Recorded data and provenance for the associated calculation.
| experiment | nonmonotone-common-law-probe |
|---|---|
| created_utc | 2026-09-24T08:32:01.576267+00:00 |
| status | conditional_inverse_fit |
| shared_law | g/g0=(1+(R/10R0)^4)^(B/4)/[(1+(R/R0)^4)^(1.15/4)*(1+(R/(C*R0))^4)^((B+1.2)/4)] |
| benchmark_ten_to_six_unit_ratio | 1.0006443553842836 |
| scope | One common radius law at all six depths for each of two reference gaps, with one fitted shape parameter and one gap amplitude fixed from depth two. Necessary local minima and sampled inverse branches only; competing depth-ten minimum, complete spatial support, physical selection and master-field derivation remain open. |
View complete data
{
"experiment": "nonmonotone-common-law-probe",
"created_utc": "2026-09-24T08:32:01.576267+00:00",
"status": "conditional_inverse_fit",
"shared_law": "g/g0=(1+(R/10R0)^4)^(B/4)/[(1+(R/R0)^4)^(1.15/4)*(1+(R/(C*R0))^4)^((B+1.2)/4)]",
"tested_depth_two_gaps": [
220.0,
500.0
],
"tested_outer_transition_scales": [
30.0,
100.0
],
"benchmark_ten_to_six_unit_ratio": 1.0006443553842836,
"fitted_common_laws": [
{
"middle_power": 1.9872341687308601,
"gamma": 91.50402480644648,
"depth_two_reference_radius": 50.49821096129994,
"points": {
"2": [
{
"depth": 2,
"radius_over_reference": 50.49821096129994,
"dimensionless_gap": 220.00000000000003,
"eta": 2.0000206611570226,
"eta_log_derivative": 1.2435240276875232,
"log_radius_curvature": 1.243457013259102,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 0.00018002251970829477,
"maximum_required_occupied_singular_slope": 0.8681728495003597
},
{
"depth": 2,
"radius_over_reference": 1992.443996759734,
"dimensionless_gap": 1.690308901981606,
"eta": 2.3499998374455906,
"eta_log_derivative": 6.502176036223382e-07,
"log_radius_curvature": -0.6999991932484516,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 0.0005111059487337946,
"maximum_required_occupied_singular_slope": 97.25242301960104
}
],
"3": [
{
"depth": 3,
"radius_over_reference": 38.49286398704804,
"dimensionless_gap": 271.75683591719877,
"eta": 1.5000135406354296,
"eta_log_derivative": 2.474071154693186,
"log_radius_curvature": 4.947981229762217,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.1105629470472607e-06,
"maximum_required_occupied_singular_slope": 0.013147600949257723
},
{
"depth": 3,
"radius_over_reference": 2767.6345774862384,
"dimensionless_gap": 1.0846523169512783,
"eta": 2.349999956337533,
"eta_log_derivative": 1.746498654529152e-07,
"log_radius_curvature": -1.699999783304791,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 0.0006824921426832025,
"maximum_required_occupied_singular_slope": 305.68517936951224
}
],
"4": [
{
"depth": 4,
"radius_over_reference": 36.112358968880045,
"dimensionless_gap": 279.1077783303025,
"eta": 1.333346170443529,
"eta_log_derivative": 2.739919858882733,
"log_radius_curvature": 8.219417360080831,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 3.0564301590355496e-08,
"maximum_required_occupied_singular_slope": 0.07302651930405109
},
{
"depth": 4,
"radius_over_reference": 2844.657845767317,
"dimensionless_gap": 1.0451937600194874,
"eta": 2.3499999608778133,
"eta_log_derivative": 1.5648874420265884e-07,
"log_radius_curvature": -1.9224913738045504,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 0.0009026003876232747,
"maximum_required_occupied_singular_slope": 169877.4834599277
}
],
"5": [
{
"depth": 5,
"radius_over_reference": 35.05113459315764,
"dimensionless_gap": 281.5488055629487,
"eta": 1.2500126161106675,
"eta_log_derivative": 2.8454473501644344,
"log_radius_curvature": 11.381189819852361,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 5.447792764076384e-10,
"maximum_required_occupied_singular_slope": 0.00026259688820562106
},
{
"depth": 5,
"radius_over_reference": 2851.1756921893084,
"dimensionless_gap": 1.0419694496085894,
"eta": 2.3499999612343254,
"eta_log_derivative": 1.5506269561373603e-07,
"log_radius_curvature": -1.953430020682678,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 0.0011276819756763344,
"maximum_required_occupied_singular_slope": 44215.80487942157
}
],
"6": [
{
"depth": 6,
"radius_over_reference": 34.44643476304896,
"dimensionless_gap": 282.65383803771203,
"eta": 1.2000125185909594,
"eta_log_derivative": 2.899936499832041,
"log_radius_curvature": 14.498749937051867,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.1583660775295308e-11,
"maximum_required_occupied_singular_slope": 0.0002455619804855119
},
{
"depth": 6,
"radius_over_reference": 2851.5387654193073,
"dimensionless_gap": 1.0417903502571115,
"eta": 2.3499999612540656,
"eta_log_derivative": 1.54983736203351e-07,
"log_radius_curvature": -1.955845952472987,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 0.0013531890838511264,
