{
  "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": 0.02628136233357228,
    "sampling_density_per_feature": 23.75206635441647,
    "edge_length_jitter_ratio": 0.0020158381613446207,
    "branch_angle_spread": 0.7759412779199437
  },
  "embedding_dimension": 2,
  "requested_embedding_dimension": 2,
  "feature_thickness_ratio": 0.6039125132385512,
  "feature_thickness_budget": 0.6039125132385512,
  "tube_sampling_mode": "solid",
  "num_components": 1,
  "component_gap_ratio": 5.9623090861070445,
  "component_node_ids": [
    [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      21
    ]
  ],
  "component_x_intervals": [
    [
      0.0,
      7.156268819086268
    ]
  ],
  "component_topology_classes": [
    "multi_cycle"
  ],
  "crowding_r": 0.006138442372859784,
  "crowding_gamma": 0.9941603271270067,
  "crowding_gamma_min": 0.048671875,
  "crowding_admissibility_epsilon_sep": 0.18397356394188458,
  "thickness_aware_min_required_clearance": 0.02,
  "thickness_crowding_order": "choose_tube_radius_then_apply_thickness_aware_crowding",
  "cycle_tree_edges": [
    [
      0,
      2
    ],
    [
      1,
      2
    ]
  ],
  "cycle_lengths": {
    "0": 8,
    "1": 6,
    "2": 5
  },
  "pair_separations": {
    "(0, 2)": 3,
    "(1, 2)": 1
  },
  "cycle_nodes": {
    "0": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7
    ],
    "2": [
      8,
      9,
      10,
      11,
      12
    ],
    "1": [
      15,
      16,
      17,
      18,
      19,
      20
    ]
  },
  "cycle_motifs": {
    "0": {
      "cycle_id": 0,
      "original_cycle_length": 8,
      "original_motif_vertices": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7
      ],
      "final_nodes": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7
      ]
    },
    "2": {
      "cycle_id": 2,
      "original_cycle_length": 5,
      "original_motif_vertices": [
        8,
        9,
        10,
        11,
        12
      ],
      "final_nodes": [
        8,
        9,
        10,
        11,
        12
      ]
    },
    "1": {
      "cycle_id": 1,
      "original_cycle_length": 6,
      "original_motif_vertices": [
        15,
        16,
        17,
        18,
        19,
        20
      ],
      "final_nodes": [
        15,
        16,
        17,
        18,
        19,
        20
      ]
    }
  },
  "attachments": [
    {
      "cycle_pair": [
        0,
        2
      ],
      "separation": 3,
      "attachment_type": "path",
      "anchor_a": 0,
      "anchor_b": 11,
      "path_nodes": [
        0,
        13,
        14,
        11
      ]
    },
    {
      "cycle_pair": [
        1,
        2
      ],
      "separation": 1,
      "attachment_type": "path",
      "anchor_a": 11,
      "anchor_b": 19,
      "path_nodes": [
        11,
        19
      ]
    }
  ],
  "edge_cycle_membership": {
    "(0, 1)": [
      0
    ],
    "(1, 2)": [
      0
    ],
    "(2, 3)": [
      0
    ],
    "(3, 4)": [
      0
    ],
    "(4, 5)": [
      0
    ],
    "(5, 6)": [
      0
    ],
    "(6, 7)": [
      0
    ],
    "(0, 7)": [
      0
    ],
    "(8, 9)": [
      2
    ],
    "(9, 10)": [
      2
    ],
    "(10, 11)": [
      2
    ],
    "(11, 12)": [
      2
    ],
    "(8, 12)": [
      2
    ],
    "(15, 16)": [
      1
    ],
    "(16, 17)": [
      1
    ],
    "(17, 18)": [
      1
    ],
    "(18, 19)": [
      1
    ],
    "(19, 20)": [
      1
    ],
    "(15, 20)": [
      1
    ]
  },
  "num_cycles_ground_truth": 3,
  "betti_1": 3,
  "leaf_count": 1,
  "branch_nodes": [
    0,
    11,
    13,
    19
  ],
  "is_planar": true,
  "max_edge_cycle_multiplicity": 1,
  "branch_params": {
    "num_initial_attachment_sites": 1,
    "max_branch_depth": 1,
    "promotion_prob": 0.4538638567368279,
    "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": [
    13
  ],
  "branch_generation_nodes": {
    "1": [
      21
    ]
  },
  "branch_parent_map": {
    "21": 13
  },
  "branch_root_map": {
    "21": 13
  },
  "branch_depth_map": {
    "21": 1
  },
  "num_leaves_after_branching": 1,
  "num_branch_nodes_after_branching": 4,
  "betti_1_after_branching": 3,
  "embedding_valid": true,
  "embedding_dimensions_attempted": [
    2
  ],
  "embedding_attempt_history": [
    {
      "dimension": 2,
      "embedding_valid": true,
      "global_embedding_attempts": 1,
      "local_placement_rejections": 0,
