Recorded data and provenance for the associated calculation.

Download recorded JSON

experiment_keyneutral-band-kinetics-20261009
created_utc2026-10-09T21:06:51.372165+00:00
scopeExact Clifford compression and finite equivariant-evaluation controls; no spatial particle solution or independent color derivation.
View complete data
{
  "experiment_key": "neutral-band-kinetics-20261009",
  "created_utc": "2026-10-09T21:06:51.372165+00:00",
  "sources": {
    "experiments/neutral-band-kinetics-checks.py": "60d605bc612befa222996f59c9960c06c4312bdf134b07a86a34f2b302ab6a2d"
  },
  "scope": "Exact Clifford compression and finite equivariant-evaluation controls; no spatial particle solution or independent color derivation.",
  "summary": {
    "checks_passed": 548,
    "case_count": 40,
    "spinor_fibre_only_singlet_loses_spatial_depth_at_d4_and_above": true,
    "separate_color_multiplicity_preserves_full_Clifford_symbol": true,
    "equivariant_source_can_retain_full_contact_count": true
  },
  "cases": [
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 2,
      "parameters": {
        "spinor_rank": 2,
        "rotation_subgroup": "SU(1)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 2,
        "squared_leakage_per_direction": [
          0,
          0
        ],
        "complete_depth_retained": true
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 3,
      "parameters": {
        "spinor_rank": 2,
        "rotation_subgroup": "SU(1)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 3,
        "squared_leakage_per_direction": [
          0,
          0,
          0
        ],
        "complete_depth_retained": true
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 4,
      "parameters": {
        "spinor_rank": 4,
        "rotation_subgroup": "SU(2)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 0,
        "squared_leakage_per_direction": [
          2,
          2,
          2,
          2
        ],
        "complete_depth_retained": false
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 5,
      "parameters": {
        "spinor_rank": 4,
        "rotation_subgroup": "SU(2)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 1,
        "squared_leakage_per_direction": [
          2,
          2,
          2,
          2,
          0
        ],
        "complete_depth_retained": false
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 6,
      "parameters": {
        "spinor_rank": 8,
        "rotation_subgroup": "SU(3)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 0,
        "squared_leakage_per_direction": [
          2,
          2,
          2,
          2,
          2,
          2
        ],
        "complete_depth_retained": false
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 7,
      "parameters": {
        "spinor_rank": 8,
        "rotation_subgroup": "SU(3)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 1,
        "squared_leakage_per_direction": [
          2,
          2,
          2,
          2,
          2,
          2,
          0
        ],
        "complete_depth_retained": false
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 8,
      "parameters": {
        "spinor_rank": 16,
        "rotation_subgroup": "SU(4)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 0,
        "squared_leakage_per_direction": [
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2
        ],
        "complete_depth_retained": false
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 9,
      "parameters": {
        "spinor_rank": 16,
        "rotation_subgroup": "SU(4)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 1,
        "squared_leakage_per_direction": [
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          0
        ],
        "complete_depth_retained": false
      }
    },
    {
      "name": "pointwise-spinor-singlet",
      "real_depth": 10,
      "parameters": {
        "spinor_rank": 32,
        "rotation_subgroup": "SU(5)"
      },
      "measurements": {
        "invariant_fibre_rank": 2,
        "retained_principal_directions": 0,
        "squared_leakage_per_direction": [
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2,
          2
        ],
        "complete_depth_retained": false
      }
    },
    {
      "name": "separate-relative-mode-multiplicity",
      "real_depth": 2,
