{ "kind": "ordinary numerical experiments, not enclosures", "integrator": "classical RK4 without clipping", "quadrature": "Gauss-Legendre / Chebyshev-U as in two_mode.py", "precision_note": "longdouble checks arithmetic; quadrature nodes originate in float64", "predicted_GS_small_time_capacity_difference_over_eps_sigma_squared": -4.420695487050275, "runs": [ { "pair": "gs", "epsilon": 0.04, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336661118624, "beta2": -0.03964949139183611, "z": -0.9912371831060062, "chi": 8.225561367809256e-06, "c_linear": 0.00021440547258906226, "kappa2": 0.7041137278257508, "kappa_perp": 0.7041295300836399, "residual_error": -4.06759585735994e-09, "coupling_error": -3.506575357532356e-07, "capacity_difference": -1.5802257889108162e-05, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve 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0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585987446, "gap_base": 0.7353114254016203, "beta1": -0.7353052944769124, "beta2": -0.015755017899141285, "z": -0.7871727475678841, "chi": 0.0022343217557902533, "c_linear": 0.11424178279782903, "kappa2": 0.7661196173783121, "kappa_perp": 0.7704302214490775, "residual_error": -1.1562947783601285e-05, "coupling_error": -5.051390016632719e-05, "capacity_difference": -0.004310604070765334, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.1973798352377906, "beta2": -0.011653473554394361, "z": -0.5800120869916802, "chi": 0.00679123134490334, "c_linear": 0.3486425336629241, "kappa2": 0.8641909695327497, "kappa_perp": 0.876368562165085, "residual_error": -5.323181456075819e-05, "coupling_error": -0.00018161932835514174, "capacity_difference": -0.01217759263233531, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.3568443262375464, "gap_base": 0.0001688676370499337, "beta1": -0.00016246577587313927, "beta2": -0.006637991030423498, "z": -0.3269002938506352, "chi": 0.011294453359299296, "c_linear": 0.5857632376199797, "kappa2": 0.8771394446896824, "kappa_perp": 0.8960489953005486, "residual_error": -9.998515341079397e-05, "coupling_error": -0.00042081139310029894, "capacity_difference": -0.018909550610866188, "estimated_distance_to_freeze": 1.1291790128931112e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556215314015, "gap_base": 5.4183970812231014e-11, "beta1": 2.954789463676446e-06, "beta2": -0.0022255773021911222, "z": -0.106649604824081, "chi": 0.01487292898679967, "c_linear": 0.7769750274429695, "kappa2": 0.8722696375616708, "kappa_perp": 0.8960634732365874, "residual_error": -9.258520570950201e-05, "coupling_error": -0.0006665715620597212, "capacity_difference": -0.023793835674916664, "estimated_distance_to_freeze": -3.5037261425507893e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562153502465, "gap_base": 5.575116923302708e-24, "beta1": 3.738788503893754e-07, "beta2": -0.00025227833192186547, "z": -0.011351955915290007, "chi": 0.01645063184689201, "c_linear": 0.8596993916389246, "kappa2": 0.8702605232207967, "kappa_perp": 0.8960634732412289, "residual_error": -2.5239213616065327e-05, "coupling_error": -0.0007433559858864812, "capacity_difference": -0.025802950020432203, "estimated_distance_to_freeze": -3.5073492998805023e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "gs", "epsilon": 0.01, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336681903283, "beta2": -0.009912372098692225, "z": -0.9912371831060062, "chi": 2.1221379595898557e-06, "c_linear": 0.00021440547258906226, "kappa2": 0.7041252556172752, "kappa_perp": 0.7041295300836399, "residual_error": -2.676321629591083e-10, "coupling_error": -2.1916766300767207e-08, "capacity_difference": -4.274466364639906e-06, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.048908534332402984, "gap_base": 0.9563669597530424, "beta1": -0.9563669430572646, "beta2": -0.009567895424032143, "z": -0.9567863899187731, "chi": 5.13831089887902e-05, "c_linear": 0.00519158968502721, "kappa2": 0.7070290953348484, "kappa_perp": 0.7071324872836825, "residual_error": -3.152484441201753e-08, "coupling_error": -5.327878614819e-07, "capacity_difference": -0.00010339194883413061, "estimated_distance_to_freeze": 0.30794708369527235, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.0956121025079325, "gap_base": 0.9112695827458732, "beta1": -0.9112694578890616, "beta2": -0.00914539231893457, "z": -0.9145157540684956, "chi": 0.00019841503692957443, "c_linear": 0.020049663975781416, "kappa2": 0.7156497120038919, "kappa_perp": 0.7160477311026894, "residual_error": -2.3477824961405658e-07, "coupling_error": -2.081602828239742e-06, "capacity_difference": -0.0003980190987974419, "estimated_distance_to_freeze": 0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { 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-0.006336076755244724, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.3568443262375464, "gap_base": 0.0001688676370499337, "beta1": -0.00016724952958806596, "beta2": -0.003295030681957097, "z": -0.3269002938506352, "chi": 0.005750632158576345, "c_linear": 0.5857632376199797, "kappa2": 0.8859671502707528, "kappa_perp": 0.8960489953005486, "residual_error": -2.602774345074506e-05, "coupling_error": -0.00010700021762345257, "capacity_difference": -0.01008184502979581, "estimated_distance_to_freeze": 1.1291790128931112e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556215314015, "gap_base": 5.4183970812231014e-11, "beta1": 7.406604445666416e-07, "beta2": -0.0010909783581801978, "z": -0.106649604824081, "chi": 0.007600482492194124, "c_linear": 0.7769750274429695, "kappa2": 0.8830771531587869, "kappa_perp": 0.8960634732365874, "residual_error": -2.4482309939387673e-05, "coupling_error": -0.0001692677822355713, "capacity_difference": -0.01298632007780054, "estimated_distance_to_freeze": -3.5037261425507893e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562153502465, "gap_base": 5.575116923302708e-24, "beta1": 9.114791787703974e-08, "beta2": -0.00012020879334653404, "z": -0.011351955915290007, "chi": 