"maximum_required_occupied_singular_slope": 2374700.1709845215
}
],
"10": [
{
"depth": 10,
"radius_over_reference": 2.432505731688093,
"dimensionless_gap": 79.57103938018322,
"eta": 1.1112704524905985,
"eta_log_derivative": 0.09710272465072638,
"log_radius_curvature": 0.8723515479113938,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.159112476946868e-11,
"maximum_required_occupied_singular_slope": 0.0006687963271046508
},
{
"depth": 10,
"radius_over_reference": 3.5906007692788924,
"dimensionless_gap": 76.01546601390835,
"eta": 1.11128585497385,
"eta_log_derivative": -0.09787758159363087,
"log_radius_curvature": -0.8798678953993355,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 1.1841914623193414e-11,
"maximum_required_occupied_singular_slope": 0.0010085640217707896
},
{
"depth": 10,
"radius_over_reference": 33.421147634798785,
"dimensionless_gap": 283.98738743801044,
"eta": 1.1111235191584155,
"eta_log_derivative": 2.980359050361176,
"log_radius_curvature": 26.82021153907155,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 9.033000743400583e-18,
"maximum_required_occupied_singular_slope": 7.16090366531835e-09
},
{
"depth": 10,
"radius_over_reference": 2851.5526256441735,
"dimensionless_gap": 1.0417835142484841,
"eta": 2.3499999612548184,
"eta_log_derivative": 1.5498072449611096e-07,
"log_radius_curvature": -1.955965144190938,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 0.0022553136362295115,
"maximum_required_occupied_singular_slope": 152546681.039117
}
]
},
"selected_inner_ten_outer_six_ratio": 1.0006443553828244,
"all_selected_minima_pass_necessary_slope_bound": true,
"depth_two_gap": 220.0,
"outer_transition_scale": 30.0,
"selected_radii_by_depth": {
"2": {
"depth": 2,
"radius_over_reference": 50.49821096129994,
"dimensionless_gap": 220.00000000000003,
"eta": 2.0000206611570226,
"eta_log_derivative": 1.2435240276875232,
"log_radius_curvature": 1.243457013259102,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 0.00018002251970829477,
"maximum_required_occupied_singular_slope": 0.8681728495003597
},
"3": {
"depth": 3,
"radius_over_reference": 38.49286398704804,
"dimensionless_gap": 271.75683591719877,
"eta": 1.5000135406354296,
"eta_log_derivative": 2.474071154693186,
"log_radius_curvature": 4.947981229762217,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.1105629470472607e-06,
"maximum_required_occupied_singular_slope": 0.013147600949257723
},
"4": {
"depth": 4,
"radius_over_reference": 36.112358968880045,
"dimensionless_gap": 279.1077783303025,
"eta": 1.333346170443529,
"eta_log_derivative": 2.739919858882733,
"log_radius_curvature": 8.219417360080831,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 3.0564301590355496e-08,
"maximum_required_occupied_singular_slope": 0.07302651930405109
},
"5": {
"depth": 5,
"radius_over_reference": 35.05113459315764,
"dimensionless_gap": 281.5488055629487,
"eta": 1.2500126161106675,
"eta_log_derivative": 2.8454473501644344,
"log_radius_curvature": 11.381189819852361,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 5.447792764076384e-10,
"maximum_required_occupied_singular_slope": 0.00026259688820562106
},
"6": {
"depth": 6,
"radius_over_reference": 34.44643476304896,
"dimensionless_gap": 282.65383803771203,
"eta": 1.2000125185909594,
"eta_log_derivative": 2.899936499832041,
"log_radius_curvature": 14.498749937051867,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.1583660775295308e-11,
"maximum_required_occupied_singular_slope": 0.0002455619804855119
},
"10": {
"depth": 10,
"radius_over_reference": 2.432505731688093,
"dimensionless_gap": 79.57103938018322,
"eta": 1.1112704524905985,
"eta_log_derivative": 0.09710272465072638,
"log_radius_curvature": 0.8723515479113938,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.159112476946868e-11,
"maximum_required_occupied_singular_slope": 0.0006687963271046508
}
},
"ten_competing_outer_minimum_unit_ratio": 7.798053584809246e-07,
"sampled_inverse_branches": {
"2": [
{
"harmonic": 76.0,
"edge_over_reference_gap": 0.7185844671043458,
"normalized_current": -0.14070147518609755,
"inverse_density": -26.598835194192127,
"standing_frequency_over_product": 0.004545407589007118
},
{
"harmonic": 78.5,
"edge_over_reference_gap": 0.6958703451003518,
"normalized_current": -0.15205775521285306,
"inverse_density": -28.365759163403595,
"standing_frequency_over_product": 0.004545407589007118
},
{
"harmonic": 81.0,
"edge_over_reference_gap": 0.6716207115368684,
"normalized_current": -0.16418166260544,
"inverse_density": -30.189486042887676,
"standing_frequency_over_product": 0.004545407589007118
},
{
"harmonic": 88.0,
"edge_over_reference_gap": 0.5939084716749483,
"normalized_current": -0.20303418860604103,