      "parameters": {
        "carrier_rank": 9,
        "singlet_rank": 1
      },
      "measurements": {
        "retained_principal_directions": 2,
        "complete_depth_retained": true
      }
    },
    {
      "name": "separate-relative-mode-multiplicity",
      "real_depth": 3,
      "parameters": {
        "carrier_rank": 9,
        "singlet_rank": 1
      },
      "measurements": {
        "retained_principal_directions": 3,
        "complete_depth_retained": true
      }
    },
    {
      "name": "separate-relative-mode-multiplicity",
      "real_depth": 4,
      "parameters": {
        "carrier_rank": 9,
        "singlet_rank": 1
      },
      "measurements": {
        "retained_principal_directions": 4,
        "complete_depth_retained": true
      }
    },
    {
      "name": "separate-relative-mode-multiplicity",
      "real_depth": 5,
      "parameters": {
        "carrier_rank": 9,
        "singlet_rank": 1
      },
      "measurements": {
        "retained_principal_directions": 5,
        "complete_depth_retained": true
      }
    },
    {
      "name": "separate-relative-mode-multiplicity",
      "real_depth": 6,
      "parameters": {
        "carrier_rank": 9,
        "singlet_rank": 1
      },
      "measurements": {
        "retained_principal_directions": 6,
        "complete_depth_retained": true
      }
    },
    {
      "name": "separate-relative-mode-multiplicity",
      "real_depth": 10,
      "parameters": {
        "carrier_rank": 9,
        "singlet_rank": 1
      },
      "measurements": {
        "retained_principal_directions": 10,
        "complete_depth_retained": true
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 2,
      "mode_index": 1,
      "measurements": {
        "full_spatial_count": 1,
        "selected_contact_eigenvalue": 1,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 2,
      "mode_index": 2,
      "measurements": {
        "full_spatial_count": 3,
        "selected_contact_eigenvalue": 3,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 2,
      "mode_index": 3,
      "measurements": {
        "full_spatial_count": 6,
        "selected_contact_eigenvalue": 6,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 3,
      "mode_index": 1,
      "measurements": {
        "full_spatial_count": 1,
        "selected_contact_eigenvalue": 1,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 3,
      "mode_index": 2,
      "measurements": {
        "full_spatial_count": 4,
        "selected_contact_eigenvalue": 4,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 3,
      "mode_index": 3,
      "measurements": {
        "full_spatial_count": 10,
        "selected_contact_eigenvalue": 10,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 4,
      "mode_index": 1,
      "measurements": {
        "full_spatial_count": 1,
        "selected_contact_eigenvalue": 1,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 4,
      "mode_index": 2,
      "measurements": {
        "full_spatial_count": 5,
        "selected_contact_eigenvalue": 5,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 4,
      "mode_index": 3,
      "measurements": {
        "full_spatial_count": 15,
        "selected_contact_eigenvalue": 15,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 5,
      "mode_index": 1,
      "measurements": {
        "full_spatial_count": 1,
        "selected_contact_eigenvalue": 1,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 5,
      "mode_index": 2,
      "measurements": {
        "full_spatial_count": 6,
        "selected_contact_eigenvalue": 6,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 5,
      "mode_index": 3,
      "measurements": {
        "full_spatial_count": 21,
        "selected_contact_eigenvalue": 21,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 6,
      "mode_index": 1,
      "measurements": {
        "full_spatial_count": 1,
        "selected_contact_eigenvalue": 1,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 6,
      "mode_index": 2,
      "measurements": {
        "full_spatial_count": 7,
        "selected_contact_eigenvalue": 7,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 6,
      "mode_index": 3,
      "measurements": {
        "full_spatial_count": 28,
        "selected_contact_eigenvalue": 28,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 10,