0.008409567453642188, "c_linear": 0.8596993916389246, "kappa2": 0.8818403479262322, "kappa_perp": 0.8960634732412289, "residual_error": -6.689234193633971e-06, "coupling_error": -0.00018742646274705864, "capacity_difference": -0.014223125314996699, "estimated_distance_to_freeze": -3.5073492998805023e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "gs", "epsilon": 0.005, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336682963152, "beta2": -0.004956185982996843, "z": -0.9912371831060062, "chi": 1.0665481425129261e-06, "c_linear": 0.00021440547258906226, "kappa2": 0.7041273658579787, "kappa_perp": 0.7041295300836399, "residual_error": -6.746681165126223e-11, "coupling_error": -5.479220432385328e-09, "capacity_difference": -2.1642256611276167e-06, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.048908534332402984, "gap_base": 0.9563669597530424, "beta1": -0.9563669555656994, "beta2": -0.004783939896971442, "z": -0.9567863899187731, "chi": 2.582473475957839e-05, "c_linear": 0.00519158968502721, "kappa2": 0.7070801344985853, "kappa_perp": 0.7071324872836825, 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"beta2": -0.003936607150725959, "z": -0.7871727475678841, "chi": 0.000568029310037486, "c_linear": 0.11424178279782903, "kappa2": 0.7693046164720817, "kappa_perp": 0.7704302214490775, "residual_error": -7.434128865375575e-07, "coupling_error": -3.1796039516591556e-06, "capacity_difference": -0.0011256049769957643, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.1973884944806418, "beta2": -0.00290351284312593, "z": -0.5800120869916802, "chi": 0.0017316551609683197, "c_linear": 0.3486425336629241, "kappa2": 0.8731380777474518, "kappa_perp": 0.876368562165085, "residual_error": -3.452408167529432e-06, "coupling_error": -1.1557507346300752e-05, "capacity_difference": -0.0032304844176331837, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.3568443262375464, "gap_base": 0.0001688676370499337, "beta1": -0.00016846092534622865, "beta2": -0.001641137272113822, "z": -0.3269002938506352, "chi": 0.0029018362355559125, "c_linear": 0.5857632376199797, "kappa2": 0.8908496207009244, "kappa_perp": 0.8960489953005486, "residual_error": -6.635802860645865e-06, "coupling_error": -2.6979952543986288e-05, "capacity_difference": -0.0051993745996241625, "estimated_distance_to_freeze": 1.1291790128931112e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556215314015, "gap_base": 5.4183970812231014e-11, "beta1": 1.8521046659175363e-07, "beta2": -0.000539531199441799, "z": -0.106649604824081, "chi": 0.003842225842205647, "c_linear": 0.7769750274429695, "kappa2": 0.8892965457834359, "kappa_perp": 0.8960634732365874, "residual_error": -6.2831753213939525e-06, "coupling_error": -4.2649295009200734e-05, "capacity_difference": -0.00676692745315155, "estimated_distance_to_freeze": -3.5037261425507893e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562153502465, "gap_base": 5.575116923302708e-24, "beta1": 2.2427901538326303e-08, "beta2": -5.847480310798466e-05, "z": -0.011351955915290007, "chi": 0.004251445408811248, "c_linear": 0.8596993916389246, "kappa2": 0.8886224750810281, "kappa_perp": 0.8960634732412289, "residual_error": -1.715023531534624e-06, "coupling_error": -4.705154938337494e-05, "capacity_difference": -0.007440998160200829, "estimated_distance_to_freeze": -3.5073492998805023e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "gs", "epsilon": 0.0025, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336683229113, "beta2": -0.002478092974701617, "z": -0.9912371831060062, "chi": 5.346438727098643e-07, "c_linear": 0.00021440547258906226, "kappa2": 0.7041284412226532, "kappa_perp": 0.7041295300836399, "residual_error": -1.6936601426875697e-11, "coupling_error": -1.3698087627914543e-09, "capacity_difference": -1.088860986708795e-06, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.048908534332402984, "gap_base": 0.9563669597530424, "beta1": -0.9563669587045317, "beta2": -0.0023919679699131555, "z": -0.9567863899187731, "chi": 1.2945668694699851e-05, "c_linear": 0.00519158968502721, "kappa2": 0.7071061466673301, "kappa_perp": 0.7071324872836825, "residual_error": -1.9951162228380726e-09, "coupling_error": -3.330551786817379e-08, "capacity_difference": -2.6340616352427126e-05, "estimated_distance_to_freeze": 0.30794708369527235, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.0956121025079325, "gap_base": 0.9112695827458732, "beta1": -0.9112695749046417, "beta2": -0.0022863042466377704, "z": -0.9145157540684956, "chi": 4.999396759347688e-05, "c_linear": 0.020049663975781416, "kappa2": 0.715946295558625, "kappa_perp": 0.7160477311026894, "residual_error": -1.4861466531360112e-08, "coupling_error": -1.3019234597666426e-07, "capacity_difference": -0.0001014355440643877, "estimated_distance_to_freeze": 0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585987446, "gap_base": 0.7353114254016203, "beta1": -0.7353113285312314, "beta2": -0.0019681185890633333, "z": -0.7871727475678841, "chi": 0.0002848086018717436, "c_linear": 0.11424178279782903, "kappa2": 0.7698634011196337, "kappa_perp": 0.7704302214490775, "residual_error": -1.8672014362279554e-07, "coupling_error": -7.958551228289868e-07, "capacity_difference": -0.0005668203294437735, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.1973889307044836, "beta2": -0.001450898581124285, "z": -0.5800120869916802, "chi": 0.0008687081624794605, "c_linear": 0.3486425336629241, "kappa2": 0.8747376276944814, "kappa_perp": 0.876368562165085, "residual_error": -8.683636450845366e-07, "coupling_error": -2.898171677849764e-06, "capacity_difference": -0.0016309344706035844, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.3568443262375464, "gap_base": 0.0001688676370499337, "beta1": -0.00016876568735430347, "beta2": -0.0008189257888749341, "z": -0.3269002938506352, "chi": 0.001457634038977926, "c_linear": 0.5857632376199797, "kappa2": 0.8934094736496427, "kappa_perp": 