Recorded data and provenance for the associated calculation.
| title | Induced Normal Curvature Gives Mixed Spatial Inertia and a Retained-Orientation Comparison |
|---|---|
| checks_passed | 270 |
| case_count | 12 |
| scope | actual squared-first-curvature-variation symbols, not the complete nonzero-background curvature Hessian; frozen real-normal response and finite-lock retained-orientation comparison |
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{
"title": "Induced Normal Curvature Gives Mixed Spatial Inertia and a Retained-Orientation Comparison",
"sources": {
"experiments/induced-curvature-response-checks.py": "8806acad8023a188818ba3454eb5ae5ae73f1ae9e09eb6738b3d561e5149c3ae",
"experiments/nested-normal-curvature-checks.py": "a77678aea22b4191f1f5180c8095cc03701e96c2a8c1b7db7e3d1ada0d872d2f"
},
"checks_passed": 270,
"case_count": 12,
"occupied_depths": [
2,
3,
4,
5,
6,
10
],
"scope": "actual squared-first-curvature-variation symbols, not the complete nonzero-background curvature Hessian; frozen real-normal response and finite-lock retained-orientation comparison",
"cases": [
{
"case": "induced-curvature-depth-2",
"real_depth": 2,
"hodge_active": false,
"axial_electric_symbol_diagonal": [
4,
4,
2,
2,
4,
4,
4,
4
],
"axial_magnetic_symbol_diagonal": [
2,
2,
2,
0,
2,
2,
2,
2
],
"independent_gauss_source_constraint_survives_induced_reduction": false,
"frozen_symbol_is_complete_variable_geometry_solution": false,
"background_curvature_second_variation_included": false,
"arbitrary_real_graph_waves_preserve_unitary_normal_carrier": false
},
{
"case": "induced-curvature-depth-3",
"real_depth": 3,
"hodge_active": true,
"axial_electric_symbol_diagonal": [
4,
4,
4,
6,
6,
6
],
"axial_magnetic_symbol_diagonal": [
4,
2,
2,
4,
4,
4
],
"independent_gauss_source_constraint_survives_induced_reduction": false,
"frozen_symbol_is_complete_variable_geometry_solution": false,
"background_curvature_second_variation_included": false,
"arbitrary_real_graph_waves_preserve_unitary_normal_carrier": false
},
{
"case": "active-depth-3-axial-symbol-4-2",
"real_depth": 3,
"electric_symbol_a": 4,
"magnetic_symbol_b": 2,
"high_frequency_locked_speed_squared": 0.5,
"compact_probe_acceleration_at_x_2": 0.11320762071319146,
"compact_unforced_displacement_acceleration_at_x_2": 0.014150952589148932,
"retained_lock_coefficient": 0.3333333333333333,
"retained_bare_speed_squared": 0.6666666666666667,
"retained_orientation_gap_squared": 0.08333333333333333,
"independent_orientation_is_exact_integrable_graph": false
},
{
"case": "active-depth-3-axial-symbol-4-4",
"real_depth": 3,
"electric_symbol_a": 4,
"magnetic_symbol_b": 4,
"high_frequency_locked_speed_squared": 1.0,
"compact_probe_acceleration_at_x_2": 0.11320762071319146,
"compact_unforced_displacement_acceleration_at_x_2": 0.0,
"retained_lock_coefficient": 0.3333333333333333,
"retained_bare_speed_squared": 0.6666666666666667,
"retained_orientation_gap_squared": 0.08333333333333333,
"independent_orientation_is_exact_integrable_graph": false
},
{
"case": "active-depth-3-axial-symbol-6-4",
"real_depth": 3,
"electric_symbol_a": 6,
"magnetic_symbol_b": 4,
"high_frequency_locked_speed_squared": 0.6666666666666666,
"compact_probe_acceleration_at_x_2": 0.11032580961956652,
