{
  "status": "PASS",
  "checks": 7987,
  "groups": {
    "valid_model_certificate": 3,
    "displayed_bound_values": 3,
    "base_period_bounds": 1,
    "anisotropic_period_bounds": 1,
    "period_bounds_remain_without_uniqueness": 1,
    "base_multiplier_exponent": 1,
    "anisotropic_multiplier_exponent": 1,
    "existence_does_not_silently_upgrade_to_uniqueness": 1,
    "rational_strict_multiplier_bound": 2,
    "reject_tampered_rational_bound": 5,
    "reject_unproved_uniqueness": 1,
    "reject_stale_period_after_model_change": 1,
    "reject_zero_radius": 1,
    "reject_extra_model_field": 1,
    "failure_of_chosen_annulus_is_not_nonexistence": 1,
    "symbolic_radial_numerator": 24,
    "symbolic_angular_numerator": 24,
    "symbolic_divergence": 24,
    "rational_circle_point": 600,
    "sampled_product_envelope": 600,
    "sampled_radial_identity": 1800,
    "sampled_angular_identity": 1800,
    "sampled_angular_envelope": 1800,
    "sampled_inner_envelope": 600,
    "sampled_outer_envelope": 600,
    "symbolic_punctured_Dulac_minus_two": 1,
    "annulus_two_boundary_flux_identity": 3,
    "symbolic_competition_weighted_divergence": 2,
    "positive_quadrant_sign_examples": 32,
    "plateau_C1_seam_values": 1,
    "nonpositive_but_zero_open_disk": 25,
    "outer_plateau_formula": 16,
    "explicit_nontrivial_periodic_circle": 4,
    "exact_omega_radial_square_identity": 6,
    "omega_radial_tolerance_time": 1
  },
  "certificates": [
    {
      "kappa": "0",
      "delta": "1/10",
      "omega": "1",
      "inner_radius": "3/4",
      "outer_radius": "5/4",
      "radial_inner_lower": "73/320",
      "radial_outer_upper": "-193/320",
      "angular_lower": "13/15",
      "angular_upper": "17/15",
      "divergence_upper": "-1/4",
      "existence": "CERTIFIED",
      "unique_cycle_and_all_annulus_distance_convergence": "CERTIFIED",
      "period_pi_coefficients": [
        "30/17",
        "30/13"
      ],
      "negative_log_multiplier_pi_coefficient": "15/34"
    },
    {
      "kappa": "1/8",
      "delta": "1/10",
      "omega": "1",
      "inner_radius": "3/4",
      "outer_radius": "5/4",
      "radial_inner_lower": "73/320",
      "radial_outer_upper": "-143/320",
      "angular_lower": "193/240",
      "angular_upper": "287/240",
      "divergence_upper": "-1/8",
      "existence": "CERTIFIED",
      "unique_cycle_and_all_annulus_distance_convergence": "CERTIFIED",
      "period_pi_coefficients": [
        "480/287",
        "480/193"
      ],
      "negative_log_multiplier_pi_coefficient": "60/287"
    },
    {
      "kappa": "1/3",
      "delta": "1/10",
      "omega": "1",
      "inner_radius": "3/4",
      "outer_radius": "5/4",
      "radial_inner_lower": "73/320",
      "radial_outer_upper": "-179/960",
      "angular_lower": "7/10",
      "angular_upper": "13/10",
      "divergence_upper": "1/12",
      "existence": "CERTIFIED",
      "unique_cycle_and_all_annulus_distance_convergence": "UNVERIFIED",
      "period_pi_coefficients": [
        "20/13",
        "20/7"
      ],
      "negative_log_multiplier_pi_coefficient": null
    }
  ],
  "strict_multiplier_rational_upper_bounds": [
    "1/3",
    "3/5",
    null
  ],
  "omega_squared_distance_tolerance": {
    "initial_radius": "3/4",
    "time": 4992,
    "distance": "1/100"
  },
  "scope": [
    "General existence uses compactness, uniqueness and the planar theorem proved in the pages.",
    "Sampled rational circle points check arithmetic only; global sine envelopes are analytic.",
    "Dulac exclusions require their domain and regularity hypotheses.",
    "UNVERIFIED declines the chosen certificate and is not a nonexistence statement."
  ]
}