0.8960489953005486, "residual_error": -1.6750542483460768e-06, "coupling_error": -6.774055072023303e-06, "capacity_difference": -0.0026395216509058628, "estimated_distance_to_freeze": 1.1291790128931112e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556215314015, "gap_base": 5.4183970812231014e-11, "beta1": 4.626230831073887e-08, "beta2": -0.00026821484089661787, "z": -0.106649604824081, "chi": 0.001931733458856513, "c_linear": 0.7769750274429695, "kappa2": 0.8926113797960767, "kappa_perp": 0.8960634732365874, "residual_error": -1.5908288364153435e-06, "coupling_error": -1.0704109750910885e-05, "capacity_difference": -0.003452093440510673, "estimated_distance_to_freeze": -3.5037261425507893e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562153502465, "gap_base": 5.575116923302708e-24, "beta1": 5.558008125934663e-09, "beta2": -2.88136803372888e-05, "z": -0.011351955915290007, "chi": 0.0021374614722308918, "c_linear": 0.8596993916389246, "kappa2": 0.8922607494020358, "kappa_perp": 0.8960634732412289, "residual_error": -4.337905490637836e-07, "coupling_error": -1.1787006866419841e-05, "capacity_difference": -0.0038027238391931117, "estimated_distance_to_freeze": -3.5073492998805023e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "gs", "epsilon": 0.005, "n_y": 16, "n_aux": 16, "step": 0.001, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.00995611640129488, "gap_base": 0.9912336683306744, "beta1": -0.9912336682951939, "beta2": -0.004956185982996545, "z": -0.9912371831059965, "chi": 1.0665481425906973e-06, "c_linear": 0.00021440547259328545, "kappa2": 0.7041273658579932, "kappa_perp": 0.7041295300836543, "residual_error": -6.746656271844342e-11, "coupling_error": -5.4792203757300474e-09, "capacity_difference": -2.1642256611276167e-06, "estimated_distance_to_freeze": 0.34689950162638045, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.04890853433232117, "gap_base": 0.9563669597475992, "beta1": -0.956366955560256, "beta2": -0.004783939896970053, "z": -0.9567863899187172, "chi": 2.582473476022263e-05, "c_linear": 0.00519158968508751, "kappa2": 0.7070801344988069, "kappa_perp": 0.7071324872839035, "residual_error": -7.94737646699073e-09, "coupling_error": -1.3321366521491912e-07, "capacity_difference": -5.2352785096632104e-05, "estimated_distance_to_freeze": 0.3079470836953542, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.09561210250708423, "gap_base": 0.9112695827338644, "beta1": -0.9112695514191966, "beta2": -0.00457263796571172, "z": -0.9145157540683634, "chi": 9.972767394706366e-05, "c_linear": 0.020049663975876715, "kappa2": 0.7158461476075271, "kappa_perp": 0.7160477311033004, "residual_error": -5.9195369902717565e-08, "coupling_error": -5.206459323199217e-07, "capacity_difference": -0.00020158349577337198, "estimated_distance_to_freeze": 0.2612435155205911, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585146932, "gap_base": 0.7353114253370396, "beta1": -0.7353110384728031, "beta2": -0.003936607150724262, "z": -0.7871727475682387, "chi": 0.0005680293100268569, "c_linear": 0.1142417827953647, "kappa2": 0.7693046164714721, "kappa_perp": 0.7704302214483806, 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-0.0001684609175959822, "beta2": -0.001641137272386791, "z": -0.3269002939061738, "chi": 0.002901836234470777, "c_linear": 0.5857632374007503, "kappa2": 0.8908496205757215, "kappa_perp": 0.8960489951728743, "residual_error": -6.635802855921996e-06, "coupling_error": -2.6979952532974697e-05, "capacity_difference": -0.005199374597152806, "estimated_distance_to_freeze": 1.1291911165556279e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556214098392, "gap_base": 5.418396257557926e-11, "beta1": 1.8521046646285006e-07, "beta2": -0.0005395311996167831, "z": -0.10664960485942429, "chi": 0.0038422258409250157, "c_linear": 0.7769750271857971, "kappa2": 0.8892965456580673, "kappa_perp": 0.8960634731082335, "residual_error": -6.283175319661614e-06, "coupling_error": -4.264929500397011e-05, "capacity_difference": -0.006766927450166271, "estimated_distance_to_freeze": -3.3821638267816923e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562141346205, "gap_base": 5.57511489264646e-24, "beta1": 2.2427901529030123e-08, "beta2": -5.8474803145240854e-05, "z": -0.01135195592268974, "chi": 0.004251445407527728, "c_linear": 0.8596993913824104, "kappa2": 0.8886224749557519, "kappa_perp": 0.896063473112872, "residual_error": -1.7150235317921558e-06, "coupling_error": -4.7051549384323835e-05, "capacity_difference": -0.007440998157120182, "estimated_distance_to_freeze": -3.385786706555649e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "gs", "epsilon": 0.005, "n_y": 24, "n_aux": 24, "step": 0.001, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.00995611640129488, "gap_base": 0.9912336683306744, "beta1": -0.9912336682951939, "beta2": -0.004956185982996545, "z": -0.9912371831059965, "chi": 1.0665481425717822e-06, "c_linear": 0.00021440547259328555, "kappa2": 0.704127365857993, "kappa_perp": 0.7041295300836542, "residual_error": -6.746656271844342e-11, "coupling_error": -5.479220394645564e-09, "capacity_difference": -2.164225661238639e-06, "estimated_distance_to_freeze": 0.34689950162638045, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.04890853433232117, "gap_base": 0.9563669597475992, "beta1": -0.9563669555602559, "beta2": -0.004783939896970054, "z": -0.9567863899187173, "chi": 2.5824734760197315e-05, "c_linear": 0.00519158968508752, "kappa2": 0.7070801344988069, "kappa_perp": 0.7071324872839034, "residual_error": -7.94737646699073e-09, "coupling_error": -1.3321366524028267e-07, "capacity_difference": -5.235278509652108e-05, "estimated_distance_to_freeze": 0.3079470836953542, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.09561210250708423, "gap_base": 0.9112695827338644, "beta1": -0.9112695514191965, "beta2": -0.0045726379657117225, "z": -0.9145157540683635, "chi": 9.972767394704314e-05, "c_linear": 0.020049663975876722, "kappa2": 0.7158461476075269, "kappa_perp": 