{ "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": 0.068573131604513, "sampling_density_per_feature": 17.041873831610662, "edge_length_jitter_ratio": 0.02119542308083181, "branch_angle_spread": 0.7904332605244404 }, "embedding_dimension": 4, "requested_embedding_dimension": 4, "feature_thickness_ratio": 0.4549965508146894, "feature_thickness_budget": 0.4549965508146894, "tube_sampling_mode": "solid", "num_components": 1, "component_gap_ratio": 7.073351393376914, "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, 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 ] ], "component_x_intervals": [ [ 0.0, 8.00765950055518 ] ], "component_topology_classes": [ "branchy_cycle" ], "crowding_r": 0.04961186670470844, "crowding_gamma": 0.9545295613870088, "crowding_gamma_min": 0.0834765625, "crowding_admissibility_epsilon_sep": 0.08449833152455281, "thickness_aware_min_required_clearance": 0.02, "thickness_crowding_order": "choose_tube_radius_then_apply_thickness_aware_crowding", "cycle_tree_edges": [ [ 0, 1 ], [ 0, 2 ] ], "cycle_lengths": { "0": 5, "1": 5, "2": 7 }, "pair_separations": { "(0, 1)": 0, "(0, 2)": -1 }, "cycle_nodes": { "0": [ 0, 1, 2, 3, 4 ], "1": [ 5, 6, 7, 8, 3 ], "2": [ 10, 11, 12, 13, 14, 2, 1 ] }, "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 ] }, "1": { "cycle_id": 1, "original_cycle_length": 5, "original_motif_vertices": [ 5, 6, 7, 8, 9 ], "final_nodes": [ 5, 6, 7, 8, 3 ] }, "2": { "cycle_id": 2, "original_cycle_length": 7, "original_motif_vertices": [ 10, 11, 12, 13, 14, 15, 16 ], "final_nodes": [ 10, 11, 12, 13, 14, 2, 1 ] } }, "attachments": [ { "cycle_pair": [ 0, 1 ], "separation": 0, "attachment_type": "shared_vertex", "anchor_a": 3, "anchor_b_original": 9, "shared_node": 3 }, { "cycle_pair": [ 0, 2 ], "separation": -1, "attachment_type": "shared_path", "shared_edges": 1, "cycle_a_path": [ 1, 2 ], "cycle_b_path_original": [ 16, 15 ], "orientation": "reversed", "shared_path_nodes": [ 1, 2 ], "cycle_a_edge_indices": [ 1 ], "cycle_b_edge_indices": [ 5 ] } ], "edge_cycle_membership": { "(0, 1)": [ 0 ], "(1, 2)": [ 0, 2 ], "(2, 3)": [ 0 ], "(3, 4)": [ 0 ], "(0, 4)": [ 0 ], "(5, 6)": [ 1 ], "(6, 7)": [ 1 ], "(7, 8)": [ 1 ], "(3, 8)": [ 1 ], "(3, 5)": [ 1 ], "(10, 11)": [ 2 ], "(11, 12)": [ 2 ], "(12, 13)": [ 2 ], "(13, 14)": [ 2 ], "(2, 14)": [ 2 ], "(1, 10)": [ 2 ] }, "num_cycles_ground_truth": 3, "betti_1": 3, "leaf_count": 14, "branch_nodes": [ 1, 2, 3, 10, 11, 21, 25, 27, 29, 39 ], "is_planar": true, "max_edge_cycle_multiplicity": 2, "branch_params": { "num_initial_attachment_sites": 3, "max_branch_depth": 3, "promotion_prob": 0.23605668602333899, "children_per_branch_point_range": [ 1, 3 ], "branch_length_range": [ 1, 4 ], "max_degree": 5, "max_total_nodes": 80, "max_total_edges": 88 }, "branch_attachment_nodes_initial": [ 10, 11, 2 ], "branch_generation_nodes": { "1": [ 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 ], "2": [ 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 ], "3": [ 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55 ] }, "branch_parent_map": { "15": 10, "16": 15, "17": 10, "18": 11, "19": 18, "20": 19, "21": 11, "22": 2, "23": 2, "24": 23, "25": 24, "26": 25, "27": 21, "28": 27, "29": 28, "30": 21, "31": 30, "32": 31, "33": 32, "34": 21, "35": 34, "36": 25, "37": 36, "38": 37, "39": 26, "40": 27, "41": 40, "42": 41, "43": 