Infinity,
    "clearance_delta": NaN,
    "accepted_steps": 1,
    "reason": "no_admissible_improvement"
  },
  "topology_class": "tree",
  "sampled_topology_spec": {
    "topology_class": "tree",
    "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": 0,
    "branch_attach_count": 3
  },
  "tube_embedding_separation_ratio": 6.0,
  "realized_post_crowding_min_nonadjacent_node_distance": Infinity,
  "realized_post_crowding_min_nonincident_edge_distance": Infinity,
  "realized_post_crowding_min_nonincident_node_edge_distance": Infinity,
  "realized_post_crowding_min_structural_distance": Infinity,
  "realized_post_crowding_separation_to_feature_scale": Infinity,
  "realized_post_crowding_separation_to_post_median_edge": Infinity,
  "realized_post_crowding_absolute_hardness": Infinity,
  "minimum_realized_component_gap": Infinity,
  "feature_thickness_radius": 0.6899001961560889,
  "effective_max_tube_radius_for_sampling": 1.0,
  "cycle_hole_radius_cap": Infinity,
  "cycle_hole_radius_fraction": 0.2,
  "crowding_applied": true,
  "crowding_isotropy_epsilon": 0.05,
  "crowding_axis": [
    -0.9081812306866524,
    0.014709631851369977,
    -0.4183186332919857
  ],
  "crowding_centroid": [
    0.906017015065438,
    0.015180871263646962,
    -0.4470651108270269
  ],
  "crowding_covariance_eigenvalues": [
    0.6420479013122696,
    0.0031271721482318215,
    2.2150602787254296e-18
  ],
  "crowding_covariance_matrix": [
    [
      0.5301045083230987,
      -0.008553309779544332,
      0.24273141163975598
    ],
    [
      -0.008553309779544332,
      0.0001399573847520267,
      -0.004002389571884603
    ],
    [
      0.24273141163975598,
      -0.004002389571884603,
      0.11493060775265085
    ]
  ],
  "crowding_isotropic_fallback_used": false,
  "crowding_linear_operator": [
    [
      0.9847653096432769,
      -0.0011616007134722202,
      0.033034084591684644
    ],
    [
      -0.0011616007134722202,
      0.9130662198239663,
      -0.000535046537488232
    ],
    [
      0.033034084591684644,
      -0.000535046537488232,
      0.9282632817464603
    ]
  ],
  "crowding_model_dimension": 3,
  "feature_scale_nominal": 1.0,
  "feature_scale_pre_crowding": 0.9884998659992024,
  "feature_scale_post_crowding_median_edge": 0.9873150502944158,
  "pre_crowding_edge_length_summary": {
    "min": 0.9823428293426004,
    "median": 0.9884998659992024,
    "mean": 0.9884998659992024,
    "max": 0.9946569026558043
  },
  "post_crowding_edge_length_summary": {
    "min": 0.9811456060921039,
    "median": 0.9873150502944158,
    "mean": 0.9873150502944158,
    "max": 0.9934844944967277
  },
  "pre_crowding_min_nonadjacent_node_distance": Infinity,
  "pre_crowding_min_nonincident_edge_distance": Infinity,
  "pre_crowding_min_nonincident_node_edge_distance": Infinity,
  "crowding_gamma_min_search_tolerance": 0.005,
  "crowding_gamma_min_search_history": [
    {
      "gamma": 0.01,
      "admissible": true,
      "realized_separation_ratio": Infinity
    },
    {
      "gamma": 1.0,
      "admissible": true,
      "realized_separation_ratio": Infinity
    }
  ],
  "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": 0.05309916701865869,
  "realized_noise_ratio": 0.05309916701865869,
  "max_admissible_noise_ratio_after_crowding": 0.05309916701865869,
  "requested_crowding_r": 0.08783090342742239,
  "realized_crowding_r": 0.08783090342742239,
  "staged_generation_order": "topology -> max-separation embedding -> admissible thickness -> thickness-constrained crowding -> clearance-capped noise -> sampling",
