{
  "seed": 16102026,
  "numerical_tolerance": 1e-07,
  "groups": {
    "one_frequency_physical_realization": {
      "passed": true,
      "cases": 120,
      "max_error": 2.061184678958507e-13
    },
    "complex_tomography": {
      "passed": true,
      "cases": 240,
      "max_error": 6.9715177555407e-14,
      "setting_counts": [
        4,
        9,
        16,
        25
      ]
    },
    "reciprocal_tomography": {
      "passed": true,
      "cases": 240,
      "max_error": 3.2695314095023566e-14,
      "setting_counts": [
        3,
        6,
        10,
        15
      ]
    },
    "physical_short_design_ambiguities": {
      "passed": true,
      "cases": 9,
      "max_error": 4.9508509587976365e-15
    },
    "canonical_and_flatness": {
      "passed": true,
      "cases": 425,
      "max_error": 1.2116813367896757e-12
    },
    "extension_interface": {
      "passed": true,
      "cases": 125,
      "max_error": 5.6568213462111505e-14,
      "defect_identities": 225
    },
    "admissibility_and_input_rejections": {
      "passed": true,
      "cases": 4,
      "max_error": 0.0
    },
    "node_independent_rank_profiles": {
      "passed": true,
      "cases": 3,
      "max_error": 0.0,
      "profiles": [
        [
          3,
          6,
          7,
          7
        ],
        [
          3,
          6,
          7,
          7
        ],
        [
          3,
          6,
          7,
          7
        ]
      ]
    },
    "damped_rank_and_known_linewidth_repair": {
      "passed": true,
      "cases": 2,
      "max_error": 0.0,
      "smallest_unshifted_eigenvalue": 1.5129267065739995e-05
    },
    "dissipative_kernel_identity": {
      "passed": true,
      "cases": 50,
      "max_error": 9.292499991001925e-15
    },
    "mixed_pole_phase_and_contrast": {
      "passed": true,
      "cases": 100,
      "max_error": 8.005932084973442e-16
    },
    "rational_witness_and_mass_bounds": {
      "passed": true,
      "cases": 40,
      "max_error": 4.422840674851928e-15
    },
    "joint_gauge_invariance": {
      "passed": true,
      "cases": 300,
      "max_error": 0.0
    }
  },
  "exact": {
    "descriptor_identity": {
      "passed": true,
      "rank": 3,
      "pivots": [
        0,
        1,
        2
      ],
      "gram": "Matrix([[6/5, 1, 16/25 - 13*I/25], [1, 11/10, 1/2 - I/2], [16/25 + 13*I/25, 1/2 + I/2, 3/5]])",
      "shifted_gram": "Matrix([[-2/5, 0, -7/25 + I/25], [0, 3/10, 0], [-7/25 - I/25, 0, -1/5]])",
      "data": "Matrix([[2/5 - 6*I/5, -I], [-I, -3/10 - 11*I/10], [4/5 - 3*I/5, 1/2 - I/2]])",
      "identity": "D* (zG-J)^(-1) D = C* (zI-L)^(-1) C"
    },
    "one_sample_distinct_visible_dimensions": {
      "passed": true,
      "functions": [
        "1/z",
        "2*z/(z**2-1)"
      ],
      "common_value_at_i": "-I"
    },
    "unbounded_extension_family": {
      "passed": true,
      "added_dimensions_tested": [
        1,
        2,
        3,
        4
      ],
      "all_visible": true
    },
    "flat_two_sample_certificate": {
      "passed": true,
      "K": "Matrix([[1, 1/2], [1/2, 1/4]])",
      "ranks": [
        1,
        1
      ]
    },
    "range_condition_counterexample": {
      "passed": true,
      "Pick": "0",
      "data": "1"
    },
    "two_channel_cross_pole_invariant": {
      "passed": true,
      "value": "-I",
      "residue_ranks": [
        1,
        1
      ]
    },
    "damped_kernel_ranks": {
      "passed": true,
      "internal_damped_order": 1,
      "ranks": [
        1,
        2,
        3,
        4,
        5,
        6
      ]
    },
    "MDS_all_maximal_minors": {
      "passed": true,
      "minors": 15,
      "distance": 3
    },
    "rational_annihilator_identity": {
      "passed": true,
      "weights": [
        "-1",
        "I*(2 - I)",
        "1 - 2*I"
      ]
    }
  },
  "elapsed_seconds": 3.6427738666534424,
  "summary": {
    "numerical_groups": 13,
    "numerical_cases": 1658,
    "exact_groups": 9,
    "all_passed": true,
    "formal_proof_assistant": "not available; symbolic checks are not formalized proofs"
  }
}