"compact_unforced_displacement_acceleration_at_x_2": 0.0061292116455314745,
"retained_lock_coefficient": 0.3333333333333333,
"retained_bare_speed_squared": 0.6666666666666667,
"retained_orientation_gap_squared": 0.05555555555555555,
"independent_orientation_is_exact_integrable_graph": false
},
{
"case": "induced-curvature-depth-4",
"real_depth": 4,
"hodge_active": true,
"axial_electric_symbol_diagonal": [
6,
6,
6,
6,
8,
8
],
"axial_magnetic_symbol_diagonal": [
6,
4,
4,
4,
6,
6
],
"independent_gauss_source_constraint_survives_induced_reduction": false,
"frozen_symbol_is_complete_variable_geometry_solution": false,
"background_curvature_second_variation_included": false,
"arbitrary_real_graph_waves_preserve_unitary_normal_carrier": false
},
{
"case": "active-depth-4-axial-symbol-6-4",
"real_depth": 4,
"electric_symbol_a": 6,
"magnetic_symbol_b": 4,
"high_frequency_locked_speed_squared": 0.6666666666666666,
"compact_probe_acceleration_at_x_2": 0.11032580961956652,
"compact_unforced_displacement_acceleration_at_x_2": 0.0061292116455314745,
"retained_lock_coefficient": 0.3333333333333333,
"retained_bare_speed_squared": 0.6666666666666667,
"retained_orientation_gap_squared": 0.05555555555555555,
"independent_orientation_is_exact_integrable_graph": false
},
{
"case": "active-depth-4-axial-symbol-6-6",
"real_depth": 4,
"electric_symbol_a": 6,
"magnetic_symbol_b": 6,
"high_frequency_locked_speed_squared": 1.0,
"compact_probe_acceleration_at_x_2": 0.11032580961956652,
"compact_unforced_displacement_acceleration_at_x_2": 0.0,
"retained_lock_coefficient": 0.3333333333333333,
"retained_bare_speed_squared": 0.6666666666666667,
"retained_orientation_gap_squared": 0.05555555555555555,
"independent_orientation_is_exact_integrable_graph": false
},
{
"case": "active-depth-4-axial-symbol-8-6",
"real_depth": 4,
"electric_symbol_a": 8,
"magnetic_symbol_b": 6,
"high_frequency_locked_speed_squared": 0.75,
"compact_probe_acceleration_at_x_2": 0.10624032162673534,
"compact_unforced_displacement_acceleration_at_x_2": 0.0033200100508354795,
"retained_lock_coefficient": 0.3333333333333333,
"retained_bare_speed_squared": 0.6666666666666667,
"retained_orientation_gap_squared": 0.041666666666666664,
"independent_orientation_is_exact_integrable_graph": false
},
{
"case": "induced-curvature-depth-5",
"real_depth": 5,
"hodge_active": false,
"axial_electric_symbol_diagonal": [
2,
2,
4,
4
],
"axial_magnetic_symbol_diagonal": [
2,
2,
4,
4
],
"independent_gauss_source_constraint_survives_induced_reduction": false,
"frozen_symbol_is_complete_variable_geometry_solution": false,
"background_curvature_second_variation_included": false,
"arbitrary_real_graph_waves_preserve_unitary_normal_carrier": false
},
{
"case": "induced-curvature-depth-6",
"real_depth": 6,
"hodge_active": false,
"axial_electric_symbol_diagonal": [
2,
2,
4,
4
],
"axial_magnetic_symbol_diagonal": [
2,
2,
4,
4
],
"independent_gauss_source_constraint_survives_induced_reduction": false,
"frozen_symbol_is_complete_variable_geometry_solution": false,
"background_curvature_second_variation_included": false,
"arbitrary_real_graph_waves_preserve_unitary_normal_carrier": false
},
{
"case": "depth-10-no-normal-connection",
"real_depth": 10,
"hodge_active": false,
"normal_curvature_response_present": false
}
]
}