0.7160477311033002, "residual_error": -5.919536990445229e-08, "coupling_error": -5.206459323404673e-07, "capacity_difference": -0.00020158349577337198, "estimated_distance_to_freeze": 0.2612435155205911, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585146932, "gap_base": 0.7353114253370394, "beta1": -0.735311038472803, "beta2": -0.003936607150724267, "z": -0.7871727475682389, "chi": 0.0005680293100268636, "c_linear": 0.11424178279536468, "kappa2": 0.7693046164714719, "kappa_perp": 0.7704302214483805, "residual_error": -7.434128830733147e-07, "coupling_error": -3.179603949959777e-06, "capacity_difference": -0.0011256049769086118, "estimated_distance_to_freeze": 0.13667339217620603, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.3407982882891465, "gap_base": 0.19738907599513789, "beta1": -0.1973884941170414, "beta2": -0.002903512843230886, "z": -0.5800120870136236, "chi": 0.001731655160634687, "c_linear": 0.34864253359522024, "kappa2": 0.873138077693647, "kappa_perp": 0.8763685621103159, "residual_error": -3.4524081627680496e-06, "coupling_error": -1.1557507341414036e-05, "capacity_difference": -0.003230484416668844, "estimated_distance_to_freeze": 0.016057329738528858, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.35684432611651384, "gap_base": 0.00016886762930040737, "beta1": -0.00016846091759699038, "beta2": -0.0016411372723867772, "z": -0.3269002939061708, "chi": 0.00290183623447078, "c_linear": 0.5857632374007624, "kappa2": 0.890849620575727, "kappa_perp": 0.8960489951728805, "residual_error": -6.63580285592308e-06, "coupling_error": -2.6979952533031943e-05, "capacity_difference": -0.005199374597153472, "estimated_distance_to_freeze": 1.1291911161503965e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556214098433, "gap_base": 5.418396257680286e-11, "beta1": 1.8521046646306936e-07, "beta2": -0.0005395311996167743, "z": -0.10664960485942229, "chi": 0.003842225840925101, "c_linear": 0.7769750271858121, "kappa2": 0.8892965456580728, "kappa_perp": 0.8960634731082402, "residual_error": -6.283175319662807e-06, "coupling_error": -4.26492950039597e-05, "capacity_difference": -0.0067669274501673815, "estimated_distance_to_freeze": -3.3821679346068834e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562141346616, "gap_base": 5.5751148929576746e-24, "beta1": 2.2427901529056655e-08, "beta2": -5.847480314523899e-05, "z": -0.011351955922689332, "chi": 0.004251445407527815, "c_linear": 0.8596993913824247, "kappa2": 0.8886224749557577, "kappa_perp": 0.8960634731128787, "residual_error": -1.715023531792332e-06, "coupling_error": -4.705154938430909e-05, "capacity_difference": -0.007440998157120959, "estimated_distance_to_freeze": -3.38579081438084e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "gs", "epsilon": 0.005, "n_y": 16, "n_aux": 16, "step": 0.001, "dtype": "longdouble", "rows": [ { "sigma": 0.01, "lambda_base": 0.00995611640129488, "gap_base": 0.9912336683306744, "beta1": -0.9912336682951939, "beta2": -0.004956185982996545, "z": -0.9912371831059965, "chi": 1.0665481425906973e-06, "c_linear": 0.00021440547259328545, "kappa2": 0.7041273658579932, "kappa_perp": 0.7041295300836543, "residual_error": -6.746656271844342e-11, "coupling_error": -5.4792203757300474e-09, "capacity_difference": -2.1642256611276167e-06, "estimated_distance_to_freeze": 0.34689950162638045, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.04890853433232117, "gap_base": 0.9563669597475992, "beta1": -0.956366955560256, "beta2": -0.004783939896970053, "z": -0.9567863899187172, "chi": 2.582473476022263e-05, "c_linear": 0.00519158968508751, "kappa2": 0.7070801344988069, "kappa_perp": 0.7071324872839035, "residual_error": -7.94737646699073e-09, "coupling_error": -1.3321366521491912e-07, "capacity_difference": -5.2352785096632104e-05, "estimated_distance_to_freeze": 0.3079470836953542, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.09561210250708423, "gap_base": 0.9112695827338644, "beta1": -0.9112695514191966, "beta2": -0.00457263796571172, "z": -0.9145157540683634, "chi": 9.972767394706366e-05, "c_linear": 0.020049663975876715, "kappa2": 0.7158461476075271, "kappa_perp": 0.7160477311033004, "residual_error": -5.9195369902717565e-08, "coupling_error": -5.206459323199217e-07, "capacity_difference": -0.00020158349577337198, "estimated_distance_to_freeze": 0.2612435155205911, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585146932, "gap_base": 0.7353114253370396, "beta1": -0.7353110384728031, "beta2": -0.003936607150724262, "z": -0.7871727475682387, "chi": 0.0005680293100268569, "c_linear": 0.1142417827953647, "kappa2": 0.7693046164714721, "kappa_perp": 0.7704302214483806, "residual_error": -7.434128830681105e-07, "coupling_error": -3.1796039499666076e-06, "capacity_difference": -0.0011256049769085008, "estimated_distance_to_freeze": 0.13667339217620603, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.3407982882891465, "gap_base": 0.19738907599513683, "beta1": -0.19738849411704043, "beta2": -0.002903512843230882, "z": -0.5800120870136235, "chi": 0.0017316551606347049, "c_linear": 0.34864253359522024, "kappa2": 0.8731380776936473, "kappa_perp": 0.8763685621103157, "residual_error": -3.4524081627641465e-06, "coupling_error": -1.1557507341396255e-05, "capacity_difference": -0.0032304844166684, "estimated_distance_to_freeze": 0.016057329738528858, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.3568443261165098, "gap_base": 0.00016886762929939765, "beta1": -0.0001684609175959822, "beta2": -0.001641137272386791, "z": -0.3269002939061738, "chi": 0.002901836234470777, "c_linear": 0.5857632374007503, "kappa2": 0.8908496205757215, "kappa_perp": 0.8960489951728743, "residual_error": -6.635802855921996e-06, "coupling_error": -2.6979952532974697e-05, "capacity_difference": -0.005199374597152806, "estimated_distance_to_freeze": 1.1291911165556279e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556214098392, "gap_base": 5.418396257557926e-11, "beta1": 