42, "44": 27, "45": 44, "46": 29, "47": 46, "48": 29, "49": 48, "50": 39, "51": 50, "52": 39, "53": 52, "54": 53, "55": 39 }, "branch_root_map": { "15": 10, "16": 10, "17": 10, "18": 11, "19": 11, "20": 11, "21": 11, "22": 2, "23": 2, "24": 2, "25": 2, "26": 2, "27": 11, "28": 11, "29": 11, "30": 11, "31": 11, "32": 11, "33": 11, "34": 11, "35": 11, "36": 2, "37": 2, "38": 2, "39": 2, "40": 11, "41": 11, "42": 11, "43": 11, "44": 11, "45": 11, "46": 11, "47": 11, "48": 11, "49": 11, "50": 2, "51": 2, "52": 2, "53": 2, "54": 2, "55": 2 }, "branch_depth_map": { "15": 1, "16": 1, "17": 1, "18": 1, "19": 1, "20": 1, "21": 1, "22": 1, "23": 1, "24": 1, "25": 1, "26": 1, "27": 2, "28": 2, "29": 2, "30": 2, "31": 2, "32": 2, "33": 2, "34": 2, "35": 2, "36": 2, "37": 2, "38": 2, "39": 2, "40": 3, "41": 3, "42": 3, "43": 3, "44": 3, "45": 3, "46": 3, "47": 3, "48": 3, "49": 3, "50": 3, "51": 3, "52": 3, "53": 3, "54": 3, "55": 3 }, "num_leaves_after_branching": 14, "num_branch_nodes_after_branching": 10, "betti_1_after_branching": 3, "node_positions_4d": { "0": [ 4.918225483434172, 0.0004854522600730299, 0.4652503674965216, -0.01953443936951027 ], "1": [ 4.399630565608221, 0.06729263015698145, 0.1959587100092437, -0.9744154750381728 ], "2": [ 3.8086377118296735, 0.015234090948535756, -0.5187048332304005, -0.7268540979190701 ], "3": [ 3.8754839982568923, -0.12133471731088515, -0.7903651253222661, 0.47038067376551806 ], "4": [ 4.617346740181054, -0.09024385568559122, -0.09791423374829411, 0.7555466543944309 ], "5": [ 1.6600445277294111, -1.3434215720437486, -3.4587542399386892, 2.467690669287607 ], "6": [ 0.8214421106755285, -1.4330689646021428, -4.060947331894665, 2.678424146248485 ], "7": [ 0.21498616679078753, -0.9631194649727637, -3.917960891469959, 2.0574451150649375 ], "8": [ 0.7345300871744498, -0.6179398071589113, -3.2311928888535713, 1.5066054381522482 ], "9": [ 3.504866210946519, 0.25154057705389093, -0.01910817728761982, -3.426844892604831 ], "10": [ 2.867456740410846, 0.3930044308531921, -0.18243138528010783, -5.082341354930337 ], "11": [ 2.4554561458515574, 0.4231576146357989, -0.3665540953321147, -5.786401519130143 ], "12": [ 2.592888266729525, 0.3627488401506794, -0.5133241451297061, -4.954599390879309 ], "13": [ 3.0836448394690827, 0.217113746214709, -0.533715821017483, -3.1974254172098466 ], "14": [ 3.6474287303350037, 0.5321050524722176, 0.5880642931189486, -2.920474468275479 ], "15": [ 3.827847691277912, 0.7844424276099052, 1.2090331256576758, -2.251393424996718 ], "16": [ 3.601127327474793, -0.120453263366589, -0.13113554009026251, -4.398458206629958 ], "17": [ 2.3337995702962937, -0.013239170909782827, 0.420439089518829, -5.548096441211051 ], "18": [ 1.8770404780722612, -0.45715236358606826, 1.07215324554266, -5.851240808846967 ], "19": [ 1.553318895243835, -0.8524589548861186, 1.7993757058108486, -6.190467244937945 ], "20": [ 2.881945869235955, 0.8198677315839573, -0.795514242126478, -5.851928081740722 ], "21": [ 3.466302925479714, 0.3128005092878588, -0.1520356969679526, 0.14070509043794877 ], "22": [ 4.273508270207142, -0.32208463669905696, -1.2704318989002061, -0.24745091382480222 ], "23": [ 4.815503203214846, -0.6822344083876736, -1.9442041165233144, 0.052470759684623225 ], "24": [ 5.269355843421744, -1.1213477023328424, -2.6321305197057407, 0.3006558943495268 ], "25": [ 