Recorded data and provenance for the associated calculation.
| experiment | inverse-current-depth-batch |
|---|---|
| created_utc | 2026-09-23T17:38:05.161043+00:00 |
| status | diagnostic_pass |
| scope | finite sampled inverse branches; no master-field derivation or full spatial Hessian |
View complete data
{
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"status": "diagnostic_pass",
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"depth": 5,
"gap": "5000.0",
"zero_mode_product_unit": "1.59999948800006144001638e-15",
"simplex_unit_at_same_radius": "1.91999938560007372801966e-13",
"finite_zero_current_inverse_curvature": "13020844270837.08333379",
"branch_points": [
{
"harmonic": "10.0",
"edge_over_gap": "0.999998032064851198318695",
"current": "-3.07507495087884834437992e-13",
"frequency": "3.84383876997134760349536e-10",
"inverse_density": "-1.53753532287439624732195e-9",
"required_fractional_coefficient": "0.14157555994511027154831",
"leading_fractional_coefficient": "0.143587294374629375849828"
},
{
"harmonic": "10.25",
"edge_over_gap": "0.999997947185377213265711",
"current": "-3.41392229556764582946162e-13",
"frequency": "4.2673971500576388681467e-10",
"inverse_density": "-1.70695865453855641712605e-9",
"required_fractional_coefficient": "0.141657611288152191725811",
"leading_fractional_coefficient": "0.143587294374629375849828"
},
{
"harmonic": "15.0",
"edge_over_gap": "0.999996001981699574534114",
"current": "-1.78606510412446549272795e-12",
"frequency": "2.23257528557576573094126e-9",
"inverse_density": "-8.93030006890212650761598e-9",
"required_fractional_coefficient": "0.142590613108734098179179",
"leading_fractional_coefficient": "0.143587294374629375849828"
},
{
"harmonic": "21.75",
"edge_over_gap": "0.999992150926490906825667",
"current": "-9.58669529230762176807709e-12",
"frequency": "1.1983303438779632659122e-8",
"inverse_density": "-4.79332079981465825383762e-8",
"required_fractional_coefficient": "0.143079882470970119135444",
"leading_fractional_coefficient": "0.143587294374629375849828"
},
{
"harmonic": "22.0",
"edge_over_gap": "0.99999198379173511949101",
"current": "-1.01038613486922031451415e-11",
"frequency": "1.26297559584772849829133e-8",
"inverse_density": "-5.05190177664711969770607e-8",
"required_fractional_coefficient": "0.143090542229684490826392",
"leading_fractional_coefficient": "0.143587294374629375849828"
}
],
"edge_and_current_decrease_with_harmonic": true,
"minimum_positive_f_second_secant": "1615871282.77274114530443"
},
{
"depth": 6,
"gap": "5000.0",
"zero_mode_product_unit": "3.19999840000017600016736e-19",
"simplex_unit_at_same_radius": "2.3039988480001267201205e-16",
"finite_zero_current_inverse_curvature": "10416680625008806.2524746",
"branch_points": [
{
"harmonic": "13.0",
"edge_over_gap": "0.999997495154608179884366",
"current": "-4.27715083919798403389177e-15",
"frequency": "4.27714346142743524323169e-12",
"inverse_density": "-2.13857141615069708643163e-11",
"required_fractional_coefficient": "0.115325354323846636889048",
"leading_fractional_coefficient": "0.116960709528514642620271"
},
{
"harmonic": "13.25",
"edge_over_gap": "0.999997411817277780391169",
"current": "-4.71364050642756056484876e-15",
"frequency": "4.71363208107366530482811e-12",
"inverse_density": "-2.35681569390378137522833e-11",
"required_fractional_coefficient": "0.115377336222467842617064",
"leading_fractional_coefficient": "0.116960709528514642620271"
},
{
"harmonic": "34.75",
"edge_over_gap": "0.999985256244176641020408",
"current": "-8.49509991440054859309255e-13",
"frequency": "8.49500728140485902100025e-10",
"inverse_density": "-4.24750301737079212085308e-9",
"required_fractional_coefficient": "0.116684592826882064280548",
"leading_fractional_coefficient": "0.116960709528514642620271"
},
{
"harmonic": "35.0",
"edge_over_gap": "0.999985056886883696452701",