1.8521046646285006e-07, "beta2": -0.0005395311996167831, "z": -0.10664960485942429, "chi": 0.0038422258409250157, "c_linear": 0.7769750271857971, "kappa2": 0.8892965456580673, "kappa_perp": 0.8960634731082335, "residual_error": -6.283175319661614e-06, "coupling_error": -4.264929500397011e-05, "capacity_difference": -0.006766927450166271, "estimated_distance_to_freeze": -3.3821638267816923e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562141346205, "gap_base": 5.57511489264646e-24, "beta1": 2.2427901529030123e-08, "beta2": -5.8474803145240854e-05, "z": -0.01135195592268974, "chi": 0.004251445407527728, "c_linear": 0.8596993913824104, "kappa2": 0.8886224749557519, "kappa_perp": 0.896063473112872, "residual_error": -1.7150235317921558e-06, "coupling_error": -4.7051549384323835e-05, "capacity_difference": -0.007440998157120182, "estimated_distance_to_freeze": -3.385786706555649e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "block", "epsilon": 0.04, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336660538056, "beta2": -0.039649487188131785, "z": -0.9912371831060062, "chi": 8.576226590936051e-06, "c_linear": 0.00021440547258906248, "kappa2": 0.7041303521656743, "kappa_perp": 0.7041295300836399, "residual_error": 1.3610846477662975e-10, "coupling_error": 7.687373551308954e-12, "capacity_difference": 8.220820344462254e-07, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.048908534332402984, "gap_base": 0.9563669597530424, "beta1": -0.9563666909026814, "beta2": -0.038271439464211486, "z": -0.9567863899187731, "chi": 0.00020766806463334587, "c_linear": 0.00519158968502721, "kappa2": 0.707152503411997, "kappa_perp": 0.7071324872836825, "residual_error": 1.613253943627546e-08, "coupling_error": 4.477232257464256e-09, "capacity_difference": 2.001612831448174e-05, "estimated_distance_to_freeze": 0.30794708369527235, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.0956121025079325, "gap_base": 0.9112695827458732, "beta1": -0.9112675720962503, "beta2": -0.03658050777470931, "z": -0.9145157540684956, "chi": 0.000802052748135813, "c_linear": 0.020049663975781413, "kappa2": 0.7161263172788119, "kappa_perp": 0.7160477311026894, "residual_error": 1.2238803051567437e-07, "coupling_error": 6.61891045565131e-08, "capacity_difference": 7.858617612255259e-05, "estimated_distance_to_freeze": 0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585987446, "gap_base": 0.7353114254016203, "beta1": -0.7352865820676188, "beta2": -0.0314851899405709, "z": -0.7871727475678842, "chi": 0.004571768283047881, "c_linear": 0.11424178279782901, "kappa2": 0.7709252096514204, "kappa_perp": 0.7704302214490774, "residual_error": 1.7199621444655144e-06, "coupling_error": 2.0969711347204253e-06, "capacity_difference": 0.0004949882023430607, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.1973517050290908, "beta2": -0.023189587409505184, "z": -0.5800120869916802, "chi": 0.013966135563416377, "c_linear": 0.34864253366292397, "kappa2": 0.8783374409272428, "kappa_perp": 0.876368562165085, "residual_error": 1.0896070162021848e-05, "coupling_error": 2.0434216899418295e-05, "capacity_difference": 0.0019688787621577886, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.35684432623754636, "gap_base": 0.00016886763704993338, "beta1": -0.0001426674348992028, "beta2": -0.013040327275612619, "z": -0.3269002938506352, "chi": 0.02350844612416298, "c_linear": 0.5857632376199798, "kappa2": 0.9011443129339507, "kappa_perp": 0.8960489953005485, "residual_error": 3.5684478412789655e-05, "coupling_error": 7.791661936378674e-05, "capacity_difference": 0.005095317633402208, "estimated_distance_to_freeze": 1.1291790128986623e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.35685562153140143, "gap_base": 5.41839708122306e-11, "beta1": 1.1792782272677764e-05, "beta2": -0.004216024387692885, "z": -0.106649604824081, "chi": 0.03123041967357304, "c_linear": 0.7769750274429695, "kappa2": 0.9050455679618916, "kappa_perp": 0.8960634732365873, "residual_error": 4.99598052703552e-05, "coupling_error": 0.00015141857585425703, "capacity_difference": 0.008982094725304313, "estimated_distance_to_freeze": -3.503726087039638e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.3568556215350246, "gap_base": 5.575116923302611e-24, "beta1": 1.367246789107647e-06, "beta2": -0.0004374463759468671, "z": -0.011351955915290007, "chi": 0.03454774935896201, "c_linear": 0.8596993916389244, "kappa2": 0.9070437958563795, "kappa_perp": 0.8960634732412289, "residual_error": 1.663186066473319e-05, "coupling_error": 0.00015977369340502978, "capacity_difference": 0.010980322615150584, "estimated_distance_to_freeze": -3.507349244369351e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "block", "epsilon": 0.02, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336677622982, "beta2": -0.019824743645107383, "z": -0.9912371831060062, "chi": 4.288110412510955e-06, "c_linear": 0.00021440547258906248, "kappa2": 0.7041297356040757, "kappa_perp": 0.7041295300836399, "residual_error": 1.701274190968327e-11, "coupling_error": 9.607297054257946e-13, "capacity_difference": 2.0552043578092594e-07, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.048908534332402984, "gap_base": 0.9563669597530424, "beta1": -0.9563668925409643, "beta2": -0.019135725781821687, "z": -0.9567863899187731, "chi": 0.00010383235334750417, "c_linear": 0.00519158968502721, "kappa2": 0.7071374912732427, "kappa_perp": 0.7071324872836825, "residual_error": 2.0165537746585915e-09, "coupling_error": 5.596469599729184e-10, "capacity_difference": 5.003989560159461e-06, "estimated_distance_to_freeze": 0.30794708369527235, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.0956121025079325, "gap_base": 0.9112695827458732, "beta1": -0.9112690800978526, "beta2": -0.01829029978315798, "z": -0.9145157540684956, "chi": 0.0004010015528182067, "c_linear": 0.020049663975781413, "kappa2": 0.7160673770038064, "kappa_perp": 0.7160477311026894, "residual_error": 1.5298211933356676e-08, "coupling_error": 