{ "A_equal_R": { "params": { "M1": 1.0, "M2": 1.0, "tau1": 0.1, "tau2": 0.1, "w": [ -0.004, 0.003, -0.002, 0.006 ] }, "P": { "-0.30": { "E": 1.9987717488829717, "isolation": 0.0014515562051098385, "inside_band": false, "weight0": 0.6407883806399609, "Gamma": 0.999999999999998, "tail": 5.284034866971501e-21, "conv_2L": 1.7763568394002505e-15, "eta_dependence": 1.3322676295501878e-15, "dense_minus_banded": 1.7763568394002505e-15, "dM1": [ 0.9993304952485663, 0.9993304952496843 ], "dM2": [ 0.9993304952487698, 0.9993304952496843 ], "dtau1": [ 0.00133695523152344, 0.0013369552328886952 ], "dtau2": [ 0.0013369552324301222, 0.0013369552328886957 ], "dtheta": [ -0.002563152083005319, -0.0025631520821777784 ], "euler_residual": -3.552713678800501e-15, "Ep": [ -0.0011330902868311732, -0.0011330902852397778, -0.0011330902852397784 ], "Epp": [ 0.003517649173797229, 0.003517649188281665 ], "green_rel_error": 1.477928061095734e-15, "eq_3a_root": 1.9987717488829722, "eq_3a_root_minus_E": 4.440892098500626e-16, "closed_E": 1.9987696954178489, "closed_Ep": -0.0011328548748095464 }, "-0.15": { "E": 1.998642641791647, "isolation": 0.001413502030640723, "inside_band": false, "weight0": 0.6277890046358329, "Gamma": 0.9999999999999988, "tail": 2.0431024738666595e-20, "conv_2L": 1.1102230246251565e-15, "eta_dependence": 8.881784197001252e-16, "dense_minus_banded": 4.440892098500626e-16, "dM1": [ 0.9994210796151296, 0.9994210796154035 ], "dM2": [ 0.9994210796141489, 0.9994210796154035 ], "dtau1": [ 0.0011558185154155372, 0.0011558185156420253 ], "dtau2": [ 0.0011558185155265595, 0.0011558185156420257 ], "dtheta": [ -0.002511154470604312, -0.0025111544704462543 ], "euler_residual": -2.4424906541753444e-15, "Ep": [ -0.0005810445112145828, -0.0005810445103634665, -0.0005810445103634664 ], "Epp": [ 0.003809572070948934, 0.003809572065239796 ], "green_rel_error": 5.00221778057326e-15, "eq_3a_root": 1.9986426417916472, "eq_3a_root_minus_E": 2.220446049250313e-16, "closed_E": 1.9986406206187968, "closed_Ep": -0.0005808746989030781 }, "+0.00": { "E": 1.9985988835265178, "isolation": 0.001401116473482178, "inside_band": false, "weight0": 0.6235021151130774, "Gamma": 1.0000000000000004, "tail": 3.165361573386918e-20, "conv_2L": 1.9984014443252818e-15, "eta_dependence": 2.4424906541753444e-15, "dense_minus_banded": 2.4424906541753444e-15, "dM1": [ 0.9994515458613776, 0.9994515458612895 ], "dM2": [ 0.9994515458604895, 0.9994515458612895 ], "dtau1": [ 0.0010948993396930893, 0.0010948993396561516 ], "dtau2": [ 0.0010948993404887493, 0.0010948993396561516 ], "dtheta": [ -0.0024940068755567126, -0.0024940068753713397 ], "euler_residual": 1.9984014443252818e-15, "Ep": [ 1.8503717077085944e-15, 7.893878378888825e-21, -2.053590192312075e-20 ], "Epp": [ 0.003905596114480344, 0.003905596125007126 ], "green_rel_error": 6.252772106673449e-15, "eq_3a_root": 1.9985988835265194, "eq_3a_root_minus_E": 1.5543122344752192e-15, "closed_E": 1.998596875762567, "closed_Ep": 0.0 }, "+0.15": { "E": 1.9986426417916483, "isolation": 0.0014135020306393908, "inside_band": false, "weight0": 0.6277890046357715, "Gamma": 0.9999999999999984, "tail": 2.043102670676963e-20, "conv_2L": 8.881784197001252e-16, "eta_dependence": 1.3322676295501878e-15, "dense_minus_banded": 2.220446049250313e-16, "dM1": [ 0.9994210796155922, 0.9994210796154032 ], "dM2": [ 0.9994210796144635, 0.9994210796154032 ], "dtau1": [ 0.001155818514656885, 0.0011558185156417791 ], "dtau2": [ 0.001155818515360026, 0.0011558185156417796 ], "dtheta": [ -0.0025111544695496, -0.002511154470446009 ], "euler_residual": -4.218847493575595e-15, "Ep": [ 0.0005810445112719442, 0.0005810445103635037, 0.0005810445103635038 ], "Epp": [ 0.003809572049299585, 0.0038095720652400445 ], "green_rel_error": 1.1937110612725393e-14, "eq_3a_root": 1.9986426417916472, "eq_3a_root_minus_E": -1.1102230246251565e-15, "closed_E": 1.9986406206187968, "closed_Ep": 0.0005808746989030781 }, "+0.30": { "E": 1.9987717488829717, "isolation": 0.0014515562051098385, "inside_band": false, "weight0": 0.6407883806399609, "Gamma": 0.999999999999998, "tail": 5.284034866971501e-21, "conv_2L": 1.7763568394002505e-15, "eta_dependence": 1.3322676295501878e-15, "dense_minus_banded": 1.7763568394002505e-15, "dM1": [ 0.9993304952485663, 0.9993304952496843 ], "dM2": [ 0.9993304952487698, 0.9993304952496843 ], "dtau1": [ 0.00133695523152344, 0.0013369552328886952 ], "dtau2": [ 0.0013369552324301222, 0.0013369552328886957 ], "dtheta": [ -0.002563152083005319, -0.0025631520821777784 ], "euler_residual": -3.552713678800501e-15, "Ep": [ 0.0011330902868274726, 0.0011330902852397778, 0.0011330902852397784 ], "Epp": [ 0.003517649173427155, 0.003517649188281665 ], "green_rel_error": 1.477928061095734e-15, "eq_3a_root": 1.9987717488829722, "eq_3a_root_minus_E": 4.440892098500626e-16, "closed_E": 1.9987696954178489, "closed_Ep": 0.0011328548748095464 } }, "max_abs_deviation": { "dM": 1.2545520178264269e-12, "dtau": 1.3652551311693628e-12, "dtheta": 8.964088152318972e-13, "euler": 4.218847493575595e-15, "V1": 1.5913954182211754e-12, "V2": 1.5913947676998719e-12, "V12": 6.505213034913027e-19, "Epp": 1.5940459455882072e-11, "eq310": 1.5543122344752192e-15, "green": 1.1937110612725393e-14, "conv": 1.9984014443252818e-15, "tail": 3.165361573386918e-20, "eta": 2.4424906541753444e-15, "solvers": 2.4424906541753444e-15, "closed_E": 2.0534651228309997e-06, "closed_Ep": 2.3541202162679145e-07 }, "closed_forms_P0": { "u": 0.7999999999999998, "a": 0.005000000000000001, "eps2": 0.010000000000000002, "compare": { "s3_1": [ 0.9994515458612895, 0.9994521720236076 ], "s3_2": [ 0.9994515458612895, 0.9994521720236076 ], "A1": [ 0.0010948993396561516, 0.0010956559527848483 ], "A2": [ 0.0010948993396561516, 0.0010956559527848483 ], "U": [ -0.0024940068753713397, -0.002498780190217697 ], "Ebind": [ -0.001401116473482178, -0.001403124237432848 ], "Epp0": [ 0.003905596125007126, 0.0039043440472151534 ] }, "item4": { "mb_over_m1_plus_m2": [ 1.2802142976293736, 1.2806248474865696 ], "mb_minus_m1_m2": [ 56.042859525874704, 56.044658939287096 ] }, "max_dE_over_P": 2.0534651228309997e-06, "max_dEp_over_P": 2.3541202162679145e-07, "rel_dev_Epp0": 0.0003206883862772754 } }, "B_unequal_R": { "params": { "M1": 1.0, "M2": 1.7, "tau1": 0.2, "tau2": 0.12, "w": [ -0.01, 0.005, -0.004, 0.008 ] }, "P": { "-0.30": { "E": 2.696652071451656, "isolation": 0.0036570933737110067, "inside_band": false, "weight0": 0.6441146800209665, "Gamma": 1.0000000000000004, "tail": 3.542800658530355e-21, "conv_2L": 4.440892098500626e-16, "eta_dependence": 1.7763568394002505e-15, "dense_minus_banded": 4.440892098500626e-16, "dM1": [ 0.9975918168031079, 0.9975918168041218 ], "dM2": [ 0.9995873147538702, 0.9995873147536779 ], "dtau1": [ 0.004803847817314022, 0.00480384781574927 ], "dtau2": [ 0.0013991144944084746, 0.0013991144950698544 ], "dtheta": [ -0.0064411427438404445, -0.006441142744538554 ], "euler_residual": -1.3322676295501878e-15, "Ep": [ -0.0015461338158921183, -0.0015461338167275206, -0.001546133816727594 ], "Epp": [ 0.004673250563932049, 0.004673250556180512 ], "green_rel_error": 4.277464579962843e-14, "eq_3a_root": 2.6966520714516546, "eq_3a_root_minus_E": -1.3322676295501878e-15, "closed_E": 2.6966438039739637, "closed_Ep": -0.001545464131327247 }, "-0.15": { "E": 2.696475088076594, "isolation": 0.0036032185712131515, "inside_band": false, "weight0": 0.6368363628390621, "Gamma": 1.0000000000000004, "tail": 7.638554699665447e-21, "conv_2L": 3.1086244689504383e-15, "eta_dependence": 6.217248937900877e-15, "dense_minus_banded": 2.6645352591003757e-15, "dM1": [ 0.9976817346970904, 0.9976817346985778 ], "dM2": [ 0.9996814413248957, 0.9996814413234609 ], "dtau1": [ 0.004623913755182525, 0.004623913756321769 ], "dtau2": [ 0.0010793486492725415, 0.0010793486503045025 ], "dtheta": [ -0.0063683592788447525, -0.006368359278489002 ], "euler_residual": 4.440892098500626e-15, "Ep": [ -0.0008001290118316481, -0.0008001290122026834, -0.0008001290122026873 ], "Epp": [ 0.005213784762444126, 0.0052137847511406704 ], "green_rel_error": 4.220620971804914e-14, "eq_3a_root": 2.696475088076597, "eq_3a_root_minus_E": 3.1086244689504383e-15, "closed_E": 2.6964669046101912, "closed_Ep": -0.0007997160499104646 }, "+0.00": { "E": 2.696414739676969, "isolation": 0.003585260323031303, "inside_band": false, "weight0": 0.6343920873760741, "Gamma": 1.0000000000000007, "tail": 9.860552537011425e-21, "conv_2L": 2.6645352591003757e-15, "eta_dependence": 3.552713678800501e-15, "dense_minus_banded": 3.552713678800501e-15, "dM1": [ 0.9977123894775822, 0.9977123894767301 ], "dM2": [ 0.9997133235958366, 0.9997133235960436 ], "dtau1": [ 0.004562573288698542, 0.0045625732893821835 ], "dtau2": [ 0.0009710432199439011, 0.0009710432203219463 ], "dtheta": [ -0.006343916422883271, -0.006343916422741831 ], "euler_residual": -2.6645352591003757e-15, "Ep": [ 1.1102230246251565e-14, -1.752348181816857e-19, 3.6871916661879243e-20 ], "Epp": [ 0.005394417406471656, 0.005394417424747923 ], "green_rel_error": 4.0500907564219975e-14, "eq_3a_root": 2.696414739676964, "eq_3a_root_minus_E": -4.884981308350689e-15, "closed_E": 2.6964065882071035, "closed_Ep": 0.0 }, "+0.15": { "E": 2.696475088076594, "isolation": 0.0036032185712131515, "inside_band": false, "weight0": 0.6368363628390621, "Gamma": 1.0000000000000004, "tail": 7.638554699665447e-21, "conv_2L": 3.1086244689504383e-15, "eta_dependence": 6.217248937900877e-15, "dense_minus_banded": 2.6645352591003757e-15, "dM1": [ 0.9976817346970904, 0.9976817346985778 ], "dM2": [ 0.9996814413248957, 0.9996814413234609 ], "dtau1": [ 0.004623913755182525, 0.004623913756321769 ], "dtau2": [ 0.0010793486492725415, 0.0010793486503045025 ], "dtheta": [ -0.0063683592788447525, -0.006368359278489002 ], "euler_residual": 4.440892098500626e-15, "Ep": [ 0.0008001290118538525, 0.0008001290122026834, 0.0008001290122026873 ], "Epp": [ 0.005213784763184274, 0.0052137847511406704 ], "green_rel_error": 3.950614916369572e-14, "eq_3a_root": 2.696475088076597, "eq_3a_root_minus_E": 3.1086244689504383e-15, "closed_E": 2.6964669046101912, "closed_Ep": 0.0007997160499104646 }, "+0.30": { "E": 2.696652071451656, "isolation": 0.0036570933737110067, "inside_band": false, "weight0": 0.6441146800209665, "Gamma": 1.0000000000000004, "tail": 3.542800658530355e-21, "conv_2L": 4.440892098500626e-16, "eta_dependence": 1.7763568394002505e-15, "dense_minus_banded": 4.440892098500626e-16, "dM1": [ 0.9975918168031079, 0.9975918168041218 ], "dM2": [ 0.9995873147538702, 0.9995873147536779 ], "dtau1": [ 0.004803847817314022, 0.00480384781574927 ], "dtau2": [ 0.0013991144944084746, 0.0013991144950698544 ], "dtheta": [ -0.0064411427438404445, -0.006441142744538554 ], "euler_residual": -1.3322676295501878e-15, "Ep": [ 0.0015461338158773152, 0.0015461338167275206, 0.001546133816727594 ], "Epp": [ 0.004673250560231305, 0.004673250556180512 ], "green_rel_error": 4.2348320426210185e-14, "eq_3a_root": 