"current": "-8.843720854916371465611e-13",
"frequency": "8.84362309818672639997612e-10",
"inverse_density": "-4.42181090018502401826982e-9",
"required_fractional_coefficient": "0.116688407250885874285187",
"leading_fractional_coefficient": "0.116960709528514642620271"
}
],
"edge_and_current_decrease_with_harmonic": true,
"minimum_positive_f_second_secant": "28592271687.6382629756175"
},
{
"depth": 10,
"gap": "5000.0",
"zero_mode_product_unit": "5.11999170559892173515808e-34",
"simplex_unit_at_same_radius": "1.85794259012773671925416e-27",
"finite_zero_current_inverse_curvature": "1.19606963257647230553981e+27",
"branch_points": [
{
"harmonic": "22.75",
"edge_over_gap": "0.999996136964842173411717",
"current": "-1.96716568809846587070156e-22",
"frequency": "1.09286659580501735468614e-19",
"inverse_density": "-9.83579686404085469440264e-19",
"required_fractional_coefficient": "0.0704342978802201767812748",
"leading_fractional_coefficient": "0.0715993349974726945009214"
},
{
"harmonic": "23.0",
"edge_over_gap": "0.999996063960056640374622",
"current": "-2.15748719863574992124499e-22",
"frequency": "1.19860038280542181889337e-19",
"inverse_density": "-1.07874007054702474686387e-18",
"required_fractional_coefficient": "0.0704556100866881378774762",
"leading_fractional_coefficient": "0.0715993349974726945009214"
},
{
"harmonic": "23.25",
"edge_over_gap": "0.999995990288539213529599",
"current": "-2.36420122886049349754534e-22",
"frequency": "1.31344108355936671767967e-19",
"inverse_density": "-1.18209667498838433394766e-18",
"required_fractional_coefficient": "0.0704763436895811720949131",
"leading_fractional_coefficient": "0.0715993349974726945009214"
}
],
"edge_and_current_decrease_with_harmonic": true,
"minimum_positive_f_second_secant": "17819670330733693942.9774"
}
],
"cross_depth_scale": [
{
"gap": "500.0",
"ten_to_six_unit_at_equal_radius": "8.06309676543163832651896e-8",
"required_ten_to_six_radius_for_equal_frequency_unit": "8.06309676543163832651896e-8",
"large_gap_formula": "8.064e-8",
"equal_radius_unit_mismatch_factor": "12402182.7976470703526329",
"ten_to_six_radius_if_one_physical_gap": "0.195196539958532886543783",
"ten_dimensionless_gap_if_one_physical_gap": "97.5982699792664432718916",
"tau_inverse_branch_edge_over_gap_if_one_physical_gap": "0.988884057848715302929421",
"scope": "same dimensionless gap and one physical gap are separate hypotheses; inverse current law fixes within-depth ratios, not physical radii"
},
{
"gap": "5000.0",
"ten_to_six_unit_at_equal_radius": "8.06399096831334236962014e-12",
"required_ten_to_six_radius_for_equal_frequency_unit": "8.06399096831334236962014e-12",
"large_gap_formula": "8.064e-12",
"equal_radius_unit_mismatch_factor": "124008075397.083333613556",
"ten_to_six_radius_if_one_physical_gap": "0.0777398020094384109010885",
"ten_dimensionless_gap_if_one_physical_gap": "388.699010047192054505442",
"tau_inverse_branch_edge_over_gap_if_one_physical_gap": "0.999345891817377945672191",
"scope": "same dimensionless gap and one physical gap are separate hypotheses; inverse current law fixes within-depth ratios, not physical radii"
}
],
"radial_minima": [
{
"depth": 2,
"gamma": "1000.0",
"stationary_radius_over_reference": "1.00000100000250001350008",
"dimensionless_reference_gap": "499.999499998249992249955",
"log_radius_curvature_of_log_frequency_unit": "3.99997599999999975999942",
"simplex_unit_times_reference_radius_over_speed": "0.0039999920000159999520001",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 3,
"gamma": "1000.0",
"stationary_radius_over_reference": "0.880112512453164512361435",
"dimensionless_reference_gap": "550.069593101551521596379",
"log_radius_curvature_of_log_frequency_unit": "7.49995042603162042482651",
"simplex_unit_times_reference_radius_over_speed": "0.0000225307115362848260909434",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 4,