8.273302578448456e-09, "capacity_difference": 1.964590111702691e-05, "estimated_distance_to_freeze": 0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585987446, "gap_base": 0.7353114254016203, "beta1": -0.7353052154937917, "beta2": -0.01574323997738175, "z": -0.7871727475678842, "chi": 0.002285097720589277, "c_linear": 0.11424178279782901, "kappa2": 0.7705539448861317, "kappa_perp": 0.7704302214490774, "residual_error": 2.1497397593300827e-07, "coupling_error": 2.6206463269676933e-07, "capacity_difference": 0.00012372343705435718, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.19737974030684985, "beta2": -0.011598880059244464, "z": -0.5800120869916802, "chi": 0.006975403364167427, "c_linear": 0.34864253366292397, "kappa2": 0.876860476844193, "kappa_perp": 0.876368562165085, "residual_error": 1.361680589138936e-06, "coupling_error": 2.5526909089475247e-06, "capacity_difference": 0.0004919146791080298, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.35684432623754636, "gap_base": 0.00016886763704993338, "beta1": -0.00016232353473943665, "beta2": -0.006533544489140062, "z": -0.3269002938506352, "chi": 0.011724995768370196, "c_linear": 0.5857632376199798, "kappa2": 0.8973214298023651, "kappa_perp": 0.8960489953005485, "residual_error": 4.461387872641866e-06, "coupling_error": 9.731015970598778e-06, "capacity_difference": 0.0012724345018165772, "estimated_distance_to_freeze": 1.1291790128986623e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.35685562153140143, "gap_base": 5.41839708122306e-11, "beta1": 2.959876588157107e-06, "beta2": -0.0021267247151800835, "z": -0.106649604824081, "chi": 0.01555843864355188, "c_linear": 0.7769750274429695, "kappa2": 0.8983078392359769, "kappa_perp": 0.8960634732365873, "residual_error": 6.26738130153669e-06, "coupling_error": 1.893809469248782e-05, "capacity_difference": 0.002244365999389597, "estimated_distance_to_freeze": -3.503726087039638e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.3568556215350246, "gap_base": 5.575116923302611e-24, "beta1": 3.4973207229597644e-07, "beta2": -0.00022493060929375946, "z": -0.011351955915290007, "chi": 0.01721402341947503, "c_linear": 0.8596993916389244, "kappa2": 0.8988121362208453, "kappa_perp": 0.8960634732412289, "residual_error": 2.108509012040675e-06, "coupling_error": 2.0035586696540153e-05, "capacity_difference": 0.002748662979616401, "estimated_distance_to_freeze": -3.507349244369351e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "block", "epsilon": 0.01, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336681894213, "beta2": -0.00991237182893388, "z": -0.9912371831060062, "chi": 2.144054845887394e-06, "c_linear": 0.00021440547258906248, "kappa2": 0.7041295814637442, "kappa_perp": 0.7041295300836399, "residual_error": 2.1261829102892094e-12, "coupling_error": 1.1999676900460547e-13, "capacity_difference": 5.138010428229478e-08, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 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"estimated_distance_to_freeze": 0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585987446, "gap_base": 0.7353114254016203, "beta1": -0.7353098729825083, "beta2": -0.007871700604602396, "z": -0.7871727475678842, "chi": 0.00114245058428138, "c_linear": 0.11424178279782901, "kappa2": 0.7704611508327827, "kappa_perp": 0.7704302214490774, "residual_error": 2.6871076445542097e-08, "coupling_error": 3.2756303089886626e-08, "capacity_difference": 3.0929383705302627e-05, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.19738674276936807, "beta2": -0.005799950670103512, "z": -0.5800120869916802, "chi": 0.003486744373445098, "c_linear": 0.34864253366292397, "kappa2": 0.8764915217821578, "kappa_perp": 0.876368562165085, "residual_error": 1.7019981328990352e-07, "coupling_error": 3.190368158584485e-07, "capacity_difference": 0.00012295961707287084, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.35684432623754636, "gap_base": 0.00016886763704993338, "beta1": -0.0001672319839913259, "beta2": -0.0032684452392791274, "z": -0.3269002938506352, "chi": 0.005858848485552179, "c_linear": 0.5857632376199798, "kappa2": 0.8963670167593012, "kappa_perp": 0.8960489953005485, "residual_error": 5.5769922722472e-07, "coupling_error": 1.2161093523805136e-06, "capacity_difference": 0.00031802145875270416, "estimated_distance_to_freeze": 1.1291790128986623e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.35685562153140143, "gap_base": 5.41839708122306e-11, "beta1": 7.406595076435279e-07, "beta2": -0.0010657119243953986, "z": -0.106649604824081, "chi": 0.0077721178704554614, "c_linear": 0.7769750274429695, "kappa2": 0.896624491759693, "kappa_perp": 0.8960634732365873, "residual_error": 7.841238454115579e-07, "coupling_error": 2.3675960257657155e-06, "capacity_difference": 0.0005610185231057496, "estimated_distance_to_freeze": -3.503726087039638e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.3568556215350246, "gap_base": 5.575116923302611e-24, "beta1": 8.793477033023006e-08, "beta2": -0.00011325506191802175, "z": -0.011351955915290007, "chi": 0.008599500373357844, "c_linear": 0.8596993916389244, "kappa2": 0.8967508635044904, "kappa_perp": 0.8960634732412289, "residual_error": 2.64497234878322e-07, "coupling_error": 2.5064569685994548e-06, "capacity_difference": 0.0006873902632614781, "estimated_distance_to_freeze": -3.507349244369351e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "block", "epsilon": 0.005, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.9912336682962019, "beta2": -0.004956185915264462, "z": -0.9912371831060062, "chi": 1.072027377896828e-06, "c_linear": 0.00021440547258906248, "kappa2": 0.7041295429286656, "kappa_perp": 0.7041295300836399, "residual_error": 2.655688169372894e-13, "coupling_error": 1.4951515570874215e-14, "capacity_difference": 1.2845025709751212e-08, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.048908534332402984, "gap_base": 0.9563669597530424, "beta1": -0.9563669555522977, "beta2": -0.004783931918086392, "z": -0.9567863899187731, "chi": 