"inverse_density": -35.598078323126266,
"standing_frequency_over_product": 0.004545407589007118
},
{
"harmonic": 95.0,
"edge_over_reference_gap": 0.49626705687113404,
"normalized_current": -0.25184806305277413,
"inverse_density": -41.45181046196752,
"standing_frequency_over_product": 0.004545407589007118
}
],
"3": [
{
"harmonic": 1.0,
"edge_over_reference_gap": 0.9999649138925012,
"normalized_current": -5.978974712362941e-07,
"inverse_density": -0.00016247942454160946,
"standing_frequency_over_product": 1.3540268742798886e-05
},
{
"harmonic": 2.5,
"edge_over_reference_gap": 0.9998715932600326,
"normalized_current": -3.923923615191541e-06,
"inverse_density": -0.0010662718251923803,
"standing_frequency_over_product": 1.3540268742798886e-05
},
{
"harmonic": 4.0,
"edge_over_reference_gap": 0.9997275343634444,
"normalized_current": -1.1959659092871853e-05,
"inverse_density": -0.0032495907290682777,
"standing_frequency_over_product": 1.3540268742798886e-05
},
{
"harmonic": 10.0,
"edge_over_reference_gap": 0.9986398212878439,
"normalized_current": -0.00013164209763451415,
"inverse_density": -0.03574549987203826,
"standing_frequency_over_product": 1.3540268742798886e-05
},
{
"harmonic": 16.0,
"edge_over_reference_gap": 0.9967221814048062,
"normalized_current": -0.0004888338325251153,
"inverse_density": -0.13258329994073229,
"standing_frequency_over_product": 1.3540268742798886e-05
},
{
"harmonic": 16.5,
"edge_over_reference_gap": 0.9965242548912571,
"normalized_current": -0.0005334147726553615,
"inverse_density": -0.14465755921818105,
"standing_frequency_over_product": 1.3540268742798886e-05
},
{
"harmonic": 17.0,
"edge_over_reference_gap": 0.9963203913621199,
"normalized_current": -0.000580629843328208,
"inverse_density": -0.15744266621444886,
"standing_frequency_over_product": 1.3540268742798886e-05
}
],
"4": [
{
"harmonic": 3.0,
"edge_over_reference_gap": 0.9998823945928482,
"normalized_current": -1.779635918076689e-07,
"inverse_density": -4.966719579278942e-05,
"standing_frequency_over_product": 4.598954294433455e-08
},
{
"harmonic": 11.5,
"edge_over_reference_gap": 0.9989240832962166,
"normalized_current": -1.3919246936299227e-05,
"inverse_density": -0.003882191012322262,
"standing_frequency_over_product": 4.598954294433455e-08
},
{
"harmonic": 20.0,
"edge_over_reference_gap": 0.9970186839000018,
"normalized_current": -0.00010525840122975115,
"inverse_density": -0.029320206361751634,
"standing_frequency_over_product": 4.598954294433455e-08
},
{
"harmonic": 46.0,
"edge_over_reference_gap": 0.9848564553405037,
"normalized_current": -0.0025389164035010165,
"inverse_density": -0.7015518142503143,
"standing_frequency_over_product": 4.598954294433455e-08
},
{
"harmonic": 72.0,
"edge_over_reference_gap": 0.961080963002222,
"normalized_current": -0.014792852413368484,
"inverse_density": -4.0245204906296665,
"standing_frequency_over_product": 4.598954294433455e-08
}
],
"5": [
{
"harmonic": 10.0,
"edge_over_reference_gap": 0.9993779357795665,
"normalized_current": -5.433362075939591e-07,
"inverse_density": -0.00015290799218435234,
"standing_frequency_over_product": 1.5912609784105911e-10
},
{
"harmonic": 12.5,
"edge_over_reference_gap": 0.999083799876007,
"normalized_current": -1.4156045156596413e-06,
"inverse_density": -0.00039830181714836627,
"standing_frequency_over_product": 1.5912609784105911e-10
},
{
"harmonic": 15.0,
"edge_over_reference_gap": 0.9987333799016651,
"normalized_current": -3.15725298095951e-06,
"inverse_density": -0.0008881189045587049,
"standing_frequency_over_product": 1.5912609784105911e-10
},
{
"harmonic": 18.5,
"edge_over_reference_gap": 0.9981474267896334,
"normalized_current": -8.098149995700239e-06,
"inverse_density": -0.00227701550873735,
"standing_frequency_over_product": 1.5912609784105911e-10
},
{
"harmonic": 22.0,
"edge_over_reference_gap": 0.9974489495353481,
"normalized_current": -1.787705723521435e-05,
"inverse_density": -0.005024118536158091,
"standing_frequency_over_product": 1.5912609784105911e-10
}
],
"6": [
{
"harmonic": 13.0,
"edge_over_reference_gap": 0.9992135705571341,
"normalized_current": -1.311027716330138e-07,
"inverse_density": -3.70349346131492e-05,
"standing_frequency_over_product": 5.541886322409713e-13
},
{
"harmonic": 24.0,
"edge_over_reference_gap": 0.9976516935688409,
"normalized_current": -3.3586145429693923e-06,
"inverse_density": -0.0009476582683319852,
"standing_frequency_over_product": 5.541886322409713e-13
},
{
"harmonic": 35.0,
"edge_over_reference_gap": 0.9952332590277545,
"normalized_current": -2.718826466648601e-05,
"inverse_density": -0.007657509214858649,
"standing_frequency_over_product": 5.541886322409713e-13
}
],
"10": [
{
"harmonic": 23.0,
"edge_over_reference_gap": 0.9825756824203797,