"gamma": "1000.0",
"stationary_radius_over_reference": "0.840897167803967830544332",
"dimensionless_reference_gap": "560.597442935054979977556",
"log_radius_curvature_of_log_frequency_unit": "10.6665712073663936658635",
"simplex_unit_times_reference_radius_over_speed": "0.000000161997680355810423698544",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 5,
"gamma": "1000.0",
"stationary_radius_over_reference": "0.821097493262177360816878",
"dimensionless_reference_gap": "564.503882435064500958059",
"log_radius_curvature_of_log_frequency_unit": "13.74983995589708289194",
"simplex_unit_times_reference_radius_over_speed": "1.4391560381931938845434e-9",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 6,
"gamma": "1000.0",
"stationary_radius_over_reference": "0.809107462285275766543132",
"dimensionless_reference_gap": "566.374592998286594302883",
"log_radius_curvature_of_log_frequency_unit": "16.7997568371472639129263",
"simplex_unit_times_reference_radius_over_speed": "1.5268295293711323773263e-11",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 10,
"gamma": "1000.0",
"stationary_radius_over_reference": "0.787511820667626099527537",
"dimensionless_reference_gap": "568.757928429159050018629",
"log_radius_curvature_of_log_frequency_unit": "28.888128310405576276696",
"simplex_unit_times_reference_radius_over_speed": "7.39783091569658116646726e-19",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 2,
"gamma": "10000.0",
"stationary_radius_over_reference": "1.00000001000000025000001",
"dimensionless_reference_gap": "4999.99994999999824999992",
"log_radius_curvature_of_log_frequency_unit": "3.99999975999999999999976",
"simplex_unit_times_reference_radius_over_speed": "0.000399999992000000159999995",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 3,
"gamma": "10000.0",
"stationary_radius_over_reference": "0.880111744549984340716181",
"dimensionless_reference_gap": "5500.69833071936139380052",
"log_radius_curvature_of_log_frequency_unit": "7.49999950425815353078252",
"simplex_unit_times_reference_radius_over_speed": "0.000000225308589726455148300959",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 4,
"gamma": "10000.0",
"stationary_radius_over_reference": "0.840896422779166330248261",
"dimensionless_reference_gap": "5605.97608496820339463791",
"log_radius_curvature_of_log_frequency_unit": "10.6666657120725235820303",
"simplex_unit_times_reference_radius_over_speed": "1.61999976803364003786629e-10",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 5,
"gamma": "10000.0",
"stationary_radius_over_reference": "0.821096751164432623105544",
"dimensionless_reference_gap": "5645.04009983849409910304",
"log_radius_curvature_of_log_frequency_unit": "13.7499983995719769202103",
"simplex_unit_times_reference_radius_over_speed": "1.43919180711708686309477e-13",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 6,
"gamma": "10000.0",
"stationary_radius_over_reference": "0.809106719077093059016495",
"dimensionless_reference_gap": "5663.74697048192715685014",
"log_radius_curvature_of_log_frequency_unit": "16.7999975684286455478458",
"simplex_unit_times_reference_radius_over_speed": "1.52688843290019294140242e-16",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
},
{
"depth": 10,
"gamma": "10000.0",
"stationary_radius_over_reference": "0.787511069694542809479598",
"dimensionless_reference_gap": "5687.57988693245443319288",
"log_radius_curvature_of_log_frequency_unit": "28.8888812842127017803785",
"simplex_unit_times_reference_radius_over_speed": "7.3987479771239837345092e-28",
"scope": "local radial minimum of one prescribed bounded curvature law; full metric and field support untested"
}
],
"radial_cross_depth": [
{
"gamma": "1000.0",
"ten_to_six_stationary_radius": "0.973309303616290887519756",
"ten_to_six_frequency_unit": "4.84522389263953101375587e-8",
