Recorded data and provenance for the associated calculation.
| title | An Actual Nested Spatial Flag Generates a Conditional Rank-Three Normal Color Geometry |
|---|---|
| checks_passed | 689 |
| dependency_checks_passed | 174 |
| case_count | 13 |
| scope | one exact nested ordinary spatial flag and induced normal connections; quadratic and higher-jet controls, not a derived force action |
View complete data
{
"title": "An Actual Nested Spatial Flag Generates a Conditional Rank-Three Normal Color Geometry",
"sources": {
"experiments/nested-normal-curvature-checks.py": "a77678aea22b4191f1f5180c8095cc03701e96c2a8c1b7db7e3d1ada0d872d2f",
"experiments/hodge-gated-gauss-checks.py": "d24406f940aea7e81ee65cb9596a57a3dc88e0f5d03c07106db93cc948ff1faa"
},
"checks_passed": 689,
"dependency_checks_passed": 174,
"case_count": 13,
"occupied_depths": [
2,
3,
4,
5,
6,
10
],
"scope": "one exact nested ordinary spatial flag and induced normal connections; quadratic and higher-jet controls, not a derived force action",
"cases": [
{
"case": "nested-normal-curvature-depth-2",
"real_depth": 2,
"even_source_carrier": 2,
"intrinsic_real_normal_rank": 8,
"intrinsic_curvature_lie_dimension": 1,
"even_shadow_real_normal_rank": 8,
"complex_normal_rank": 4,
"even_shadow_curvature_lie_dimension": 1,
"quadratic_first_normal_real_rank": 2,
"symmetric_complex_second_fundamental_dimension": 1,
"full_second_fundamental_normal_isomorphism": false,
"odd_shadow_equals_intrinsic_normal_connection": true,
"independent_gauge_action_or_force_derived": false
},
{
"case": "nested-normal-curvature-depth-3",
"real_depth": 3,
"even_source_carrier": 4,
"intrinsic_real_normal_rank": 7,
"intrinsic_curvature_lie_dimension": 10,
"even_shadow_real_normal_rank": 6,
"complex_normal_rank": 3,
"even_shadow_curvature_lie_dimension": 9,
"quadratic_first_normal_real_rank": 6,
"symmetric_complex_second_fundamental_dimension": 3,
"full_second_fundamental_normal_isomorphism": true,
"odd_shadow_equals_intrinsic_normal_connection": false,
"independent_gauge_action_or_force_derived": false
},
{
"case": "nested-normal-curvature-depth-4",
"real_depth": 4,
"even_source_carrier": 4,
"intrinsic_real_normal_rank": 6,
"intrinsic_curvature_lie_dimension": 9,
"even_shadow_real_normal_rank": 6,
"complex_normal_rank": 3,
"even_shadow_curvature_lie_dimension": 9,
"quadratic_first_normal_real_rank": 6,
"symmetric_complex_second_fundamental_dimension": 3,
"full_second_fundamental_normal_isomorphism": true,
"odd_shadow_equals_intrinsic_normal_connection": true,
"independent_gauge_action_or_force_derived": false
},
{
"case": "nested-normal-curvature-depth-5",
"real_depth": 5,
"even_source_carrier": 6,
"intrinsic_real_normal_rank": 5,
"intrinsic_curvature_lie_dimension": 10,
"even_shadow_real_normal_rank": 4,
"complex_normal_rank": 2,
"even_shadow_curvature_lie_dimension": 4,
"quadratic_first_normal_real_rank": 4,
"symmetric_complex_second_fundamental_dimension": 6,
"full_second_fundamental_normal_isomorphism": false,
"odd_shadow_equals_intrinsic_normal_connection": false,
"independent_gauge_action_or_force_derived": false
},
{
"case": "nested-normal-curvature-depth-6",
"real_depth": 6,
"even_source_carrier": 6,
"intrinsic_real_normal_rank": 4,
"intrinsic_curvature_lie_dimension": 4,
"even_shadow_real_normal_rank": 4,
"complex_normal_rank": 2,
"even_shadow_curvature_lie_dimension": 4,
"quadratic_first_normal_real_rank": 4,
"symmetric_complex_second_fundamental_dimension": 6,
"full_second_fundamental_normal_isomorphism": false,
"odd_shadow_equals_intrinsic_normal_connection": true,
"independent_gauge_action_or_force_derived": false
},
{
"case": "nested-normal-curvature-depth-10",
"real_depth": 10,
"even_source_carrier": 10,
"intrinsic_real_normal_rank": 0,
"intrinsic_curvature_lie_dimension": 0,
"even_shadow_real_normal_rank": 0,
"complex_normal_rank": 0,
"even_shadow_curvature_lie_dimension": 0,
"quadratic_first_normal_real_rank": 0,
"symmetric_complex_second_fundamental_dimension": 15,
"full_second_fundamental_normal_isomorphism": false,
"odd_shadow_equals_intrinsic_normal_connection": true,
"independent_gauge_action_or_force_derived": false
},
{
"case": "actual-complex-graph-diagonal-1-x-0",
"complex_base_rank": 2,
"complex_normal_rank": 3,
"diagonal_second_derivative": 1.0,
"position_x1": 0.0,
"pointwise_curvature_lie_dimension": 9,
"traceless_curvature_lie_dimension": 8
},
{
"case": "actual-complex-graph-diagonal-1-x-0.4",
"complex_base_rank": 2,
"complex_normal_rank": 3,
"diagonal_second_derivative": 1.0,
"position_x1": 0.4,
"pointwise_curvature_lie_dimension": 9,
"traceless_curvature_lie_dimension": 8
},
{
"case": "actual-complex-graph-diagonal-1.41421-x-0",
"complex_base_rank": 2,
"complex_normal_rank": 3,
"diagonal_second_derivative": 1.4142135623730951,
"position_x1": 0.0,
"pointwise_curvature_lie_dimension": 4,
"traceless_curvature_lie_dimension": 3
},
{
"case": "actual-complex-graph-diagonal-1.41421-x-0.4",
"complex_base_rank": 2,
"complex_normal_rank": 3,
"diagonal_second_derivative": 1.4142135623730951,
"position_x1": 0.4,
"pointwise_curvature_lie_dimension": 9,
"traceless_curvature_lie_dimension": 8
},
{
"case": "quadratic-curve-control",
"real_depth": 2,
"complex_normal_rank": 4,
"normal_graph_degrees": [
2
],
"transported_curvature_lie_dimension": 1,
"traceless_transport_lie_dimension": 1,
"pointwise_only_curvature_lie_dimension": 1,
"quadratic_selection_is_universal": false
},
{
"case": "higher-normal-jet-curve",
"real_depth": 2,
"complex_normal_rank": 4,
"normal_graph_degrees": [
2,
3,
4,
5
],
"transported_curvature_lie_dimension": 16,
"traceless_transport_lie_dimension": 15,
"pointwise_only_curvature_lie_dimension": 1,
"quadratic_selection_is_universal": false
},
{
"case": "exact-rational-curvature-and-higher-jet-certificate",
"all_occupied_intrinsic_and_shadow_dimensions_exact": true,
"covariant_curvature_jet_maximum_order": 6,
"depth_two_exact_normal_holonomy_dimension": 16,
"depth_two_exact_traceless_holonomy_dimension": 15,
"four_base_parallel_second_fundamental_obstruction_squared": 1536,
"higher_jet_control_embeds_in_one_common_nested_flag": true
}
]
}