"normalized_current": -0.00020844187957408492,
"inverse_density": -0.01634949970377549,
"standing_frequency_over_product": 7.769917724439038e-18
}
]
},
"minimum_eta_between_selected_ten_and_six": -0.3356725817892511,
"mean_eta_between_selected_ten_and_six": 0.5217585514807151,
"eta_turning_points_between_selected_ten_and_six": [
{
"radius_over_reference": 2.9568133196955766,
"eta": 1.1203753622383352
},
{
"radius_over_reference": 16.084734859729924,
"eta": -0.3356746246330803
}
]
},
{
"middle_power": 2.3550611927422223,
"gamma": 144.55956292509845,
"depth_two_reference_radius": 52.05556168824198,
"points": {
"2": [
{
"depth": 2,
"radius_over_reference": 52.055561688242,
"dimensionless_gap": 500.0,
"eta": 2.0000039999999966,
"eta_log_derivative": 1.2596388910379754,
"log_radius_curvature": 1.2596258525025656,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 7.684081912283914e-05,
"maximum_required_occupied_singular_slope": 0.38199923600229213
}
],
"3": [
{
"depth": 3,
"radius_over_reference": 39.92707522966595,
"dimensionless_gap": 614.8177420211412,
"eta": 1.5000026454966544,
"eta_log_derivative": 2.569462882520505,
"log_radius_curvature": 5.138893284169713,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 3.975471746226833e-07,
"maximum_required_occupied_singular_slope": 0.0025687636609990783
}
],
"4": [
{
"depth": 4,
"radius_over_reference": 37.558798371649424,
"dimensionless_gap": 630.7438591224777,
"eta": 1.3333358469330654,
"eta_log_derivative": 2.876828916121294,
"log_radius_curvature": 8.63041664086238,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.546452310390813e-09,
"maximum_required_occupied_singular_slope": 0.00632786933069553
}
],
"5": [
{
"depth": 5,
"radius_over_reference": 36.50996915905635,
"dimensionless_gap": 635.9813480759395,
"eta": 1.250002472394019,
"eta_log_derivative": 3.0060329204913736,
"log_radius_curvature": 12.024007824715069,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.009017289715266e-11,
"maximum_required_occupied_singular_slope": 1.0087000834938867e-05
}
],
"6": [
{
"depth": 6,
"radius_over_reference": 35.914623638457854,
"dimensionless_gap": 638.3393409288651,
"eta": 1.2000024541978296,
"eta_log_derivative": 3.075679647581745,
"log_radius_curvature": 15.37820462352624,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.891427937816059e-13,
"maximum_required_occupied_singular_slope": 4.180537631263786e-06
}
],
"10": [
{
"depth": 10,
"radius_over_reference": 2.4650686879553017,
"dimensionless_gap": 125.56274363543152,
"eta": 1.111174764363584,
"eta_log_derivative": 0.08421469425836751,
"log_radius_curvature": 0.7573705347984793,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.8926466895948179e-13,
"maximum_required_occupied_singular_slope": 1.106656912462216e-05
},
{
"depth": 10,
"radius_over_reference": 3.3924091183444243,
"dimensionless_gap": 121.01316694110383,
"eta": 1.111179659151815,
"eta_log_derivative": -0.0849878489675335,
"log_radius_curvature": -0.7645566659058282,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 1.9167177153504906e-13,
"maximum_required_occupied_singular_slope": 1.542342426093957e-05
},
{
"depth": 10,
"radius_over_reference": 34.90950841251641,
"dimensionless_gap": 641.1689020412346,
"eta": 1.1111135439550974,
"eta_log_derivative": 3.18484312074024,
"log_radius_curvature": 28.662955627711952,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 5.675765730146634e-21,
"maximum_required_occupied_singular_slope": 4.699835107468992e-12
}
]
},
"selected_inner_ten_outer_six_ratio": 1.0006443553858924,
"all_selected_minima_pass_necessary_slope_bound": true,
"depth_two_gap": 500.0,
"outer_transition_scale": 30.0,
"selected_radii_by_depth": {
"2": {
"depth": 2,
"radius_over_reference": 52.055561688242,
"dimensionless_gap": 500.0,
"eta": 2.0000039999999966,
"eta_log_derivative": 1.2596388910379754,
"log_radius_curvature": 1.2596258525025656,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 7.684081912283914e-05,
"maximum_required_occupied_singular_slope": 0.38199923600229213
},
"3": {
"depth": 3,
"radius_over_reference": 39.92707522966595,
"dimensionless_gap": 614.8177420211412,
"eta": 1.5000026454966544,
"eta_log_derivative": 2.569462882520505,
"log_radius_curvature": 5.138893284169713,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 3.975471746226833e-07,
"maximum_required_occupied_singular_slope": 0.0025687636609990783
},
"4": {
"depth": 4,
"radius_over_reference": 37.558798371649424,
"dimensionless_gap": 630.7438591224777,
"eta": 1.3333358469330654,
"eta_log_derivative": 2.876828916121294,
"log_radius_curvature": 8.63041664086238,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.546452310390813e-09,
"maximum_required_occupied_singular_slope": 0.00632786933069553