      "min_nonadjacent_node_distance": 1.791581611880235,
      "min_nonincident_edge_distance": 2.5715156734066724,
      "min_nonincident_node_edge_distance": 1.791581611880235,
      "failure_reason": null,
      "refinement_applied": true,
      "refinement_iterations": 24,
      "refinement_objective_delta": -32.833805034889394,
      "refinement_clearance_delta": 0.042851822540101114
    }
  ],
  "embedding_constructive_success": true,
  "embedding_rejected": false,
  "min_nonadjacent_node_distance": 1.791581611880235,
  "min_nonincident_edge_distance": 2.5715156734066724,
  "min_nonincident_node_edge_distance": 1.791581611880235,
  "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": 220.34517209164812,
    "objective_after": 187.51136705675873,
    "objective_delta": -32.833805034889394,
    "clearance_before": 1.748729789340134,
    "clearance_after": 1.791581611880235,
    "clearance_delta": 0.042851822540101114,
    "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": 3,
    "branch_attach_count": 1
  },
  "tube_embedding_separation_ratio": 6.0,
  "realized_post_crowding_min_nonadjacent_node_distance": 1.791053651031687,
  "realized_post_crowding_min_nonincident_edge_distance": 2.5714489747019833,
  "realized_post_crowding_min_nonincident_node_edge_distance": 1.791053651031687,
  "realized_post_crowding_min_structural_distance": 1.791053651031687,
  "realized_post_crowding_separation_to_feature_scale": 1.791053651031687,
  "realized_post_crowding_separation_to_post_median_edge": 1.7675712750241295,
  "realized_post_crowding_absolute_hardness": 0.5583305667164005,
  "minimum_realized_component_gap": Infinity,
  "feature_thickness_radius": 0.0819867819709423,
  "effective_max_tube_radius_for_sampling": 0.13575936940150257,
  "cycle_hole_radius_cap": 0.13575936940150257,
  "cycle_hole_radius_fraction": 0.2,
  "crowding_applied": true,
  "crowding_isotropy_epsilon": 0.05,
  "crowding_axis": [
    0.2685501804761637,
    0.9632656957279336
  ],
  "crowding_centroid": [
    3.5871099378131457,
    -3.6350993884962195
  ],
  "crowding_covariance_eigenvalues": [
    12.492016215289924,
    3.8429315446082364
  ],
  "crowding_covariance_matrix": [
    [
      4.466696606892779,
      2.23738999402992
    ],
    [
      2.23738999402992,
      11.868251153005382
    ]
  ],
  "crowding_isotropic_fallback_used": false,
  "crowding_linear_operator": [
    [
      0.9945814796595622,
      0.001510636807468469
    ],
    [
      0.001510636807468469,
      0.9995788474674445
    ]
  ],
  "crowding_model_dimension": 2,
  "feature_scale_nominal": 1.0,
  "feature_scale_pre_crowding": 1.0164685203255055,
  "feature_scale_post_crowding_median_edge": 1.0132851084079972,
  "pre_crowding_edge_length_summary": {
    "min": 0.9754244142187157,
    "median": 1.0164685203255055,
    "mean": 1.328324744946028,
    "max": 4.682691038678485
  },
  "post_crowding_edge_length_summary": {
    "min": 0.969916070021843,
    "median": 1.0132851084079972,
    "mean": 1.3253271123376111,
    "max": 4.682660617234755
  },
  "pre_crowding_min_nonadjacent_node_distance": 1.791581611880235,
  "pre_crowding_min_nonincident_edge_distance": 2.5715156734066724,
  "pre_crowding_min_nonincident_node_edge_distance": 1.791581611880235,
  "crowding_gamma_min_search_tolerance": 0.005,
  "crowding_gamma_min_search_history": [
    {
      "gamma": 0.01,
      "admissible": false,
      "realized_separation_ratio": 0.03853928417791832
    },
    {
      "gamma": 1.0,
      "admissible": true,
      "realized_separation_ratio": 1.7625549400256033
    },
    {
      "gamma": 0.505,
      "admissible": true,
      "realized_separation_ratio": 1.3859453211732649
    },
    {
      "gamma": 0.2575,
      "admissible": true,
      "realized_separation_ratio": 0.8542072850012304
    },
    {
      "gamma": 0.13375,
      "admissible": true,
      "realized_separation_ratio": 0.5154544141078853
    },
    {
      "gamma": 0.07187500000000001,
      "admissible": true,
      "realized_separation_ratio": 0.2769998023864315
    },
    {
      "gamma": 0.0409375,
      "admissible": false,
      "realized_separation_ratio": 0.1577699638079871
    },
    {
      "gamma": 0.056406250000000005,
      "admissible": true,
      "realized_separation_ratio": 0.21738502795313516
    },
    {
      "gamma": 0.048671875,
      "admissible": true,
