{
  "schema": "essential-normal-core-finite-calibration/v1",
  "exact_normalization_and_grading": true,
  "exact_invariant_phase": true,
  "normalized_dimension": 8,
  "essential_dimension": 4,
  "essential_source_identity_rank": 4,
  "essential_source_nondegenerate": true,
  "source_products": [
    {
      "left": [
        0,
        0
      ],
      "right": [
        0,
        0
      ],
      "exact_product": true
    },
    {
      "left": [
        0,
        0
      ],
      "right": [
        0,
        1
      ],
      "exact_product": true
    },
    {
      "left": [
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        0
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      "right": [
        1,
        0
      ],
      "exact_product": true
    },
    {
      "left": [
        0,
        0
      ],
      "right": [
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        1
      ],
      "exact_product": true
    },
    {
      "left": [
        0,
        1
      ],
      "right": [
        0,
        0
      ],
      "exact_product": true
    },
    {
      "left": [
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        1
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      "right": [
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      "exact_product": true
    },
    {
      "left": [
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      "right": [
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      "exact_product": true
    },
    {
      "left": [
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      "right": [
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      "exact_product": true
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    {
      "left": [
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      "right": [
        0,
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      "exact_product": true
    },
    {
      "left": [
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      "right": [
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        1
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      "exact_product": true
    },
    {
      "left": [
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        0
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      "right": [
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      "exact_product": true
    },
    {
      "left": [
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        0
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      "right": [
        1,
        1
      ],
      "exact_product": true
    },
    {
      "left": [
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        1
      ],
      "right": [
        0,
        0
      ],
      "exact_product": true
    },
    {
      "left": [
        1,
        1
      ],
      "right": [
        0,
        1
      ],
      "exact_product": true
    },
    {
      "left": [
        1,
        1
      ],
      "right": [
        1,
        0
      ],
      "exact_product": true
    },
    {
      "left": [
        1,
        1
      ],
      "right": [
        1,
        1
      ],
      "exact_product": true
    }
  ],
  "symmetrization_tests": [
    {
      "x": "-1",
      "positive_seed_entries": [
        "1/32",
        "1/8",
        "3/32",
        "3/16"
      ],
      "exact_phase_commutation": true,
      "exact_bounded_perturbation": true,
      "exact_reference_projection_commutation": true,
      "exact_essential_reference_perturbation": true,
      "exact_compression_formula": true,
      "exact_reference_commutator": true,
      "exact_full_arrow_error": true,
      "positive_regulator_minus_identity": true,
      "averaged_projection_commutator_zero": false,
      "essential_operator": [
        [
          "0",
          "12",
          "0",
          "0"
        ],
        [
          "12",
          "0",
          "0",
          "0"
        ],
        [
          "0",
          "0",
          "0",
          "24/5"
        ],
        [
          "0",
          "0",
          "24/5",
          "0"
        ]
      ]
    },
    {
      "x": "-1/2",
      "positive_seed_entries": [
        "3/64",
        "7/64",
        "7/64",
        "11/64"
      ],
      "exact_phase_commutation": true,
      "exact_bounded_perturbation": true,
      "exact_reference_projection_commutation": true,
      "exact_essential_reference_perturbation": true,
      "exact_compression_formula": true,
      "exact_reference_commutator": true,
      "exact_full_arrow_error": true,
      "positive_regulator_minus_identity": true,
