{
  "status": "PASS",
  "checks": 15931,
  "groups": {
    "central_risk_exactly_two": 6,
    "certificate_weighted_equality": 504,
    "certified_grid_global_comparison": 64,
    "continuous_domain_derivative_rejects_grid": 1,
    "directional_upper_certificate": 2016,
    "em_exact_likelihood_monotonicity": 504,
    "em_fixed_point_not_global": 1,
    "em_preserves_zero_weights": 504,
    "em_probability_simplex": 504,
    "even_dimension_integral_recurrence": 24,
    "family_risk_sign_boundary": 324,
    "frozen_derivative_underestimates_risk_by_one": 121,
    "invalid_partition_rejected": 1,
    "joint_scale_equivariance": 540,
    "likelihood_tangent_amgm_check": 2016,
    "one_extra_midpoint_still_passes": 1,
    "positive_inverse_moment_bracket": 54,
    "posterior_mean_support": 1960,
    "posterior_pairwise_variance": 1960,
    "preserved_subspace_translation": 180,
    "projection_orthogonality": 180,
    "refit_no_uniform_dominance": 121,
    "refit_risk_equals_correct_sure": 121,
    "refit_sampling_covariance": 1,
    "residual_dimension_rejected": 1,
    "residual_zero_group_sums": 180,
    "risk_bracket_width": 54,
    "singular_inverse_moment_rejected": 1,
    "strict_joint_risk_dominance": 54,
    "symmetric_grid_optimum": 1,
    "terminal_asymmetric_grid_certificate": 1,
    "terminal_continuous_domain_violation": 1,
    "terminal_grid_posterior": 1,
    "terminal_residual_dimension_coefficient": 1,
    "terminal_three_point_positive": 1,
    "terminal_three_point_zero": 1,
    "terminal_two_group_output": 1,
    "too_narrow_density_negative_variance": 1,
    "tweedie_first_derivative_identity": 1960,
    "tweedie_second_derivative_identity": 1960,
    "unnormalized_mixing_weights_rejected": 1,
    "wrong_full_dimension_has_zero_risk_gain": 1,
    "zero_prior_mass_rejected": 1,
    "zero_variance_rejected": 1
  },
  "exact_em_candidates": 504,
  "certified_five_dimensional_risks": [
    {
      "lambda": "0",
      "risk_sigma_squared_units": [
        "2.0000000000000000",
        "2.0000000000000000"
      ]
    },
    {
      "lambda": "1/2",
      "risk_sigma_squared_units": [
        "2.2797098060728026",
        "2.2797098060728027"
      ]
    },
    {
      "lambda": "1",
      "risk_sigma_squared_units": [
        "2.5230061310636869",
        "2.5230061310636870"
      ]
    },
    {
      "lambda": "2",
      "risk_sigma_squared_units": [
        "2.9213577811074578",
        "2.9213577811074579"
      ]
    },
    {
      "lambda": "4",
      "risk_sigma_squared_units": [
        "3.4699865838860850",
        "3.4699865838860851"
      ]
    },
    {
      "lambda": "9",
      "risk_sigma_squared_units": [
        "4.1310556263889566",
        "4.1310556263889567"
      ]
    },
    {
      "lambda": "16",
      "risk_sigma_squared_units": [
        "4.4755244790987596",
        "4.4755244790987597"
      ]
    },
    {
      "lambda": "25",
      "risk_sigma_squared_units": [
        "4.6550656945180742",
        "4.6550656945180743"
      ]
    },
    {
      "lambda": "36",
      "risk_sigma_squared_units": [
        "4.7571562521134936",
        "4.7571562521134937"
      ]
    }
  ],
  "terminal1_output": [
    "5/2",
    "3/2",
    "2",
    "-1/2",
    "1/2",
    "0"
  ],
  "terminal2_positive_posterior": [
    "1/33",
    "16/33",
    "16/33"
  ],
  "terminal2_mean_in_a_units": "5/11",
  "terminal2_variance_in_a_squared_units": "112/363",
  "terminal3_weights": [
    "31/45",
    "0",
    "14/45"
  ],
  "terminal3_certificate": [
    "3",
    "48/17",
    "3"
  ],
  "terminal4_covariance": [
    [
      "5/8",
      "3/8"
    ],
    [
      "3/8",
      "5/8"
    ]
  ],
  "scope": "Exact finite rational kernel, posterior, projection and likelihood checks; certified inverse-moment series bounds; not an arbitrary-prior risk theorem or a continuous-domain optimizer."
}