Recorded data and provenance for the associated calculation.
| title | Independent normal color and kinetic compatibility across nested spatial sectors |
|---|---|
| created_utc | 2026-10-09T23:09:28.636574+00:00 |
| checks_passed | 1451 |
| scope | Finite ordinary spatial parent, full tangent Clifford symbols, exact real commutants and derivative-form controls. |
View complete data
{
"title": "Independent normal color and kinetic compatibility across nested spatial sectors",
"created_utc": "2026-10-09T23:09:28.636574+00:00",
"checks_passed": 1451,
"cases": [
{
"real_depth": 2,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 8,
"full_triplet_kinetic_compatibility": true,
"retained_spatial_symbol_directions": 2,
"squared_leak_by_tangent_direction": [
0.0,
0.0
],
"spatial_three_form_can_be_nonzero": false,
"combined_kinetic_and_three_form_candidate": false,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 3,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 8,
"full_triplet_kinetic_compatibility": true,
"retained_spatial_symbol_directions": 3,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": true,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 4,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 8,
"full_triplet_kinetic_compatibility": true,
"retained_spatial_symbol_directions": 4,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0,
0.0
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": true,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 5,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 3,
"full_triplet_kinetic_compatibility": false,
"retained_spatial_symbol_directions": 4,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0,
0.0,
11.999999999999998
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": false,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 6,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 3,
"full_triplet_kinetic_compatibility": false,
"retained_spatial_symbol_directions": 4,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0,
0.0,
11.999999999999998,
11.999999999999998
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": false,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 7,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 0,
"full_triplet_kinetic_compatibility": false,
"retained_spatial_symbol_directions": 4,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0,
0.0,
11.999999999999998,
11.999999999999998,
11.999999999999998
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": false,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 8,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 0,
"full_triplet_kinetic_compatibility": false,
"retained_spatial_symbol_directions": 4,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0,
0.0,
11.999999999999998,
11.999999999999998,
11.999999999999998,
11.999999999999998
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": false,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 9,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 0,
"full_triplet_kinetic_compatibility": false,
"retained_spatial_symbol_directions": 4,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0,
0.0,
11.999999999999998,
11.999999999999998,
11.999999999999998,
11.999999999999998,
11.999999999999998
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": false,
"all_color_interactions_proved_absent": false
}
},
{
"real_depth": 10,
"geometry": "one flat nested flag in the selected ten-dimensional parent",
"parameters": {
"parent_depth": 10,
"normal_complex_rank": 3,
"projected_full_spinor_rank": 12
},
"measurements": {
"independent_normal_su3_subalgebra_dimension": 0,
"full_triplet_kinetic_compatibility": false,
"retained_spatial_symbol_directions": 4,
"squared_leak_by_tangent_direction": [
0.0,
0.0,
0.0,
0.0,
11.999999999999998,
11.999999999999998,
11.999999999999998,
11.999999999999998,
11.999999999999998,
11.999999999999998
],
"spatial_three_form_can_be_nonzero": true,
"combined_kinetic_and_three_form_candidate": false,
"all_color_interactions_proved_absent": false
}
},
{
"geometry": "independent spin and normal color volume",
"parameters": {
"spin_rank": 2,
"color_rank": 3
},
"measurements": {
"third_contraction": "tr(rho_a) tr(rho_b)-tr(rho_a rho_b)",
"pair_operator": "I_spin tensor (I_color-swap_color)",
"same_chiral_pointwise_field_volume_vanishes": true,
"distinct_modes_or_spatial_jets_needed_for_chiral_source": true
}
},
{
"geometry": "independent spin and normal color volume",
"parameters": {
"spin_rank": 4,
"color_rank": 3
},
"measurements": {
"third_contraction": "tr(rho_a) tr(rho_b)-tr(rho_a rho_b)",
"pair_operator": "I_spin tensor (I_color-swap_color)",
"same_chiral_pointwise_field_volume_vanishes": false,
"distinct_modes_or_spatial_jets_needed_for_chiral_source": false
}
},
{
"geometry": "charge character versus independent observer spin",
"parameters": {
"observer_sector_depth": 3,
"containing_base_depth": 4
},
"measurements": {
"ambient_Q_commutes_with_observer_spin": false,
"fixed_projective_stabilizer_observer_commutant_dimension": 8,
"both_rays_stabilizer_observer_commutant_dimension": 9,
"auxiliary_branch_operator": "(I-i gamma1 gamma2 gamma3)/2",
"normal_branch_charge": "N_normal/3-branch",
"normal_charge_weights_with_spin_multiplicities": {
"0": 2,
"2/3": 6,
"-1": 2,
"-1/3": 6
},
"normal_branch_charge_commutes_with_Cl3": true,
"normal_branch_charge_commutes_with_Cl4": false,
"physical_total_charge_generator_derived": false
}
},
{
"geometry": "normal connection and standard color contractions",
"parameters": {
"connection_metric": "g=g_B+|dy+A y|^2",
"normal_group": "SU3"
},
"measurements": {
"qq_antisymmetric_casimir": "-2/3",
"qq_symmetric_casimir": "1/3",
"determinant_singlet_present": true,
"observer_spin_and_color_commute": true,
"normal_curvature_can_couple_a_depth_two_triplet": true,