2.595795716924403e-05, "c_linear": 0.00519158968502721, "kappa2": 0.7071328000321997, "kappa_perp": 0.7071324872836825, "residual_error": 3.1507473713388023e-11, "coupling_error": 8.744107980138702e-12, "capacity_difference": 3.1274851719498287e-07, "estimated_distance_to_freeze": 0.30794708369527235, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.0956121025079325, "gap_base": 0.9112695827458732, "beta1": -0.9112695513306528, "beta2": -0.00457257853131129, "z": -0.9145157540684956, "chi": 0.0001002484491468549, "c_linear": 0.020049663975781413, "kappa2": 0.7160489589589527, "kappa_perp": 0.7160477311026894, "residual_error": 2.390311880720586e-10, "coupling_error": 1.2926794784064426e-10, "capacity_difference": 1.2278562633305512e-06, "estimated_distance_to_freeze": 0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585987446, "gap_base": 0.7353114254016203, "beta1": -0.7353110373004571, "beta2": -0.003935860378978441, "z": -0.7871727475678842, "chi": 0.0005712130084702264, "c_linear": 0.11424178279782901, "kappa2": 0.7704379537027859, "kappa_perp": 0.7704302214490774, "residual_error": 3.3588609801502023e-09, "coupling_error": 4.09448108133325e-09, "capacity_difference": 7.732253708536696e-06, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.19738849298786984, "beta2": -0.002900039160305316, "z": -0.5800120869916802, "chi": 0.0017432525463658554, "c_linear": 0.34864253366292397, "kappa2": 0.8763993008787234, "kappa_perp": 0.876368562165085, "residual_error": 2.127465308478585e-08, "coupling_error": 3.987805123552464e-08, "capacity_difference": 3.073871363845626e-05, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.35684432623754636, "gap_base": 0.00016886763704993338, "beta1": -0.000168458747079487, "beta2": -0.001634431756048084, "z": -0.3269002938506352, "chi": 0.0029289681933988964, "c_linear": 0.5857632376199798, "kappa2": 0.8961284952175532, "kappa_perp": 0.8960489953005485, "residual_error": 6.971320509210031e-08, "coupling_error": 1.520052989971432e-07, "capacity_difference": 7.94999170047328e-05, "estimated_distance_to_freeze": 1.1291790128986623e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.35685562153140143, "gap_base": 5.41839708122306e-11, "beta1": 1.8516990093807042e-07, "beta2": -0.0005331499867205073, "z": -0.106649604824081, "chi": 0.003885171097137801, "c_linear": 0.7769750274429695, "kappa2": 0.8962037232965875, "kappa_perp": 0.8960634732365873, "residual_error": 9.803739989776555e-08, "coupling_error": 2.959599229531741e-07, "capacity_difference": 0.00014025006000017992, "estimated_distance_to_freeze": -3.503726087039638e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.3568556215350246, "gap_base": 5.575116923302611e-24, "beta1": 2.201515807799107e-08, "beta2": -5.672668816090519e-05, "z": -0.011351955915290007, "chi": 0.004298810328179832, "c_linear": 0.8596993916389244, "kappa2": 0.8962353348491056, "kappa_perp": 0.8960634732412289, "residual_error": 3.3091415544843393e-08, "coupling_error": 3.1336998521005327e-07, "capacity_difference": 0.0001718616078766333, "estimated_distance_to_freeze": -3.507349244369351e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "block", "epsilon": 0.0025, "n_y": 16, "n_aux": 16, "step": 0.002, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.009956116401250086, "gap_base": 0.9912336683317954, "beta1": -0.991233668322897, "beta2": -0.0024780929577319214, "z": -0.9912371831060062, "chi": 5.36013683317646e-07, "c_linear": 0.00021440547258906248, "kappa2": 0.7041295332948962, "kappa_perp": 0.7041295300836399, "residual_error": 3.309418711294754e-14, "coupling_error": 1.8449898015338983e-15, "capacity_difference": 3.211256371926652e-09, "estimated_distance_to_freeze": 0.34689950162642524, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.048908534332402984, "gap_base": 0.9563669597530424, "beta1": -0.9563669587028563, "beta2": -0.0023919659708589508, "z": -0.9567863899187731, "chi": 1.2978975305437755e-05, "c_linear": 0.00519158968502721, "kappa2": 0.7071325654708013, "kappa_perp": 0.7071324872836825, "residual_error": 3.937981885027142e-12, "coupling_error": 1.0928697301916838e-12, "capacity_difference": 7.818711877938256e-08, "estimated_distance_to_freeze": 0.30794708369527235, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.0956121025079325, "gap_base": 0.9112695827458732, "beta1": -0.9112695748920714, "beta2": -0.0022862893552931403, "z": -0.9145157540684956, "chi": 5.0124176097620274e-05, "c_linear": 0.020049663975781413, "kappa2": 0.7160480380665982, "kappa_perp": 0.7160477311026894, "residual_error": 2.987809869306468e-11, "coupling_error": 1.6158166743897393e-11, "capacity_difference": 3.069639088471021e-07, "estimated_distance_to_freeze": 0.26124351551974284, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585987446, "gap_base": 0.7353114254016203, "beta1": -0.7353113283765548, "beta2": -0.0019679314490641388, "z": -0.7871727475678842, "chi": 0.0002856049688022534, "c_linear": 0.11424178279782901, "kappa2": 0.7704321545067411, "kappa_perp": 0.7704302214490774, "residual_error": 4.1985557175036603e-10, "coupling_error": 5.118076808717509e-10, "capacity_difference": 1.933057663716653e-06, "estimated_distance_to_freeze": 0.1366733921678009, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.34079828835148707, "gap_base": 0.19738907635874084, "beta1": -0.197388930517678, "beta2": -0.0014500275581591578, "z": -0.5800120869916802, "chi": 0.0008716113188639308, "c_linear": 0.34864253366292397, "kappa2": 0.8763762467690828, "kappa_perp": 0.876368562165085, "residual_error": 2.6593200426038716e-09, "coupling_error": 4.98470662088548e-09, "capacity_difference": 7.684603997804018e-06, "estimated_distance_to_freeze": 0.01605732967618828, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.35684432623754636, "gap_base": 0.00016886763704993338, "beta1": -0.00016876541601339534, "beta2": -0.0008172420204517927, "z": -0.3269002938506352, "chi": 