},
"5": {
"depth": 5,
"radius_over_reference": 36.50996915905635,
"dimensionless_gap": 635.9813480759395,
"eta": 1.250002472394019,
"eta_log_derivative": 3.0060329204913736,
"log_radius_curvature": 12.024007824715069,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.009017289715266e-11,
"maximum_required_occupied_singular_slope": 1.0087000834938867e-05
},
"6": {
"depth": 6,
"radius_over_reference": 35.914623638457854,
"dimensionless_gap": 638.3393409288651,
"eta": 1.2000024541978296,
"eta_log_derivative": 3.075679647581745,
"log_radius_curvature": 15.37820462352624,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.891427937816059e-13,
"maximum_required_occupied_singular_slope": 4.180537631263786e-06
},
"10": {
"depth": 10,
"radius_over_reference": 2.4650686879553017,
"dimensionless_gap": 125.56274363543152,
"eta": 1.111174764363584,
"eta_log_derivative": 0.08421469425836751,
"log_radius_curvature": 0.7573705347984793,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.8926466895948179e-13,
"maximum_required_occupied_singular_slope": 1.106656912462216e-05
}
},
"ten_competing_outer_minimum_unit_ratio": 3.000783490964064e-08,
"sampled_inverse_branches": {
"2": [
{
"harmonic": 76.0,
"edge_over_reference_gap": 0.9520336128519833,
"normalized_current": -0.023983042303798954,
"inverse_density": -11.703926209306465,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 78.5,
"edge_over_reference_gap": 0.9487612976929445,
"normalized_current": -0.025619188987256552,
"inverse_density": -12.481421031522492,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 81.0,
"edge_over_reference_gap": 0.9453718844983703,
"normalized_current": -0.02731388421495785,
"inverse_density": -13.283915647657166,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 88.0,
"edge_over_reference_gap": 0.9352475608094362,
"normalized_current": -0.03237601157915972,
"inverse_density": -15.663899436924739,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 95.0,
"edge_over_reference_gap": 0.9241644875237308,
"normalized_current": -0.037917509553456484,
"inverse_density": -18.23988146218563,
"standing_frequency_over_product": 0.001999996000012
}
],
"3": [
{
"harmonic": 1.0,
"edge_over_reference_gap": 0.9999931456230808,
"normalized_current": -5.1634444878351494e-08,
"inverse_density": -3.174564683363982e-05,
"standing_frequency_over_product": 2.645482658083498e-06
},
{
"harmonic": 2.5,
"edge_over_reference_gap": 0.999974919330428,
"normalized_current": -3.388547801352519e-07,
"inverse_density": -0.00020833083043950157,
"standing_frequency_over_product": 2.645482658083498e-06
},
{
"harmonic": 4.0,
"edge_over_reference_gap": 0.9999467968516174,
"normalized_current": -1.0327177281293436e-06,
"inverse_density": -0.0006349130230990138,
"standing_frequency_over_product": 2.645482658083498e-06
},
{
"harmonic": 10.0,
"edge_over_reference_gap": 0.9997349819103921,
"normalized_current": -1.1361338832695215e-05,
"inverse_density": -0.0069840433745101274,
"standing_frequency_over_product": 2.645482658083498e-06
},
{
"harmonic": 16.0,
"edge_over_reference_gap": 0.9993637764227753,
"normalized_current": -4.21496226747272e-05,
"inverse_density": -0.025904451784469918,
"standing_frequency_over_product": 2.645482658083498e-06
},
{
"harmonic": 16.5,
"edge_over_reference_gap": 0.999325622738155,
"normalized_current": -4.5989209147220555e-05,
"inverse_density": -0.028263550520664864,
"standing_frequency_over_product": 2.645482658083498e-06
},
{
"harmonic": 17.0,
"edge_over_reference_gap": 0.999286355588747,
"normalized_current": -5.0055001093444916e-05,
"inverse_density": -0.030761536481488706,
"standing_frequency_over_product": 2.645482658083498e-06
}
],
"4": [
{
"harmonic": 3.0,
"edge_over_reference_gap": 0.9999769790126875,
"normalized_current": -6.823554804064069e-09,
"inverse_density": -4.3038503763213685e-06,
"standing_frequency_over_product": 3.9850703703745535e-09
},
{
"harmonic": 11.5,
"edge_over_reference_gap": 0.9997898787105596,
"normalized_current": -5.334233235404545e-07,
"inverse_density": -0.000336406455007161,
"standing_frequency_over_product": 3.9850703703745535e-09
},
{
"harmonic": 20.0,
"edge_over_reference_gap": 0.9994204441416062,
"normalized_current": -4.029666616680311e-06,
"inverse_density": -0.0025407065287842276,
"standing_frequency_over_product": 3.9850703703745535e-09
},
{
"harmonic": 46.0,
"edge_over_reference_gap": 0.9971423232663807,
"normalized_current": -9.656530536352137e-05,
"inverse_density": -0.06079217577123139,
"standing_frequency_over_product": 3.9850703703745535e-09
},
{
"harmonic": 72.0,
"edge_over_reference_gap": 0.9930699967074913,
"normalized_current": -0.0005554583662402014,
"inverse_density": -0.34874098418967686,
