{
  "schema": "AN02-entire-logarithm-example-checks154/v1",
  "status": "PASS",
  "quadrature_count": 41,
  "checks": [
    {
      "name": "actual polynomial angular error N=1, r=0.25",
      "actual": 0.6931471805599454,
      "expected": 0.6931471805599453,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 2.417606215558525e-14,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=1, r=0.75",
      "actual": 0.6931471805599452,
      "expected": 0.6931471805599453,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 2.4176064235379843e-14,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=1, r=0.99",
      "actual": 0.6931471805599454,
      "expected": 0.6931471805599453,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 6.089639509301546e-13,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=1, r=1.01",
      "actual": 0.6931471805599452,
      "expected": 0.6931471805599453,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 7.834540359191934e-13,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=1, r=1.5",
      "actual": 0.6931471805599452,
      "expected": 0.6931471805599453,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 6.777888817770474e-13,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=1, r=2",
      "actual": 0.6931471805599454,
      "expected": 0.6931471805599453,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 1.9367815682937263e-12,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "physical polar disk error N=1, R=2",
      "actual": 8.710344361214407,
      "expected": 8.710344361214409,
      "relative_error": 2.0393646516549297e-16,
      "tolerance": 2e-08,
      "passed": true,
      "details": {
        "actual_polynomial_evaluated_in_nested_quadrature": true,
        "split_radial_singular_circle": 1,
        "proof_locator": "GD33"
      }
    },
    {
      "name": "actual polynomial angular error N=3, r=0.25",
      "actual": 0.23104906018664848,
      "expected": 0.23104906018664842,
      "relative_error": 2.4025698778611885e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 8.058687385195115e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=3, r=0.75",
      "actual": 0.23104906018664842,
      "expected": 0.23104906018664842,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 2.2044241628919968e-13,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=3, r=0.99",
      "actual": 0.23104906018664842,
      "expected": 0.23104906018664842,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 8.062570909141667e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=3, r=1.01",
      "actual": 0.23104906018664848,
      "expected": 0.23104906018664842,
      "relative_error": 2.4025698778611885e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 8.185607159995888e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=3, r=1.5",
      "actual": 0.23104906018664842,
      "expected": 0.23104906018664842,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 8.058687385200738e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=3, r=2",
      "actual": 0.23104906018664842,
      "expected": 0.23104906018664842,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 8.058687385195113e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "physical polar disk error N=3, R=2",
      "actual": 2.9034481204048026,
      "expected": 2.903448120404803,
      "relative_error": 1.5295234887411972e-16,
      "tolerance": 2e-08,
      "passed": true,
      "details": {
        "actual_polynomial_evaluated_in_nested_quadrature": true,
        "split_radial_singular_circle": 1,
        "proof_locator": "GD33"
      }
    },
    {
      "name": "actual polynomial angular error N=13, r=0.25",
      "actual": 0.05331901388922656,
      "expected": 0.05331901388922656,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 1.8596970888911802e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=13, r=0.75",
      "actual": 0.053319013889226545,
      "expected": 0.05331901388922656,
      "relative_error": 2.602784034349621e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 1.85969708889118e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=13, r=0.99",
      "actual": 0.05331901388922657,
      "expected": 0.05331901388922656,
      "relative_error": 2.602784034349621e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 1.859714585925332e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=13, r=1.01",
      "actual": 0.05331901388922656,
      "expected": 0.05331901388922656,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 1.859658724563872e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=13, r=1.5",
      "actual": 0.053319013889226545,
      "expected": 0.05331901388922656,
      "relative_error": 2.602784034349621e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 1.85969708889118e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=13, r=2",