2.6966520714516546, "eq_3a_root_minus_E": -1.3322676295501878e-15, "closed_E": 2.6966438039739637, "closed_Ep": 0.001545464131327247 } }, "max_abs_deviation": { "dM": 1.4873657860903222e-12, "dtau": 1.5647518003536476e-12, "dtheta": 6.981091052460364e-13, "euler": 4.440892098500626e-15, "V1": 8.502053228109929e-13, "V2": 8.502788317182874e-13, "V12": 7.35089072945172e-17, "Epp": 1.8276266784689188e-11, "eq310": 4.884981308350689e-15, "green": 4.277464579962843e-14, "conv": 3.1086244689504383e-15, "tail": 9.860552537011425e-21, "eta": 6.217248937900877e-15, "solvers": 3.552713678800501e-15, "closed_E": 8.267477692225356e-06, "closed_Ep": 6.69684564871386e-07 }, "closed_forms_P0": { "u": 0.8252427184466018, "a": 0.012117647058823532, "eps2": 0.04000000000000001, "compare": { "s3_1": [ 0.9977123894767301, 0.997712813740429 ], "s3_2": [ 0.9997133235960436, 0.9997150909849669 ], "A1": [ 0.0045625732893821835, 0.004574372519142084 ], "A2": [ 0.0009710432203219463, 0.0009686906511124409 ], "U": [ -0.006343916422741831, -0.0063649433780238966 ], "Ebind": [ -0.003585260323031081, -0.003593411792896635 ], "Epp0": [ 0.005394417424747923, 0.005391481449620242 ] }, "item4": { "mb_over_m1_plus_m2": [ 1.295838032493856, 1.2965436916468096 ], "mb_minus_m1_m2": [ 42.321274092871064, 42.32598992467248 ] }, "max_dE_over_P": 8.267477692225356e-06, "max_dEp_over_P": 6.69684564871386e-07, "rel_dev_Epp0": 0.0005445581432701723 } }, "C_above_band_R": { "params": { "M1": 1.0, "M2": 0.8, "tau1": 0.1, "tau2": 0.15, "w": [ 0.02, -0.005, 0.003, -0.01 ] }, "P": { "-0.30": { "E": 1.8313465315612105, "isolation": 0.012743087345902016, "inside_band": false, "weight0": 0.9036658105468726, "Gamma": 1.000000000000001, "tail": 5.5580167244561765e-28, "conv_2L": 2.220446049250313e-16, "eta_dependence": 1.3322676295501878e-15, "dense_minus_banded": 2.220446049250313e-16, "dM1": [ 0.9966369378430021, 0.996636937842992 ], "dM2": [ 0.9881027121923698, 0.9881027121927409 ], "dtau1": [ 0.006793044051933705, 0.006793044052046955 ], "dtau2": [ 0.019361128223926993, 0.019361128223725578 ], "dtheta": [ 0.018073251688214647, 0.01807325168825412 ], "euler_residual": 8.881784197001252e-16, "Ep": [ 0.0008867732218753588, 0.0008867732246106974, 0.00088677322461067 ], "Epp": [ -0.0026292340571387744, -0.002629234044505366 ], "green_rel_error": 4.9737813445611155e-15, "eq_3a_root": 1.8313465315612096, "eq_3a_root_minus_E": -8.881784197001252e-16, "closed_E": 1.8315472483142752, "closed_Ep": 0.0009016494129372725 }, "-0.15": { "E": 1.8314483719913548, "isolation": 0.012601844860038236, "inside_band": false, "weight0": 0.8994257891125012, "Gamma": 0.9999999999999997, "tail": 2.381395421773662e-28, "conv_2L": 0.0, "eta_dependence": 8.881784197001252e-16, "dense_minus_banded": 4.440892098500626e-16, "dM1": [ 0.9965405216444585, 0.9965405216446359 ], "dM2": [ 0.9879941423733782, 0.9879941423726564 ], "dtau1": [ 0.0069871784095232314, 0.006987178410096289 ], "dtau2": [ 0.01953691097944521, 0.019536910979863466 ], "dtheta": [ 0.017988447059746893, 0.01798844705863354 ], "euler_residual": -4.440892098500626e-16, "Ep": [ 0.00046191115759726864, 0.000461911158908447, 0.00046191115890853256 ], "Epp": [ -0.002996418482966353, -0.002996418484758176 ], "green_rel_error": 5.684320109558415e-16, "eq_3a_root": 1.831448371991355, "eq_3a_root_minus_E": 2.220446049250313e-16, "closed_E": 1.8316508007415573, "closed_Ep": 0.0004696922820371139 }, "+0.00": { "E": 1.8314832491433681, "isolation": 0.012554657226293786, "inside_band": false, "weight0": 0.8979827973644506, "Gamma": 0.9999999999999993, "tail": 1.265245303041117e-28, "conv_2L": 0.0, "eta_dependence": 0.0, "dense_minus_banded": 0.0, "dM1": [ 0.9965076038347213, 0.9965076038341719 ], "dM2": [ 0.9879570643803874, 0.9879570643793468 ], "dtau1": [ 0.007053461200556832, 0.0070534612009323285 ], "dtau2": [ 0.01959694681237985, 0.01959694681368228 ], "dtheta": [ 0.01795958579122366, 0.0179595857911024 ], "euler_residual": -1.7763568394002505e-15, "Ep": [ 1.8503717077085944e-15, -1.6041830992033249e-19, 5.73573563285171e-19 ], "Epp": [ -0.0031210110453446425, -0.003121011047160065 ], "green_rel_error": 1.5631878954715505e-15, "eq_3a_root": 1.8314832491433677, "eq_3a_root_minus_E": -4.440892098500626e-16, "closed_E": 1.8316862658330455, "closed_Ep": -0.0 }, "+0.15": { "E": 1.8314483719913548, "isolation": 0.012601844860038236, "inside_band": false, "weight0": 0.8994257891125012, "Gamma": 0.9999999999999997, "tail": 2.381395421773662e-28, "conv_2L": 0.0, "eta_dependence": 8.881784197001252e-16, "dense_minus_banded": 4.440892098500626e-16, "dM1": [ 0.9965405216444585, 0.9965405216446359 ], "dM2": [ 0.9879941423733782, 0.9879941423726564 ], "dtau1": [ 0.0069871784095232314, 0.006987178410096289 ], "dtau2": [ 0.01953691097944521, 0.019536910979863466 ], "dtheta": [ 0.017988447059746893, 0.01798844705863354 ], "euler_residual": -4.440892098500626e-16, "Ep": [ -0.0004619111575861664, -0.000461911158908447, -0.00046191115890853256 ], "Epp": [ -0.0029964184811159815, -0.002996418484758176 ], "green_rel_error": 2.2737280438233693e-15, "eq_3a_root": 1.831448371991355, "eq_3a_root_minus_E": 2.220446049250313e-16, "closed_E": 1.8316508007415573, "closed_Ep": -0.0004696922820371139 }, "+0.30": { "E": 1.8313465315612105, "isolation": 0.012743087345902016, "inside_band": false, "weight0": 0.9036658105468726, "Gamma": 1.000000000000001, "tail": 5.5580167244561765e-28, "conv_2L": 2.220446049250313e-16, "eta_dependence": 1.3322676295501878e-15, "dense_minus_banded": 2.220446049250313e-16, "dM1": [ 0.9966369378430021, 0.996636937842992 ], "dM2": [ 0.9881027121923698, 0.9881027121927409 ], "dtau1": [ 0.006793044051933705, 0.006793044052046955 ], "dtau2": [ 0.019361128223926993, 0.019361128223725578 ], "dtheta": [ 0.018073251688214647, 0.01807325168825412 ], "euler_residual": 8.881784197001252e-16, "Ep": [ -0.0008867732218772092, -0.0008867732246106974, -0.00088677322461067 ], "Epp": [ -0.002629234056953737, -0.002629234044505366 ], "green_rel_error": 2.8421607683206314e-15, "eq_3a_root": 1.8313465315612096, "eq_3a_root_minus_E": -8.881784197001252e-16, "closed_E": 1.8315472483142752, "closed_Ep": -0.0009016494129372725 } }, "max_abs_deviation": { "dM": 1.0406120409811592e-12, "dtau": 1.3024269163164348e-12, "dtheta": 1.1133524657758187e-12, "euler": 1.7763568394002505e-15, "V1": 2.7353386482936726e-12, "V2": 2.7353112179787087e-12, "V12": 8.55435514091063e-17, "Epp": 1.2633408642132027e-11, "eq310": 8.881784197001252e-16, "green": 4.9737813445611155e-15, "conv": 2.220446049250313e-16, "tail": 5.5580167244561765e-28, "eta": 1.3322676295501878e-15, "solvers": 4.440892098500626e-16, "closed_E": 0.00020301668967737108, "closed_Ep": 1.4876191061913725e-05 }, "closed_forms_P0": { "u": 2.098360655737705, "a": 0.00953125, "eps2": 0.035156249999999986, "compare": { "s3_1": [ 0.9965076038341719, 0.9964244816984306 ], "s3_2": [ 0.9879570643793468, 0.9874298184710452 ], "A1": [ 0.0070534612009323285, 0.007151036603138771 ], "A2": [ 0.01959694681368228, 0.02011229044632779 ], "U": [ 0.0179595857911024, 0.018054602308312292 ], "Ebind": [ 0.031483249143368086, 0.031686265833045575 ], "Epp0": [ -0.003121011047160065, -0.0031736605620080204 ] }, "item4": { "mb_over_m1_plus_m2": [ -2.3636728831961515, -2.3244606775654373 ], "mb_minus_m1_m2": [ -455.9645463888116, -447.7617655945683 ] }, "max_dE_over_P": 0.00020301668967737108, "max_dEp_over_P": 1.4876191061913725e-05, "rel_dev_Epp0": 0.016589522987500434 } }, "D_wide_R": { "params": { "M1": 1.3, "M2": 1.0, "tau1": 0.15, "tau2": 0.2, "w": [ -0.004, 0.002, 0.001, 0.003 ] }, "P": { "-0.30": { "E": 2.2999698406707054, "isolation": 0.0005676902764646385, "inside_band": false, "weight0": 0.27803153364811334, "Gamma": 1.0000000000000016, "tail": 2.5420251273295236e-08, "conv_2L": 3.1086244689504383e-15, "eta_dependence": 3.9968028886505635e-15, "dense_minus_banded": 2.220446049250313e-15, "dM1": [ 0.9995878102232201, 0.9995878102226097 ], "dM2": [ 0.9994525069865201, 0.9994525069865698 ], "dtau1": [ 0.0010710953159964731, 0.0010710953162301957 ], "dtau2": [ 0.0010942109083626288, 0.0010942109070576644 ], "dtheta": [ -0.0011121258306120059, -0.0011121258285397067 ], "euler_residual": 5.329070518200751e-15, "Ep": [ -0.003402250763991551, -0.0034022507589530036, -0.003402250758953079 ], "Epp": [ 0.010746616826059116, 0.01074661686468223 ], "green_rel_error": 2.3374007407359554e-13, "eq_3a_root": 2.299969840670707, "eq_3a_root_minus_E": 1.7763568394002505e-15, "closed_E": 2.299969153832336, "closed_Ep": -0.003403264820215837 }, "-0.15": { "E": 2.2995833452872985, "isolation": 0.0005521813277367116, "inside_band": false, "weight0": 0.27073149336333957, "Gamma": 0.9999999999999983, "tail": 4.14179099418866e-08, "conv_2L": 4.440892098500626e-16, "eta_dependence": 4.440892098500626e-15, "dense_minus_banded": 0.0, "dM1": [ 0.9998046921911036, 0.9998046921896625 ], "dM2": [ 0.9995861016039997, 0.9995861016019525 ], "dtau1": [ 0.0005071638142783996, 0.0005071638149982289 ], "dtau2": [ 0.0008269056284149201, 0.0008269056293956405 ], "dtheta": [ -0.0010829256051521814, -0.0010829256056103754 ], "euler_residual": -1.3322676295501878e-15, "Ep": [ -0.0017343104155761089, -0.0017343104135742542, -0.0017343104135741697 ], "Epp": [ 0.01141561427608906, 0.01141561422753753 ], "green_rel_error": 2.1441330315987695e-13, "eq_3a_root": 2.2995833452873002, "eq_3a_root_minus_E": 1.7763568394002505e-15, "closed_E": 2.299582581337323, "closed_Ep": -0.0017344866586560333 }, "+0.00": { "E": 2.2994528607227624, "isolation": 0.000547139277237374, "inside_band": false, "weight0": 0.2683527421411404, "Gamma": 0.9999999999999991, "tail": 4.853656656034339e-08, "conv_2L": 4.440892098500626e-15, "eta_dependence": 1.7763568394002505e-15, "dense_minus_banded": 1.7763568394002505e-15, "dM1": [ 0.9998771296688006, 0.9998771296692601 ], "dM2": [ 0.9996319144148039, 0.9996319144145291 ], "dtau1": [ 0.0003188390674072986, 0.00031883906936428863 ], "dtau2": [ 0.000735249248003574, 0.0007352492475109331 ], "dtheta": [ -0.00107341058008803, -0.0010734105786802063 ], "euler_residual": -4.440892098500626e-16, "Ep": [ 1.1102230246251565e-14, -2.2352182505058147e-19, 5.295571825345954e-19 ], "Epp": [ 0.01163513175472808, 0.011635131655509572 ], "green_rel_error": 2.302157628221212e-13, "eq_3a_root": 2.299452860722764, "eq_3a_root_minus_E": 1.3322676295501878e-15, "closed_E": 2.2994520877886893, "closed_Ep": 0.0 }, "+0.15": { "E": 2.2995833452872985, "isolation": 0.0005521813277367116, "inside_band": false, "weight0": 0.27073149336333957, "Gamma": 0.9999999999999983, "tail": 4.14179099418866e-08, "conv_2L": 4.440892098500626e-16, "eta_dependence": 4.440892098500626e-15, "dense_minus_banded": 0.0, "dM1": [ 0.9998046921911036, 0.9998046921896625 ], "dM2": [ 0.9995861016039997, 0.9995861016019525 ], "dtau1": [ 0.0005071638142783996, 0.0005071638149982289 ], "dtau2": [ 0.0008269056284149201, 0.0008269056293956405 ], "dtheta": [ -0.0010829256051521814, -0.0010829256056103754 ], "euler_residual": -1.3322676295501878e-15, "Ep": [ 0.0017343104155650066, 0.0017343104135742542, 0.0017343104135741697 ], "Epp": [ 0.011415614271278093, 0.01141561422753753 ], "green_rel_error": 2.1464067675813775e-13, "eq_3a_root": 2.2995833452873002, "eq_3a_root_minus_E": 1.7763568394002505e-15, "closed_E": 2.299582581337323, "closed_Ep": 0.0017344866586560333 }, "+0.30": { "E": 2.2999698406707054, "isolation": 0.0005676902764646385, "inside_band": false, "weight0": 0.27803153364811334, "Gamma": 1.0000000000000016, "tail": 2.5420251273295236e-08, "conv_2L": 3.1086244689504383e-15, "eta_dependence": 3.9968028886505635e-15, "dense_minus_banded": 2.220446049250313e-15, "dM1": [ 0.9995878102232201, 0.9995878102226097 ], "dM2": [ 0.9994525069865201, 0.9994525069865698 ], "dtau1": [ 0.0010710953159964731, 0.0010710953162301957 ], "dtau2": [ 0.0010942109083626288, 0.0010942109070576644 ], "dtheta": [ -0.0011121258306120059, -0.0011121258285397067 ], "euler_residual": 5.329070518200751e-15, "Ep": [ 0.0034022507639841493, 0.0034022507589530036, 0.003402250758953079 ], "Epp": [ 0.010746616826799265, 0.01074661686468223 ], "green_rel_error": 2.328305796219475e-13, "eq_3a_root": 2.299969840670707, "eq_3a_root_minus_E": 1.7763568394002505e-15, "closed_E": 2.299969153832336, "closed_Ep": 0.003403264820215837 } }, "max_abs_deviation": { "dM": 2.0472512574087887e-12, "dtau": 1.956990017086546e-12, "dtheta": 2.0722991465188523e-12, "euler": 5.329070518200751e-15, "V1": 5.038547270380667e-12, "V2": 5.038471809909462e-12, "V12": 8.456776945386935e-17, "Epp": 9.921850840921564e-11, "eq310": 1.7763568394002505e-15, "green": 2.3374007407359554e-13, "conv": 4.440892098500626e-15, "tail": 4.853656656034339e-08, "eta": 4.440892098500626e-15, "solvers": 2.220446049250313e-15, "closed_E": 7.729340731899015e-07, "closed_Ep": 1.0140562316878453e-06 }, "closed_forms_P0": { "u": 0.2791946308724832, "a": 0.014326923076923077, "eps2": 0.04000000000000001, "compare": { "s3_1": [ 0.9998771296692601, 0.9998773988238779 ], "s3_2": [ 0.9996319144145291, 0.9996316515775179 ], "A1": [ 0.00031883906936428863, 0.00031876305791723347 ], "A2": [ 0.0007352492475109331, 0.0007366968449642731 ], "U": [ -0.0010734105786802063, -0.0010756421627509882 ], "Ebind": [ -0.000547139277237596, -0.000547912211310236 ], "Epp0": [ 0.011635131655509572, 0.011635552241296749 ] }, "item4": { "mb_over_m1_plus_m2": [ 1.0382810672392517, 1.0382435368968217 ], "mb_minus_m1_m2": [ 3.168821677026937, 3.161249157372777 ] }, "max_dE_over_P": 7.729340731899015e-07, "max_dEp_over_P": 1.0140562316878453e-06, "rel_dev_Epp0": 3.61466115621009e-05 } }, "E_order_one": { "params": { "M1": 1.0, "M2": 1.3, "tau1": 1.0, "tau2": 0.8, "w": [ -0.6, 0.2, -0.15, 0.3 ] }, "P": { "-0.30": { "E": 2.0202430653650967, "isolation": 0.29440305721726867, "inside_band": false, "weight0": 0.701707383851894, "Gamma": 1.0000000000000004, "tail": 1.7199875421734497e-30, "conv_2L": 4.440892098500626e-16, "eta_dependence": 4.440892098500626e-16, "dense_minus_banded": 4.440892098500626e-16, "dM1": [ 0.8503318666591339, 0.8503318666583716 ], "dM2": [ 0.9328219265201905, 0.9328219265196965 ], "dtau1": [ 0.23778305062290467, 0.23778305062442884 ], "dtau2": [ 0.13944747911154295, 0.13944747911219654 ], "dtheta": [ -0.41998783550600827, -0.41998783550550445 ], "euler_residual": 1.3322676295501878e-15, "Ep": [ -0.0533071623368205, -0.05330716251086799, -0.05330716251086764 ], "Epp": [ 0.15802105920115217, 0.15802105937262773 ], "green_rel_error": 1.9938464141953312e-15, "eq_3a_root": 2.020243065365098, "eq_3a_root_minus_E": 1.3322676295501878e-15, "closed_E": 1.9741936617317075, "closed_Ep": -0.049718216265647104 }, "-0.15": { "E": 2.0141207903858516, "isolation": 0.2895782974541672, "inside_band": false, "weight0": 0.6956259399840091, "Gamma": 0.9999999999999998, "tail": 2.1615467344399323e-30, "conv_2L": 4.440892098500626e-16, "eta_dependence": 8.881784197001252e-16, "dense_minus_banded": 2.6645352591003757e-15, "dM1": [ 0.8549045880839415, 0.8549045880838624 ], "dM2": [ 0.9371204279218225, 0.9371204279213157 ], "dtau1": [ 0.22858232492573016, 0.22858232492677993 ], "dtau2": [ 0.12864136876322704, 0.1286413687625461 ], "dtheta": [ -0.416264047684541, -0.41626404768504804 ], "euler_residual": -4.440892098500626e-16, "Ep": [ -0.02776996948270864, -0.027769969570427034, -0.027769969570427072 ], "Epp": [ 0.1801269900647551, 0.1801269902164982 ], "green_rel_error": 3.588255397739565e-15, "eq_3a_root": 2.014120790385851, "eq_3a_root_minus_E": -4.440892098500626e-16, "closed_E": 1.9684934526588127, "closed_Ep": -0.025810794086150356 }, "+0.00": { "E": 2.012023935088437, "isolation": 0.2879760649115628, "inside_band": false, "weight0": 0.6935661601144257, "Gamma": 0.9999999999999994, "tail": 2.2610645562733344e-30, "conv_2L": 8.881784197001252e-16, "eta_dependence": 8.881784197001252e-16, "dense_minus_banded": 8.881784197001252e-16, "dM1": [ 0.8564696712686226, 0.8564696712688329 ], "dM2": [ 0.938590891190379, 0.9385908911908176 ], "dtau1": [ 0.2254381116959895, 0.22543811169631017 ], "dtau2": [ 0.1249503925203251, 0.1249503925193654 ], "dtheta": [ -0.41500239894528185, -0.4150023989441348 ], "euler_residual": -4.440892098500626e-16, "Ep": [ -7.401486830834377e-15, -3.140156509536244e-17, 1.9141900210567238e-17 ], "Epp": [ 0.1876436174034583, 0.18764361764368498 ], "green_rel_error": 4.983365620674174e-16, "eq_3a_root": 2.012023935088438, "eq_3a_root_minus_E": 8.881784197001252e-16, "closed_E": 1.9665456848909921, "closed_Ep": 0.0 }, "+0.15": { "E": 2.0141207903858516, "isolation": 0.2895782974541672, "inside_band": false, "weight0": 0.6956259399840091, "Gamma": 0.9999999999999998, "tail": 2.1615467344399323e-30, "conv_2L": 4.440892098500626e-16, "eta_dependence": 8.881784197001252e-16, "dense_minus_banded": 2.6645352591003757e-15, "dM1": [ 0.8549045880839415, 0.8549045880838624 ], "dM2": [ 0.9371204279218225, 0.9371204279213157 ], "dtau1": [ 0.22858232492580416, 0.22858232492677993 ], "dtau2": [ 0.12864136876322704, 0.1286413687625461 ], "dtheta": [ -0.416264047684541, -0.41626404768504804 ], "euler_residual": -4.440892098500626e-16, "Ep": [ 0.027769969482642026, 0.027769969570427034, 0.027769969570427072 ], "Epp": [ 0.18012699007659747, 0.1801269902164982 ], "green_rel_error": 3.1895603535462812e-15, "eq_3a_root": 2.014120790385851, "eq_3a_root_minus_E": -4.440892098500626e-16, "closed_E": 1.9684934526588127, "closed_Ep": 0.025810794086150356 }, "+0.30": { "E": 2.0202430653650967, "isolation": 0.29440305721726867, "inside_band": false, "weight0": 0.701707383851894, "Gamma": 1.0000000000000004, "tail": 1.7199875421734497e-30, "conv_2L": 4.440892098500626e-16, "eta_dependence": 4.440892098500626e-16, "dense_minus_banded": 4.440892098500626e-16, "dM1": [ 0.8503318666591339, 0.8503318666583716 ], "dM2": [ 0.9328219265201905, 0.9328219265196965 ], "dtau1": [ 0.23778305062290467, 0.23778305062442884 ], "dtau2": [ 0.13944747911157998, 0.13944747911219654 ], "dtheta": [ -0.41998783550600827, -0.41998783550550445 ], "euler_residual": 1.3322676295501878e-15, "Ep": [ 0.0533071623368205, 0.05330716251086799, 0.05330716251086764 ], "Epp": [ 0.15802105920041204, 0.15802105937262773 ], "green_rel_error": 3.9876928283906716e-16, "eq_3a_root": 2.020243065365098, "eq_3a_root_minus_E": 1.3322676295501878e-15, "closed_E": 1.9741936617317075, "closed_Ep": 0.049718216265647104 } }, "max_abs_deviation": { "dM": 7.622791287076325e-13, "dtau": 1.5241696793566462e-12, "dtheta": 1.1470269178914805e-12, "euler": 1.3322676295501878e-15, "V1": 1.7404749169669387e-10, "V2": 1.7404713781310477e-10, "V12": 3.5388358909926865e-16, "Epp": 2.4022667188816627e-10, "eq310": 1.3322676295501878e-15, "green": 3.588255397739565e-15, "conv": 8.881784197001252e-16, "tail": 2.2610645562733344e-30, "eta": 8.881784197001252e-16, "solvers": 2.6645352591003757e-15, "closed_E": 0.04604940363338916, "closed_Ep": 0.003588946071173396 }, "closed_forms_P0": { "u": 1.6082474226804122, "a": 0.3730769230769231, "eps2": 1.0, "compare": { "s3_1": [ 0.8564696712688329, 0.8820100594684337 ], "s3_2": [ 0.9385908911908176, 0.9553174189702944 ], "A1": [ 0.22543811169631017, 0.23597988106313272 ], "A2": [ 0.1249503925193654, 0.11617471067723459 ], "U": [ -0.4150023989441348, -0.5095316109791912 ], "Ebind": [ -0.287976064911563, -0.3334543151090077 ], "Epp0": [ 0.18764361764368498, 0.1741988413604073 ] }, "item4": { "mb_over_m1_plus_m2": [ 1.7581035334915232, 1.893795071426206 ], "mb_minus_m1_m2": [ 2.298001335896179, 2.339805527406449 ] }, "max_dE_over_P": 0.04604940363338916, "max_dEp_over_P": 0.003588946071173396, "rel_dev_Epp0": 0.07718062978077568 } }, "epsilon_scan_set_B": [ { "eps": 1.0, "dE_P0": 8.151469865325112e-06, "dE_P03": 8.267477692225356e-06, "rel_dEpp0": 0.0005445581432701723, "d_s3_1": -4.2426369883941106e-07, "d_s3_2": -1.7673889233238427e-06 }, { "eps": 0.5, "dE_P0": 5.094345443268367e-07, "dE_P03": 5.167414247608804e-07, "rel_dEpp0": 0.00013707918516712943, "d_s3_1": -2.720324154825704e-08, "d_s3_2": -1.10197183156302e-07, "ratio_to_previous": { "dE_P0": 16.001015157102092, "dE_P03": 15.99925474535178, "rel_dEpp0": 3.972580830607048, "d_s3_1": 15.596071449308377, "d_s3_2": 16.038421969616095 } }, { "eps": 0.25, "dE_P0": 3.183914820681366e-08, "dE_P03": 3.2296711527379784e-08, "rel_dEpp0": 3.432847031626075e-05, "d_s3_1": -1.7109325067821146e-09, "d_s3_2": -6.883195680096321e-09, "ratio_to_previous": { "dE_P0": 16.000256697125344, "dE_P03": 15.999815471083144, "rel_dEpp0": 3.9931632229530947, "d_s3_1": 15.899657900252487, "d_s3_2": 16.00959616402478 } }, { "eps": 0.125, "dE_P0": 1.9899379921639593e-09, "dE_P03": 2.018550659954599e-09, "rel_dEpp0": 8.585780804080197e-06, "d_s3_1": -1.0710143882874945e-10, "d_s3_2": -4.3013559380966626e-10, "ratio_to_previous": { "dE_P0": 16.00007052088601, "dE_P03": 15.999950939109054, "rel_dEpp0": 3.9982933526496423, "d_s3_1": 15.974878820422024, "d_s3_2": 16.002385710823354 } } ], "settings": { "L": 120, "L_check": 240, "P_values": [ -0.3, -0.15, 0.0, 0.15, 0.3 ], "eta": 0.5, "h_P": 0.01, "h_rel_parameters": 0.001 }, "new_in_v2": { "I3_clock": [ { "part": 1, "N": 4, "D": 0.06, "lambda0": 78.53981633974483, "g0": 0.28810180056785306, "D_over_g0": 0.2082597188970672, "D_over_M": 0.06, "sum_q_minus_1": 2.9976021664879227e-15, "Gamma_level0": 0.8564696712688329, "Gamma_mean_level": 0.8621903822649348, "Gamma_first_order": 0.8623337319853568, "Gamma_fit": 0.8621456724086228, "d2E_dM2": 0.19546869055079613, "d2E_dM2_closed": 0.17218462083533354, "Gamma_closed_11_20_at_mean": 0.8870173806068575, "Gamma_closed_11_26": 0.8871755980934937, "dev_mean_level": 0.0009467967298583124, "dev_level0": 0.07097572305973499, "dev_first_order": 0.002645333718387599, "dev_mean_level_first_revolution": 0.0003598364085480865, "dev_level0_first_revolution": 0.03789662732937604, "set": "E_order_one" }, { "part": 1, "N": 4, "D": 0.03, "lambda0": 