{
  "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": 0.05563980845512021,
    "sampling_density_per_feature": 23.615571403714146,
    "edge_length_jitter_ratio": 0.003933106229303314,
    "branch_angle_spread": 1.0751924960790853
  },
  "embedding_dimension": 5,
  "requested_embedding_dimension": 5,
  "feature_thickness_ratio": 0.7150133661003452,
  "feature_thickness_budget": 0.7150133661003452,
  "tube_sampling_mode": "solid",
  "num_components": 1,
  "component_gap_ratio": 5.836052854133409,
  "component_node_ids": [
    [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12
    ]
  ],
  "component_x_intervals": [
    [
      0.0,
      2.8147496835310197
    ]
  ],
  "component_topology_classes": [
    "single_cycle"
  ],
  "crowding_r": 0.0538842669291317,
  "crowding_gamma": 0.9514473287010047,
  "crowding_gamma_min": 0.0989453125,
  "crowding_admissibility_epsilon_sep": 0.2686725640244242,
  "thickness_aware_min_required_clearance": 0.02,
  "thickness_crowding_order": "choose_tube_radius_then_apply_thickness_aware_crowding",
  "cycle_tree_edges": [],
  "cycle_lengths": {
    "0": 6
  },
  "pair_separations": {},
  "cycle_nodes": {
    "0": [
      0,
      1,
      2,
      3,
      4,
      5
    ]
  },
  "cycle_motifs": {
    "0": {
      "cycle_id": 0,
      "original_cycle_length": 6,
      "original_motif_vertices": [
        0,
        1,
        2,
        3,
        4,
        5
      ],
      "final_nodes": [
        0,
        1,
        2,
        3,
        4,
        5
      ]
    }
  },
  "attachments": [],
  "edge_cycle_membership": {
    "(0, 1)": [
      0
    ],
    "(1, 2)": [
      0
    ],
    "(2, 3)": [
      0
    ],
    "(3, 4)": [
      0
    ],
    "(4, 5)": [
      0
    ],
    "(0, 5)": [
      0
    ]
  },
  "num_cycles_ground_truth": 1,
  "betti_1": 1,
  "leaf_count": 2,
  "branch_nodes": [
    1
  ],
  "is_planar": true,
  "max_edge_cycle_multiplicity": 1,
  "branch_params": {
    "num_initial_attachment_sites": 1,
    "max_branch_depth": 1,
    "promotion_prob": 0.3141786463677987,
    "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": [
    1
  ],
  "branch_generation_nodes": {
    "1": [
      6,
      7,
      8,
      9,
      10,
      11,
      12
    ]
  },
  "branch_parent_map": {
    "6": 1,
    "7": 6,
    "8": 7,
    "9": 1,
    "10": 9,
    "11": 10,
    "12": 11
  },
  "branch_root_map": {
    "6": 1,
    "7": 1,
    "8": 1,
    "9": 1,
    "10": 1,
    "11": 1,
    "12": 1
  },
  "branch_depth_map": {
    "6": 1,
    "7": 1,
    "8": 1,
    "9": 1,
    "10": 1,
    "11": 1,
    "12": 1
  },
  "num_leaves_after_branching": 2,
  "num_branch_nodes_after_branching": 1,
  "betti_1_after_branching": 1,
  "node_positions_5d": {
    "0": [
      2.1907861792951615,
      0.371778105876272,
      0.7482497953551905,
      0.10364936355055687,
      0.44068544606527577
    ],
    "1": [
      1.3506842063358397,
      0.036537374436246994,
      0.708518408194841,
      0.3603940327747815,
      0.16205121275974987
    ],
    "2": [
      1.0912728228893809,
      -0.33107052292305394,
      -0.023518272770315707,
      0.2551211291900255,
      -0.2657534134426992
    ],
    "3": [
      1.6583680505995193,
      -0.3666145957107879,
      -0.7017339009667379,
      -0.0949106393331497,
      -0.41043934569328316
    ],
    "4": [
      2.4912971530106454,
      -0.030625197345382868,
      -0.6532675694807119,
      -0.35198269342105715,
      -0.12410931944994967
    ],
    "5": [
      2.7562857528612223,
      0.3385763546755719,
      0.07173190969852294,
      -0.25442208445294556,
      0.3028168068420449
    ],
    "6": [
      1.2312213268792047,
      0.2886436388635013,
      1.138732034518973,
      -0.15512045202660396,
      0.8439804271131457
    ],
    "7": [
      0.9957419089273764,
      0.46826082124430596,
      1.4281376768175043,
      -0.6432208533139722,
      1.5930450286883084
    ],
    "8": [
      0.7697968606440213,
      0.6208166061718208,
      1.6447901959821052,
      -1.2207527577543185,
      2.3129048857086683
    ],
    "9": [
      1.0373964147410022,
      -0.23942860839923694,
      0.8226500936872186,
      1.1595534990778733,
      -0.29489689972536687
    ],
    "10": [
      0.7280709510804826,
