Recorded data and provenance for the associated calculation.
| experiment | rational-common-law-probe |
|---|---|
| created_utc | 2026-09-24T08:40:14.645953+00:00 |
| status | conditional_inverse_fit |
| shared_law | g/g0=(1+(R/(b*R0))^4)/[(1+(R/R0)^4)*(1+(R/(C*R0))^4)] |
| middle_scale_b | 1.34 |
| outer_scale_C | 18.0075313793418 |
| gamma | 179.03876542237558 |
| depth_two_gap | 500 |
| benchmark_ten_to_six_unit_ratio | 1.0006443553842836 |
| fitted_ten_to_six_unit_ratio | 1.0006443553842854 |
| minimum_eta_between_selected_ten_and_six | 0.03654904551978487 |
| mean_eta_between_selected_ten_and_six | 0.3954584381500321 |
| competing_outer_ten_unit_ratio | 4.844821836918648e-8 |
| scope | One positive rational gap law, one tuned outer scale, all six maintained depths and sampled inverse branches. Fixed-metric depth-two control at h=500 is available separately. No selection of competing tau radius, complete support or master-field origin. |
View complete data
{
"experiment": "rational-common-law-probe",
"created_utc": "2026-09-24T08:40:14.645953+00:00",
"status": "conditional_inverse_fit",
"shared_law": "g/g0=(1+(R/(b*R0))^4)/[(1+(R/R0)^4)*(1+(R/(C*R0))^4)]",
"middle_scale_b": 1.34,
"outer_scale_C": 18.0075313793418,
"gamma": 179.03876542237558,
"depth_two_gap": 500.0,
"benchmark_ten_to_six_unit_ratio": 1.0006443553842836,
"fitted_ten_to_six_unit_ratio": 1.0006443553842854,
"selected_radii_by_depth": {
"2": {
"depth": 2,
"radius_over_reference": 18.007168478378276,
"dimensionless_gap": 499.99999999999983,
"eta": 2.0000039999999455,
"eta_log_derivative": 3.999661560129363,
"log_radius_curvature": 3.9996375615471176,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 0.00022213331345385639,
"maximum_required_occupied_singular_slope": 0.38199923600229213
},
"3": {
"depth": 3,
"radius_over_reference": 15.848057669884675,
"dimensionless_gap": 550.076608269075,
"eta": 1.5000033048644055,
"eta_log_derivative": 3.749298197961631,
"log_radius_curvature": 7.498540222833411,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 1.251197830135133e-06,
"maximum_required_occupied_singular_slope": 0.003209002127122015
},
"4": {
"depth": 4,
"radius_over_reference": 15.14176139024492,
"dimensionless_gap": 560.6068987508706,
"eta": 1.3333365152286552,
"eta_log_derivative": 3.554657240065699,
"log_radius_curvature": 10.663863562412482,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 8.996080059011542e-09,
"maximum_required_occupied_singular_slope": 0.00901238997502416
},
"5": {
"depth": 5,
"radius_over_reference": 14.785138116791387,
"dimensionless_gap": 564.5144791950684,
"eta": 1.2500031380366061,
"eta_log_derivative": 3.436480851140647,
"log_radius_curvature": 13.74574458969365,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 7.991800155450959e-11,
"maximum_required_occupied_singular_slope": 1.6249384585273878e-05
},
"6": {
"depth": 6,
"radius_over_reference": 14.569171810856838,
"dimensionless_gap": 566.3858108222875,
"eta": 1.2000031173927115,
"eta_log_derivative": 3.3588993232456588,
"log_radius_curvature": 16.794228610083167,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 8.478497269290176e-13,
"maximum_required_occupied_singular_slope": 7.601945772951173e-06
},
"10": {
"depth": 10,
"radius_over_reference": 1.067214828960502,
"dimensionless_gap": 116.63969767719243,
"eta": 1.1111849175636799,
"eta_log_derivative": 0.6598051262799716,
"log_radius_curvature": 5.934156006888249,
"stationary_type": "minimum",
"frequency_unit_times_reference_radius_over_speed": 8.483960434656292e-13,
"maximum_required_occupied_singular_slope": 2.1476569515090983e-05
}
},
"sampled_inverse_branches": {
"2": [
{
"harmonic": 76.0,
"edge_over_reference_gap": 0.9520336128519833,
"normalized_current": -0.02398304230379897,
"inverse_density": -11.703926209306468,
"standing_frequency_over_product": 0.001999996000012001
},
{
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"edge_over_reference_gap": 0.9487612976929445,
"normalized_current": -0.02561918898725657,
"inverse_density": -12.481421031522496,
"standing_frequency_over_product": 0.001999996000012001
},
{
"harmonic": 81.0,
"edge_over_reference_gap": 0.9453718844983703,
"normalized_current": -0.027313884214957868,
"inverse_density": -13.28391564765717,
"standing_frequency_over_product": 0.001999996000012001
},
{
"harmonic": 88.0,
"edge_over_reference_gap": 0.9352475608094362,
"normalized_current": -0.032376011579159744,
"inverse_density": -15.663899436924744,
"standing_frequency_over_product": 0.001999996000012001
},
{
"harmonic": 95.0,
"edge_over_reference_gap": 0.9241644875237307,
"normalized_current": -0.03791750955345651,
