Recorded data and provenance for the associated calculation.
| experiment | scalar-current-cancellation-and-scale |
|---|
View complete data
{
"experiment": "scalar-current-cancellation-and-scale",
"cancellation": [
{
"depth": 2,
"partner_rank": 2,
"maintained_indices": [
76,
81,
95
],
"null_field_norm_squared": 2.0,
"null_current_norms": [
0.0,
0.0,
0.0
],
"one_sided_probes": [
{
"direction": -1,
"current": -9.99999999995449e-06,
"one_sided_energy_slope": 1.664213562365521,
"other_bilinears": [
0.0,
-9.99999999995449e-06
]
},
{
"direction": 1,
"current": 9.999999999843467e-06,
"one_sided_energy_slope": 1.1642135623548713,
"other_bilinears": [
0.0,
9.999999999843467e-06
]
}
]
},
{
"depth": 3,
"partner_rank": 2,
"maintained_indices": [
1,
4,
16,
17
],
"null_field_norm_squared": 2.0,
"null_current_norms": [
0.0,
0.0,
0.0
],
"one_sided_probes": [
{
"direction": -1,
"current": -9.99999999995449e-06,
"one_sided_energy_slope": 1.664213562365521,
"other_bilinears": [
0.0,
-9.99999999995449e-06
]
},
{
"direction": 1,
"current": 9.999999999843467e-06,
"one_sided_energy_slope": 1.1642135623548713,
"other_bilinears": [
0.0,
9.999999999843467e-06
]
}
]
},
{
"depth": 4,
"partner_rank": 4,
"maintained_indices": [
3,
20,
72
],
"null_field_norm_squared": 2.0,
"null_current_norms": [
0.0,
0.0,
0.0
],
"one_sided_probes": [
{
"direction": -1,
"current": -9.99999999995449e-06,
"one_sided_energy_slope": 2.3749999999891913,
"other_bilinears": [
0.0,
-9.99999999995449e-06
]
},
{
"direction": 1,
"current": 9.999999999843467e-06,
"one_sided_energy_slope": 1.6249999999745632,
"other_bilinears": [
0.0,
9.999999999843467e-06
]
}
]
},
{
"depth": 5,
"partner_rank": 4,
"maintained_indices": [
10,
15,
22
],
"null_field_norm_squared": 2.0,
"null_current_norms": [
0.0,
0.0,
0.0
],
"one_sided_probes": [
{
"direction": -1,
"current": -9.99999999995449e-06,
"one_sided_energy_slope": 2.3749999999891913,
"other_bilinears": [
0.0,
-9.99999999995449e-06
]
},
{
"direction": 1,
"current": 9.999999999843467e-06,
"one_sided_energy_slope": 1.6249999999745632,
"other_bilinears": [
0.0,
9.999999999843467e-06
]
}
]
},
{
"depth": 6,
"partner_rank": 8,
"maintained_indices": [
13,
35
],
"null_field_norm_squared": 2.0,
"null_current_norms": [
0.0,
0.0,
0.0
],
"one_sided_probes": [
{
"direction": -1,
"current": -9.99999999995449e-06,
"one_sided_energy_slope": 3.265927124731326,
"other_bilinears": [
0.0,
-9.99999999995449e-06
]
},
{
"direction": 1,
"current": 9.999999999843467e-06,
"one_sided_energy_slope": 2.390927124708764,
"other_bilinears": [
0.0,
9.999999999843467e-06
]
}
]
},
{
"depth": 10,
"partner_rank": 32,
"maintained_indices": [
23
],
"null_field_norm_squared": 2.0,
"null_current_norms": [
0.0,
0.0,
0.0
],
"one_sided_probes": [
{
"direction": -1,
"current": -9.99999999995449e-06,
"one_sided_energy_slope": 6.1412292494644305,
"other_bilinears": [
0.0,
-9.99999999995449e-06
]
},
{
"direction": 1,
"current": 9.999999999843467e-06,
"one_sided_energy_slope": 5.172479249411413,
"other_bilinears": [
0.0,
9.999999999843467e-06
]
}
]
}
],
"dilation": [
{
"depth": 2,
"radii": [
0.7,
1.0,
1.4
],
"energies": [
1.7585714285714285,
1.6,
1.4942857142857142
],
"virial_residual_max": 1.1102230246251565e-16
},
{
"depth": 3,
"radii": [
0.7,
1.0,
1.4
],
"energies": [
1.7585714285714285,
1.6,
1.4942857142857142
],
"virial_residual_max": 1.1102230246251565e-16
},
{
"depth": 4,
"radii": [
0.7,
1.0,
1.4
],
"energies": [
1.7585714285714285,
1.6,
1.4942857142857142
],
"virial_residual_max": 1.1102230246251565e-16
},
{