"three_form_zero_alone_removes_all_depth_two_color_coupling": false
}
},
{
"real_depth": 2,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 2,
"contact_form_degree": 2
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": true,
"measured_force_derived": false
}
},
{
"real_depth": 3,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 2,
"contact_form_degree": 2
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": true,
"measured_force_derived": false
}
},
{
"real_depth": 4,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 2,
"contact_form_degree": 2
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": true,
"measured_force_derived": false
}
},
{
"real_depth": 5,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 2,
"contact_form_degree": 2
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 6,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 2,
"contact_form_degree": 2
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 10,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 2,
"contact_form_degree": 2
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 2,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 3,
"contact_form_degree": 3
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 3,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 3,
"contact_form_degree": 3
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": true,
"measured_force_derived": false
}
},
{
"real_depth": 4,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 3,
"contact_form_degree": 3
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": true,
"measured_force_derived": false
}
},
{
"real_depth": 5,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 3,
"contact_form_degree": 3
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 6,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 3,
"contact_form_degree": 3
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 10,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 3,
"contact_form_degree": 3
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 2,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 4,
"contact_form_degree": 4
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 3,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 4,
"contact_form_degree": 4
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 4,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 4,
"contact_form_degree": 4
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": true,
"measured_force_derived": false
}
},
{
"real_depth": 5,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 4,
"contact_form_degree": 4
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 6,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 4,
"contact_form_degree": 4
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 10,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 4,
"contact_form_degree": 4
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 2,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 5,
"contact_form_degree": 5
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 3,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 5,
"contact_form_degree": 5
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 4,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 5,
"contact_form_degree": 5
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 5,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 5,
"contact_form_degree": 5
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 6,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 5,
"contact_form_degree": 5
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 10,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 5,
"contact_form_degree": 5
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 2,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 6,
"contact_form_degree": 6
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 3,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 6,
"contact_form_degree": 6
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 4,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 6,
"contact_form_degree": 6
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": true,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 5,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 6,
"contact_form_degree": 6
},
"measurements": {
"spatial_form_nonzero": false,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 6,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 6,
"contact_form_degree": 6
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
},
{
"real_depth": 10,
"geometry": "determinant spatial differential-form candidate",
"parameters": {
"normal_complex_rank": 6,
"contact_form_degree": 6
},
"measurements": {
"spatial_form_nonzero": true,
"base_color_kinetics_preserved": false,
"combined_candidate_allowed": false,
"measured_force_derived": false
}
}
],
"scope": "Finite ordinary spatial parent, full tangent Clifford symbols, exact real commutants and derivative-form controls.",
"limitations": [
"The selected ten-dimensional parent is within the infinite containing manifold; higher ambient normals are not excluded.",
"The normal SU3 triplet is distinct from the base middle-Hodge spin-one triplet.",
"Depth two also admits the triplet kinematically, and its normal curvature need not vanish.",
"A determinant three-form vanishes at depth two but does not remove an independently present covariant kinetic connection.",
"Residual SU2 and higher equivalent-mode interactions are not excluded at five/six.",
"No occupied particle representation, strong dynamics or all-sector force absence is derived."
],
"sources": {
"experiments/normal-color-kinetics-checks.py": "15e50b931c5d5d468a43cbd65b3ea8e17f271e5ce6d69c7054000a84e5514a43",
"experiments/spinor-hodge-source-checks.py": "c1a9212b8dd1f0e9e525e36db80c322b9487986ca656aa028c2a4cbb8456b38e"
}
}