      "averaged_projection_commutator_zero": false,
      "essential_operator": [
        [
          "0",
          "64/7",
          "0",
          "0"
        ],
        [
          "64/7",
          "0",
          "0",
          "0"
        ],
        [
          "0",
          "0",
          "0",
          "1728/385"
        ],
        [
          "0",
          "0",
          "1728/385",
          "0"
        ]
      ]
    },
    {
      "x": "0",
      "positive_seed_entries": [
        "1/16",
        "3/32",
        "1/8",
        "5/32"
      ],
      "exact_phase_commutation": true,
      "exact_bounded_perturbation": true,
      "exact_reference_projection_commutation": true,
      "exact_essential_reference_perturbation": true,
      "exact_compression_formula": true,
      "exact_reference_commutator": true,
      "exact_full_arrow_error": true,
      "positive_regulator_minus_identity": true,
      "averaged_projection_commutator_zero": false,
      "essential_operator": [
        [
          "0",
          "8",
          "0",
          "0"
        ],
        [
          "8",
          "0",
          "0",
          "0"
        ],
        [
          "0",
          "0",
          "0",
          "108/25"
        ],
        [
          "0",
          "0",
          "108/25",
          "0"
        ]
      ]
    },
    {
      "x": "1/2",
      "positive_seed_entries": [
        "5/64",
        "5/64",
        "9/64",
        "9/64"
      ],
      "exact_phase_commutation": true,
      "exact_bounded_perturbation": true,
      "exact_reference_projection_commutation": true,
      "exact_essential_reference_perturbation": true,
      "exact_compression_formula": true,
      "exact_reference_commutator": true,
      "exact_full_arrow_error": true,
      "positive_regulator_minus_identity": true,
      "averaged_projection_commutator_zero": true,
      "essential_operator": [
        [
          "0",
          "192/25",
          "0",
          "0"
        ],
        [
          "192/25",
          "0",
          "0",
          "0"
        ],
        [
          "0",
          "0",
          "0",
          "64/15"
        ],
        [
          "0",
          "0",
          "64/15",
          "0"
        ]
      ]
    },
    {
      "x": "1",
      "positive_seed_entries": [
        "3/32",
        "1/16",
        "5/32",
        "1/8"
      ],
      "exact_phase_commutation": true,
      "exact_bounded_perturbation": true,
      "exact_reference_projection_commutation": true,
      "exact_essential_reference_perturbation": true,
      "exact_compression_formula": true,
      "exact_reference_commutator": true,
      "exact_full_arrow_error": true,
      "positive_regulator_minus_identity": true,
      "averaged_projection_commutator_zero": false,
      "essential_operator": [
        [
          "0",
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          "0",
          "0"
        ],
        [
          "8",
          "0",
          "0",
          "0"
        ],
        [
          "0",
          "0",
          "0",
          "108/25"
        ],
        [
          "0",
          "0",
          "108/25",
          "0"
        ]
      ]
    }
  ],
  "all_fraction_checks": true,
  "text_canvas_overflows": [],
  "finite_model_proves_original_inverse": false,
  "finite_model_proves_physical_sum": false,
  "proof_scope": "ENC.1–29 retain the actual B-source inverse. A full joint core is proved for a global compact-coordinate carrier; the smooth oscillatory seed does not supply the boundary convergence. General holonomy normal-source/mixed/physical/Bott obligations remain.",
  "flat_coordinate_seed_zero_normal_derivative": true,
  "oscillatory_seed_samples": [
    {
      "m": 1,
      "N_m": 4,
      "chi_midpoint": "1/2",
      "chi_midpoint_derivative": "2",
      "weight_midpoint": "3/2",
      "selected_vector_coefficient": "1/4",
      "cutoff_derivative_midpoint": "2",
      "derivative_times_vector": "1/2"
    },
    {
      "m": 2,
      "N_m": 16,
      "chi_midpoint": "1/2",
      "chi_midpoint_derivative": "2",
      "weight_midpoint": "5/2",
      "selected_vector_coefficient": "1/16",
      "cutoff_derivative_midpoint": "8",
      "derivative_times_vector": "1/2"
    },
    {
      "m": 3,
      "N_m": 256,
      "chi_midpoint": "1/2",
      "chi_midpoint_derivative": "2",
      "weight_midpoint": "7/2",
      "selected_vector_coefficient": "1/256",
      "cutoff_derivative_midpoint": "128",
      "derivative_times_vector": "1/2"
    }
  ],
  "finite_samples_prove_infinite_joint_core": false,
  "finite_samples_prove_physical_sum": false
}