"standing_frequency_over_product": 3.9850703703745535e-09
}
],
"5": [
{
"harmonic": 10.0,
"edge_over_reference_gap": 0.9998783103828366,
"normalized_current": -9.236537293730667e-09,
"inverse_density": -5.873756941246619e-06,
"standing_frequency_over_product": 6.112429940626263e-12
},
{
"harmonic": 12.5,
"edge_over_reference_gap": 0.9998209193679505,
"normalized_current": -2.406074655210848e-08,
"inverse_density": -1.5300234275058275e-05,
"standing_frequency_over_product": 6.112429940626263e-12
},
{
"harmonic": 15.0,
"edge_over_reference_gap": 0.99975267077926,
"normalized_current": -5.365239462813338e-08,
"inverse_density": -3.41159072261687e-05,
"standing_frequency_over_product": 6.112429940626263e-12
},
{
"harmonic": 18.5,
"edge_over_reference_gap": 0.9996388513440724,
"normalized_current": -1.3756860073560074e-07,
"inverse_density": -8.746853132740285e-05,
"standing_frequency_over_product": 6.112429940626263e-12
},
{
"harmonic": 22.0,
"edge_over_reference_gap": 0.9995036681897649,
"normalized_current": -3.0356743240655386e-07,
"inverse_density": -0.00019299487202846006,
"standing_frequency_over_product": 6.112429940626263e-12
}
],
"6": [
{
"harmonic": 13.0,
"edge_over_reference_gap": 0.9998462209121444,
"normalized_current": -9.878637727580544e-10,
"inverse_density": -6.305198451632829e-07,
"standing_frequency_over_product": 9.43471146193445e-15
},
{
"harmonic": 24.0,
"edge_over_reference_gap": 0.9995431182100855,
"normalized_current": -2.5283436212469005e-08,
"inverse_density": -1.61338901502461e-05,
"standing_frequency_over_product": 9.43471146193445e-15
},
{
"harmonic": 35.0,
"edge_over_reference_gap": 0.9990798311808293,
"normalized_current": -2.0437274751349293e-07,
"inverse_density": -0.00013036924739066709,
"standing_frequency_over_product": 9.43471146193445e-15
}
],
"10": [
{
"harmonic": 23.0,
"edge_over_reference_gap": 0.9934837651774074,
"normalized_current": -2.1680769850345813e-06,
"inverse_density": -0.000270763692104371,
"standing_frequency_over_product": 1.2856878560081666e-19
}
]
},
"minimum_eta_between_selected_ten_and_six": -0.627913055794991,
"mean_eta_between_selected_ten_and_six": 0.39301670528098337,
"eta_turning_points_between_selected_ten_and_six": [
{
"radius_over_reference": 2.892951908534323,
"eta": 1.117739191238489
},
{
"radius_over_reference": 16.238873553188817,
"eta": -0.6279150332661001
}
]
},
{
"middle_power": 1.0722438446455953,
"gamma": 165.06247819840866,
"depth_two_reference_radius": 153.08386443347973,
"points": {
"2": [
{
"depth": 2,
"radius_over_reference": 153.08386443347987,
"dimensionless_gap": 500.0,
"eta": 2.0000039999999997,
"eta_log_derivative": 1.184319004307863,
"log_radius_curvature": 1.1843062670507951,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.6129416152556913e-05,
"maximum_required_occupied_singular_slope": 0.38199923600229213
}
],
"3": [
{
"depth": 3,
"radius_over_reference": 113.73031000227732,
"dimensionless_gap": 629.3120456935706,
"eta": 1.5000025250379547,
"eta_log_derivative": 2.127935162193552,
"log_radius_curvature": 4.255843781951526,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.332112013262833e-07,
"maximum_required_occupied_singular_slope": 0.002451799472859694
}
],
"4": [
{
"depth": 4,
"radius_over_reference": 105.41438664589454,
"dimensionless_gap": 649.5777541404216,
"eta": 1.3333357032865427,
"eta_log_derivative": 2.2468123374709394,
"log_radius_curvature": 6.740384349263663,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 8.306408661155049e-10,
"maximum_required_occupied_singular_slope": 0.005793265682979452
}
],
"5": [
{
"depth": 5,
"radius_over_reference": 101.59855075984204,
"dimensionless_gap": 656.6025668625464,
"eta": 1.2500023195347933,
"eta_log_derivative": 2.2695569874117125,
"log_radius_curvature": 9.078139082231779,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 6.354411996514216e-12,
"maximum_required_occupied_singular_slope": 8.878299652498881e-06
}
],
"6": [
{
"depth": 6,
"radius_over_reference": 99.38635967191601,
"dimensionless_gap": 659.8630282703183,
"eta": 1.200002296700564,
"eta_log_derivative": 2.2714600666043223,
"log_radius_curvature": 11.35716531940114,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 5.790609335449679e-14,
"maximum_required_occupied_singular_slope": 3.54178396606366e-06
}
],
"10": [
{
"depth": 10,
"radius_over_reference": 2.3673572718432045,
"dimensionless_gap": 143.86677017246902,
"eta": 1.1111595566531134,
"eta_log_derivative": 0.12417183627416616,
"log_radius_curvature": 1.1169623243695466,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 5.794340545753187e-14,
"maximum_required_occupied_singular_slope": 3.2537355115250656e-06
},
{
"depth": 10,
"radius_over_reference": 4.301408944614657,
"dimensionless_gap": 133.70889623886237,