5.765694183965603, -1.5784585187052111, -3.3023603009967983, 0.5984826257328555 ], "26": [ 2.5148919632567006, 1.2495111935236627, -1.537819247910864, -5.669153434887244 ], "27": [ 2.337516347400337, 1.743363913944682, -2.2664189234341015, -5.34713157717381 ], "28": [ 2.1328356391129724, 2.2545836534482677, -2.94286805933878, -4.987924650741718 ], "29": [ 3.5102870195046525, 0.40818582737003895, -1.1497893629323443, -6.3292895198814385 ], "30": [ 4.203329720831353, -0.07967862798799401, -1.4780320281687815, -6.645745223095405 ], "31": [ 4.839513681535632, -0.6260787462253514, -1.7913209728821826, -6.946127642864884 ], "32": [ 5.436964706857614, -1.2474776554131104, -2.187490996055279, -7.153417678148604 ], "33": [ 2.6889959547375697, 1.3196190270618726, -0.4857120985115062, -6.639069513826175 ], "34": [ 2.5994251305866243, 1.823577832128075, -0.20538683553370585, -7.461013267560826 ], "35": [ 4.918077841199502, -1.0328566789534892, -3.5356980414755776, 0.3231755433300121 ], "36": [ 4.547517518581194, -0.9435729565016044, -4.43048629984844, 0.32377260917378514 ], "37": [ 4.212642559530355, -0.9552833172302453, -5.343491740036745, 0.3787771844248957 ], "38": [ 6.283501249091808, -2.0016507541537716, -3.971033054774095, 0.9038834364389423 ], "39": [ 2.47170872510155, 1.3217079044512563, -2.1893696891872425, -6.362357078421188 ], "40": [ 2.360731104893766, 1.5132219220604477, -2.901743110643854, -6.967165771363278 ], "41": [ 2.273495873476138, 1.7441274683829893, -3.581311919497204, -7.611092698446333 ], "42": [ 2.062397206374627, 2.0354638197027, -4.2233134467236635, -8.25843277375918 ], "43": [ 2.3037248659911462, 1.3685712585201475, -1.3318789163921494, -4.724623044920178 ], "44": [ 2.155020615406781, 1.5522151899093333, -0.9318936217565412, -3.8512397750583913 ], "45": [ 2.4308418397619986, 3.1290846003015265, -3.1594189724420425, -5.179518074569924 ], "46": [ 2.7347868940139097, 3.9571607628274146, -3.5173881491770373, -5.364801835145068 ], "47": [ 1.6965567137072457, 1.768188791182843, -3.425719390690429, -4.443282667311999 ], "48": [ 1.270608214804235, 1.2904006724700303, -3.8956761117856264, -3.909577393128421 ], "49": [ 6.798997549017582, -2.43784126801225, -4.29552350042921, 0.28241135357387126 ], "50": [ 7.284833695663526, -2.9549061034001727, -4.632628107875963, -0.283114993898129 ], "51": [ 6.851130244302, -1.4031604453662052, -4.24445929080227, 1.3428090942298754 ], "52": [ 7.378887639172282, -0.8015177302200349, -4.577714572004637, 1.790904150104999 ], "53": [ 7.887820901452619, -0.15297827552644294, -4.899116544038936, 2.2130854088393077 ], "54": [ 6.092208355794204, -2.6948969954370834, -4.155016680531206, 1.5670799343419617 ] }, "embedding_valid": true, "embedding_dimensions_attempted": [ 4 ], "embedding_attempt_history": [ { "dimension": 4, "embedding_valid": true, "global_embedding_attempts": 1, "local_placement_rejections": 0, "min_nonadjacent_node_distance": 1.344438149536375, "min_nonincident_edge_distance": 1.3867056508102389, "min_nonincident_node_edge_distance": 1.0488917259267805, "failure_reason": null, "refinement_applied": true, "refinement_iterations": 24, "refinement_objective_delta": -47.6742095144468, "refinement_clearance_delta": 0.032642407060578194 } ], "embedding_constructive_success": true, "embedding_rejected": false, "min_nonadjacent_node_distance": 