157.07963267948966, "g0": 0.28810180056785306, "D_over_g0": 0.1041298594485336, "D_over_M": 0.03, "sum_q_minus_1": 1.9984014443252818e-15, "Gamma_level0": 0.8564696712688329, "Gamma_mean_level": 0.8593655981103847, "Gamma_first_order": 0.8594017016270948, "Gamma_fit": 0.8593541025206765, "d2E_dM2": 0.19546869055079613, "d2E_dM2_closed": 0.17218462083533354, "Gamma_closed_11_20_at_mean": 0.884552755442187, "Gamma_closed_11_26": 0.8845928287809637, "dev_mean_level": 0.0002475659342767722, "dev_level0": 0.03606318054154545, "dev_first_order": 0.0006866642287148839, "dev_mean_level_first_revolution": 9.234651743539324e-05, "dev_level0_first_revolution": 0.019233635157828832, "set": "E_order_one", "ratio_to_previous": { "dev_mean_level": 3.824422502329495, "dev_level0": 1.9680938284955107, "dev_first_order": 3.8524414229913124 } }, { "part": 1, "N": 4, "D": 0.015, "lambda0": 314.1592653589793, "g0": 0.28810180056785306, "D_over_g0": 0.0520649297242668, "D_over_M": 0.015, "sum_q_minus_1": 1.3322676295501878e-15, "Gamma_level0": 0.8564696712688329, "Gamma_mean_level": 0.8579266273579921, "Gamma_first_order": 0.8579356864479638, "Gamma_fit": 0.8579237667072714, "d2E_dM2": 0.19546869055079613, "d2E_dM2_closed": 0.17218462083533354, "Gamma_closed_11_20_at_mean": 0.8832913598005296, "Gamma_closed_11_26": 0.8833014441246987, "dev_mean_level": 6.07722356592566e-05, "dev_level0": 0.018160681641319787, "dev_first_order": 0.00017070048426082174, "dev_mean_level_first_revolution": 2.3218168594296706e-05, "dev_level0_first_revolution": 0.009685663579682813, "set": "E_order_one", "ratio_to_previous": { "dev_mean_level": 4.073668371603898, "dev_level0": 1.9857834223299913, "dev_first_order": 4.022626131896003 } }, { "part": 1, "N": 4, "D": 0.1, "lambda0": 47.12388980384689, "g0": 0.003589344384700155, "D_over_g0": 27.86024111429858, "D_over_M": 0.1, "sum_q_minus_1": 1.1102230246251565e-15, "Gamma_level0": 0.9977123894767301, "Gamma_mean_level": 0.9978093967582963, "Gamma_first_order": 0.9978119032690593, "Gamma_fit": 0.9978328312332096, "d2E_dM2": 0.001990275846584925, "d2E_dM2_closed": 0.0019957745654456236, "Gamma_closed_11_20_at_mean": 0.9978100720044616, "Gamma_closed_11_26": 0.9978126024687013, "dev_mean_level": 0.00046856157329266956, "dev_level0": 0.0014255752432916768, "dev_first_order": 0.000470726417796663, "dev_mean_level_first_revolution": 0.00041275611907753973, "dev_level0_first_revolution": 0.0009115174225038936, "set": "B_unequal_R" }, { "part": 1, "N": 4, "D": 0.05, "lambda0": 94.24777960769379, "g0": 0.003589344384700155, "D_over_g0": 13.93012055714929, "D_over_M": 0.05, "sum_q_minus_1": 2.6645352591003757e-15, "Gamma_level0": 0.9977123894767301, "Gamma_mean_level": 0.9977615159617519, "Gamma_first_order": 0.9977621463728947, "Gamma_fit": 0.9977620037487646, "d2E_dM2": 0.001990275846584925, "d2E_dM2_closed": 0.0019957745654456236, "Gamma_closed_11_20_at_mean": 0.9977620715654857, "Gamma_closed_11_26": 0.9977627081045651, "dev_mean_level": 0.0001306954843264263, "dev_level0": 0.0005874380983595939, "dev_first_order": 0.00013091300811862716, "dev_mean_level_first_revolution": 0.0001251309988861138, "dev_level0_first_revolution": 0.000351697595908973, "set": "B_unequal_R", "ratio_to_previous": { "dev_mean_level": 3.5851397292532745, "dev_level0": 2.426766747462515, "dev_first_order": 3.5957192074458564 } }, { "part": 1, "N": 4, "D": 0.025, "lambda0": 188.49555921538757, "g0": 0.003589344384700155, "D_over_g0": 6.965060278574645, "D_over_M": 0.025, "sum_q_minus_1": 2.220446049250313e-15, "Gamma_level0": 0.9977123894767301, "Gamma_mean_level": 0.9977371098586924, "Gamma_first_order": 0.9977372679248124, "Gamma_fit": 0.9977368501719874, "d2E_dM2": 0.001990275846584925, "d2E_dM2_closed": 0.0019957745654456236, "Gamma_closed_11_20_at_mean": 0.997737601306593, "Gamma_closed_11_26": 0.997737760922497, "dev_mean_level": 3.2593668840674717e-05, "dev_level0": 0.00030208804183140536, "dev_first_order": 3.2613523463176364e-05, "dev_mean_level_first_revolution": 3.2593668840674717e-05, "dev_level0_first_revolution": 0.00014078240854031865, "set": "B_unequal_R", "ratio_to_previous": { "dev_mean_level": 4.009842677278695, "dev_level0": 1.9445923605524305, "dev_first_order": 4.014071287527085 } }, { "part": 2, "N": 5, "D": 0.1, "lambda0": 50.26548245743669, "g0": 0.003589344384700155, "D_over_g0": 27.86024111429858, "D_over_M": 0.05882352941176471, "sum_q_minus_1": 2.6645352591003757e-15, "Gamma_level0": 0.9997133235960436, "Gamma_mean_level": 0.999727645111026, "Gamma_first_order": 0.9997282035003875, "Gamma_fit": 0.9997277089609488, "d2E_dM2": 0.00029759808687771037, "d2E_dM2_closed": 0.0002951748287156396, "Gamma_closed_11_20_at_mean": 0.9997292967392039, "Gamma_closed_11_26": 0.9997298497264027, "dev_mean_level": 7.2552162198036285e-06, "dev_level0": 0.00021994915284728744, "dev_first_order": 1.3051467231628422e-05, "dev_mean_level_first_revolution": 5.6901172710288606e-06, "dev_level0_first_revolution": 0.00010832143266170657, "set": "B_unequal_R" }, { "part": 2, "N": 5, "D": 0.05, "lambda0": 100.53096491487338, "g0": 0.003589344384700155, "D_over_g0": 13.93012055714929, "D_over_M": 0.029411764705882356, "sum_q_minus_1": 1.7763568394002505e-15, "Gamma_level0": 0.9997133235960436, "Gamma_mean_level": 0.9997206215820752, "Gamma_first_order": 0.9997207635482155, "Gamma_fit": 0.9997205698052849, "d2E_dM2": 0.00029759808687771037, "d2E_dM2_closed": 0.0002951748287156396, "Gamma_closed_11_20_at_mean": 0.9997223297657317, "Gamma_closed_11_26": 0.9997224703556848, "dev_mean_level": 1.8887657756705423e-06, "dev_level0": 0.00011137972002434049, "dev_first_order": 3.4333857857338224e-06, "dev_mean_level_first_revolution": 1.8887657756705423e-06, "dev_level0_first_revolution": 5.356949068496819e-05, "set": "B_unequal_R", "ratio_to_previous": { "dev_mean_level": 3.841247185468463, "dev_level0": 1.9747684120522175, "dev_first_order": 3.801340148217254 } }, { "part": 2, "N": 5, "D": 0.025, "lambda0": 201.06192982974676, "g0": 0.003589344384700155, "D_over_g0": 6.965060278574645, "D_over_M": 0.014705882352941178, "sum_q_minus_1": 1.3322676295501878e-15, "Gamma_level0": 0.9997133235960436, "Gamma_mean_level": 0.9997170077773905, "Gamma_first_order": 0.9997170435721295, "Gamma_fit": 0.9997169942914724, "d2E_dM2": 0.00029759808687771037, "d2E_dM2_closed": 0.0002951748287156396, "Gamma_closed_11_20_at_mean": 0.999718745222923, "Gamma_closed_11_26": 0.9997187806703258, "dev_mean_level": 4.854379966889866e-07, "dev_level0": 5.6639805733671444e-05, "dev_first_order": 8.02049628600976e-07, "dev_mean_level_first_revolution": 4.854379966889866e-07, "dev_level0_first_revolution": 2.6731036821658893e-05, "set": "B_unequal_R", "ratio_to_previous": { "dev_mean_level": 3.890848653284651, "dev_level0": 1.9664566038249502, "dev_first_order": 4.280764759810082 } } ], "I4_w22": [ { "eps": 2.0, "w22": 0.032, "dE": 2.86729628928839e-07, "w22_times_weight": 2.867347376495886e-07, "weight_22_at_0": 8.960460551549645e-06 }, { "eps": 1.0, "w22": 0.008, "dE": 4.444423051808144e-09, "w22_times_weight": 4.444422510851054e-09, "weight_22_at_0": 5.555528138563818e-07, "ratio_to_previous": { "dE": 64.51447703930604, "weight_22_at_0": 16.128908589896998 } }, { "eps": 0.5, "w22": 0.002, "dE": 6.930322982157122e-11, "w22_times_weight": 6.93040919254433e-11, "weight_22_at_0": 3.465204596272165e-08, "ratio_to_previous": { "dE": 64.13009989939573, "weight_22_at_0": 16.0323235878782 } }, { "eps": 0.25, "w22": 0.0005, "dE": 1.0800249583553523e-12, "w22_times_weight": 1.0823293910994822e-12, "weight_22_at_0": 2.1646587821989643e-09, "ratio_to_previous": { "dE": 64.16817434210526, "weight_22_at_0": 16.00808693161351 } } ], "I5_j_zero": [ { "eps": 1.0, "E": 2.001000623469512, "closed_E": 2.001, "dE": 6.234695120177491e-07, "one_minus_weight_r0_11": 0.0024954676847248614, "weight_r_not_0_in_11": 3.044137799612656e-07 }, { "eps": 0.5, "E": 2.000250039038553, "closed_E": 2.0002500000000003, "dE": 3.9038552834824713e-08, "one_minus_weight_r0_11": 0.0006247164369600489, "weight_r_not_0_in_11": 1.906156910091994e-08, "ratio_to_previous": { "dE": 15.970610249199023, "one_minus_weight": 3.9945606311691275 } }, { "eps": 0.25, "E": 2.000062502441032, "closed_E": 2.0000625000000003, "dE": 2.441031821120987e-09, "one_minus_weight_r0_11": 0.0001562322727233223, "weight_r_not_0_in_11": 1.1919065734389278e-09, "ratio_to_previous": { "dE": 15.992643970080312, "one_minus_weight": 3.998638860399753 } } ], "I2_degenerate": { "X_P0_0.3": { "P0": 0.3, "E0": 1.0, "W0_block_11_22": [ [ -0.8709984901538393, 0.1699989926373006 ], [ 0.1699989926373006, 2.488875934645938 ] ], "level": 0.9999999999999982, "splitting": 2.1094237467877974e-15, "isolation": 0.5367646288937746, "tail": 1.329247076629414e-30, "xi": { "M1": { "branch_overlap_min": 0.9999971099677671, "second_order_branches": false, "matrix_eigenvalues": [ -0.6284491302935782, 0.8930763706569885 ], "slopes_finite_difference": [ -0.6284491302942693, 0.8930763706587833 ], "max_abs_deviation": 1.794786541609028e-12 }, "M2": { "branch_overlap_min": 0.9999992632573971, "second_order_branches": false, "matrix_eigenvalues": [ -0.9193836682493896, 0.8379556562603612 ], "slopes_finite_difference": [ -0.919383668249835, 0.8379556562611896 ], "max_abs_deviation": 8.284484209752918e-13 }, "tau1": { "branch_overlap_min": 0.9999994652353024, "second_order_branches": false, "matrix_eigenvalues": [ 0.13701364783169456, 0.6017382679216703 ], "slopes_finite_difference": [ 0.13701364783985648, 0.6017382679187796 ], "max_abs_deviation": 8.161915587834301e-12 }, "tau2": { "branch_overlap_min": 0.9999997344706929, "second_order_branches": false, "matrix_eigenvalues": [ -0.1562399942386677, 0.5336387103127493 ], "slopes_finite_difference": [ -0.15623999423875992, 0.5336387103116194 ], "max_abs_deviation": 1.1299849944634843e-12 }, "theta": { "branch_overlap_min": 0.9999958486105363, "second_order_branches": false, "matrix_eigenvalues": [ -0.726064560740659, 2.016971420266951 ], "slopes_finite_difference": [ -0.7260645607407579, 2.016971420271583 ], "max_abs_deviation": 4.632294547946003e-12 }, "P": { "branch_overlap_min": 0.9999549236248141, "second_order_branches": false, "matrix_eigenvalues": [ -0.031846375003745014, 0.05626498105111962 ], "slopes_finite_difference": [ -0.03184637502647488, 0.05626498076378439 ], "max_abs_deviation": 2.8733523199653277e-10, "second_derivative_11_24": [ -0.10636246132447708, 0.1732240845088477 ], "second_derivative_finite_difference": [ -0.10636246133695812, 0.1732240843798268 ], "max_abs_deviation_second": 1.290208773152557e-10, "term_of_11_9_from_the_level": { "numerator": 0.0006549251905570781, "denominator": -2.1094237467877974e-15 } } }, "every_eigenvector": { "euler": 1.5543122344752192e-15, "V12": 1.0755285551056204e-16, "mean_rule": 4.083622329176251e-12, "norm_Pi_V1_minus_V2_Pi": 1.623807045561269e-16 }, "overlap_of_branch_0_of_M1_with_branch_0_of": { "M2": 0.9912457291055672, "tau1": 