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experiment_keysymmetric-Hodge-feedback-20261009
created_utc2026-10-09T22:03:49.617721+00:00
scopeA conditional common raw-Hodge reciprocal contact kernel and filtered color-volume action. It selects 3/4 among maintained sectors, allows 7/8 controls, and retains alternative interactions and nested-source ordering as explicit physical premises.
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{
  "experiment_key": "symmetric-Hodge-feedback-20261009",
  "created_utc": "2026-10-09T22:03:49.617721+00:00",
  "sources": {
    "experiments/symmetric-hodge-feedback-checks.py": "7da35c7ba35a56c5a6ed159acdc003a006e4da20c79533b38c6636e3102512ad",
    "experiments/sawtooth-sector-coupling-checks.py": "4b76b045f19240c04e8cf1be656643d8594a68423dd1292d29624e5106e584b9"
  },
  "scope": "A conditional common raw-Hodge reciprocal contact kernel and filtered color-volume action. It selects 3/4 among maintained sectors, allows 7/8 controls, and retains alternative interactions and nested-source ordering as explicit physical premises.",
  "summary": {
    "checks_passed": 4021,
    "case_count": 31
  },
  "cases": [
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 1,
      "parameters": {
        "even_carrier_depth": 2,
        "middle_degree": 1,
        "odd_depth_uses_declared_isometric_shadow": true,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 1,
        "symmetric_filter_active": false,
        "nonabelian_volume_channel_active": false,
        "isotropic_pair_coefficient_sigma2_units": 0,
        "complementary_Hermitian_channel_available": true
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 2,
      "parameters": {
        "even_carrier_depth": 2,
        "middle_degree": 1,
        "odd_depth_uses_declared_isometric_shadow": false,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 1,
        "symmetric_filter_active": false,
        "nonabelian_volume_channel_active": false,
        "isotropic_pair_coefficient_sigma2_units": 0,
        "complementary_Hermitian_channel_available": true
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 3,
      "parameters": {
        "even_carrier_depth": 4,
        "middle_degree": 2,
        "odd_depth_uses_declared_isometric_shadow": true,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 3,
        "symmetric_filter_active": true,
        "nonabelian_volume_channel_active": true,
        "isotropic_pair_coefficient_sigma2_units": 1,
        "complementary_Hermitian_channel_available": false
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 4,
      "parameters": {
        "even_carrier_depth": 4,
        "middle_degree": 2,
        "odd_depth_uses_declared_isometric_shadow": false,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 3,
        "symmetric_filter_active": true,
        "nonabelian_volume_channel_active": true,
        "isotropic_pair_coefficient_sigma2_units": 1,
        "complementary_Hermitian_channel_available": false
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 5,
      "parameters": {
        "even_carrier_depth": 6,
        "middle_degree": 3,
        "odd_depth_uses_declared_isometric_shadow": true,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 10,
        "symmetric_filter_active": false,
        "nonabelian_volume_channel_active": false,
        "isotropic_pair_coefficient_sigma2_units": 0,
        "complementary_Hermitian_channel_available": true
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 6,
      "parameters": {
        "even_carrier_depth": 6,
        "middle_degree": 3,
        "odd_depth_uses_declared_isometric_shadow": false,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 10,
        "symmetric_filter_active": false,
        "nonabelian_volume_channel_active": false,
        "isotropic_pair_coefficient_sigma2_units": 0,
        "complementary_Hermitian_channel_available": true
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 7,
      "parameters": {
        "even_carrier_depth": 8,
        "middle_degree": 4,
        "odd_depth_uses_declared_isometric_shadow": true,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 35,
        "symmetric_filter_active": true,
        "nonabelian_volume_channel_active": true,
        "isotropic_pair_coefficient_sigma2_units": 33,
        "complementary_Hermitian_channel_available": false
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 8,
      "parameters": {
        "even_carrier_depth": 8,
        "middle_degree": 4,
        "odd_depth_uses_declared_isometric_shadow": false,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