"depth": 5,
"radii": [
0.7,
1.0,
1.4
],
"energies": [
1.7585714285714285,
1.6,
1.4942857142857142
],
"virial_residual_max": 1.1102230246251565e-16
},
{
"depth": 6,
"radii": [
0.7,
1.0,
1.4
],
"energies": [
1.7585714285714285,
1.6,
1.4942857142857142
],
"virial_residual_max": 1.1102230246251565e-16
},
{
"depth": 10,
"radii": [
0.7,
1.0,
1.4
],
"energies": [
1.7585714285714285,
1.6,
1.4942857142857142
],
"virial_residual_max": 1.1102230246251565e-16
}
],
"quadratic_current": [
{
"depth": 2,
"partner_rank": 2,
"traceless_test_p2": 2.0,
"aligned_angle_second_order_per_b": -4
},
{
"depth": 3,
"partner_rank": 2,
"traceless_test_p2": 2.0,
"aligned_angle_second_order_per_b": -4
},
{
"depth": 4,
"partner_rank": 4,
"traceless_test_p2": 2.0,
"aligned_angle_second_order_per_b": -8
},
{
"depth": 5,
"partner_rank": 4,
"traceless_test_p2": 2.0,
"aligned_angle_second_order_per_b": -8
},
{
"depth": 6,
"partner_rank": 8,
"traceless_test_p2": 2.0,
"aligned_angle_second_order_per_b": -16
},
{
"depth": 10,
"partner_rank": 32,
"traceless_test_p2": 2.0,
"aligned_angle_second_order_per_b": -64
}
],
"smooth_polynomial_control": [
{
"depth": 2,
"partner_rank": 2,
"coherent_source_coefficient_at_rho": 3.2,
"aligned_pair_mixed_energy": 3.8399999999999985,
"misalignment_excess": 0.3317760000000076,
"formula_error": 7.438494264988549e-15
},
{
"depth": 3,
"partner_rank": 2,
"coherent_source_coefficient_at_rho": 3.2,
"aligned_pair_mixed_energy": 3.8399999999999985,
"misalignment_excess": 0.3317760000000076,
"formula_error": 7.438494264988549e-15
},
{
"depth": 4,
"partner_rank": 4,
"coherent_source_coefficient_at_rho": 6.4,
"aligned_pair_mixed_energy": 15.359999999999994,
"misalignment_excess": 1.3271040000000305,
"formula_error": 2.9753977059954195e-14
},
{
"depth": 5,
"partner_rank": 4,
"coherent_source_coefficient_at_rho": 6.4,
"aligned_pair_mixed_energy": 15.359999999999994,
"misalignment_excess": 1.3271040000000305,
"formula_error": 2.9753977059954195e-14
},
{
"depth": 6,
"partner_rank": 8,
"coherent_source_coefficient_at_rho": 12.8,
"aligned_pair_mixed_energy": 61.439999999999976,
"misalignment_excess": 5.308416000000122,
"formula_error": 1.1901590823981678e-13
},
{
"depth": 10,
"partner_rank": 32,
"coherent_source_coefficient_at_rho": 51.2,
"aligned_pair_mixed_energy": 983.0400000000005,
"misalignment_excess": 84.93465600000127,
"formula_error": 1.2221335055073723e-12
}
],
"analytic_results": {
"smooth_positive_homogeneous_current_potential": "Impossible at the full zero current: degree-one homogeneity plus differentiability forces a linear functional, which cannot be positive on both X and -X.",
"local_quadratic_homogeneous_binding": "At fixed canonical norm, E(R)=K/R+V. A stationary radius requires K=0, then dilation is flat. No strict localized scale minimum follows from this class.",
"smooth_quartic_two_invariant_alignment": "For U=a(Tr C)^2+b Tr(C^2), positivity on accessible traceless C forces b>=0. The prepared coherent-pair angle coefficient is -2*b*r*rho*sigma*k, so alignment cannot be a strict minimum in this class.",
"smooth_higher_polynomial_control": "H=(Tr C)^2+[Tr(C^2)-(Tr C)^2/r]^2 is smooth and nonnegative with a prepared aligned angular minimum. Its coherent source is 2*r*rho, dependent on the spatial density, and aligned pairs have mixed energy 2*r^2*rho*sigma. It does not preserve the conditional constant self frequency."
},
"sources": {
"experiments/scalar-current-cancellation-and-scale.py": "75216dbaa1533ba59dc96293df651f0d099f28a5a084dccc0129258e42aafa38"
}
}