0.27691133128244105, "tau2": 0.727218460602937, "theta": 0.00125015493571443, "P": 0.5106343791399865 }, "U_in_the_branch_vectors_of_M1": [ 2.0135422002964525, -0.7226353407701603 ] }, "X_P0_0": { "P0": 0.0, "E0": 1.0, "W0_block_11_22": [ [ -0.8690861691877569, 0.17779417922648388 ], [ 0.17779417922648388, 2.4886177820527084 ] ], "level": 0.9999999999999998, "splitting": 3.552713678800501e-15, "isolation": 0.5397467369356923, "tail": 3.220867649153723e-30, "xi": { "M1": { "branch_overlap_min": 0.9999971876593898, "second_order_branches": false, "matrix_eigenvalues": [ -0.6311961096511747, 0.8954732540945399 ], "slopes_finite_difference": [ -0.6311961096529725, 0.8954732540947807 ], "max_abs_deviation": 1.797784143775516e-12 }, "M2": { "branch_overlap_min": 0.9999993323005603, "second_order_branches": false, "matrix_eigenvalues": [ -0.9189017363386298, 0.8450716129595568 ], "slopes_finite_difference": [ -0.9189017363377326, 0.8450716129607921 ], "max_abs_deviation": 1.2353451595004117e-12 }, "tau1": { "branch_overlap_min": 0.9999994664039994, "second_order_branches": false, "matrix_eigenvalues": [ 0.12086946671832857, 0.6053049489183279 ], "slopes_finite_difference": [ 0.12086946671909422, 0.6053049489162521 ], "max_abs_deviation": 2.075783989141655e-12 }, "tau2": { "branch_overlap_min": 0.999999739781839, "second_order_branches": false, "matrix_eigenvalues": [ -0.17900441992705343, 0.5381300536834165 ], "slopes_finite_difference": [ -0.17900441992700963, 0.5381300536826712 ], "max_abs_deviation": 7.452927164308676e-13 }, "theta": { "branch_overlap_min": 0.9999959710756143, "second_order_branches": false, "matrix_eigenvalues": [ -0.7256826731364663, 2.0243054354253944 ], "slopes_finite_difference": [ -0.7256826731369959, 2.024305435429141 ], "max_abs_deviation": 3.746780663504978e-12 }, "P": { "branch_overlap_min": 0.9999515656387844, "second_order_branches": true, "matrix_eigenvalues": [ -1.5990099605146319e-18, 1.4220717080865478e-17 ], "slopes_finite_difference": [ 1.7578531223231646e-14, -5.551115123125783e-15 ], "max_abs_deviation": 1.758013023319216e-14, "second_derivative_11_24": [ -0.10630609567694373, 0.19294340823060183 ], "second_derivative_finite_difference": [ -0.1063060956525234, 0.19294340782016753 ], "max_abs_deviation_second": 4.1043429765963424e-10, "term_of_11_9_from_the_level": { "numerator": 9.381668279642345e-35, "denominator": -3.552713678800501e-15 } } }, "every_eigenvector": { "euler": 1.5543122344752192e-15, "V12": 3.495273306657225e-17, "mean_rule": 2.8810287489022812e-12, "norm_Pi_V1_minus_V2_Pi": 6.395302922133256e-17 }, "overlap_of_branch_0_of_M1_with_branch_0_of": { "M2": 0.990444344926481, "tau1": 0.28434210754965816, "tau2": 0.7171408387658194, "theta": 0.0013826601406883624, "P": 0.511202997513944 }, "U_in_the_branch_vectors_of_M1": [ 2.0205031364803183, -0.7218803741913904 ] } }, "I1_listing": { "scan": [ { "kappa": 0.04, "centred": { "total_contract_listing_B_minus_A": 1.2827761084789717e-15, "Cbod_listing_B_minus_A": 5.162369185311951e-16, "Cbod_minus_listed_Cpair_A": 1.3390402313457069e-15, "Cbod_minus_listed_Cpair_A_minus_gradient": 1.3390402313457069e-15, "Cbod_minus_listed_Cpair_B": 2.589160095474978, "view_minus_evolution_by_Cbod": 0.04140756807593813, "view_minus_evolution_by_listed_Cpair_A": 0.04140756807593793, "view_minus_evolution_by_listed_Cpair_B": 1.0252105518165358 }, "not_centred": { "total_contract_listing_B_minus_A": 1.4541908674370036e-15, "Cbod_listing_B_minus_A": 1.2727338794797184e-15, "Cbod_minus_listed_Cpair_A": 0.6533790368880953, "Cbod_minus_listed_Cpair_A_minus_gradient": 1.337937461793145e-15, "Cbod_minus_listed_Cpair_B": 2.4911510444119456, "view_minus_evolution_by_Cbod": 0.04147399211699122, "view_minus_evolution_by_listed_Cpair_A": 0.15258106910530397, "view_minus_evolution_by_listed_Cpair_B": 1.0454209777590693 } }, { "kappa": 0.02, "centred": { "total_contract_listing_B_minus_A": 1.277058133722624e-15, "Cbod_listing_B_minus_A": 1.0104924317347425e-15, "Cbod_minus_listed_Cpair_A": 1.2979632982043458e-15, "Cbod_minus_listed_Cpair_A_minus_gradient": 1.2979632982043458e-15, "Cbod_minus_listed_Cpair_B": 2.589160095474978, "view_minus_evolution_by_Cbod": 0.010524595210457292, "view_minus_evolution_by_listed_Cpair_A": 0.010524595210457895, "view_minus_evolution_by_listed_Cpair_B": 1.0344041743048134 }, "not_centred": { "total_contract_listing_B_minus_A": 1.4352611847732062e-15, "Cbod_listing_B_minus_A": 9.818780061564638e-16, "Cbod_minus_listed_Cpair_A": 0.3266895184440475, "Cbod_minus_listed_Cpair_A_minus_gradient": 1.5067593816740945e-15, "Cbod_minus_listed_Cpair_B": 2.5195368069500708, "view_minus_evolution_by_Cbod": 0.010533024092336463, "view_minus_evolution_by_listed_Cpair_A": 0.07442241670320898, "view_minus_evolution_by_listed_Cpair_B": 1.0437996321633354 } }, { "kappa": 0.01, "centred": { "total_contract_listing_B_minus_A": 1.4427560722082318e-15, "Cbod_listing_B_minus_A": 8.320400019456291e-16, "Cbod_minus_listed_Cpair_A": 1.2946481703345058e-15, "Cbod_minus_listed_Cpair_A_minus_gradient": 1.2946481703345058e-15, "Cbod_minus_listed_Cpair_B": 2.589160095474978, "view_minus_evolution_by_Cbod": 0.00264233315616465, "view_minus_evolution_by_listed_Cpair_A": 0.0026423331561647428, "view_minus_evolution_by_listed_Cpair_B": 1.036936456151247 }, "not_centred": { "total_contract_listing_B_minus_A": 1.3322676295501878e-15, "Cbod_listing_B_minus_A": 1.2047738841180856e-15, "Cbod_minus_listed_Cpair_A": 0.16334475922202352, "Cbod_minus_listed_Cpair_A_minus_gradient": 1.7886148401916585e-15, "Cbod_minus_listed_Cpair_B": 2.5493580271163903, "view_minus_evolution_by_Cbod": 0.0026433907275934454, "view_minus_evolution_by_listed_Cpair_A": 0.03695338761977342, "view_minus_evolution_by_listed_Cpair_B": 1.0414064786548582 } } ], "mean_of_X_not_centred": -0.6020967706836465 } }, "new_in_v3": { "I3_root_against_dense": [ { "sign": -1, "u": 1.0, "root_minus_dense": -2.995867443011946e-15 }, { "sign": -1, "u": 0.5, "root_minus_dense": 9.686262208985497e-16 }, { "sign": 1, "u": 1.0, "root_minus_dense": -8.281569874313277e-15 }, { "sign": 1, "u": 0.5, "root_minus_dense": -2.8831104170734534e-15 } ], "I3_wide": [ { "eps_factor": 1.0, "sign": -1, "u": 2.0, "w11": -0.024235294117647063, "a": 0.012117647058823532, "found": true, "E_bind": -0.014920001571574897, "E_bind_leading": -0.014978235492056277, "isolation": 0.014920001571574897, "isolation_leading": 0.014978235492056277, "rel_dev_isolation": -0.0038879025845376994, "remainder": 5.82339204813799e-05, "remainder_over_isolation": 0.003903077369128786, "rel_dev_E_bind": -0.0038879025845376994, "wide_form": -0.024235294117647063, "rel_dev_wide_form": -0.6243493005938658, "Epp0": 0.0031404151650026376, "rel_dev_Epp0": 0.004562116682309792, "mb_minus_m1_m2": 175.3736798984645, "minus_4_m1_m2_E_bind": 176.13890744220365, "rel_dev_11_16": -0.004363411568840803, "leading_function": 176.82639122566437, "rel_dev_leading_function": -0.008215466690975592, "P_half_pi": { "isolation": 0.017532317636902654, "isolation_leading": 0.017602563555805258, "remainder": 6.498322307038791e-05, "remainder_over_isolation": 0.003706482189987756, "closed_form_minus_exact_edge": -0.017597300859973044 } }, { "eps_factor": 1.0, "sign": -1, "u": 1.0, "w11": -0.012117647058823532, "a": 0.012117647058823532, "found": true, "E_bind": -0.005006099041962584, "E_bind_leading": -0.005019293755815151, "isolation": 0.005006099041962584, "isolation_leading": 0.005019293755815151, "rel_dev_isolation": -0.0026287988897401816, "remainder": 1.3194713852566695e-05, "remainder_over_isolation": 0.002635727687759421, "rel_dev_E_bind": -0.0026287988897401816, "wide_form": -0.006058823529411766, "rel_dev_wide_form": -0.21028838595180344, "Epp0": 0.0049475706098375295, "rel_dev_Epp0": 0.0009484862427336612, "mb_minus_m1_m2": 59.063843814237046, "minus_4_m1_m2_E_bind": 59.09978035650273, "rel_dev_11_16": -0.000608435549482786, "leading_function": 59.25555128392888, "rel_dev_leading_function": -0.00323526598838393, "P_half_pi": { "isolation": 0.006554166297161543, "isolation_leading": 0.0065734022494556635, "remainder": 1.3973256461904254e-05, "remainder_over_isolation": 0.002131965505354319, "closed_form_minus_exact_edge": -0.006568139553623447 } }, { "eps_factor": 1.0, "sign": -1, "u": 0.5, "w11": -0.006058823529411766, "a": 0.012117647058823532, "found": true, "E_bind": -0.001428217778920135, "E_bind_leading": -0.0014302942166163728, "isolation": 0.001428217778920135, "isolation_leading": 0.0014302942166163728, "rel_dev_isolation": -0.001451755640283511, "remainder": 2.076437696237705e-06, "remainder_over_isolation": 0.0014538662988831327, "rel_dev_E_bind": -0.001451755640283511, "wide_form": -0.0015147058823529415, "rel_dev_wide_form": -0.06055666349301393, "Epp0": 0.006252906186268668, "rel_dev_Epp0": 9.590195197753653e-05, "mb_minus_m1_m2": 16.870080654370653, "minus_4_m1_m2_E_bind": 16.860904334473815, "rel_dev_11_16": 0.0005439404875910067, "leading_function": 16.885417835054408, "rel_dev_leading_function": -0.0009083092188524076, "P_half_pi": { "isolation": 0.002055058279317434, "isolation_leading": 0.0020595196414825417, "remainder": -8.013336671086266e-07, "remainder_over_isolation": 0.00038993233193113195, "closed_form_minus_exact_edge": -0.0020542569456503254 } }, { "eps_factor": 1.0, "sign": -1, "u": 0.25, "w11": -0.003029411764705883, "a": 0.012117647058823532, "found": true, "E_bind": -0.0003726666887699605, "E_bind_leading": -0.00037293763054761786, "isolation": 0.0003726666887699605, "isolation_leading": 0.00037293763054761786, "rel_dev_isolation": -0.0007265069423525296, "remainder": 2.709417776573472e-07, "remainder_over_isolation": 0.0007270351384279317, "rel_dev_E_bind": -0.0007265069423525296, "wide_form": -0.00037867647058823536, "rel_dev_wide_form": -0.016126426105083313, "Epp0": 0.0067815876724185795, "rel_dev_Epp0": 1.3316406762168568e-06, "mb_minus_m1_m2": 4.402539554989673, "minus_4_m1_m2_E_bind": 4.3995372979787, "rel_dev_11_16": 0.0006819375438819743, "leading_function": 4.402735916187166, "rel_dev_leading_function": -4.459981275987202e-05, "P_half_pi": { "isolation": 0.0005608837656039265, "isolation_leading": 0.000562102253175132, "remainder": -4.04420826101079e-06, "remainder_over_isolation": 0.007210421319034302, "closed_form_minus_exact_edge": -0.0005568395573429157 } }, { "eps_factor": 1.0, "sign": -1, "u": 0.125, "w11": -0.0015147058823529415, "a": 0.012117647058823532, "found": true, "E_bind": -9.426848538950456e-05, "E_bind_leading": -9.430217756986083e-05, "isolation": 9.426848538950456e-05, "isolation_leading": 9.430217756986083e-05, "rel_dev_isolation": -0.0003572789221256669, "remainder": 3.3692180356263116e-08, "remainder_over_isolation": 0.0003574066159761834, "rel_dev_E_bind": -0.0003572789221256669, "wide_form": -9.466911764705884e-05, "rel_dev_wide_form": -0.0042499065928440416, "Epp0": 0.006936299435021802, "rel_dev_Epp0": -1.720825363171211e-06, "mb_minus_m1_m2": 