{
  "schema": "eligible-kernel-finite-checks/v1",
  "scope": "finite algebra only",
  "count": 20,
  "all_passed": true,
  "checks": [
    {
      "name": "exact_unit_features",
      "passed": true,
      "detail": "v0=(1,0), v1=(3/5,4/5), v2=(0,1)"
    },
    {
      "name": "exact_midpoint_norm",
      "passed": true,
      "detail": "||V||^2=4/5"
    },
    {
      "name": "nonnegative_gram_normalization",
      "passed": true,
      "detail": "sum of squared midpoint weights = 1/2"
    },
    {
      "name": "normalized_feature_coordinates",
      "passed": true,
      "detail": "W=(2/sqrt(5),1/sqrt(5)); floating rendering only"
    },
    {
      "name": "rational_feature_gram_psd",
      "passed": true,
      "detail": "all 7 principal minors nonnegative, checked exactly"
    },
    {
      "name": "cnd_1_-1_0",
      "passed": true,
      "detail": "zero-sum CND identity, exact rational arithmetic"
    },
    {
      "name": "cnd_2_-1_-1",
      "passed": true,
      "detail": "zero-sum CND identity, exact rational arithmetic"
    },
    {
      "name": "cnd_3_-5_2",
      "passed": true,
      "detail": "zero-sum CND identity, exact rational arithmetic"
    },
    {
      "name": "invariant_weighted_gram_sample",
      "passed": true,
      "detail": "weights 1/3 and 2/3"
    },
    {
      "name": "nonabelian_common_source_cancellation",
      "passed": true,
      "detail": "36 reduced free-group word checks; inverse factors retain their order"
    },
    {
      "name": "right_coset_direction",
      "passed": true,
      "detail": "all 36 ordered pairs in S3, with right cosets Hc"
    },
    {
      "name": "orthogonal_coset_extension_psd",
      "passed": true,
      "detail": "all 63 principal minors of the six-label rational Gram matrix"
    },
    {
      "name": "upper_normalization_bound_sample",
      "passed": true,
      "detail": "25 convex pairs; epsilon=2/2501; bound=8epsilon"
    },
    {
      "name": "lower_normalization_constant",
      "passed": true,
      "detail": "eta=1/(2M), normalization at most M, for M=1,...,8"
    },
    {
      "name": "lower_series_R_0",
      "passed": true,
      "detail": "N=2ceil(R)+1, each of the first N defects at least 1/2"
    },
    {
      "name": "lower_series_R_1_2",
      "passed": true,
      "detail": "N=2ceil(R)+1, each of the first N defects at least 1/2"
    },
    {
      "name": "lower_series_R_3_2",
      "passed": true,
      "detail": "N=2ceil(R)+1, each of the first N defects at least 1/2"
    },
    {
      "name": "lower_series_R_2",
      "passed": true,
      "detail": "N=2ceil(R)+1, each of the first N defects at least 1/2"
    },
    {
      "name": "lower_series_R_7_3",
      "passed": true,
      "detail": "N=2ceil(R)+1, each of the first N defects at least 1/2"
    },
    {
      "name": "probability_average_witness",
      "passed": true,
      "detail": "three exact finite-probability examples; not a replacement for compact Haar proof"
    }
  ]
}