Recorded data and provenance for the associated calculation.
| experiment | real-curvature-contact |
|---|---|
| created_utc | 2026-10-10T00:06:54.395206+00:00 |
| status | passed |
| checks | 145 |
| scope | A candidate maximal-degree real-transgression-gradient energy has the occupied-sector zeros. Lower curvature norms and J-weighted terms remain allowed, so no complete force exclusion follows. |
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{
"experiment": "real-curvature-contact",
"created_utc": "2026-10-10T00:06:54.395206+00:00",
"status": "passed",
"checks": 145,
"cases": [
{
"real_depth": 2,
"geometry": "ordinary real normal SU3 curvature at one physical spatial point",
"parameters": {
"character_degree": 1,
"curvature_power": 0,
"source_form_degree": 0,
"trace_prescription": "unweighted real metric trace"
},
"measurements": {
"gradient_norm_squared_exact": "0",
"normal_complex_structure_weighted_gradient_norm_squared_exact": "0",
"active_unweighted_channel": false,
"all_higher_color_forces_excluded": false
}
},
{
"real_depth": 3,
"geometry": "ordinary real normal SU3 curvature at one physical spatial point",
"parameters": {
"character_degree": 2,
"curvature_power": 1,
"source_form_degree": 2,
"trace_prescription": "unweighted real metric trace"
},
"measurements": {
"gradient_norm_squared_exact": "280",
"normal_complex_structure_weighted_gradient_norm_squared_exact": "0",
"active_unweighted_channel": true,
"all_higher_color_forces_excluded": false
}
},
{
"real_depth": 4,
"geometry": "ordinary real normal SU3 curvature at one physical spatial point",
"parameters": {
"character_degree": 2,
"curvature_power": 1,
"source_form_degree": 2,
"trace_prescription": "unweighted real metric trace"
},
"measurements": {
"gradient_norm_squared_exact": "520",
"normal_complex_structure_weighted_gradient_norm_squared_exact": "0",
"active_unweighted_channel": true,
"all_higher_color_forces_excluded": false
}
},
{
"real_depth": 5,
"geometry": "ordinary real normal SU3 curvature at one physical spatial point",
"parameters": {
"character_degree": 3,
"curvature_power": 2,
"source_form_degree": 4,
"trace_prescription": "unweighted real metric trace"
},
"measurements": {
"gradient_norm_squared_exact": "0",
"normal_complex_structure_weighted_gradient_norm_squared_exact": "76040/3",
"active_unweighted_channel": false,
"all_higher_color_forces_excluded": false
}
},
{
"real_depth": 6,
"geometry": "ordinary real normal SU3 curvature at one physical spatial point",
"parameters": {
"character_degree": 3,
"curvature_power": 2,
"source_form_degree": 4,
"trace_prescription": "unweighted real metric trace"
},
"measurements": {
"gradient_norm_squared_exact": "0",
"normal_complex_structure_weighted_gradient_norm_squared_exact": "187456/3",
"active_unweighted_channel": false,
"all_higher_color_forces_excluded": false
}
},
{
"real_depth": 10,
"geometry": "ordinary real normal SU3 curvature at one physical spatial point",
"parameters": {
"character_degree": 5,
"curvature_power": 4,
"source_form_degree": 8,
"trace_prescription": "unweighted real metric trace"
},
"measurements": {
"gradient_norm_squared_exact": "0",
"normal_complex_structure_weighted_gradient_norm_squared_exact": "109706201824/3",
"active_unweighted_channel": false,
"all_higher_color_forces_excluded": false
}
},
{
"real_depth": 2,
"geometry": "independent Cartan curvature character",
"parameters": {
"normal_rotation_weights": [
1,
2,
-3
]
},
"measurements": {
"real_top_trace_exact": "0",
"complex_structure_weighted_top_trace_exact": "0"
}
},
{
"real_depth": 4,
"geometry": "independent Cartan curvature character",
"parameters": {
"normal_rotation_weights": [
1,
2,
-3
]
},
"measurements": {
"real_top_trace_exact": "-56",
"complex_structure_weighted_top_trace_exact": "0"
}
},
{
"real_depth": 6,
"geometry": "independent Cartan curvature character",
"parameters": {
"normal_rotation_weights": [
1,
2,
-3
]
},
"measurements": {
"real_top_trace_exact": "0",
"complex_structure_weighted_top_trace_exact": "-216"
}
},
{
"real_depth": 10,
"geometry": "independent Cartan curvature character",
"parameters": {
"normal_rotation_weights": [
1,
2,
-3
]
},
"measurements": {
"real_top_trace_exact": "0",
"complex_structure_weighted_top_trace_exact": "50400"
}
},
{
"real_depth": 10,
"geometry": "traceless complex normal rank-three invariant",
"parameters": {
"matrix_eigenvalues": [
"x",
"y",
"-x-y"
]
},
"measurements": {
"fifth_trace_identity": "tr F^5 = (5/6)(tr F^2)(tr F^3)",
"independent_fifth_character": false
}
},
{
"real_depth": 3,
"geometry": "two-site positive normal-connection Gauss control",
"parameters": {
"spatial_stiffness": [
[
2,
-1
],
[
-1,
2
]
],
"source_coupling": 1
},
"measurements": {
"full_antisymmetric_energy_exact": "2/3",
"full_symmetric_energy_exact": "1",
"pair_antisymmetric_energy_exact": "-2/9",
"pair_symmetric_energy_exact": "1/9",
"same_field_reduction_derived": false
}
},
{
"real_depth": 3,
"geometry": "ordinary noncompact radial Laplace Green function",
"parameters": {
"radial_kernel": "1/(4*pi*r)"
},
"measurements": {
"away_source_laplacian_exact": "0",
"source_flux_exact": "1",
"four_to_three_marginal_exact": "1/(4*pi*r)",
"localized_particle_profile_derived": false
}
},
{
"real_depth": 4,
"geometry": "ordinary noncompact radial Laplace Green function",
"parameters": {
"radial_kernel": "1/(4*pi**2*r**2)"
},
"measurements": {
"away_source_laplacian_exact": "0",
"source_flux_exact": "1",
"four_to_three_marginal_exact": "1/(4*pi*r)",
"localized_particle_profile_derived": false
}
},
{
"real_depth": 2,
"geometry": "inactive-curvature connection-source control",
"parameters": {
"constraint": "k q - rho = 0"
},
"measurements": {
"zero_stiffness_requires_zero_source": true,
"zero_stiffness_implies_zero_coupling": false
}
}
],
"scope": "A candidate maximal-degree real-transgression-gradient energy has the occupied-sector zeros. Lower curvature norms and J-weighted terms remain allowed, so no complete force exclusion follows.",
"sources": {
"experiments/real-curvature-contact-checks.py": "1a738f26f37e011b2946b6347468044dc4384afb978985827a692fd1ad8f6c7e"
}
}