{
  "status": "PASS",
  "assertions": 5983,
  "categories": {
    "DE_analytic_error_budget": 3,
    "DE_certificate_contains_closed_form": 3,
    "DE_finite_evaluation_width": 3,
    "DE_total_radius_under_tolerance": 3,
    "Gaussian_coarse_rational_tolerance": 2,
    "Gaussian_dual_signed_correction": 2,
    "Gaussian_shift_changes_correction_sign": 2,
    "Gaussian_two_scales_enclosures_overlap": 2,
    "Machin_tangent_identity": 1,
    "Poisson_kernel_exact_errors": 30,
    "e_coarse_bounds": 1,
    "exp_doubling_enclosures": 6,
    "exp_reciprocal_enclosures": 6,
    "identical_mesh_values_do_not_certify_integral": 6,
    "periodic_frequency_filter_labels": 3750,
    "periodic_minimal_N": 1,
    "pi_coarse_bounds": 1,
    "rational_square_root_enclosure": 1,
    "reject_false_even_symmetry_on_asymmetric_input": 1,
    "reject_unproved_DE_contract": 3,
    "reject_zero_denominator_interval": 1,
    "rounded_interval_arithmetic": 1250,
    "rounded_interval_division": 905
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    "N10_error": "2/1023",
    "N11_error": "2/2047",
    "half_shift_N11_error": "-2/2049"
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      "certified_radius_display": "1.0648137794966733235E-11",
      "finite_sum_width_display": "6.8011844099730746324E-190",
      "status": "CERTIFIED"
    },
    {
      "model": "x^2(1-x^2)^(-1/2)",
      "h": "1/12",
      "N": 48,
      "nodes": 97,
      "strip_half_width": "pi/6",
      "one_boundary_L1_bound": 512,
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      "integral_interval": [
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      "status": "CERTIFIED"
    },
    {
      "model": "1/((5-x)sqrt(1-x^2))",
      "h": "1/10",
      "N": 40,
      "nodes": 81,
      "strip_half_width": "pi/6",
      "one_boundary_L1_bound": 32,
      "finite_sum_interval": [
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      "discretization_bound": "13177032454057536/1237940039285174383767029575",
      "tail_bound": "4953122964800970993/5192296858534827628530496329220096",
      "integral_interval": [
        "1462889359789449981691854497969393058044913285745429170299679515098340248969063247830098074103830120909458837414238287626191346492001413293262098069476197767996646704359055887239481355295143421/2281220308811097609320585802850145662446614253624279965289596258949637583604338693252956405658685699889321154786797203655344352360687718999126330659861107094125997337180132475041437096123301888",
        "1462889359838018421229864143989011129717296370723458173843780545003054923324119710569081010476994872570802967046702706105564015537232262251780879073917074247356528333266777657064597171184350267/2281220308811097609320585802850145662446614253624279965289596258949637583604338693252956405658685699889321154786797203655344352360687718999126330659861107094125997337180132475041437096123301888"
      ],
      "midpoint_display": "0.64127491508093204776145349923368022873001721095295",
      "certified_radius_display": "1.0645275984615890553E-11",
      "finite_sum_width_display": "2.0076973636916971844E-190",
      "status": "CERTIFIED"
    }
  ],
  "scope": "Fraction interval endpoints certify the three stated models using the proved analytic constants. Decimal strings are display only; finite tests do not certify arbitrary functions."
}