      "mode_index": 1,
      "measurements": {
        "full_spatial_count": 1,
        "selected_contact_eigenvalue": 1,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 10,
      "mode_index": 2,
      "measurements": {
        "full_spatial_count": 11,
        "selected_contact_eigenvalue": 11,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "reference-normalized-multiplicity",
      "real_depth": 10,
      "mode_index": 3,
      "measurements": {
        "full_spatial_count": 66,
        "selected_contact_eigenvalue": 66,
        "selected_carrier_rank": 1,
        "reference_carrier_rank": 1
      }
    },
    {
      "name": "invariant-evaluation-with-kinetic-complement",
      "real_depth": 2,
      "mode_index": 5,
      "parameters": {
        "kinetic_radius": 1,
        "contact_coefficient": 1,
        "scope": "abstract equivariant evaluation control with spatial shell weights"
      },
      "measurements": {
        "source_space_rank": 5,
        "contact_eigenvalue": 15,
        "dressed_frequency": 18.765486041016864,
        "kinetic_mean": 3.6666666666666665,
        "kinetic_variance": 1.5555555555555556
      }
    },
    {
      "name": "invariant-evaluation-with-kinetic-complement",
      "real_depth": 3,
      "mode_index": 5,
      "parameters": {
        "kinetic_radius": 1,
        "contact_coefficient": 1,
        "scope": "abstract equivariant evaluation control with spatial shell weights"
      },
      "measurements": {
        "source_space_rank": 5,
        "contact_eigenvalue": 35,
        "dressed_frequency": 39.53333749334899,
        "kinetic_mean": 4.5,
        "kinetic_variance": 1.2
      }
    },
    {
      "name": "invariant-evaluation-with-kinetic-complement",
      "real_depth": 4,
      "mode_index": 5,
      "parameters": {
        "kinetic_radius": 1,
        "contact_coefficient": 1,
        "scope": "abstract equivariant evaluation control with spatial shell weights"
      },
      "measurements": {
        "source_space_rank": 5,
        "contact_eigenvalue": 70,
        "dressed_frequency": 75.21350022183711,
        "kinetic_mean": 5.2,
        "kinetic_variance": 0.96
      }
    },
    {
      "name": "invariant-evaluation-with-kinetic-complement",
      "real_depth": 5,
      "mode_index": 10,
      "parameters": {
        "kinetic_radius": 1,
        "contact_coefficient": 1,
        "scope": "abstract equivariant evaluation control with spatial shell weights"
      },
      "measurements": {
        "source_space_rank": 10,
        "contact_eigenvalue": 2002,
        "dressed_frequency": 2012.0013366131188,
        "kinetic_mean": 10.0,
        "kinetic_variance": 2.6785714285714284
      }
    },
    {
      "name": "invariant-evaluation-with-kinetic-complement",
      "real_depth": 6,
      "mode_index": 13,
      "parameters": {
        "kinetic_radius": 1,
        "contact_coefficient": 1,
        "scope": "abstract equivariant evaluation control with spatial shell weights"
      },
      "measurements": {
        "source_space_rank": 13,
        "contact_eigenvalue": 18564,
        "dressed_frequency": 18577.28590224809,
        "kinetic_mean": 13.285714285714286,
        "kinetic_variance": 3.489795918367347
      }
    },
    {
      "name": "invariant-evaluation-with-kinetic-complement",
      "real_depth": 6,
      "mode_index": 35,
      "parameters": {
        "kinetic_radius": 1,
        "contact_coefficient": 1,
        "scope": "abstract equivariant evaluation control with spatial shell weights"
      },
      "measurements": {
        "source_space_rank": 35,
        "contact_eigenvalue": 3838380,
        "dressed_frequency": 3838412.142862701,
        "kinetic_mean": 32.14285714285714,
        "kinetic_variance": 21.336734693877553
      }
    },
    {
      "name": "invariant-evaluation-with-kinetic-complement",
      "real_depth": 10,
      "mode_index": 23,
      "parameters": {
        "kinetic_radius": 1,
        "contact_coefficient": 1,
        "scope": "abstract equivariant evaluation control with spatial shell weights"
      },
      "measurements": {
        "source_space_rank": 23,
        "contact_eigenvalue": 64512240,
        "dressed_frequency": 64512265.00000007,
        "kinetic_mean": 25.0,
        "kinetic_variance": 5.0
      }
    }
  ]
}