      "realized_separation_ratio": 0.18757752712904424
    },
    {
      "gamma": 0.0448046875,
      "admissible": false,
      "realized_separation_ratio": 0.17267375265994309
    }
  ],
  "crowding_gamma_min_search_iterations": 10,
  "crowding_gamma_min_search_bracket": [
    0.0448046875,
    0.048671875
  ],
  "crowding_relative_budget_definition": "gamma = 1 - r * (1 - gamma_min)",
  "requested_noise_ratio": 0.02628136233357228,
  "realized_noise_ratio": 0.02628136233357228,
  "max_admissible_noise_ratio_after_crowding": 0.26784668118163374,
  "requested_crowding_r": 0.006138442372859784,
  "realized_crowding_r": 0.006138442372859784,
  "staged_generation_order": "topology -> max-separation embedding -> admissible thickness -> thickness-constrained crowding -> clearance-capped noise -> sampling",
  "tube_no_overlap_required_centerline_clearance": 0.2890990132761737,
  "tube_no_overlap_post_crowding_margin": 1.5019546377555133,
  "tube_no_overlap_satisfied": true,
  "tube_no_overlap_constraint_active": true,
  "max_admissible_tube_radius_after_crowding": 0.832964100848699,
  "realized_tube_radius_budget_fraction": 0.09842774963219515,
  "point_cloud_params": {
    "feature_scale": 1.0,
    "sampling_density_per_feature": 23.75206635441647,
    "noise_ratio": 0.02628136233357228,
    "sigma": 0.02628136233357228,
    "embedding_dimension": 2,
    "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": 0.0819867819709423,
    "feature_thickness_radius": 0.0819867819709423,
    "tube_sampling_mode": "solid"
  },
  "num_clean_points": 775,
  "num_edge_sampled_points": 753,
  "num_node_sampled_points": 22,
  "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,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    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,
      395,
      396,
      397,
      398,
      399,
      400,
      401,
      402,
      403,
      404,
      405,
      406,
      407,
      408,
      409,
      410,
      411,
      412,
      413,
      414,
      415,
      416,
      417,
      418,
      419,
      420,
      421,
      422,
      423,
      424,
      425,
      426,
      427,
      428,
      429,
      430,
      431,
      432,
      433,
      434,
      435,
      436,
      437,
      438,
      439,
      440,
      441,
      442,
      443,
      444,
      445,
      446,
      447,
      448,
      449,
      450,
      451,
      452,
      453,
      454,
      455,
      456,
      457,
      458,
      459,
      460,
      461,
      462,
      463,
      464,
      465,
      466,
      467,
      468,
      469,
      470,
      471,
      472,
      473,
      474,
      475,
      476,
      477,
      478,
      479,
      480,
      481,
      482,
      483,
      484,
      485,
      486,
      487,
      488,
      489,
      490,
      491,
      492,
      493,
      494,
      495,
      496,
      497,
      498,
      499,
      500,
      501,
      502,
      503,
      504,
      505,
      506,
      507,
      508,
      509,
      510,
      511,
      512,
      513,
      514,
      515,
      516,
      517,
      518,
      519,
      520,
      521,
      522,
      523,
      524,
      525,
      526,
      527,
      528,
      529,
      530,
      531,
      532,
      533,
      534,
      535,
      536,
      537,
      538,
      539,
      540,
      541,
      542,
      543,
      544,
      545,
      546,
      547,
      548,
      549,
      550,
      551,
      552,
      553,
      554,
      555,
      556,
      557,
      558,
      559,
      560,
      561,
      562,
      563,
      564,
      565,
      566,
      567,
      568,
      569,
      570,
      571,
      572,
      573,
      574,
      575,
      576,
      577,
      578,
      579,
      580,
      581,
      582,
      583,
      584,
      585,
      586,
      587,
      588,
      589,
      590,
      591,
      592,
      593,
      594,
      595,
      596,
      597,
      598,
      599,
      600,
      601,
      602,
      603,
      604,
      605,
      606,
      607,
      608,
      609,
      610,
      611,
      612,
      613,
      614,
      615,
      616,
      617,
      618,
      619,
      620,
      621,
      622,
      623,
      624,
      625,
      626,
      627,
      628,
      629,