"eta": 1.1111672210036796,
"eta_log_derivative": -0.12387466833935942,
"log_radius_curvature": -1.1144218722115027,
"stationary_type": "maximum",
"frequency_unit_times_reference_radius_over_speed": 6.162039029608502e-14,
"maximum_required_occupied_singular_slope": 6.287088953376867e-06
},
{
"depth": 10,
"radius_over_reference": 95.56083953724104,
"dimensionless_gap": 663.902858186267,
"eta": 1.1111133801717417,
"eta_log_derivative": 2.2530925822996712,
"log_radius_curvature": 20.277414605758143,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.5153129119127828e-21,
"maximum_required_occupied_singular_slope": 3.43476245318555e-12
}
]
},
"selected_inner_ten_outer_six_ratio": 1.0006443553842712,
"all_selected_minima_pass_necessary_slope_bound": true,
"depth_two_gap": 500.0,
"outer_transition_scale": 100.0,
"selected_radii_by_depth": {
"2": {
"depth": 2,
"radius_over_reference": 153.08386443347987,
"dimensionless_gap": 500.0,
"eta": 2.0000039999999997,
"eta_log_derivative": 1.184319004307863,
"log_radius_curvature": 1.1843062670507951,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 2.6129416152556913e-05,
"maximum_required_occupied_singular_slope": 0.38199923600229213
},
"3": {
"depth": 3,
"radius_over_reference": 113.73031000227732,
"dimensionless_gap": 629.3120456935706,
"eta": 1.5000025250379547,
"eta_log_derivative": 2.127935162193552,
"log_radius_curvature": 4.255843781951526,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.332112013262833e-07,
"maximum_required_occupied_singular_slope": 0.002451799472859694
},
"4": {
"depth": 4,
"radius_over_reference": 105.41438664589454,
"dimensionless_gap": 649.5777541404216,
"eta": 1.3333357032865427,
"eta_log_derivative": 2.2468123374709394,
"log_radius_curvature": 6.740384349263663,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 8.306408661155049e-10,
"maximum_required_occupied_singular_slope": 0.005793265682979452
},
"5": {
"depth": 5,
"radius_over_reference": 101.59855075984204,
"dimensionless_gap": 656.6025668625464,
"eta": 1.2500023195347933,
"eta_log_derivative": 2.2695569874117125,
"log_radius_curvature": 9.078139082231779,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 6.354411996514216e-12,
"maximum_required_occupied_singular_slope": 8.878299652498881e-06
},
"6": {
"depth": 6,
"radius_over_reference": 99.38635967191601,
"dimensionless_gap": 659.8630282703183,
"eta": 1.200002296700564,
"eta_log_derivative": 2.2714600666043223,
"log_radius_curvature": 11.35716531940114,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 5.790609335449679e-14,
"maximum_required_occupied_singular_slope": 3.54178396606366e-06
},
"10": {
"depth": 10,
"radius_over_reference": 2.3673572718432045,
"dimensionless_gap": 143.86677017246902,
"eta": 1.1111595566531134,
"eta_log_derivative": 0.12417183627416616,
"log_radius_curvature": 1.1169623243695466,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 5.794340545753187e-14,
"maximum_required_occupied_singular_slope": 3.2537355115250656e-06
}
},
"ten_competing_outer_minimum_unit_ratio": 2.6168453510343894e-08,
"sampled_inverse_branches": {
"2": [
{
"harmonic": 76.0,
"edge_over_reference_gap": 0.9520336128519833,
"normalized_current": -0.023983042303798954,
"inverse_density": -11.703926209306465,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 78.5,
"edge_over_reference_gap": 0.9487612976929445,
"normalized_current": -0.025619188987256552,
"inverse_density": -12.481421031522492,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 81.0,
"edge_over_reference_gap": 0.9453718844983703,
"normalized_current": -0.02731388421495785,
"inverse_density": -13.283915647657166,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 88.0,
"edge_over_reference_gap": 0.9352475608094362,
"normalized_current": -0.03237601157915972,
"inverse_density": -15.663899436924739,
"standing_frequency_over_product": 0.001999996000012
},
{
"harmonic": 95.0,
"edge_over_reference_gap": 0.9241644875237308,
"normalized_current": -0.037917509553456484,
"inverse_density": -18.23988146218563,
"standing_frequency_over_product": 0.001999996000012
}
],
"3": [
{
"harmonic": 1.0,
"edge_over_reference_gap": 0.999993457732688,
"normalized_current": -4.8148268040835883e-08,
"inverse_density": -3.030017029160471e-05,
"standing_frequency_over_product": 2.525025203768994e-06
},
{
"harmonic": 2.5,
"edge_over_reference_gap": 0.9999760614121108,
"normalized_current": -3.1597633380177755e-07,
"inverse_density": -0.00019884488857849252,
"standing_frequency_over_product": 2.525025203768994e-06
},
{
"harmonic": 4.0,
"edge_over_reference_gap": 0.9999492196903415,
"normalized_current": -9.629910205604361e-07,
"inverse_density": -0.0006060034845768872,
"standing_frequency_over_product": 2.525025203768994e-06