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        "isotropic_pair_coefficient_sigma2_units": 33,
        "complementary_Hermitian_channel_available": false
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 9,
      "parameters": {
        "even_carrier_depth": 10,
        "middle_degree": 5,
        "odd_depth_uses_declared_isometric_shadow": true,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 126,
        "symmetric_filter_active": false,
        "nonabelian_volume_channel_active": false,
        "isotropic_pair_coefficient_sigma2_units": 0,
        "complementary_Hermitian_channel_available": true
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
      "real_depth": 10,
      "parameters": {
        "even_carrier_depth": 10,
        "middle_degree": 5,
        "odd_depth_uses_declared_isometric_shadow": false,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
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        "symmetric_filter_active": false,
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        "isotropic_pair_coefficient_sigma2_units": 0,
        "complementary_Hermitian_channel_available": true
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
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      "parameters": {
        "even_carrier_depth": 12,
        "middle_degree": 6,
        "odd_depth_uses_declared_isometric_shadow": true,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
        "channel_rank": 462,
        "symmetric_filter_active": true,
        "nonabelian_volume_channel_active": true,
        "isotropic_pair_coefficient_sigma2_units": 460,
        "complementary_Hermitian_channel_available": false
      }
    },
    {
      "name": "all-sector-symmetric-Hodge-rule",
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      "parameters": {
        "even_carrier_depth": 12,
        "middle_degree": 6,
        "odd_depth_uses_declared_isometric_shadow": false,
        "common_kernel": "Hermitian part of raw real Hodge star"
      },
      "measurements": {
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        "isotropic_pair_coefficient_sigma2_units": 460,
        "complementary_Hermitian_channel_available": false
      }
    },
    {
      "name": "filtered-color-pair",
      "parameters": {
        "active_rank": 3,
        "third_slot_covariance": "sigma^2 I"
      },
      "measurements": {
        "pair_operator": "sigma^2 (I-swap)",
        "qq_pair_weights": [
          "-2/3",
          "1/3"
        ],
        "odd_middle_degree_pair_operator": "0",
        "higher_control_rank35_pair_coefficient": "33 sigma^2"
      }
    },
    {
      "name": "allowed-alternative-channel",
      "parameters": {
        "odd_middle_degree": true
      },
      "measurements": {
        "symmetric_Hodge_source": "0",
        "complementary_source": -0.9999999999999998,
        "time_reversal_forbids_complementary_squared_energy": false,
        "generic_norm_overlap_also_remains_allowed": true
      }
    },
    {
      "name": "nested-source-ordering",
      "real_depth": 6,
      "parameters": {
        "child_depth": 4,
        "normal_contractions": 1
      },
      "measurements": {
        "filter_parent_then_restrict": "0",
        "restrict_then_filter_squared_Hilbert_Schmidt_norm": 6,
        "intrinsic_source_first_is_an_additional_physical_premise": true
      }
    },
    {
      "name": "nested-source-ordering",
      "real_depth": 10,
      "parameters": {
        "child_depth": 4,
        "normal_contractions": 3
      },
      "measurements": {
        "filter_parent_then_restrict": "0",
        "restrict_then_filter_squared_Hilbert_Schmidt_norm": 6,
        "intrinsic_source_first_is_an_additional_physical_premise": true
      }
    },
    {
      "name": "position-versus-velocity-Hodge-contact",
      "parameters": {
        "common_bare_stiffness": 2,
        "static_coefficient": 0.3,
        "gyro_coefficient": 0.4
      },
      "measurements": {
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        "odd_middle_degree_velocity_active": true,
        "reciprocity_alone_forces_symmetric_fibre_filter": false,
        "velocity_term_requires_time_reversal_parities_or_circulation": true
      }
    },
    {
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        "interaction_order": "velocity"
      },
      "measurements": {
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    {
      "name": "all-sector-Hodge-order-response",
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}