"scope": "one g(R)=g0/(1+(R/R0)^4), one g0 and R0 across depths; necessary radial stationarity only"
},
{
"gamma": "10000.0",
"ten_to_six_stationary_radius": "0.973309269502565360014684",
"ten_to_six_frequency_unit": "4.84563758405759863975856e-12",
"scope": "one g(R)=g0/(1+(R/R0)^4), one g0 and R0 across depths; necessary radial stationarity only"
}
],
"equal_radius_shared_gap": {
"gap": "6.54402899291197214658177",
"reference_unit_ratio_ten_over_six": "1",
"required_occupied_slopes": [
{
"depth": 6,
"index": 13,
"required_harmonic_singular_slope": "320.713097130076558224392",
"maximum_possible_harmonic_singular_slope": "1"
},
{
"depth": 6,
"index": 35,
"required_harmonic_singular_slope": "27129.6238090051486077542",
"maximum_possible_harmonic_singular_slope": "1"
},
{
"depth": 10,
"index": 23,
"required_harmonic_singular_slope": "1045652.01882671540388644",
"maximum_possible_harmonic_singular_slope": "1"
}
],
"slope_bound": "|d sigma_min(B_n)/dn| <= ||dB_n/dn|| = 1",
"consequence": "the equal-radius shared-gap reference-unit crossing has no exact inverse-current occupied branch at the tested charged-lepton indices"
},
"occupied_inverse_branch_gap_bounds": [
{
"depth": 2,
"index": 76,
"necessary_reference_gap_above": "152.996731991242218166867",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 2,
"index": 81,
"necessary_reference_gap_above": "162.996932486473499278329",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 2,
"index": 95,
"necessary_reference_gap_above": "190.997382181013151183492",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 3,
"index": 1,
"necessary_reference_gap_above": "3.0",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 3,
"index": 4,
"necessary_reference_gap_above": "8.48528137423857029281013",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 3,
"index": 16,
"necessary_reference_gap_above": "29.3938769133981371783674",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 3,
"index": 17,
"necessary_reference_gap_above": "31.1287648325467613629936",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 4,
"index": 3,
"necessary_reference_gap_above": "6.77095883505677005138497",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 4,
"index": 20,
"necessary_reference_gap_above": "34.0542746054365695149843",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 4,
"index": 72,
"necessary_reference_gap_above": "116.6521187711671178201",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 5,
"index": 10,
"necessary_reference_gap_above": "17.7367079802232374847943",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 5,
"index": 15,
"necessary_reference_gap_above": "25.2753887689771889830211",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 5,
"index": 22,
"necessary_reference_gap_above": "35.7855962599782631567845",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 6,
"index": 13,
"necessary_reference_gap_above": "21.9567112709623834993349",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 6,
"index": 35,
"necessary_reference_gap_above": "53.5700319186637621181274",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
},
{
"depth": 10,
"index": 23,
"necessary_reference_gap_above": "35.213863438981703025316",
"reason": "the inverse target slope mu_d(g)*P_d'(n) cannot exceed the singular-value Lipschitz bound one"
}
],
"stable_linear_elimination": {
"potential": "a*x^2/2 + b*x*k, with a>0",
"eliminated_current_curvature": "-b^2/a <= 0",
"inverse_branch_secants": "positive at all sampled branches",
"consequence": "a stable linearly coupled eliminated coordinate alone cannot supply the inverse branch curvature"
},
"scope": "finite sampled inverse branches; no master-field derivation or full spatial Hessian",
"sources": {
"experiments/inverse-current-depth-batch.py": "fce44c5eb1886f4dccc148ef5185d2009529ea02d75eb310da2d508b41310db7"
}
}