0.0014644270944480062, "c_linear": 0.5857632376199798, "kappa2": 0.8960688699393231, "kappa_perp": 0.8960489953005485, "residual_error": 8.714174795274553e-09, "coupling_error": 1.900039805656159e-08, "capacity_difference": 1.987463877461959e-05, "estimated_distance_to_freeze": 1.1291790128986623e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.35685562153140143, "gap_base": 5.41839708122306e-11, "beta1": 4.6254690733489603e-08, "beta2": -0.00026661175670046773, "z": -0.106649604824081, "chi": 0.0019424745639210455, "c_linear": 0.7769750274429695, "kappa2": 0.896098535465762, "kappa_perp": 0.8960634732365873, "residual_error": 1.2255359734794549e-08, "coupling_error": 3.6995313621585035e-08, "capacity_difference": 3.506222917470936e-05, "estimated_distance_to_freeze": -3.503726087039638e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.3568556215350246, "gap_base": 5.575116923302611e-24, "beta1": 5.505757772187373e-09, "beta2": -2.8375752446227208e-05, "z": -0.011351955915290007, "chi": 0.0021492876523087597, "c_linear": 0.8596993916389244, "kappa2": 0.8961064395209801, "kappa_perp": 0.8960634732412289, "residual_error": 4.13734199780939e-09, "coupling_error": 3.9173211448511464e-08, "capacity_difference": 4.296627975119982e-05, "estimated_distance_to_freeze": -3.507349244369351e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "block", "epsilon": 0.005, "n_y": 16, "n_aux": 16, "step": 0.001, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.00995611640129488, "gap_base": 0.9912336683306744, "beta1": -0.9912336682950807, "beta2": -0.004956185915264158, "z": -0.9912371831059965, "chi": 1.0720273779751456e-06, "c_linear": 0.000214405472593285, "kappa2": 0.7041295429286801, "kappa_perp": 0.7041295300836543, "residual_error": 2.65824688649996e-13, "coupling_error": 1.5008720576241744e-14, "capacity_difference": 1.2845025820773515e-08, "estimated_distance_to_freeze": 0.34689950162638045, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.05, "lambda_base": 0.04890853433232117, "gap_base": 0.9563669597475992, "beta1": -0.9563669555468545, "beta2": -0.004783931918084979, "z": -0.9567863899187172, "chi": 2.5957957169891455e-05, "c_linear": 0.005191589685087513, "kappa2": 0.7071328000324206, "kappa_perp": 0.7071324872839035, "residual_error": 3.1508607355179574e-11, "coupling_error": 8.744453891453702e-12, "capacity_difference": 3.1274851708396056e-07, "estimated_distance_to_freeze": 0.3079470836953542, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.1, "lambda_base": 0.09561210250708423, "gap_base": 0.9112695827338644, "beta1": -0.9112695513186437, "beta2": -0.0045725785313086515, "z": -0.9145157540683634, "chi": 0.00010024844914811336, "c_linear": 0.020049663975876715, "kappa2": 0.7160489589595638, "kappa_perp": 0.7160477311033004, "residual_error": 2.390331656568212e-10, "coupling_error": 1.292687297808036e-10, "capacity_difference": 1.2278562633305512e-06, "estimated_distance_to_freeze": 0.2612435155205911, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.25, "lambda_base": 0.22018222585146932, "gap_base": 0.7353114253370396, "beta1": -0.7353110372358764, "beta2": -0.003935860378976714, "z": -0.7871727475682387, "chi": 0.0005712130084596532, "c_linear": 0.1142417827953647, "kappa2": 0.7704379537020893, "kappa_perp": 0.7704302214483806, "residual_error": 3.358864479954815e-09, "coupling_error": 4.094482829717673e-09, "capacity_difference": 7.73225370875874e-06, "estimated_distance_to_freeze": 0.13667339217620603, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 0.5, "lambda_base": 0.3407982882891465, "gap_base": 0.19738907599513683, "beta1": -0.1973884926242683, "beta2": -0.0029000391604110903, "z": -0.5800120870136235, "chi": 0.0017432525460307656, "c_linear": 0.3486425335952202, "kappa2": 0.8763993008239519, "kappa_perp": 0.8763685621103154, "residual_error": 2.127465702737863e-08, "coupling_error": 3.987805466463927e-08, "capacity_difference": 3.073871363645786e-05, "estimated_distance_to_freeze": 0.016057329738528858, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 1.0, "lambda_base": 0.3568443261165098, "gap_base": 0.00016886762929939765, "beta1": -0.00016845873932923753, "beta2": -0.0016344317563234195, "z": -0.3269002939061738, "chi": 0.002928968192310033, "c_linear": 0.5857632374007503, "kappa2": 0.8961284950898684, "kappa_perp": 0.8960489951728743, "residual_error": 6.971320744958952e-08, "coupling_error": 1.520053062812471e-07, "capacity_difference": 7.949991699407466e-05, "estimated_distance_to_freeze": 1.1291911165556279e-05, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 2.0, "lambda_base": 0.3568556214098392, "gap_base": 5.4183962575579296e-11, "beta1": 1.851699008108489e-07, "beta2": -0.0005331499868964311, "z": -0.10664960485942429, "chi": 0.003885171095857815, "c_linear": 0.7769750271857971, "kappa2": 0.8962037231682263, "kappa_perp": 0.8960634731082335, "residual_error": 9.803740069031733e-08, "coupling_error": 2.959599288291162e-07, "capacity_difference": 0.00014025005999274143, "estimated_distance_to_freeze": -3.3821638267816923e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." }, { "sigma": 4.0, "lambda_base": 0.35685562141346205, "gap_base": 5.575114892646492e-24, "beta1": 2.2015158069246227e-08, "beta2": -5.672668819780076e-05, "z": -0.01135195592268974, "chi": 0.004298810326902694, "c_linear": 0.8596993913824104, "kappa2": 0.896235334720754, "kappa_perp": 0.8960634731128719, "residual_error": 3.309141564793747e-08, "coupling_error": 3.1336999064233984e-07, "capacity_difference": 0.00017186160788207339, "estimated_distance_to_freeze": -3.385786706555649e-09, "distance_resolution_note": "Do not resolve distances smaller than root-refinement difference or 1e-9." } ] }, { "pair": "block", "epsilon": 0.005, "n_y": 24, "n_aux": 24, "step": 0.001, "dtype": "float64", "rows": [ { "sigma": 0.01, "lambda_base": 0.00995611640129488, "gap_base": 0.9912336683306744, "beta1": 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