1.1135376861431183, "minus_4_m1_m2_E_bind": 1.1128918414038733, "rel_dev_11_16": 0.0005799936071153297, "leading_function": 1.113289596310861, "rel_dev_leading_function": 0.00022284393304250458, "P_half_pi": { "isolation": 0.00014385659177961092, "isolation_leading": 0.0001442167993358466, "remainder": -4.902488275980617e-06, "remainder_over_isolation": 0.03407899641812212, "closed_form_minus_exact_edge": -0.0001389541035036303 } }, { "eps_factor": 1.0, "sign": -1, "u": 0.0625, "w11": -0.0007573529411764707, "a": 0.012117647058823532, "found": true, "E_bind": -2.3640040486996213e-05, "E_bind_leading": -2.3644211866057432e-05, "isolation": 2.3640040486996213e-05, "isolation_leading": 2.3644211866057432e-05, "rel_dev_isolation": -0.00017642284229435075, "remainder": 4.171379061219667e-09, "remainder_over_isolation": 0.00017645397280576726, "rel_dev_E_bind": -0.00017642284229435075, "wide_form": -2.366727941176471e-05, "rel_dev_wide_form": -0.0011522368070173508, "Epp0": 0.006976674138363447, "rel_dev_Epp0": -5.848281355921224e-07, "mb_minus_m1_m2": 0.2792168829598296, "minus_4_m1_m2_E_bind": 0.27908381130481635, "rel_dev_11_16": 0.00047658885667166206, "leading_function": 0.2791330567520875, "rel_dev_leading_function": 0.00030030913829228313, "P_half_pi": { "isolation": 3.619953080777425e-05, "isolation_leading": 3.630043971993013e-05, "remainder": -5.161786920060418e-06, "remainder_over_isolation": 0.14259264705585264, "closed_form_minus_exact_edge": -3.103774388771383e-05 } }, { "eps_factor": 1.0, "sign": -1, "u": 0.03125, "w11": -0.00037867647058823536, "a": 0.012117647058823532, "found": true, "E_bind": -5.914857966156118e-06, "E_bind_leading": -5.9153760217540985e-06, "isolation": 5.914857966156118e-06, "isolation_leading": 5.9153760217540985e-06, "rel_dev_isolation": -8.757779658904613e-05, "remainder": 5.180555979809014e-10, "remainder_over_isolation": 8.758546713127071e-05, "rel_dev_E_bind": -8.757779658904613e-05, "wide_form": -5.9168198529411775e-06, "rel_dev_wide_form": -0.00033168789449984393, "Epp0": 0.006986879432227972, "rel_dev_Epp0": -1.5738681444477128e-07, "mb_minus_m1_m2": 0.06985682630956092, "minus_4_m1_m2_E_bind": 0.06982818432267639, "rel_dev_11_16": 0.0004100098501126479, "leading_function": 0.06983430025681395, "rel_dev_leading_function": 0.00032256430814269464, "P_half_pi": { "isolation": 9.063926823905943e-06, "isolation_leading": 9.09076442331784e-06, "remainder": -5.235858232804404e-06, "remainder_over_isolation": 0.5776589258195379, "closed_form_minus_exact_edge": -3.82806859110154e-06 } }, { "eps_factor": 1.0, "sign": -1, "u": 0.015625, "w11": -0.00018933823529411768, "a": 0.012117647058823532, "found": true, "E_bind": -1.4790501695772618e-06, "E_bind_leading": -1.4791146907486286e-06, "isolation": 1.4790501695772618e-06, "isolation_leading": 1.4791146907486286e-06, "rel_dev_isolation": -4.362147963937128e-05, "remainder": 6.452117136678624e-11, "remainder_over_isolation": 4.362338255586523e-05, "rel_dev_E_bind": -4.362147963937128e-05, "wide_form": -1.4792049632352944e-06, "rel_dev_wide_form": -0.00010465747627536955, "Epp0": 0.006989437832072702, "rel_dev_Epp0": -3.995139304396111e-08, "mb_minus_m1_m2": 0.017467486621242756, "minus_4_m1_m2_E_bind": 0.017461008946398227, "rel_dev_11_16": 0.0003708418380381662, "leading_function": 0.017461770654657777, "rel_dev_leading_function": 0.00032734175119027376, "P_half_pi": { "isolation": 2.2667477633762922e-06, "isolation_leading": 2.2736737380017052e-06, "remainder": -5.255769857590888e-06, "remainder_over_isolation": 2.3186390398208596, "closed_form_minus_exact_edge": 2.9890220942145954e-06 } }, { "eps_factor": 1.0, "sign": -1, "u": 0.0078125, "w11": -9.466911764705884e-05, "a": 0.012117647058823532, "found": true, "E_bind": -3.6978754861694177e-07, "E_bind_leading": -3.697955982609469e-07, "isolation": 3.6978754861694177e-07, "isolation_leading": 3.697955982609469e-07, "rel_dev_isolation": -2.1767819960438747e-05, "remainder": 8.049644005107028e-12, "remainder_over_isolation": 2.1768293808739222e-05, "rel_dev_E_bind": -2.1767819960438747e-05, "wide_form": -3.698012408088236e-07, "rel_dev_wide_form": -3.7027184752530755e-05, "Epp0": 0.006990077876856824, "rel_dev_Epp0": -9.768734677709186e-09, "mb_minus_m1_m2": 0.004367039993908861, "minus_4_m1_m2_E_bind": 0.0043655474489500065, "rel_dev_11_16": 0.00034177496907204655, "leading_function": 0.004365642479480729, "rel_dev_leading_function": 0.00032011655436761, "P_half_pi": { "isolation": 5.667204262919945e-07, "isolation_leading": 5.68479915422776e-07, "remainder": -5.260936343085519e-06, "remainder_over_isolation": 9.283124621971712, "closed_form_minus_exact_edge": 4.694215916793525e-06 } }, { "eps_factor": 1.0, "sign": 1, "u": 2.0, "w11": 0.024235294117647063, "a": 0.012117647058823532, "found": true, "E_bind": 0.03894297934044144, "E_bind_leading": 0.03921352960970334, "isolation": 0.014909045200069634, "isolation_leading": 0.014978235492056277, "rel_dev_isolation": -0.0046193887139335315, "remainder": -0.00027055026926189885, "remainder_over_isolation": 0.018146720036815986, "rel_dev_E_bind": -0.006899411298975533, "E_bind_minus_2a": 0.014707685222794378, "w2_over_2a": 0.024235294117647063 }, { "eps_factor": 1.0, "sign": 1, "u": 1.0, "w11": 0.012117647058823532, "a": 0.012117647058823532, "found": true, "E_bind": 0.029031083268790715, "E_bind_leading": 0.029254587873462214, "isolation": 0.004997149128418907, "isolation_leading": 0.005019293755815151, "rel_dev_isolation": -0.004411901050937384, "remainder": -0.00022350460467149974, "remainder_over_isolation": 0.044726422791832185, "rel_dev_E_bind": -0.007639984731223919, "E_bind_minus_2a": 0.004795789151143651, "w2_over_2a": 0.006058823529411766 }, { "eps_factor": 1.0, "sign": 1, "u": 0.5, "w11": 0.006058823529411766, "a": 0.012117647058823532, "found": true, "E_bind": 0.025457764579939205, "E_bind_leading": 0.025665588334263436, "isolation": 0.0014238304395673973, "isolation_leading": 0.0014302942166163728, "rel_dev_isolation": -0.004519194004899729, "remainder": -0.0002078237543242309, "remainder_over_isolation": 0.1459610277663217, "rel_dev_E_bind": -0.008097369583645476, "E_bind_minus_2a": 0.0012224704622921419, "w2_over_2a": 0.0015147058823529415 }, { "eps_factor": 1.0, "sign": 1, "u": 0.25, "w11": 0.003029411764705883, "a": 0.012117647058823532, "found": true, "E_bind": 0.02440508745573683, "E_bind_leading": 0.02460823174819468, "isolation": 0.00037115331536502136, "isolation_leading": 0.00037293763054761786, "rel_dev_isolation": -0.004784486832225624, "remainder": -0.00020314429245785193, "remainder_over_isolation": 0.5473325551681085, "rel_dev_E_bind": -0.00825513570160339, "E_bind_minus_2a": 0.00016979333808976593, "w2_over_2a": 0.00037867647058823536 }, { "eps_factor": 1.0, "sign": 1, "u": 0.125, "w11": 0.0015147058823529415, "a": 0.012117647058823532, "found": true, "E_bind": 0.02412776826458304, "E_bind_leading": 0.024329596295216922, "isolation": 9.383412421123255e-05, "isolation_leading": 9.430217756986083e-05, "rel_dev_isolation": -0.004963335637520493, "remainder": -0.00020182803063388197, "remainder_over_isolation": 2.150902268555748, "rel_dev_E_bind": -0.008295576637807195, "E_bind_minus_2a": -0.00010752585306402287, "w2_over_2a": 9.466911764705884e-05 }, { "eps_factor": 1.0, "sign": 1, "u": 0.0625, "w11": 0.0007573529411764707, "a": 0.012117647058823532, "found": true, "E_bind": 0.024057460547305596, "E_bind_leading": 0.02425893832951312, "isolation": 2.3526406933788158e-05, "isolation_leading": 2.3644211866057432e-05, "rel_dev_isolation": -0.004982400468098929, "remainder": -0.00020147778220752297, "remainder_over_isolation": 8.563899399281604, "rel_dev_E_bind": -0.008305300894491646, "E_bind_minus_2a": -0.00017783357034146727, "w2_over_2a": 2.366727941176471e-05 }, { "eps_factor": 1.0, "sign": 1, "u": 0.03125, "w11": 0.00037867647058823536, "a": 0.012117647058823532, "found": true, "E_bind": 0.02403982108711964, "E_bind_leading": 0.024241209493668817, "isolation": 5.886946747832994e-06, "isolation_leading": 5.9153760217540985e-06, "rel_dev_isolation": -0.004805996071349377, "remainder": -0.00020138840654917653, "remainder_over_isolation": 34.209313448148365, "rel_dev_E_bind": -0.008307688054994699, "E_bind_minus_2a": -0.00019547303052742243, "w2_over_2a": 5.9168198529411775e-06 }, { "eps_factor": 1.0, "sign": 1, "u": 0.015625, "w11": 0.00018933823529411768, "a": 0.012117647058823532, "found": true, "E_bind": 0.024035406843661206, "E_bind_leading": 0.024236773232337812, "isolation": 1.472703289397831e-06, "isolation_leading": 1.4791146907486286e-06, "rel_dev_isolation": -0.004334620831568261, "remainder": -0.00020136638867660622, "remainder_over_isolation": 136.73249060164883, "rel_dev_E_bind": -0.00830830023230708, "E_bind_minus_2a": -0.0001998872739858576, "w2_over_2a": 1.4792049632352944e-06 }, { "eps_factor": 1.0, "sign": 1, "u": 0.0078125, "w11": 9.466911764705884e-05, "a": 0.012117647058823532, "found": true, "E_bind": 0.024034302704737207, "E_bind_leading": 0.024235663913245324, "isolation": 3.685643653987547e-07, "isolation_leading": 3.697955982609469e-07, "rel_dev_isolation": -0.0033294957213724215, "remainder": -0.00020136120850811762, "remainder_over_isolation": 546.3393301472926, "rel_dev_E_bind": -0.008308466779738982, "E_bind_minus_2a": -0.00020099141290985667, "w2_over_2a": 3.698012408088236e-07 }, { "eps_factor": 0.5, "sign": -1, "u": 2.0, "w11": -0.006058823529411766, "a": 0.003029411764705883, "found": true, "E_bind": -0.0037409280422991387, "E_bind_leading": -0.0037445588730140693, "isolation": 0.0037409280422991387, "isolation_leading": 0.0037445588730140693, "rel_dev_isolation": -0.0009696284230158297, "remainder": 3.6308307149305642e-06, "remainder_over_isolation": 0.0009705695148038961, "rel_dev_E_bind": -0.0009696284230158297, "wide_form": -0.006058823529411766, "rel_dev_wide_form": -0.6196044032132921, "Epp0": 0.0007824348657223055, "rel_dev_Epp0": 0.0011471523070140561, "mb_minus_m1_m2": 705.8394335257601, "minus_4_m1_m2_E_bind": 706.6197413231706, "rel_dev_11_16": -0.001105503263699453, "leading_function": 707.3055649026575, "rel_dev_leading_function": -0.00207284015515858, "P_half_pi": { "isolation": 0.00439625566701661, "isolation_leading": 0.004400640888951314, "remainder": 4.055689716441716e-06, "remainder_over_isolation": 0.0009225327241247529, "closed_form_minus_exact_edge": -0.004400311356733052 } }, { "eps_factor": 0.5, "sign": -1, "u": 1.0, "w11": -0.003029411764705883, "a": 0.003029411764705883, "found": true, "E_bind": -0.0012539989102265665, "E_bind_leading": -0.0012548234389537878, "isolation": 0.0012539989102265665, "isolation_leading": 0.0012548234389537878, "rel_dev_isolation": -0.0006570874448350358, "remainder": 8.245287272212569e-07, "remainder_over_isolation": 0.0006575194926383827, "rel_dev_E_bind": -0.0006570874448350358, "wide_form": -0.0015147058823529415, "rel_dev_wide_form": -0.20790047742487403, "Epp0": 