{
  "n": 24,
  "avg_matrix_size": 3.6,
  "avg_rank": 2.62,
  "avg_spectral_gap": -0.8021,
  "avg_density": 0.1375,
  "unique_gaps": 7,
  "unique_ranks": 7,
  "records": [
    {
      "name": "apply_chain",
      "proof_status": "verified",
      "trace_tags": 6,
      "unique_states": 6,
      "matrix_size": 6,
      "rank": 5,
      "spectral_gap": -1.434362,
      "laplacian_zero_count": 6,
      "density": 0.138889,
      "eigenvalue_max": 0.900969,
      "symmetric_eigenvalues": [
        0.900969
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.236068
    },
    {
      "name": "calc_chain",
      "proof_status": "failed",
      "trace_tags": 1,
      "unique_states": 1,
      "matrix_size": 1,
      "rank": 0,
      "spectral_gap": 0.0,
      "laplacian_zero_count": 1,
      "density": 0.0,
      "eigenvalue_max": 0.0,
      "symmetric_eigenvalues": [
        0.0
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 0.0
    },
    {
      "name": "cases_and_elim",
      "proof_status": "verified",
      "trace_tags": 6,
      "unique_states": 6,
      "matrix_size": 6,
      "rank": 5,
      "spectral_gap": -1.434362,
      "laplacian_zero_count": 6,
      "density": 0.138889,
      "eigenvalue_max": 0.900969,
      "symmetric_eigenvalues": [
        0.900969
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.236068
    },
    {
      "name": "cases_or_swap",
      "proof_status": "failed",
      "trace_tags": 7,
      "unique_states": 7,
      "matrix_size": 7,
      "rank": 6,
      "spectral_gap": -1.752772,
      "laplacian_zero_count": 7,
      "density": 0.122449,
      "eigenvalue_max": 0.920991,
      "symmetric_eigenvalues": [
        0.920991
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.44949
    },
    {
      "name": "constructor_example",
      "proof_status": "verified",
      "trace_tags": 6,
      "unique_states": 6,
      "matrix_size": 6,
      "rank": 5,
      "spectral_gap": -1.434362,
      "laplacian_zero_count": 6,
      "density": 0.138889,
      "eigenvalue_max": 0.900969,
      "symmetric_eigenvalues": [
        0.900969
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.236068
    },
    {
      "name": "fail_bad_coercion",
      "proof_status": "failed",
      "trace_tags": 2,
      "unique_states": 2,
      "matrix_size": 2,
      "rank": 1,
      "spectral_gap": 0.05,
      "laplacian_zero_count": 2,
      "density": 0.25,
      "eigenvalue_max": 0.5,
      "symmetric_eigenvalues": [
        0.5
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.0
    },
    {
      "name": "fail_missing_lemma",
      "proof_status": "failed",
      "trace_tags": 1,
      "unique_states": 1,
      "matrix_size": 1,
      "rank": 0,
      "spectral_gap": 0.0,
      "laplacian_zero_count": 1,
      "density": 0.0,
      "eigenvalue_max": 0.0,
      "symmetric_eigenvalues": [
        0.0
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 0.0
    },
    {
      "name": "fail_type_mismatch",
      "proof_status": "failed",
      "trace_tags": 1,
      "unique_states": 1,
      "matrix_size": 1,
      "rank": 0,
      "spectral_gap": 0.0,
      "laplacian_zero_count": 1,
      "density": 0.0,
      "eigenvalue_max": 0.0,
      "symmetric_eigenvalues": [
        0.0
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 0.0
    },
    {
      "name": "fail_unsat",
      "proof_status": "failed",
      "trace_tags": 1,
      "unique_states": 1,
      "matrix_size": 1,
      "rank": 0,
      "spectral_gap": 0.0,
      "laplacian_zero_count": 1,
      "density": 0.0,
      "eigenvalue_max": 0.0,
      "symmetric_eigenvalues": [
        0.0
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 0.0
    },
    {
      "name": "have_chain",
      "proof_status": "verified",
      "trace_tags": 6,
      "unique_states": 6,
      "matrix_size": 6,
      "rank": 5,
      "spectral_gap": -1.434362,
      "laplacian_zero_count": 6,
      "density": 0.138889,
      "eigenvalue_max": 0.900969,
      "symmetric_eigenvalues": [
        0.900969
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.236068
    },
    {
      "name": "induct_add_succ",
      "proof_status": "failed",
      "trace_tags": 3,
      "unique_states": 3,
      "matrix_size": 3,
      "rank": 2,
      "spectral_gap": -1.307107,
      "laplacian_zero_count": 3,
      "density": 0.222222,
      "eigenvalue_max": 0.666667,
      "symmetric_eigenvalues": [
        0.666667
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.414214
    },
    {
      "name": "induct_add_zero",
      "proof_status": "failed",
      "trace_tags": 3,
      "unique_states": 3,
      "matrix_size": 3,
      "rank": 2,
      "spectral_gap": -1.307107,
      "laplacian_zero_count": 3,
      "density": 0.222222,
      "eigenvalue_max": 0.666667,
      "symmetric_eigenvalues": [
        0.666667
