{
  "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"
  }
}