"inverse_density": -18.239881462185632,
"standing_frequency_over_product": 0.001999996000012001
}
],
"3": [
{
"harmonic": 1.0,
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"normalized_current": -7.209555969970827e-08,
"inverse_density": -3.965788435014651e-05,
"standing_frequency_over_product": 3.3048425614026924e-06
},
{
"harmonic": 2.5,
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"normalized_current": -4.7313362659032307e-07,
"inverse_density": -0.00026025490207590287,
"standing_frequency_over_product": 3.3048425614026924e-06
},
{
"harmonic": 4.0,
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"normalized_current": -1.4419614841580743e-06,
"inverse_density": -0.0007931578217866447,
"standing_frequency_over_product": 3.3048425614026924e-06
},
{
"harmonic": 10.0,
"edge_over_reference_gap": 0.9996688735328182,
"normalized_current": -1.5864095242782457e-05,
"inverse_density": -0.008724736222906166,
"standing_frequency_over_product": 3.3048425614026924e-06
},
{
"harmonic": 16.0,
"edge_over_reference_gap": 0.9992048879614013,
"normalized_current": -5.885774903070964e-05,
"inverse_density": -0.03236083977090167,
"standing_frequency_over_product": 3.3048425614026924e-06
},
{
"harmonic": 16.5,
"edge_over_reference_gap": 0.9991571859346089,
"normalized_current": -6.42197166144407e-05,
"inverse_density": -0.03530791684891619,
"standing_frequency_over_product": 3.3048425614026924e-06
},
{
"harmonic": 17.0,
"edge_over_reference_gap": 0.9991080894329639,
"normalized_current": -6.989763435700175e-05,
"inverse_density": -0.03842849720076337,
"standing_frequency_over_product": 3.3048425614026924e-06
}
],
"4": [
{
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"edge_over_reference_gap": 0.9999708578044672,
"normalized_current": -1.0934245097015955e-08,
"inverse_density": -6.12969619878972e-06,
"standing_frequency_over_product": 5.6756874042122116e-09
},
{
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"normalized_current": -8.54800054355084e-07,
"inverse_density": -0.0004791220016929777,
"standing_frequency_over_product": 5.6756874042122116e-09
},
{
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"normalized_current": -6.457882864171918e-06,
"inverse_density": -0.0036185643198785853,
"standing_frequency_over_product": 5.6756874042122116e-09
},
{
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"inverse_density": -0.08658237009734011,
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{
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"inverse_density": -9.46215288345276e-06,
"standing_frequency_over_product": 9.846655758344745e-12
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{
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{
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"standing_frequency_over_product": 9.846655758344745e-12
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{
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"normalized_current": -2.4968517877639144e-07,
"inverse_density": -0.000140904811635865,
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{
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],
"6": [
{
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"normalized_current": -2.024609968058246e-09,
"inverse_density": -1.1465429520269612e-06,
"standing_frequency_over_product": 1.715620602974566e-14
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{
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{
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"standing_frequency_over_product": 1.715620602974566e-14
}
],
"10": [
{
"harmonic": 23.0,
"edge_over_reference_gap": 0.9923942956283687,
"normalized_current": -4.533122783629959e-06,
"inverse_density": -0.0005254218674599672,
"standing_frequency_over_product": 2.4950971076332247e-19
}
]
},
"minimum_eta_between_selected_ten_and_six": 0.03654904551978487,
"mean_eta_between_selected_ten_and_six": 0.3954584381500321,
"eta_turning_points": [
{
"radius_over_reference": 1.1576214844641843,
"eta": 1.1384285887927228
},
{
"radius_over_reference": 4.684562151657011,
"eta": 0.03654903139019216
}
],
"competing_outer_ten_unit_ratio": 4.844821836918648e-08,
"scope": "One positive rational gap law, one tuned outer scale, all six maintained depths and sampled inverse branches. Fixed-metric depth-two control at h=500 is available separately. No selection of competing tau radius, complete support or master-field origin.",
"sources": {
"experiments/rational-common-law-probe.py": "c5c1d814e6f89023d9fa7a27a83f6f52360ff958af3f3f98287118ed1a196cc4",
"experiments/nonmonotone-common-law-probe.py": "43a676540502034807ba79aa3835e5bf767ec06fbd77fe4a0c3ef5293beb4bd1"
}
}