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.414214
    },
    {
      "name": "induct_factorial",
      "proof_status": "verified",
      "trace_tags": 2,
      "unique_states": 2,
      "matrix_size": 2,
      "rank": 1,
      "spectral_gap": 0.05,
      "laplacian_zero_count": 2,
      "density": 0.25,
      "eigenvalue_max": 0.5,
      "symmetric_eigenvalues": [
        0.5
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.0
    },
    {
      "name": "induct_mul_zero",
      "proof_status": "failed",
      "trace_tags": 3,
      "unique_states": 3,
      "matrix_size": 3,
      "rank": 2,
      "spectral_gap": -1.307107,
      "laplacian_zero_count": 3,
      "density": 0.222222,
      "eigenvalue_max": 0.666667,
      "symmetric_eigenvalues": [
        0.666667
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.414214
    },
    {
      "name": "intro_all",
      "proof_status": "verified",
      "trace_tags": 8,
      "unique_states": 8,
      "matrix_size": 8,
      "rank": 7,
      "spectral_gap": -1.611768,
      "laplacian_zero_count": 8,
      "density": 0.109375,
      "eigenvalue_max": 0.939693,
      "symmetric_eigenvalues": [
        0.939693
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.645751
    },
    {
      "name": "intro_apply",
      "proof_status": "verified",
      "trace_tags": 8,
      "unique_states": 8,
      "matrix_size": 8,
      "rank": 7,
      "spectral_gap": -1.611768,
      "laplacian_zero_count": 8,
      "density": 0.109375,
      "eigenvalue_max": 0.939693,
      "symmetric_eigenvalues": [
        0.939693
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.645751
    },
    {
      "name": "omega_chain_ineq",
      "proof_status": "verified",
      "trace_tags": 2,
      "unique_states": 2,
      "matrix_size": 2,
      "rank": 1,
      "spectral_gap": 0.05,
      "laplacian_zero_count": 2,
      "density": 0.25,
      "eigenvalue_max": 0.5,
      "symmetric_eigenvalues": [
        0.5
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.0
    },
    {
      "name": "omega_chain_unsat",
      "proof_status": "failed",
      "trace_tags": 1,
      "unique_states": 1,
      "matrix_size": 1,
      "rank": 0,
      "spectral_gap": 0.0,
      "laplacian_zero_count": 1,
      "density": 0.0,
      "eigenvalue_max": 0.0,
      "symmetric_eigenvalues": [
        0.0
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 0.0
    },
    {
      "name": "omega_distrib",
      "proof_status": "failed",
      "trace_tags": 1,
      "unique_states": 1,
      "matrix_size": 1,
      "rank": 0,
      "spectral_gap": 0.0,
      "laplacian_zero_count": 1,
      "density": 0.0,
      "eigenvalue_max": 0.0,
      "symmetric_eigenvalues": [
        0.0
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 0.0
    },
    {
      "name": "omega_reorder_sum",
      "proof_status": "verified",
      "trace_tags": 2,
      "unique_states": 2,
      "matrix_size": 2,
      "rank": 1,
      "spectral_gap": 0.05,
      "laplacian_zero_count": 2,
      "density": 0.25,
      "eigenvalue_max": 0.5,
      "symmetric_eigenvalues": [
        0.5
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.0
    },
    {
      "name": "rw_chain_3step",
      "proof_status": "verified",
      "trace_tags": 6,
      "unique_states": 6,
      "matrix_size": 6,
      "rank": 5,
      "spectral_gap": -1.434362,
      "laplacian_zero_count": 6,
      "density": 0.138889,
      "eigenvalue_max": 0.900969,
      "symmetric_eigenvalues": [
        0.900969
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 2.236068
    },
    {
      "name": "rw_chain_eq",
      "proof_status": "verified",
      "trace_tags": 4,
      "unique_states": 4,
      "matrix_size": 4,
      "rank": 3,
      "spectral_gap": -1.037132,
      "laplacian_zero_count": 4,
      "density": 0.1875,
      "eigenvalue_max": 0.809017,
      "symmetric_eigenvalues": [
        0.809017
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.732051
    },
    {
      "name": "rw_chain_mixed",
      "proof_status": "verified",
      "trace_tags": 4,
      "unique_states": 4,
      "matrix_size": 4,
      "rank": 3,
      "spectral_gap": -1.037132,
      "laplacian_zero_count": 4,
      "density": 0.1875,
      "eigenvalue_max": 0.809017,
      "symmetric_eigenvalues": [
        0.809017
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.732051
    },
    {
      "name": "rw_then_omega",
      "proof_status": "failed",
      "trace_tags": 3,
      "unique_states": 3,
      "matrix_size": 3,
      "rank": 2,
      "spectral_gap": -1.307107,
      "laplacian_zero_count": 3,
      "density": 0.222222,
      "eigenvalue_max": 0.666667,
      "symmetric_eigenvalues": [
        0.666667
      ],
      "laplacian_eigenvalues": [
        0.0
      ],
      "frobenius_norm": 1.414214
    }
  ]
}