      -0.5261236856226084,
      0.9038723484008977,
      1.9443166104699792,
      -0.7610368788489745
    ],
    "11": [
      0.4222507285458791,
      -0.8089969917585433,
      0.9938969828415656,
      2.724653901730995,
      -1.2225818150007293
    ],
    "12": [
      0.015624263495262802,
      -1.1472991494243,
      1.0355936998186612,
      3.4353614362142726,
      -1.6762205907672778
    ]
  },
  "embedding_valid": true,
  "embedding_dimensions_attempted": [
    5
  ],
  "embedding_attempt_history": [
    {
      "dimension": 5,
      "embedding_valid": true,
      "global_embedding_attempts": 1,
      "local_placement_rejections": 0,
      "min_nonadjacent_node_distance": 2.5476796437282703,
      "min_nonincident_edge_distance": 2.7292717953002126,
      "min_nonincident_node_edge_distance": 2.5476796437282703,
      "failure_reason": null,
      "refinement_applied": true,
      "refinement_iterations": 24,
      "refinement_objective_delta": -0.042416477029489474,
      "refinement_clearance_delta": 0.055397220406408376
    }
  ],
  "embedding_constructive_success": true,
  "embedding_rejected": false,
  "min_nonadjacent_node_distance": 2.5476796437282703,
  "min_nonincident_edge_distance": 2.7292717953002126,
  "min_nonincident_node_edge_distance": 2.5476796437282703,
  "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": 0.996233405158844,
    "objective_after": 0.9538169281293545,
    "objective_delta": -0.042416477029489474,
    "clearance_before": 2.492282423321862,
    "clearance_after": 2.5476796437282703,
    "clearance_delta": 0.055397220406408376,
    "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": 2.424239830874306,
  "realized_post_crowding_min_nonincident_edge_distance": 2.602311018973834,
  "realized_post_crowding_min_nonincident_node_edge_distance": 2.424239830874306,
  "realized_post_crowding_min_structural_distance": 2.424239830874306,
  "realized_post_crowding_separation_to_feature_scale": 2.424239830874306,
  "realized_post_crowding_separation_to_post_median_edge": 2.4604177057760475,
  "realized_post_crowding_absolute_hardness": 0.41250044127826596,
  "minimum_realized_component_gap": Infinity,
  "feature_thickness_radius": 0.1243362820122121,
  "effective_max_tube_radius_for_sampling": 0.17389364717800634,
  "cycle_hole_radius_cap": 0.17389364717800634,
  "cycle_hole_radius_fraction": 0.2,
  "crowding_applied": true,
  "crowding_isotropy_epsilon": 0.05,
  "crowding_axis": [
    -0.2591002847400637,
    -0.27859299039759383,
    0.01542273595125495,
    0.7474710172408687,
    -0.5443364821042433
  ],
  "crowding_centroid": [
    1.2875997399465382,
    -0.1019650653781688,
    0.6244348770844396,
    0.5586646532851106,
    0.06926504186530098
  ],
  "crowding_covariance_eigenvalues": [
    3.0438521335898363,
    1.0787611792510965,
    0.1654838551247081,
    0.0047691596026201285,
    7.952268180476566e-05
  ],
  "crowding_covariance_matrix": [
    [
      0.6329622843907673,
      0.21211408925823788,
      -0.37581042711043394,
      -0.6217633540585654,
      0.174565988814237
    ],
    [
      0.21211408925823788,
      0.260521688226506,
      0.06892031550750374,
      -0.6034952507450525,
      0.49679797488894667
    ],
    [
      -0.37581042711043394,
      0.06892031550750374,
      0.5534007195736012,
      0.1615172274389285,
      0.2948392196563821
    ],
    [
      -0.6217633540585654,
      -0.6034952507450525,
      0.1615172274389285,
      1.7444914128308655,
      -1.1748520529299673
    ],
    [
      0.174565988814237,
      0.49679797488894667,
      0.2948392196563821,
      -1.1748520529299673,
      1.1015697452283277
    ]
  ],
  "crowding_isotropic_fallback_used": false,
  "crowding_linear_operator": [
    [
      0.9547068131223749,
      0.003504702872151985,
      -0.00019401818727622853,
      -0.009403193588021675,
      0.006847758909961168
    ],
    [
      0.003504702872151985,
      0.9552156983675506,
      -0.0002086146182318225,
      -0.010110617298636144,
      0.007362931438542194
    ],
    [
      -0.00019401818727622853,
      -0.0002086146182318225,
      0.9514588774774759,
      0.0005597175315808041,
      -0.00040760733872653384
    ],
    [
      -0.009403193588021675,
      -0.010110617298636144,