      630,
      631,
      632,
      633,
      634,
      635,
      636,
      637,
      638,
      639,
      640,
      641,
      642,
      643,
      644,
      645,
      646,
      647,
      648,
      649,
      650,
      651,
      652,
      653,
      654,
      655,
      656,
      657,
      658,
      659,
      660,
      661,
      662,
      663,
      664,
      665,
      666,
      667,
      668,
      669,
      670,
      671,
      672,
      673,
      674,
      675,
      676,
      677,
      678,
      679,
      680,
      681,
      682,
      683,
      684,
      685,
      686,
      687,
      688,
      689,
      690,
      691,
      692,
      693,
      694,
      695,
      696,
      697,
      698,
      699,
      700,
      701,
      702,
      703,
      704,
      705,
      706,
      707,
      708,
      709,
      710,
      711,
      712,
      713,
      714,
      715,
      716,
      717,
      718,
      719,
      720,
      721,
      722,
      723,
      724,
      725,
      726,
      727,
      728,
      729,
      730,
      731,
      732,
      733,
      734,
      735,
      736,
      737,
      738,
      739,
      740,
      741,
      742,
      743,
      744,
      745,
      746,
      747,
      748,
      749,
      750,
      751,
      752,
      753,
      754,
      755,
      756,
      757,
      758,
      759,
      760,
      761,
      762,
      763,
      764,
      765,
      766,
      767,
      768,
      769,
      770,
      771,
      772,
      773,
      774
    ]
  ],
  "nearest_feature_changed_rate": 0.06064516129032258,
  "nonincident_feature_confusion_rate": 0.06193548387096774,
  "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": 775,
  "num_nearest_feature_changes": 47,
  "num_nonincident_feature_confusions": 48,
  "num_cross_component_confusions": 0,
  "sample_id": 0,
  "difficulty": "full",
  "difficulty_coordinate": {
    "noise_ratio": 0.02628136233357228,
    "crowding_r": 0.006138442372859784,
    "sampling_density_per_feature": 23.75206635441647,
    "feature_thickness_ratio": 0.6039125132385512,
    "num_components": 1,
    "requested_embedding_dimension": 2
  },
  "realized_geometry": {
    "realized_separation_to_feature_scale": 1.791053651031687,
    "realized_absolute_hardness": 0.5583305667164005,
    "crowding_gamma": 0.9941603271270067,
    "crowding_gamma_min": 0.048671875,
    "feature_thickness_radius": 0.0819867819709423,
    "feature_thickness_budget": 0.6039125132385512,
    "effective_max_tube_radius_for_sampling": 0.13575936940150257,
    "max_admissible_tube_radius_before_crowding": 0.13575936940150257,
    "cycle_hole_radius_cap": 0.13575936940150257,
    "cycle_hole_radius_fraction": 0.2,
    "requested_noise_ratio": 0.02628136233357228,
    "realized_noise_ratio": 0.02628136233357228,
    "max_admissible_noise_ratio_after_crowding": 0.26784668118163374,
    "requested_crowding_r": 0.006138442372859784,
    "realized_crowding_r": 0.006138442372859784,
    "thickness_aware_min_required_clearance": 0.18397356394188458,
    "thickness_clearance_noise_margin": 0.10512544933428912,
    "minimum_realized_component_gap": Infinity
  },
  "graph_summary": {
    "num_nodes": 22,
    "num_edges": 24,
    "num_components": 1,
    "num_clean_points": 775,
    "topology_classes": [
      "multi_cycle"
    ]
  },
  "seed_bundle": {
    "point_cloud_seed": 910100634,
    "component_seed_bundles": [
      {
        "topology_seed": 547243252,
        "branch_seed": 676834051,
        "embedding_seed": 349745244,
        "topology_class": "multi_cycle"
      }
    ]
  },
  "scheduled_normalized_axes": {
    "noise_ratio": 0.034896457408734885,
    "crowding_r": 0.01023073728809964,
    "sampling_density_per_feature": 0.05804342537597811,
    "feature_thickness_ratio": 0.27984093316100234
  },
  "scheduled_vector_magnitude": 0.14405070099355216,
  "scheduled_sample_rank": 0,
  "actual_normalized_axes": {
    "noise_ratio": 0.034896457408734885,
    "crowding_r": 0.01023073728809964,
    "sampling_density_per_feature": 0.05804342537597811,
    "feature_thickness_ratio": 0.27984093316100234
  },
  "actual_difficulty_coordinate": [
    0.02628136233357228,
    0.006138442372859784,
    23.75206635441647,
    0.6039125132385512
  ],
  "difficulty_relaxation_factor": 1.0
}