},
{
"harmonic": 10.0,
"edge_over_reference_gap": 0.9997470567649708,
"normalized_current": -1.0594186218306805e-05,
"inverse_density": -0.0066660384405485915,
"standing_frequency_over_product": 2.525025203768994e-06
},
{
"harmonic": 16.0,
"edge_over_reference_gap": 0.9993927898759672,
"normalized_current": -3.930315101394869e-05,
"inverse_density": -0.024724942578526372,
"standing_frequency_over_product": 2.525025203768994e-06
},
{
"harmonic": 16.5,
"edge_over_reference_gap": 0.9993563788838966,
"normalized_current": -4.288339560199158e-05,
"inverse_density": -0.02697662430838718,
"standing_frequency_over_product": 2.525025203768994e-06
},
{
"harmonic": 17.0,
"edge_over_reference_gap": 0.9993189056136176,
"normalized_current": -4.6674560078298295e-05,
"inverse_density": -0.029360869301355202,
"standing_frequency_over_product": 2.525025203768994e-06
}
],
"4": [
{
"harmonic": 3.0,
"edge_over_reference_gap": 0.9999782947017919,
"normalized_current": -6.065942489370154e-09,
"inverse_density": -3.940245265914349e-06,
"standing_frequency_over_product": 3.648395726024194e-09
},
{
"harmonic": 11.5,
"edge_over_reference_gap": 0.9998018938643657,
"normalized_current": -4.741944937034619e-07,
"inverse_density": -0.0003079855990389827,
"standing_frequency_over_product": 3.648395726024194e-09
},
{
"harmonic": 20.0,
"edge_over_reference_gap": 0.9994536190035641,
"normalized_current": -3.5821807865789086e-06,
"inverse_density": -0.0023260582871828454,
"standing_frequency_over_product": 3.648395726024194e-09
},
{
"harmonic": 46.0,
"edge_over_reference_gap": 0.9973069664921128,
"normalized_current": -8.583442951328435e-05,
"inverse_density": -0.05565622918516231,
"standing_frequency_over_product": 3.648395726024194e-09
},
{
"harmonic": 72.0,
"edge_over_reference_gap": 0.9934739664898093,
"normalized_current": -0.0004936544837165133,
"inverse_density": -0.3192780658479055,
"standing_frequency_over_product": 3.648395726024194e-09
}
],
"5": [
{
"harmonic": 10.0,
"edge_over_reference_gap": 0.9998858370738944,
"normalized_current": -7.874384327123977e-09,
"inverse_density": -5.169921077871685e-06,
"standing_frequency_over_product": 5.379992081473342e-12
},
{
"harmonic": 12.5,
"edge_over_reference_gap": 0.9998319978708733,
"normalized_current": -2.0512349912287747e-08,
"inverse_density": -1.3466849998486369e-05,
"standing_frequency_over_product": 5.379992081473342e-12
},
{
"harmonic": 15.0,
"edge_over_reference_gap": 0.9997679747913197,
"normalized_current": -4.573978489145375e-08,
"inverse_density": -3.002789348941857e-05,
"standing_frequency_over_product": 5.379992081473342e-12
},
{
"harmonic": 18.5,
"edge_over_reference_gap": 0.9996612065354751,
"normalized_current": -1.1727950956343188e-07,
"inverse_density": -7.698742189569079e-05,
"standing_frequency_over_product": 5.379992081473342e-12
},
{
"harmonic": 22.0,
"edge_over_reference_gap": 0.9995344049173497,
"normalized_current": -2.587947133407337e-07,
"inverse_density": -0.00016986883645107506,
"standing_frequency_over_product": 5.379992081473342e-12
}
],
"6": [
{
"harmonic": 13.0,
"edge_over_reference_gap": 0.9998560954047878,
"normalized_current": -8.096211633196945e-10,
"inverse_density": -5.341816222275148e-07,
"standing_frequency_over_product": 7.99316086295214e-15
},
{
"harmonic": 24.0,
"edge_over_reference_gap": 0.9995724889412922,
"normalized_current": -2.072118286874302e-08,
"inverse_density": -1.3668765049417459e-05,
"standing_frequency_over_product": 7.99316086295214e-15
},
{
"harmonic": 35.0,
"edge_over_reference_gap": 0.9991390873902266,
"normalized_current": -1.67491088987038e-07,
"inverse_density": -0.0001104499039647228,
"standing_frequency_over_product": 7.99316086295214e-15
}
],
"10": [
{
"harmonic": 23.0,
"edge_over_reference_gap": 0.9950886479522424,
"normalized_current": -5.556705294484964e-07,
"inverse_density": -7.961759030423543e-05,
"standing_frequency_over_product": 3.7801130474330063e-20
}
]
},
"minimum_eta_between_selected_ten_and_six": 0.10864105850613336,
"mean_eta_between_selected_ten_and_six": 0.5924420522838425,
"eta_turning_points_between_selected_ten_and_six": [
{
"radius_over_reference": 3.1907245363330885,
"eta": 1.1280135496185764
},
{
"radius_over_reference": 28.7329328703565,
"eta": 0.10864104824992327
}
]
}
],
"scope": "One common radius law at all six depths for each of two reference gaps, with one fitted shape parameter and one gap amplitude fixed from depth two. Necessary local minima and sampled inverse branches only; competing depth-ten minimum, complete spatial support, physical selection and master-field derivation remain open.",
"sources": {
"experiments/nonmonotone-common-law-probe.py": "43a676540502034807ba79aa3835e5bf767ec06fbd77fe4a0c3ef5293beb4bd1"
}
}