      0.0005597175315808041,
      0.9785743335346839,
      -0.01975490425795523
    ],
    [
      0.006847758909961168,
      0.007362931438542194,
      -0.00040760733872653384,
      -0.01975490425795523,
      0.9658335923019334
    ]
  ],
  "crowding_model_dimension": 5,
  "feature_scale_nominal": 1.0,
  "feature_scale_pre_crowding": 1.0060404401726002,
  "feature_scale_post_crowding_median_edge": 0.9852960435064294,
  "pre_crowding_edge_length_summary": {
    "min": 0.9980492877333329,
    "median": 1.0060404401726002,
    "mean": 1.0073938529083797,
    "max": 1.0184267615154352
  },
  "post_crowding_edge_length_summary": {
    "min": 0.9612164057112892,
    "median": 0.9852960435064294,
    "mean": 0.9849072481390727,
    "max": 1.0172462512900253
  },
  "pre_crowding_min_nonadjacent_node_distance": 2.5476796437282703,
  "pre_crowding_min_nonincident_edge_distance": 2.7292717953002126,
  "pre_crowding_min_nonincident_node_edge_distance": 2.5476796437282703,
  "node_positions_5d_pre_crowding": {
    "0": [
      2.224891999196947,
      0.3830677041725178,
      0.7552814543655568,
      0.1150023200635957,
      0.43446213137804285
    ],
    "1": [
      1.3505669597036192,
      0.04001772180231255,
      0.7130078191068401,
      0.359901498231838,
      0.15977663061797795
    ],
    "2": [
      1.0820498291131835,
      -0.3419063591094142,
      -0.056630895376601494,
      0.23733590222469794,
      -0.2811779915898431
    ],
    "3": [
      1.6737159317088062,
      -0.38396106775940175,
      -0.7691960784821935,
      -0.11795645996839212,
      -0.4424242847171936
    ],
    "4": [
      2.540467039376401,
      -0.04016187625443907,
      -0.7177396668317079,
      -0.36309868022662567,
      -0.15972386008516307
    ],
    "5": [
      2.8147496835310197,
      0.3433336283844858,
      0.044508467912673114,
      -0.2483610977070604,
      0.280105097036374
    ],
    "6": [
      1.214573357334225,
      0.29376954870214783,
      1.1657964935984435,
      -0.15181769061458247,
      0.854583386361943
    ],
    "7": [
      0.957066356865684,
      0.4717885154958457,
      1.4705664974976886,
      -0.635945596945962,
      1.620841195093667
    ],
    "8": [
      0.7089587885152762,
      0.6206968978806725,
      1.698907755442443,
      -1.2122758368505315,
      2.3550982825842963
    ],
    "9": [
      1.034591937464836,
      -0.23573036195801697,
      0.8321720134405267,
      1.1614736932242276,
      -0.29254820752205823
    ],
    "10": [
      0.7227245540879697,
      -0.5228162171222067,
      0.9167507840889366,
      1.9480789970573393,
      -0.7546534906324106
    ],
    "11": [
      0.4144401824070305,
      -0.8059939842130583,
      1.0105871408850737,
      2.730324298977156,
      -1.2121416487408145
    ],
    "12": [
      0.0,
      -1.1476499999376397,
      1.0536416164500355,
      3.4399791452407373,
      -1.6617516955359053
    ]
  },
  "crowding_gamma_min_search_tolerance": 0.005,
  "crowding_gamma_min_search_history": [
    {
      "gamma": 0.01,
      "admissible": false,
      "realized_separation_ratio": 0.11672636207842269
    },
    {
      "gamma": 1.0,
      "admissible": true,
      "realized_separation_ratio": 2.5323829361085926
    },
    {
      "gamma": 0.505,
      "admissible": true,
      "realized_separation_ratio": 1.2826299189589605
    },
    {
      "gamma": 0.2575,
      "admissible": true,
      "realized_separation_ratio": 0.6613195946146455
    },
    {
      "gamma": 0.13375,
      "admissible": true,
      "realized_separation_ratio": 0.3570359329134802
    },
    {
      "gamma": 0.07187500000000001,
      "admissible": false,
      "realized_separation_ratio": 0.21458665759411294
    },
    {
      "gamma": 0.1028125,
      "admissible": true,
      "realized_separation_ratio": 0.2839638027712803
    },
    {
      "gamma": 0.08734375,
      "admissible": false,
      "realized_separation_ratio": 0.24861624322608128
    },
    {
      "gamma": 0.095078125,
      "admissible": false,
      "realized_separation_ratio": 0.26615763858347813
    },
    {
      "gamma": 0.0989453125,
      "admissible": true,
      "realized_separation_ratio": 0.27503082075358604
    }
  ],
  "crowding_gamma_min_search_iterations": 10,