      "actual": 0.053319013889226545,
      "expected": 0.05331901388922656,
      "relative_error": 2.602784034349621e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 1.85969708889118e-15,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "physical polar disk error N=13, R=2",
      "actual": 0.6700264893241852,
      "expected": 0.6700264893241853,
      "relative_error": 1.6569837794696305e-16,
      "tolerance": 2e-08,
      "passed": true,
      "details": {
        "actual_polynomial_evaluated_in_nested_quadrature": true,
        "split_radial_singular_circle": 1,
        "proof_locator": "GD33"
      }
    },
    {
      "name": "actual polynomial angular error N=32, r=0.25",
      "actual": 0.021660849392498294,
      "expected": 0.02166084939249829,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 7.55501942362042e-16,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=32, r=0.75",
      "actual": 0.021660849392498294,
      "expected": 0.02166084939249829,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 7.55501942362042e-16,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=32, r=0.99",
      "actual": 0.021660849392498287,
      "expected": 0.02166084939249829,
      "relative_error": 1.6017132519074588e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 5.932193739667248e-13,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=32, r=1.01",
      "actual": 0.021660849392498304,
      "expected": 0.02166084939249829,
      "relative_error": 6.406853007629835e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 7.696702208698036e-13,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=32, r=1.5",
      "actual": 0.021660849392498273,
      "expected": 0.02166084939249829,
      "relative_error": 8.008566259537295e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 7.555019423620414e-16,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "actual polynomial angular error N=32, r=2",
      "actual": 0.021660849392498256,
      "expected": 0.02166084939249829,
      "relative_error": 1.601713251907459e-15,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "periodicity_reduction": "t=N*theta; one complete period repeated N times",
        "quadrature_error": 7.555019423620407e-16,
        "proof_locator": "GD32"
      }
    },
    {
      "name": "physical polar disk error N=32, R=2",
      "actual": 0.2721982612879501,
      "expected": 0.27219826128795027,
      "relative_error": 6.11809395496479e-16,
      "tolerance": 2e-08,
      "passed": true,
      "details": {
        "actual_polynomial_evaluated_in_nested_quadrature": true,
        "split_radial_singular_circle": 1,
        "proof_locator": "GD33"
      }
    },
    {
      "name": "two-seed weighted error, N=8",
      "actual": 6.683562225603598,
      "expected": 6.683562225603598,
      "relative_error": 0.0,
      "tolerance": 3e-09,
      "passed": true,
      "details": {
        "actual_complex_seed_polynomial_and_cutoff_coefficient_evaluated": true,
        "rescaling_exponent": 0.1111111111111111,
        "two_disjoint_centers": [
          -0.5,
          0.5
        ],
        "proof_locator": "L147.15"
      }
    },
    {
      "name": "two-seed weighted error, N=32",
      "actual": 4.391801595010659,
      "expected": 4.391801595010657,
      "relative_error": 4.044711039356367e-16,
      "tolerance": 3e-09,
      "passed": true,
      "details": {
        "actual_complex_seed_polynomial_and_cutoff_coefficient_evaluated": true,
        "rescaling_exponent": 0.4444444444444444,
        "two_disjoint_centers": [
          -0.5,
          0.5
        ],
        "proof_locator": "L147.15"
      }
    },
    {
      "name": "two-seed weighted error, N=128",
      "actual": 0.9778968648291271,
      "expected": 0.9778968648291271,
      "relative_error": 0.0,
      "tolerance": 3e-09,
      "passed": true,
      "details": {
        "actual_complex_seed_polynomial_and_cutoff_coefficient_evaluated": true,
        "rescaling_exponent": 1.7777777777777777,
        "two_disjoint_centers": [
          -0.5,
          0.5
        ],
        "proof_locator": "L147.15"
      }
    },
    {
      "name": "two-seed weighted error, N=512",
      "actual": 0.01439044549995347,
      "expected": 0.014390445499953438,
      "relative_error": 2.169844051574606e-15,
      "tolerance": 3e-09,
      "passed": true,
      "details": {
        "actual_complex_seed_polynomial_and_cutoff_coefficient_evaluated": true,
        "rescaling_exponent": 7.111111111111111,
        "two_disjoint_centers": [
          -0.5,
          0.5
        ],
        "proof_locator": "L147.15"
      }
    },
    {
      "name": "two-seed weighted error, N=2048",
      "actual": 1.0258771760879618e-06,
      "expected": 1.0258771760879663e-06,
      "relative_error": 4.334751836513969e-15,