1.344438149536375, "min_nonincident_edge_distance": 1.3867056508102389, "min_nonincident_node_edge_distance": 1.0488917259267805, "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": 280.38732290687375, "objective_after": 232.71311339242695, "objective_delta": -47.6742095144468, "clearance_before": 1.0162493188662023, "clearance_after": 1.0488917259267805, "clearance_delta": 0.032642407060578194, "accepted_steps": 24, "reason": "accepted" }, "topology_class": "branchy_cycle", "sampled_topology_spec": { "topology_class": "branchy_cycle", "children_per_branch_point_range": [ 1, 3 ], "branch_length_range": [ 1, 4 ], "max_branch_depth_range": [ 1, 3 ], "promotion_prob_range": [ 0.2, 0.6 ], "max_degree": 5, "num_cycles": 3, "branch_attach_count": 3 }, "tube_embedding_separation_ratio": 6.0, "realized_post_crowding_min_nonadjacent_node_distance": 1.3059063607687496, "realized_post_crowding_min_nonincident_edge_distance": 1.323693412843518, "realized_post_crowding_min_nonincident_node_edge_distance": 1.0012096418586636, "realized_post_crowding_min_structural_distance": 1.0012096418586636, "realized_post_crowding_separation_to_feature_scale": 1.0012096418586636, "realized_post_crowding_separation_to_post_median_edge": 1.0236164013381974, "realized_post_crowding_absolute_hardness": 0.9987918196069128, "minimum_realized_component_gap": Infinity, "feature_thickness_radius": 0.032249165762276405, "effective_max_tube_radius_for_sampling": 0.07087782468797399, "cycle_hole_radius_cap": 0.07087782468797399, "cycle_hole_radius_fraction": 0.2, "crowding_applied": true, "crowding_isotropy_epsilon": 0.05, "crowding_axis": [ -0.27947651219072894, 0.2752761899678826, 0.2502115672128296, -0.8851610418468333 ], "crowding_centroid": [ 3.58448658826314, 0.10200581791705353, -1.9901132842098421, -2.7528672547303854 ], "crowding_covariance_eigenvalues": [ 13.460256478231248, 3.1045613900909252, 2.720613686678543, 0.8891763408645619 ], "crowding_covariance_matrix": [ [ 3.3684253182110404, -1.396351516030446, -0.9119192773611973, 2.4943197826066745 ], [ -1.396351516030446, 2.0197954917797243, 0.5428141687281473, -2.9635518876860774 ], [ -0.9119192773611973, 0.5428141687281473, 3.6871190095078745, -2.305872164360821 ], [ 2.4943197826066745, -2.9635518876860774, -2.305872164360821, 11.099268076366648 ] ], "crowding_isotropic_fallback_used": false, "crowding_linear_operator": [ [ 0.9580811264315972, -0.0034981876875226766, -0.003179668476964157, 0.011248555345177552 ], [ -0.0034981876875226766, 0.9579751739390813, 0.0031318804461905295, -0.01107949800071269 ], [ -0.003179668476964157, 0.0031318804461905295, 0.9573762758625906, -0.01007068050096588 ], [ 0.011248555345177552, -0.01107949800071269, -0.01007068050096588, 0.9901561079277575 ] ], "crowding_model_dimension": 4, "feature_scale_nominal": 1.0, "feature_scale_pre_crowding": 1.0137542106998592, "feature_scale_post_crowding_median_edge": 0.9781101988496463, "pre_crowding_edge_length_summary": { "min": 0.8489316143908057, "median": 1.0137542106998592, "mean": 1.2194830119244404, "max": 4.332114192733192 }, "post_crowding_edge_length_summary": { "min": 0.8368127577776215, "median": 0.9781101988496463, "mean": 1.1837884723046264, "max": 4.184640487938936 }, "pre_crowding_min_nonadjacent_node_distance": 1.3444381495363753, "pre_crowding_min_nonincident_edge_distance": 