{
  "status": "PASS",
  "assertions": 38464,
  "groups": {
    "transport_polynomial_identity": 1,
    "transport_residual": 860,
    "transport_inverse_label": 860,
    "transport_capstone": 1,
    "hamilton_energy": 961,
    "hamilton_action_derivative": 961,
    "hamilton_label_gradient": 961,
    "hamilton_PDE": 930,
    "projection_collapse": 31,
    "all_minimizer_displacement": 1950,
    "initial_uniform_bound": 1950,
    "minimizer_value": 1964,
    "competitor_lower_bound": 17550,
    "spatial_Lipschitz": 1950,
    "temporal_Lipschitz": 1950,
    "two_leg_cost": 1382,
    "exact_semigroup": 1382,
    "constant_shift_contraction": 510,
    "absolute_value_envelopes": 390,
    "all_absolute_value_labels": 390,
    "positive_envelope_PDE": 390,
    "downward_cusp_subtest": 61,
    "eikonal_upper_test": 61,
    "upward_HJ_cusp_rejected": 1,
    "negative_tent_rejected": 1,
    "positive_join_derivatives": 6,
    "nearest_boundary_direction": 270,
    "square_upper_contact_norm": 720,
    "residual_error_capstone": 1,
    "strict_eikonal_gap": 19
  },
  "capstone": {
    "transport_at_log2_x2": {
      "u": "5/4",
      "ut": "-1",
      "ux": "7/8"
    },
    "Hamilton_3_4_5": {
      "X": "3",
      "P": "-4",
      "U": "-6",
      "ut": "-25/2",
      "H": "25/2"
    },
    "envelopes_at_t_half": [
      {
        "x": "0",
        "plus": "0",
        "plus_labels": [
          "0"
        ],
        "minus": "-1/4",
        "minus_labels": [
          "-1/2",
          "1/2"
        ]
      },
      {
        "x": "1/4",
        "plus": "1/16",
        "plus_labels": [
          "0"
        ],
        "minus": "-1/2",
        "minus_labels": [
          "3/4"
        ]
      },
      {
        "x": "1",
        "plus": "3/4",
        "plus_labels": [
          "1/2"
        ],
        "minus": "-5/4",
        "minus_labels": [
          "3/2"
        ]
      }
    ],
    "uniform_error_at_T3": "1/40"
  },
  "limits": [
    "Finite exact tests do not replace the comparison and existence proofs.",
    "The residual error certificate is conditional on a verified global residual bound."
  ]
}