      "tolerance": 3e-09,
      "passed": true,
      "details": {
        "actual_complex_seed_polynomial_and_cutoff_coefficient_evaluated": true,
        "rescaling_exponent": 28.444444444444443,
        "two_disjoint_centers": [
          -0.5,
          0.5
        ],
        "proof_locator": "L147.15"
      }
    },
    {
      "name": "local complex-gradient kernel L1 norm, real dimension=2",
      "actual": 0.5,
      "expected": 0.5,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "point-estimate-bounded-data-factor": 2.0,
        "proof_locator": "GD11\u2013GD12"
      }
    },
    {
      "name": "local complex-gradient kernel L1 norm, real dimension=4",
      "actual": 0.5,
      "expected": 0.5,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "point-estimate-bounded-data-factor": 2.0,
        "proof_locator": "GD11\u2013GD12"
      }
    },
    {
      "name": "local complex-gradient kernel L1 norm, real dimension=6",
      "actual": 0.5,
      "expected": 0.5,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "point-estimate-bounded-data-factor": 2.0,
        "proof_locator": "GD11\u2013GD12"
      }
    },
    {
      "name": "actual shrinking bump square norm, epsilon=0.5",
      "actual": 0.21782449922354785,
      "expected": 0.21782449922354785,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "point_value": 1,
        "data_supremum_scales_as": "epsilon^(-1)",
        "proof_locator": "L147.12"
      }
    },
    {
      "name": "actual shrinking bump square norm, epsilon=0.25",
      "actual": 0.05445612480588696,
      "expected": 0.05445612480588696,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "point_value": 1,
        "data_supremum_scales_as": "epsilon^(-1)",
        "proof_locator": "L147.12"
      }
    },
    {
      "name": "actual shrinking bump square norm, epsilon=0.125",
      "actual": 0.01361403120147174,
      "expected": 0.01361403120147174,
      "relative_error": 0.0,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "point_value": 1,
        "data_supremum_scales_as": "epsilon^(-1)",
        "proof_locator": "L147.12"
      }
    },
    {
      "name": "affine antiholomorphic physical L2 norm ((1+2j), (0.5-0.75j), 0.75)",
      "actual": 9.239549780632188,
      "expected": 9.23954978063219,
      "relative_error": 1.9225577886098128e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "cross_term_removed_by_actual_angular_integration": true,
        "proof_locator": "L147.11"
      }
    },
    {
      "name": "affine antiholomorphic physical L2 norm ((-2+0.25j), (1+1j), 0.5)",
      "actual": 3.3870295796514958,
      "expected": 3.3870295796514953,
      "relative_error": 1.3111465353537205e-16,
      "tolerance": 2e-09,
      "passed": true,
      "details": {
        "cross_term_removed_by_actual_angular_integration": true,
        "proof_locator": "L147.11"
      }
    }
  ],
  "disk_error_samples": [
    {
      "N": 1,
      "R": 2,
      "actual_error": 8.710344361214407,
      "exact_error": 8.710344361214409
    },
    {
      "N": 3,
      "R": 2,
      "actual_error": 2.9034481204048026,
      "exact_error": 2.903448120404803
    },
    {
      "N": 13,
      "R": 2,
      "actual_error": 0.6700264893241852,
      "exact_error": 0.6700264893241853
    },
    {
      "N": 32,
      "R": 2,
      "actual_error": 0.2721982612879501,
      "exact_error": 0.27219826128795027
    }
  ],
  "weighted_error_samples": [
    {
      "N": 8,
      "weighted_error_squared_norm": 5.980714255845453,
      "guaranteed_correction_squared_norm_bound": 0.3737946409903408,
      "actual_correction_values_or_attained_norm_claimed": false
    },
    {
      "N": 32,
      "weighted_error_squared_norm": 2.8159370525962273,
      "guaranteed_correction_squared_norm_bound": 0.04399901644681605,
      "actual_correction_values_or_attained_norm_claimed": false
    },
    {
      "N": 128,
      "weighted_error_squared_norm": 0.16527759124996844,
      "guaranteed_correction_squared_norm_bound": 0.0006456155908201892,
      "actual_correction_values_or_attained_norm_claimed": false
    },
    {
      "N": 512,
      "weighted_error_squared_norm": 1.1742428469230745e-05,
      "guaranteed_correction_squared_norm_bound": 1.1467215301983149e-08,
      "actual_correction_values_or_attained_norm_claimed": false
    },
    {
      "N": 2048,
      "weighted_error_squared_norm": 4.548101042934248e-19,
      "guaranteed_correction_squared_norm_bound": 1.1103762311851192e-22,
      "actual_correction_values_or_attained_norm_claimed": false
    }
  ],
  "exact_geometric_cutoff_radii": {
    "inner": 0.08333333333333333,
    "outer": 0.16666666666666666,
    "center_ball_radius": 0.25
  },
  "quadratures_replace_density_lemma_or_global_existence_proofs": false,
  "weighted_correction_was_numerically_solved_or_norm_attained": false,
  "whole_course_complete": false
}