0.001236015533987851, "rel_dev_Epp0": 0.00023868300751412127, "mb_minus_m1_m2": 236.82909833329205, "minus_4_m1_m2_E_bind": 236.86646082057365, "rel_dev_11_16": -0.00015776138804116655, "leading_function": 237.02220513571552, "rel_dev_leading_function": -0.0008147203014709179, "P_half_pi": { "isolation": 0.0016421467066022716, "isolation_leading": 0.0016433505623639159, "remainder": 8.743235433815314e-07, "remainder_over_isolation": 0.000532427181972416, "closed_form_minus_exact_edge": -0.001643021030145653 } }, { "eps_factor": 0.5, "sign": -1, "u": 0.5, "w11": -0.0015147058823529415, "a": 0.003029411764705883, "found": true, "E_bind": -0.00035744380650213004, "E_bind_leading": -0.0003575735541540932, "isolation": 0.00035744380650213004, "isolation_leading": 0.0003575735541540932, "rel_dev_isolation": -0.00036285583890591135, "remainder": 1.297476519631518e-07, "remainder_over_isolation": 0.000362987551058263, "rel_dev_E_bind": -0.00036285583890591135, "wide_form": -0.00037867647058823536, "rel_dev_wide_form": -0.059401404360264934, "Epp0": 0.0015631145010291626, "rel_dev_Epp0": 2.421926232755241e-05, "mb_minus_m1_m2": 67.52617710591068, "minus_4_m1_m2_E_bind": 67.51716345040234, "rel_dev_11_16": 0.00013348387091724544, "leading_function": 67.54167134021763, "rel_dev_leading_function": -0.00022940258953483094, "P_half_pi": { "isolation": 0.0005146005172142594, "isolation_leading": 0.0005148799103706354, "remainder": -5.013906188681711e-08, "remainder_over_isolation": 9.743297997102708e-05, "closed_form_minus_exact_edge": -0.0005145503781523726 } }, { "eps_factor": 0.5, "sign": -1, "u": 0.25, "w11": -0.0007573529411764707, "a": 0.003029411764705883, "found": true, "E_bind": -9.32174855774465e-05, "E_bind_leading": -9.323440763690446e-05, "isolation": 9.32174855774465e-05, "isolation_leading": 9.323440763690446e-05, "rel_dev_isolation": -0.0001815001552202796, "remainder": 1.6922059457968983e-08, "remainder_over_isolation": 0.0001815331035067437, "rel_dev_E_bind": -0.0001815001552202796, "wide_form": -9.466911764705884e-05, "rel_dev_wide_form": -0.01557252977400154, "Epp0": 0.0016953953089124342, "rel_dev_Epp0": 3.82485740065091e-07, "mb_minus_m1_m2": 17.610718062060016, "minus_4_m1_m2_E_bind": 17.607747275739893, "rel_dev_11_16": 0.00016869194712300364, "leading_function": 17.610943664748664, "rel_dev_leading_function": -1.2810369105852032e-05, "P_half_pi": { "isolation": 0.00014044920565403824, "isolation_leading": 0.000140525563293783, "remainder": -2.531745785180634e-07, "remainder_over_isolation": 0.0018026059837012974, "closed_form_minus_exact_edge": -0.00014019603107552018 } }, { "eps_factor": 0.5, "sign": -1, "u": 0.125, "w11": -0.00037867647058823536, "a": 0.003029411764705883, "found": true, "E_bind": -2.357344078414307e-05, "E_bind_leading": -2.3575544392465207e-05, "isolation": 2.357344078414307e-05, "isolation_leading": 2.3575544392465207e-05, "rel_dev_isolation": -8.922840919878494e-05, "remainder": 2.103608322135005e-09, "remainder_over_isolation": 8.923637161826711e-05, "rel_dev_E_bind": -8.922840919878494e-05, "wide_form": -2.366727941176471e-05, "rel_dev_wide_form": -0.0039806928687627224, "Epp0": 0.001734077118230059, "rel_dev_Epp0": -4.1784198334296267e-07, "mb_minus_m1_m2": 4.453399344528918, "minus_4_m1_m2_E_bind": 4.4527610370048025, "rel_dev_11_16": 0.00014333040330192682, "leading_function": 4.453158385243444, "rel_dev_leading_function": 5.410974967170186e-05, "P_half_pi": { "isolation": 3.6031617005733785e-05, "isolation_leading": 3.605419983396165e-05, "remainder": -3.069493900349513e-07, "remainder_over_isolation": 0.008518890228715126, "closed_form_minus_exact_edge": -3.5724667615698834e-05 } }, { "eps_factor": 0.5, "sign": -1, "u": 0.0625, "w11": -0.00018933823529411768, "a": 0.003029411764705883, "found": true, "E_bind": -5.9107925685195424e-06, "E_bind_leading": -5.911052966514358e-06, "isolation": 5.9107925685195424e-06, "isolation_leading": 5.911052966514358e-06, "rel_dev_isolation": -4.4052725680315715e-05, "remainder": 2.6039799481567346e-10, "remainder_over_isolation": 4.405466640844994e-05, "rel_dev_E_bind": -4.4052725680315715e-05, "wide_form": -5.9168198529411775e-06, "rel_dev_wide_form": -0.0010197083304421806, "Epp0": 0.0017441693054188734, "rel_dev_Epp0": -1.4288256349048713e-07, "mb_minus_m1_m2": 1.116614147131088, "minus_4_m1_m2_E_bind": 1.1164830407203579, "rel_dev_11_16": 0.0001174142483031938, "leading_function": 1.11653222700835, "rel_dev_leading_function": 7.337013724852108e-05, "P_half_pi": { "isolation": 9.06878191169391e-06, "isolation_leading": 9.075109929982533e-06, "remainder": -3.23204199974194e-07, "remainder_over_isolation": 0.035639207461526046, "closed_form_minus_exact_edge": -8.745577711719715e-06 } }, { "eps_factor": 0.5, "sign": -1, "u": 0.03125, "w11": -9.466911764705884e-05, "a": 0.003029411764705883, "found": true, "E_bind": -1.4788116688554939e-06, "E_bind_leading": -1.4788440054385246e-06, "isolation": 1.4788116688554939e-06, "isolation_leading": 1.4788440054385246e-06, "rel_dev_isolation": -2.1866121721995138e-05, "remainder": 3.233658303076162e-11, "remainder_over_isolation": 2.1866599859729316e-05, "rel_dev_E_bind": -2.1866121721995138e-05, "wide_form": -1.4792049632352944e-06, "rel_dev_wide_form": -0.00026595298649821245, "Epp0": 0.00174672006608934, "rel_dev_Epp0": -3.8287971381824763e-08, "mb_minus_m1_m2": 0.27935912095148296, "minus_4_m1_m2_E_bind": 0.2793310930060377, "rel_dev_11_16": 0.00010032944458660201, "leading_function": 0.2793372010272558, "rel_dev_leading_function": 7.847119591148674e-05, "P_half_pi": { "isolation": 2.271007870434643e-06, "isolation_leading": 2.27269110582946e-06, "remainder": -3.278489828680009e-07, "remainder_over_isolation": 0.14436276823877967, "closed_form_minus_exact_edge": -1.943158887566642e-06 } }, { "eps_factor": 0.5, "sign": -1, "u": 0.015625, "w11": -4.733455882352942e-05, "a": 0.003029411764705883, "found": true, "E_bind": -3.6977464552042225e-07, "E_bind_leading": -3.6977867268715714e-07, "isolation": 3.6977464552042225e-07, "isolation_leading": 3.6977867268715714e-07, "rel_dev_isolation": -1.0890749067868521e-05, "remainder": 4.0271667348853154e-12, "remainder_over_isolation": 1.0890867677575528e-05, "rel_dev_E_bind": -1.0890749067868521e-05, "wide_form": -3.698012408088236e-07, "rel_dev_wide_form": -7.192296368484605e-05, "Epp0": 0.0017473595112347943, "rel_dev_Epp0": -9.495944133114093e-09, "mb_minus_m1_m2": 0.0698525170723201, "minus_4_m1_m2_E_bind": 0.06984632193163531, "rel_dev_11_16": 8.868886826754983e-05, "leading_function": 0.06984708261863111, "rel_dev_leading_function": 7.780502041381135e-05, "P_half_pi": { "isolation": 5.679840086416418e-07, "isolation_leading": 5.684184345004263e-07, "remainder": -3.2909779240403343e-07, "remainder_over_isolation": 0.5794138345392593, "closed_form_minus_exact_edge": -2.3888621623760833e-07 } }, { "eps_factor": 0.5, "sign": -1, "u": 0.0078125, "w11": -2.366727941176471e-05, "a": 0.003029411764705883, "found": true, "E_bind": -9.244839714904354e-08, "E_bind_leading": -9.244889956523672e-08, "isolation": 9.244839714904354e-08, "isolation_leading": 9.244889956523672e-08, "rel_dev_isolation": -5.434528648181909e-06, "remainder": 5.024161931801709e-13, "remainder_over_isolation": 5.434558182444041e-06, "rel_dev_E_bind": -5.434528648181909e-06, "wide_form": -9.24503102022059e-08, "rel_dev_wide_form": -2.069319989697024e-05, "Epp0": 0.0017475194826295998, "rel_dev_Epp0": -2.0919139606119022e-09, "mb_minus_m1_m2": 0.017463766994126217, "minus_4_m1_m2_E_bind": 0.017462475017041557, "rel_dev_11_16": 7.398043532616647e-05, "leading_function": 0.017462569917922915, "rel_dev_leading_function": 6.855097553959524e-05, "P_half_pi": { "isolation": 1.4200961198575397e-07, "isolation_leading": 1.42119978855694e-07, "remainder": -3.2942185139287795e-07, "remainder_over_isolation": 2.3197151712936495, "closed_form_minus_exact_edge": 1.8741223940712398e-07 } }, { "eps_factor": 0.5, "sign": 1, "u": 2.0, "w11": 0.006058823529411766, "a": 0.003029411764705883, "found": true, "E_bind": 0.009786148616199895, "E_bind_leading": 0.009803382402425835, "isolation": 0.003740092506917366, "isolation_leading": 0.0037445588730140693, "rel_dev_isolation": -0.001192761617100195, "remainder": -1.7233786225940434e-05, "remainder_over_isolation": 0.004607850258801419, "rel_dev_E_bind": -0.0017579428730308383, "E_bind_minus_2a": 0.003727325086788129, "w2_over_2a": 0.006058823529411766 }, { "eps_factor": 0.5, "sign": 1, "u": 1.0, "w11": 0.003029411764705883, "a": 0.003029411764705883, "found": true, "E_bind": 0.007299453794610978, "E_bind_leading": 0.007313646968365554, "isolation": 0.0012533976853284492, "isolation_leading": 0.0012548234389537878, "rel_dev_isolation": -0.001136218515751735, "remainder": -1.419317375457585e-05, "remainder_over_isolation": 0.011323759346864096, "rel_dev_E_bind": -0.00194064244773736, "E_bind_minus_2a": 0.001240630265199212, "w2_over_2a": 0.0015147058823529415 }, { "eps_factor": 0.5, "sign": 1, "u": 0.5, "w11": 0.0015147058823529415, "a": 0.003029411764705883, "found": true, "E_bind": 0.006403213593810778, "E_bind_leading": 0.006416397083565859, "isolation": 0.00035715748452824943, "isolation_leading": 0.0003575735541540932, "rel_dev_isolation": -0.001163591717033028, "remainder": -1.3183489755081053e-05, "remainder_over_isolation": 0.03691225951065937, "rel_dev_E_bind": -0.002054656154128547, "E_bind_minus_2a": 0.00034439006439901214, "w2_over_2a": 0.00037867647058823536 }, { "eps_factor": 0.5, "sign": 1, "u": 0.25, "w11": 0.0007573529411764707, "a": 0.003029411764705883, "found": true, "E_bind": 0.00613917534216912, "E_bind_leading": 0.00615205793704867, "isolation": 9.31192328865911e-05, "isolation_leading": 9.323440763690446e-05, "rel_dev_isolation": -0.0012353245248460578, "remainder": -1.2882594879550652e-05, "remainder_over_isolation": 0.13834515685111176, "rel_dev_E_bind": -0.0020940301621624234, "E_bind_minus_2a": 8.035181275735381e-05, "w2_over_2a": 9.466911764705884e-05 }, { "eps_factor": 0.5, "sign": 1, "u": 0.125, "w11": 0.00037867647058823536, "a": 0.003029411764705883, "found": true, "E_bind": 0.0060696011944169626, "E_bind_leading": 0.006082399073804231, "isolation": 2.354508513443404e-05, "isolation_leading": 2.3575544392465207e-05, "rel_dev_isolation": -0.0012919853524528055, "remainder": -1.2797879387268021e-05, "remainder_over_isolation": 0.5435478068648592, "rel_dev_E_bind": -0.0021040841339046833, "E_bind_minus_2a": 1.0777665005196752e-05, "w2_over_2a": 2.366727941176471e-05 }, { "eps_factor": 0.5, "sign": 1, "u": 0.0625, "w11": 0.00018933823529411768, "a": 0.003029411764705883, "found": true, "E_bind": 0.0060519593553679816, "E_bind_leading": 0.00606473458237828, "isolation": 5.903246085453041e-06, "isolation_leading": 5.911052966514358e-06, "rel_dev_isolation": -0.001320725952811132, "remainder": -1.2775227010298172e-05, "remainder_over_isolation": 