  "tube_no_overlap_required_centerline_clearance": 1.6121970603868125,
  "tube_no_overlap_post_crowding_margin": Infinity,
  "tube_no_overlap_satisfied": true,
  "tube_no_overlap_constraint_active": false,
  "max_admissible_tube_radius_after_crowding": Infinity,
  "realized_tube_radius_budget_fraction": 0.6899001961560889,
  "point_cloud_params": {
    "feature_scale": 1.0,
    "sampling_density_per_feature": 21.57048393202728,
    "noise_ratio": 0.05309916701865869,
    "sigma": 0.05309916701865869,
    "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": 0.6899001961560889,
    "feature_thickness_radius": 0.6899001961560889,
    "tube_sampling_mode": "solid"
  },
  "num_clean_points": 112,
  "num_edge_sampled_points": 109,
  "num_node_sampled_points": 3,
  "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
  ],
  "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
    ]
  ],
  "nearest_feature_changed_rate": 0.08035714285714286,
  "nonincident_feature_confusion_rate": 0.03571428571428571,
  "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": 112,
  "num_nearest_feature_changes": 9,
  "num_nonincident_feature_confusions": 4,
  "num_cross_component_confusions": 0,
  "sample_id": 29,
  "difficulty": "full",
  "difficulty_coordinate": {
    "noise_ratio": 0.05309916701865869,
    "crowding_r": 0.08783090342742239,
    "sampling_density_per_feature": 21.57048393202728,
    "feature_thickness_ratio": 0.6899001961560889,
    "num_components": 1,
    "requested_embedding_dimension": 3
  },
  "realized_geometry": {
    "realized_separation_to_feature_scale": Infinity,
    "realized_absolute_hardness": Infinity,
    "crowding_gamma": 0.9130474056068518,
    "crowding_gamma_min": 0.01,
    "feature_thickness_radius": 0.6899001961560889,
    "feature_thickness_budget": 0.6899001961560889,
    "effective_max_tube_radius_for_sampling": 1.0,
    "max_admissible_tube_radius_before_crowding": 1.0,
    "cycle_hole_radius_cap": Infinity,
    "cycle_hole_radius_fraction": 0.2,
    "requested_noise_ratio": 0.05309916701865869,
    "realized_noise_ratio": 0.05309916701865869,
    "max_admissible_noise_ratio_after_crowding": 0.05309916701865869,
    "requested_crowding_r": 0.08783090342742239,
    "realized_crowding_r": 0.08783090342742239,
    "thickness_aware_min_required_clearance": 1.3998003923121778,
    "thickness_clearance_noise_margin": 0.21239666807463475,
    "minimum_realized_component_gap": Infinity
  },
  "graph_summary": {
    "num_nodes": 3,
    "num_edges": 2,
    "num_components": 1,
    "num_clean_points": 112,
    "topology_classes": [
      "tree"
    ]
  },
  "seed_bundle": {
    "point_cloud_seed": 693040600,
    "component_seed_bundles": [
      {
        "topology_seed": 580876993,
        "branch_seed": 954450508,
        "embedding_seed": 131818864,
        "topology_class": "tree"
      }
    ]
  },
  "scheduled_normalized_axes": {
    "noise_ratio": 0.18388426121477044,
    "crowding_r": 0.14638483904570398,
    "sampling_density_per_feature": 0.1595123752545452,
    "feature_thickness_ratio": 0.4361821748292525
  },
  "scheduled_vector_magnitude": 0.2602599806554314,
  "scheduled_sample_rank": 29,
  "actual_normalized_axes": {
    "noise_ratio": 0.18388426121477044,
    "crowding_r": 0.14638483904570398,
    "sampling_density_per_feature": 0.1595123752545452,
    "feature_thickness_ratio": 0.4361821748292525
  },
  "actual_difficulty_coordinate": [
    0.05309916701865869,
    0.08783090342742239,
    21.57048393202728,
    0.6899001961560889
  ],
  "difficulty_relaxation_factor": 1.0
}