1.386705650810239, "pre_crowding_min_nonincident_node_edge_distance": 1.0488917259267807, "node_positions_4d_pre_crowding": { "0": [ 4.952394034203628, 0.02457411777366677, 0.6085063410512113, 0.017663345855372194 ], "1": [ 4.421625122786361, 0.08222202399531044, 0.3151685899875462, -0.9430195661472207 ], "2": [ 3.7991895903687385, 0.030924007676009186, -0.430593655284853, -0.6940848919986273 ], "3": [ 3.853457352214153, -0.09662451602852798, -0.7010826251084508, 0.5102576824770217 ], "4": [ 4.626959628764557, -0.060408003124932885, 0.027666939001775765, 0.7972886465782206 ], "5": [ 1.5038206119407307, -1.3486965529332875, -3.470924170039181, 2.5119354782310115 ], "6": [ 0.6235724509750971, -1.4409422797112557, -4.10028372861394, 2.7273306871575063 ], "7": [ 0.0, -0.9602020227195464, -3.961026058327739, 2.1140577326464114 ], "8": [ 0.5524041329643441, -0.6065682790672721, -3.248804474717499, 1.5626671179405656 ], "9": [ 3.51642574994549, 0.24354224852146647, 0.06103881469431517, -3.4103266154400282 ], "10": [ 2.8705073863388773, 0.3702183517199311, -0.12963107698314458, -5.07546554514142 ], "11": [ 2.4482075729930965, 0.39262106210801667, -0.33087512376331424, -5.7835239507571625 ], "12": [ 2.581162541898776, 0.3401928800392881, -0.47476720192689414, -4.947012817604716 ], "13": [ 3.0721621625013853, 0.21040741459096063, -0.4754179246005065, -3.1794062632196045 ], "14": [ 3.6623325333247805, 0.5408669405867812, 0.700220826797045, -2.890751584958107 ], "15": [ 3.845783315496967, 0.8107038844118168, 1.355750650381411, -2.2074161281782483 ], "16": [ 3.6266276495590306, -0.15538671207761273, -0.06470076040718535, -4.398594156351897 ], "17": [ 2.319422339318327, -0.06325080857411569, 0.4948013991270053, -5.538089905780462 ], "18": [ 1.8467207894021906, -0.5340390012667238, 1.1723539952465782, -5.837254690847991 ], "19": [ 1.5137540585596625, -0.9542596056902675, 1.9286896598335266, -6.173080584609263 ], "20": [ 2.8942240497677005, 0.8090069083334996, -0.7795624005805583, -5.854673179782041 ], "21": [ 3.4339092111491443, 0.34920364730493864, -0.04051480721930596, 0.19377793686280742 ], "22": [ 4.275085485483027, -0.31151105232301446, -1.2081752524289062, -0.22706231375446081 ], "23": [ 4.833783817101658, -0.6798387539678549, -1.9058827743941664, 0.05827637836897833 ], "24": [ 5.300742168340946, -1.131483590791495, -2.6189568961372274, 0.2913178010692963 ], "25": [ 5.811460006692777, -1.6012444791406095, -3.312819851883735, 0.5739899012662721 ], "26": [ 2.507998660675475, 1.2607780560183184, -1.5557184694632449, -5.66853273103697 ], "27": [ 2.3184214503481293, 1.7818518391875542, -2.3156669233543026, -5.343054392077912 ], "28": [ 2.100139188326356, 2.3212176942537965, -3.020891720259871, -4.978933933745614 ], "29": [ 3.553095801674209, 0.37712428567390094, -1.1512498941019174, -6.3528784407560615 ], "30": [ 4.277421865809042, -0.13227557289297728, -1.4935793623648401, -6.689890663150174 ], "31": [ 4.942038071295036, -0.7028591034240748, -1.8201151288765005, -7.010515467522727 ], "32": [ 5.564572372242369, -1.3505328380855348, -2.23213374472065, -7.238376360067533 ], "33": [ 2.704940080225626, 1.319900437098221, -0.46651342911513727, -6.638589165009115 ], "34": [ 2.6239025231099715, 1.835258340343074, -0.1842942179935218, -7.459146797707761 ], "35": [ 4.9310865491779845, -1.037157907525647, -3.564095383436939, 0.30970342128608597 ], "36": [ 4.5415923066762955, -0.9423585587372717, -4.500360701871254, 0.3062694311543153 ], "37": [ 4.1882786072786065, -0.9521776573106053, -5.454632411863811, 0.3560190487884787 ], "38": [ 6.344629621103221, -2.0354319769841656, -4.005016116744239, 0.8644713248978525 ], "39": [ 2.469182170564441, 1.330086664512506, -2.244057670308274, -6.374412488864386 ], "40": [ 2.358787044513191, 1.5249428671597356, -2.9956205688335724, -6.989443536292987 ], "41": [ 2.2738915965355644, 1.760450200109951, -3.7133768628576, -7.64347269598108 ], "42": [ 2.060079990455206, 2.0584320928013136, -4.392535233517992, -8.298392759203958 ], "43": [ 2.2775496327818403, 1.3945937860274569, -1.331710929650698, -4.708218372043686 ], "44": [ 2.114028058850155, 1.594603214721781, -0.9057479736931595, -3.8177240498083314 ], "45": [ 2.41597390105157, 3.2337988492933936, -3.2510105253977604, -5.168149168045772 ], "46": [ 2.7372926984920234, 4.098470294527082, -3.6286238334260896, -5.3530905412441525 ], "47": [ 1.6348914751502557, 1.8197156491178237, -3.5194155870023174, -4.434273876334306 ], "48": [ 1.1806312352957185, 1.3270678799893554, -4.00457825946246, -3.90054910994343 ], "49": [ 6.887408511394449, -2.495086259791085, -4.347404839040231, 0.22202880265683209 ], "50": [ 7.3982270039571745, -3.0385934302012485, -4.70221419499278, -0.3646133148604562 ], "51": [ 6.933296534873572, -1.4025199599046394, -4.286093967516686, 1.305296467654222 ], "52": [ 7.48004505587943, -0.7661601336384078, -4.629718899838444, 1.7552608034056851 ], "53": [ 8.00765950055518, -0.08124752486225643, -4.961451201919786, 2.179935329916433 ], "54": [ 6.133967084089212, -2.7515990716845744, -4.188581013621049, 1.526773709883065 ] }, "crowding_gamma_min_search_tolerance": 0.005, "crowding_gamma_min_search_history": [ { "gamma": 0.01, "admissible": false, "realized_separation_ratio": 0.010348088896825529 }, { "gamma": 1.0, "admissible": true, "realized_separation_ratio": 1.0346607835075368 }, { "gamma": 0.505, "admissible": true, "realized_separation_ratio": 0.5225577663360738 }, { "gamma": 0.2575, "admissible": true, "realized_separation_ratio": 0.2664604831758698 }, { "gamma": 0.13375, "admissible": true, "realized_separation_ratio": 0.13840529512182068 }, { "gamma": 0.07187500000000001, "admissible": false, "realized_separation_ratio": 0.07437682857662187 }, { "gamma": 0.1028125, "admissible": true, "realized_separation_ratio": 0.10639111060943304 }, { "gamma": 0.08734375, "admissible": true, "realized_separation_ratio": 0.09038397996267791 }, { "gamma": 0.07960937500000001, "admissible": false, "realized_separation_ratio": 0.08238040663380652 }, { "gamma": 0.0834765625, "admissible": true, "realized_separation_ratio": 0.08638219391784119 } ], "crowding_gamma_min_search_iterations": 10, "crowding_gamma_min_search_bracket": [ 0.07960937500000001, 0.0834765625 ], "crowding_relative_budget_definition": "gamma = 1 - r * (1 - gamma_min)", "requested_noise_ratio": 0.068573131604513, "realized_noise_ratio": 0.068573131604513, "max_admissible_noise_ratio_after_crowding": 0.15278521838901846, "requested_crowding_r": 0.04961186670470844, "realized_crowding_r": 0.04961186670470844, "staged_generation_order": "topology -> max-separation embedding -> admissible thickness -> thickness-constrained crowding -> clearance-capped noise -> sampling", "tube_no_overlap_required_centerline_clearance": 0.35879085794260485, "tube_no_overlap_post_crowding_margin": 0.6424187839160587, "tube_no_overlap_satisfied": true, "tube_no_overlap_constraint_active": true, "max_admissible_tube_radius_after_crowding": 0.35345855772030577, "realized_tube_radius_budget_fraction": 0.0912388880050696, "point_cloud_params": { "feature_scale": 1.0, "sampling_density_per_feature": 17.041873831610662, "noise_ratio": 0.068573131604513, "sigma": 0.068573131604513, "embedding_dimension": 4, "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": 0.032249165762276405, "feature_thickness_radius": 0.032249165762276405, "tube_sampling_mode": "solid" }, "num_clean_points": 1190, "num_edge_sampled_points": 1135, "num_node_sampled_points": 55, "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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189 ] ], "nearest_feature_changed_rate": 0.13361344537815126, "nonincident_feature_confusion_rate": 0.07899159663865546, "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": 1190, "num_nearest_feature_changes": 159, "num_nonincident_feature_confusions": 94, "num_cross_component_confusions": 0, "sample_id": 15, "difficulty": "full", "difficulty_coordinate": { "noise_ratio": 0.068573131604513, "crowding_r": 0.04961186670470844, "sampling_density_per_feature": 17.041873831610662, "feature_thickness_ratio": 0.4549965508146894, "num_components": 1, "requested_embedding_dimension": 4 }, "realized_geometry": { "realized_separation_to_feature_scale": 1.0012096418586636, "realized_absolute_hardness": 0.9987918196069128, "crowding_gamma": 0.9545295613870088, "crowding_gamma_min": 0.0834765625, "feature_thickness_radius": 0.032249165762276405, "feature_thickness_budget": 0.4549965508146894, "effective_max_tube_radius_for_sampling": 0.07087782468797399, "max_admissible_tube_radius_before_crowding": 0.07087782468797399, "cycle_hole_radius_cap": 0.07087782468797399, "cycle_hole_radius_fraction": 0.2, "requested_noise_ratio": 0.068573131604513, "realized_noise_ratio": 0.068573131604513, "max_admissible_noise_ratio_after_crowding": 0.15278521838901846, "requested_crowding_r": 0.04961186670470844, "realized_crowding_r": 0.04961186670470844, "thickness_aware_min_required_clearance": 0.08449833152455281, "thickness_clearance_noise_margin": 0.274292526418052, "minimum_realized_component_gap": Infinity }, "graph_summary": { "num_nodes": 55, "num_edges": 57, "num_components": 1, "num_clean_points": 1190, "topology_classes": [ "branchy_cycle" ] }, "seed_bundle": { "point_cloud_seed": 348665641, "component_seed_bundles": [ { "topology_seed": 962453431, "branch_seed": 46638087, "embedding_seed": 17805380, "topology_class": "branchy_cycle" } ] }, "scheduled_normalized_axes": { "noise_ratio": 0.2698507311361833, "crowding_r": 0.0826864445078474, "sampling_density_per_feature": 0.37014540318089945, "feature_thickness_ratio": 0.009084637844889948 }, "scheduled_vector_magnitude": 0.23278026942849206, "scheduled_sample_rank": 15, "actual_normalized_axes": { "noise_ratio": 0.2698507311361833, "crowding_r": 0.0826864445078474, "sampling_density_per_feature": 0.37014540318089945, "feature_thickness_ratio": 0.009084637844889948 }, "actual_difficulty_coordinate": [ 0.068573131604513, 0.04961186670470844, 17.041873831610662, 0.4549965508146894 ], "difficulty_relaxation_factor": 1.0 }