2.16410205933635, "rel_dev_E_bind": -0.002106477511384905, "E_bind_minus_2a": -6.864174043784248e-06, "w2_over_2a": 5.9168198529411775e-06 }, { "eps_factor": 0.5, "sign": 1, "u": 0.03125, "w11": 9.466911764705884e-05, "a": 0.003029411764705883, "found": true, "E_bind": 0.006047532994613864, "E_bind_leading": 0.006060302373417204, "isolation": 1.4768853313354077e-06, "isolation_leading": 1.4788440054385246e-06, "rel_dev_isolation": -0.0013244629561426175, "remainder": -1.2769378803340406e-05, "remainder_over_isolation": 8.646154533740452, "rel_dev_E_bind": -0.0021070530835807415, "E_bind_minus_2a": -1.1290534797901881e-05, "w2_over_2a": 1.4792049632352944e-06 }, { "eps_factor": 0.5, "sign": 1, "u": 0.015625, "w11": 4.733455882352942e-05, "a": 0.003029411764705883, "found": true, "E_bind": 0.006046425406422311, "E_bind_leading": 0.006059193308084453, "isolation": 3.69297139782461e-07, "isolation_leading": 3.6977867268715714e-07, "rel_dev_isolation": -0.0013022192469806068, "remainder": -1.2767901662141985e-05, "remainder_over_isolation": 34.57351895458241, "rel_dev_E_bind": -0.002107194970179688, "E_bind_minus_2a": -1.2398122989454828e-05, "w2_over_2a": 3.698012408088236e-07 }, { "eps_factor": 0.5, "sign": 1, "u": 0.0078125, "w11": 2.366727941176471e-05, "a": 0.003029411764705883, "found": true, "E_bind": 0.0060461484433444205, "E_bind_leading": 0.006058915978311331, "isolation": 9.233406189201182e-08, "isolation_leading": 9.244889956523672e-08, "rel_dev_isolation": -0.0012421745825526417, "remainder": -1.2767534966910514e-05, "remainder_over_isolation": 138.2754609219145, "rel_dev_E_bind": -0.002107230899489867, "E_bind_minus_2a": -1.2675086067345277e-05, "w2_over_2a": 9.24503102022059e-08 } ], "I3_tight": [ { "eps_factor": 1.0, "u": 2, "w11": -0.024235294117647063, "w11_over_M": 0.024235294117647063, "in_a_band": false, "weight0": 0.8899626325872354, "tail": 4.286374863774783e-28, "E_bind_minus_w11": [ 0.009315292546071038, 0.009257058625590786, 0.009088235294117649 ], "rel_dev_leading": 0.006290758526608752, "rel_dev_tight_form": 0.024374677534862485, "rel_dev_Epp0": 0.0045621178035695755, "rel_dev_1_minus_s3": [ 0.00928390170775158, 0.01327732749960934 ] }, { "eps_factor": 1.0, "u": 4, "w11": -0.048470588235294126, "w11_over_M": 0.048470588235294126, "in_a_band": false, "weight0": 0.9647145657474384, "tail": 3.0273500468074624e-29, "E_bind_minus_w11": [ 0.010806881355552272, 0.01062589653663306, 0.01060294117647059 ], "rel_dev_leading": 0.017032428115148907, "rel_dev_tight_form": 0.01887132581287241, "rel_dev_Epp0": 0.013706571931081648, "rel_dev_1_minus_s3": [ 0.0317904044214823, 0.027299425644829782 ] }, { "eps_factor": 1.0, "u": 8, "w11": -0.09694117647058825, "w11_over_M": 0.09694117647058825, "in_a_band": false, "weight0": 0.9863204057314806, "tail": 3.21343946132194e-29, "E_bind_minus_w11": [ 0.011822029025570335, 0.011363229638264638, 0.01136029411764706 ], "rel_dev_leading": 0.04037579120646583, "rel_dev_tight_form": 0.03905716243164097, "rel_dev_Epp0": 0.03300064567553019, "rel_dev_1_minus_s3": [ 0.082875105370223, 0.05723557773482265 ] }, { "eps_factor": 1.0, "u": 16, "w11": -0.1938823529411765, "w11_over_M": 0.1938823529411765, "in_a_band": false, "weight0": 0.9914083650647069, "tail": 2.2642392220475766e-29, "E_bind_minus_w11": [ 0.012809255083744753, 0.01173933966896662, 0.011738970588235297 ], "rel_dev_leading": 0.09113931830480161, "rel_dev_tight_form": 0.08355556107768297, "rel_dev_Epp0": 0.07258383439270044, "rel_dev_1_minus_s3": [ 0.19916186754658335, 0.12156633757158962 ] }, { "eps_factor": 1.0, "u": 32, "w11": -0.387764705882353, "w11_over_M": 0.387764705882353, "in_a_band": false, "weight0": 0.9912773154710773, "tail": 6.013579122618436e-31, "E_bind_minus_w11": [ 0.014433007998646552, 0.01192835502612738, 0.011928308823529413 ], "rel_dev_leading": 0.2099747171368628, "rel_dev_tight_form": 0.17353965128766058, "rel_dev_Epp0": 0.15338733715504924, "rel_dev_1_minus_s3": [ 0.4966985526284478, 0.2691234124894872 ] }, { "eps_factor": 1.0, "u": 64, "w11": -0.775529411764706, "w11_over_M": 0.775529411764706, "in_a_band": false, "weight0": 0.9861623291256749, "tail": 6.974237998173349e-31, "E_bind_minus_w11": [ 0.018647839621440676, 0.012022983718615654, 0.012022977941176472 ], "rel_dev_leading": 0.5510159589227006, "rel_dev_tight_form": 0.35526161822236796, "rel_dev_Epp0": 0.2896168417438294, "rel_dev_1_minus_s3": [ 1.5473588086792234, 0.6646755990942441 ] }, { "eps_factor": 1.0, "u": 128, "w11": -1.551058823529412, "w11_over_M": 1.551058823529412, "in_a_band": false, "weight0": 0.9228376830703742, "tail": 1.7339401159402546e-30, "E_bind_minus_w11": [ 0.04408761817019391, 0.012070313222246165, 0.012070312500000003 ], "rel_dev_leading": 2.652566205899141, "rel_dev_tight_form": 0.7262199002585195, "rel_dev_Epp0": -2.100942686626407, "rel_dev_1_minus_s3": [ 14.09861440831093, 2.1683818548196707 ] }, { "eps_factor": 0.5, "u": 2, "w11": -0.006058823529411766, "w11_over_M": 0.006058823529411766, "in_a_band": false, "weight0": 0.8933174652797004, "tail": 3.2881135039312895e-27, "E_bind_minus_w11": [ 0.0023178954871142347, 0.0023142646563976965, 0.002272058823529412 ], "rel_dev_leading": 0.001568891745592245, "rel_dev_tight_form": 0.019775120940370317, "rel_dev_Epp0": 0.0011471534541653713, "rel_dev_1_minus_s3": [ 0.002321542434251817, 0.0033016666492830813 ] }, { "eps_factor": 0.5, "u": 4, "w11": -0.012117647058823532, "w11_over_M": 0.012117647058823532, "in_a_band": false, "weight0": 0.9688137746658395, "tail": 1.9499254398139794e-28, "E_bind_minus_w11": [ 0.0026676749434621713, 0.002656474134158265, 0.0026507352941176473 ], "rel_dev_leading": 0.0042164194862207415, "rel_dev_tight_form": 0.0063499675573438965, "rel_dev_Epp0": 0.003438100481649809, "rel_dev_1_minus_s3": [ 0.007853212388524905, 0.006741000605532999 ] }, { "eps_factor": 0.5, "u": 8, "w11": -0.024235294117647063, "w11_over_M": 0.024235294117647063, "in_a_band": false, "weight0": 0.9908688818219815, "tail": 1.784534891696209e-29, "E_bind_minus_w11": [ 0.0028687199714216155, 0.0028408074095661595, 0.002840073529411765 ], "rel_dev_leading": 0.00982557344840167, "rel_dev_tight_form": 0.00998579237263595, "rel_dev_Epp0": 0.008232547622203813, "rel_dev_1_minus_s3": [ 0.019925354733248402, 0.013912535400511995 ] }, { "eps_factor": 0.5, "u": 16, "w11": -0.048470588235294126, "w11_over_M": 0.048470588235294126, "in_a_band": false, "weight0": 0.9965930526536041, "tail": 1.1893173796815703e-29, "E_bind_minus_w11": [ 0.0029975713921960023, 0.002934834917241655, 0.0029347426470588242 ], "rel_dev_leading": 0.021376491940238725, "rel_dev_tight_form": 0.020959882824058498, "rel_dev_Epp0": 0.017935604197695944, "rel_dev_1_minus_s3": [ 0.045165705842932, 0.028583657961672254 ] }, { "eps_factor": 0.5, "u": 32, "w11": -0.09694117647058825, "w11_over_M": 0.09694117647058825, "in_a_band": false, "weight0": 0.9979766747369238, "tail": 2.010353993912508e-30, "E_bind_minus_w11": [ 0.003117420656284009, 0.002982088756531845, 0.0029820772058823533 ], "rel_dev_leading": 0.04538158009406616, "rel_dev_tight_form": 0.043415202927084645, "rel_dev_Epp0": 0.037587548717591956, "rel_dev_1_minus_s3": [ 0.09875791234091236, 0.058933872292668554 ] }, { "eps_factor": 0.5, "u": 64, "w11": -0.1938823529411765, "w11_over_M": 0.1938823529411765, "in_a_band": false, "weight0": 0.9981809983832776, "tail": 2.9166490403288004e-31, "E_bind_minus_w11": [ 0.003297572192952569, 0.0030057459296539135, 0.003005744485294118 ], "rel_dev_leading": 0.0970894646881405, "rel_dev_tight_form": 0.08849774639722303, "rel_dev_Epp0": 0.07770770279836432, "rel_dev_1_minus_s3": [ 0.21919239231328952, 0.12381374991384912 ] }, { "eps_factor": 0.5, "u": 128, "w11": -0.387764705882353, "w11_over_M": 0.387764705882353, "in_a_band": false, "weight0": 0.997863504625092, "tail": 1.4577500693434633e-30, "E_bind_minus_w11": [ 0.0036759003083068897, 0.0030175783055615413, 0.0030175781250000007 ], "rel_dev_leading": 0.2181623593767325, "rel_dev_tight_form": 0.17909141382838822, "rel_dev_Epp0": 0.15959171799045976, "rel_dev_1_minus_s3": [ 0.5279806621488864, 0.27277057353440065 ] } ], "I2_flat_member": { "M": 1.0, "tau": 1.0, "w": 1.0, "c_star": 0.41421356237309515, "L": 240, "P": [ { "P": 0.8, "Delta": 0.29713862190152907, "sign_changes_above": 1, "sign_changes_below": 0, "root": 0.3003429150020171, "root_finer_q": 0.3003429150020171, "root_minus_Delta": 0.0032042931004880315, "root_minus_Delta_over_P3": 0.006258384961890685, "root_over_P": 0.37542864375252133 }, { "P": 0.4, "Delta": 0.16130235882109156, "sign_changes_above": 1, "sign_changes_below": 0, "root": 0.16171255346925908, "root_finer_q": 0.1617125534692591, "root_minus_Delta": 0.00041019464816752227, "root_minus_Delta_over_P3": 0.006409291377617534, "root_over_P": 0.4042813836731477 }, { "P": 0.2, "Delta": 0.08229153124290134, "sign_changes_above": 1, "sign_changes_below": 0, "root": 0.08234317712266383, "root_finer_q": 0.08234317712266381, "root_minus_Delta": 5.164587976248802e-05, "root_minus_Delta_over_P3": 0.006455734970311001, "root_over_P": 0.4117158856133191 }, { "P": 0.1, "Delta": 0.04135235515316027, "sign_changes_above": 1, "sign_changes_below": 0, "root": 0.0413588231100566, "root_finer_q": 0.0413588231100566, "root_minus_Delta": 6.467956896329119e-06, "root_minus_Delta_over_P3": 0.006467956896329117, "root_over_P": 0.413588231100566 }, { "P": 0.05, "Delta": 0.020702049748055673, "sign_changes_above": 1, "sign_changes_below": 0, "root": 0.02070285862952574, "root_finer_q": 0.02070285862952574, "root_minus_Delta": 8.088814700685232e-07, "root_minus_Delta_over_P3": 0.006471051760548184, "root_over_P": 0.41405717259051483 }, { "P": -0.2, "Delta": 0.08229153124290112, "sign_changes_above": 1, "sign_changes_below": 0, "root": 0.08234317712266383, "root_finer_q": 0.08234317712266381, "root_minus_Delta": 5.164587976271007e-05, "root_minus_Delta_over_P3": 0.006455734970338757, "root_over_P": 0.4117158856133191 } ], "max_weight_of_v_on_the_flat_bands_at_P0": 7.703719777548943e-32, "P0_discrete_root": -1.816160202538259, "P0_equation_at_plus_minus_0.3": [ 1.053944184776615, 0.9460558152233852 ], "dense": [ { "P": 0.8, "E": 0.3003429150020165, "E_minus_root": -6.106226635438361e-16, "tail": 2.5895460575642306e-08, "weight_on_v_at_r0": 0.006282874936772755, "next_below": 0.29713618685757637, "next_above": 2.12475875363549, "eigenvalues_between_Delta_and_1": 1, "eigenvalues_between_minus_1_and_minus_Delta": 0 }, { "P": 0.4, "E": 0.16171255341103397, "E_minus_root": -5.822511917052964e-11, "tail": 0.00019208097907288073, "weight_on_v_at_r0": 0.0008160833844589366, "next_below": 0.16130089343034437, "next_above": 2.037558991872855, "eigenvalues_between_Delta_and_1": 1, "eigenvalues_between_minus_1_and_minus_Delta": 0 } ], "dense_P0": { "dimension": 1924, "eigenvalues_at_zero": 962, "two_times_sites": 962, "max_abs_of_them": 7.048522331707946e-15, "nearest_other_eigenvalue": -1.8161602025381942 } } } }