  "crowding_gamma_min_search_bracket": [
    0.095078125,
    0.0989453125
  ],
  "crowding_relative_budget_definition": "gamma = 1 - r * (1 - gamma_min)",
  "requested_noise_ratio": 0.05563980845512021,
  "realized_noise_ratio": 0.05563980845512021,
  "max_admissible_noise_ratio_after_crowding": 0.35926121114164694,
  "requested_crowding_r": 0.0538842669291317,
  "realized_crowding_r": 0.0538842669291317,
  "staged_generation_order": "topology -> max-separation embedding -> admissible thickness -> thickness-constrained crowding -> clearance-capped noise -> sampling",
  "tube_no_overlap_required_centerline_clearance": 0.49123179784490506,
  "tube_no_overlap_post_crowding_margin": 1.9330080330294008,
  "tube_no_overlap_satisfied": true,
  "tube_no_overlap_constraint_active": true,
  "max_admissible_tube_radius_after_crowding": 1.0908402985269126,
  "realized_tube_radius_budget_fraction": 0.11398211285384095,
  "point_cloud_params": {
    "feature_scale": 1.0,
    "sampling_density_per_feature": 23.615571403714146,
    "noise_ratio": 0.05563980845512021,
    "sigma": 0.05563980845512021,
    "embedding_dimension": 5,
    "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": 0.1243362820122121,
    "feature_thickness_radius": 0.1243362820122121,
    "tube_sampling_mode": "solid"
  },
  "num_clean_points": 334,
  "num_edge_sampled_points": 321,
  "num_node_sampled_points": 13,
  "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
  ],
  "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
    ]
  ],
  "nearest_feature_changed_rate": 0.10778443113772455,
  "nonincident_feature_confusion_rate": 0.0718562874251497,
  "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": 334,
  "num_nearest_feature_changes": 36,
  "num_nonincident_feature_confusions": 24,
  "num_cross_component_confusions": 0,
  "sample_id": 31,
  "difficulty": "full",
  "difficulty_coordinate": {
    "noise_ratio": 0.05563980845512021,
    "crowding_r": 0.0538842669291317,
    "sampling_density_per_feature": 23.615571403714146,
    "feature_thickness_ratio": 0.7150133661003452,
    "num_components": 1,
    "requested_embedding_dimension": 5
  },
  "realized_geometry": {
    "realized_separation_to_feature_scale": 2.424239830874306,
    "realized_absolute_hardness": 0.41250044127826596,
    "crowding_gamma": 0.9514473287010047,
    "crowding_gamma_min": 0.0989453125,
    "feature_thickness_radius": 0.1243362820122121,
    "feature_thickness_budget": 0.7150133661003452,
    "effective_max_tube_radius_for_sampling": 0.17389364717800634,
    "max_admissible_tube_radius_before_crowding": 0.17389364717800634,
    "cycle_hole_radius_cap": 0.17389364717800634,
    "cycle_hole_radius_fraction": 0.2,
    "requested_noise_ratio": 0.05563980845512021,
    "realized_noise_ratio": 0.05563980845512021,
    "max_admissible_noise_ratio_after_crowding": 0.35926121114164694,
    "requested_crowding_r": 0.0538842669291317,
    "realized_crowding_r": 0.0538842669291317,
    "thickness_aware_min_required_clearance": 0.2686725640244242,
    "thickness_clearance_noise_margin": 0.22255923382048085,
    "minimum_realized_component_gap": Infinity
  },
  "graph_summary": {
    "num_nodes": 13,
    "num_edges": 13,
    "num_components": 1,
    "num_clean_points": 334,
    "topology_classes": [
      "single_cycle"
    ]
  },
  "seed_bundle": {
    "point_cloud_seed": 959085582,
    "component_seed_bundles": [
      {
        "topology_seed": 691217824,
        "branch_seed": 449301264,
        "embedding_seed": 567224568,
        "topology_class": "single_cycle"
      }
    ]
  },
  "scheduled_normalized_axes": {
    "noise_ratio": 0.1979989358617789,
    "crowding_r": 0.08980711154855284,
    "sampling_density_per_feature": 0.06439202773422578,
    "feature_thickness_ratio": 0.4818424838188094
  },
  "scheduled_vector_magnitude": 0.26626462792469074,
  "scheduled_sample_rank": 31,
  "actual_normalized_axes": {
    "noise_ratio": 0.1979989358617789,
    "crowding_r": 0.08980711154855284,
    "sampling_density_per_feature": 0.06439202773422578,
    "feature_thickness_ratio": 0.4818424838188094
  },
  "actual_difficulty_coordinate": [
    0.05563980845512021,
    0.0538842669291317,
    23.615571403714146,
    0.7150133661003452
  ],
  "difficulty_relaxation_factor": 1.0
}