{
  "status": "PASS",
  "scope": "Finite checks of explicit models; not a replacement for the proofs.",
  "assertions": 14508,
  "groups": {
    "exact_cylinder": 7421,
    "exact_capstone": 10,
    "exact_missing_point": 1200,
    "exact_index": 2160,
    "exact_paraboloid": 204,
    "exact_projective": 552,
    "float_sphere": 2816,
    "float_capstone": 2,
    "float_integrals": 135,
    "input_validation": 8
  },
  "exact_models": {
    "cylinder_cases": 2460,
    "index_cases": 720,
    "cylinder_main": {
      "distance_squared": "25",
      "lift_indices": [
        -1,
        0
      ],
      "next_squared": "97"
    },
    "cylinder_perturbed": {
      "distance_squared": "20",
      "lift_indices": [
        0
      ],
      "next_squared": "32"
    },
    "negative_index_coefficient_of_pi": "-15/8",
    "sharp_length_coefficient_of_pi": "2/3",
    "punctured_plane_infimum": "2; not attained (geometric equality proof in text)",
    "projective_fiber_size": 2,
    "paraboloid_witnesses": [
      {
        "k": "1/11",
        "radius": 2,
        "curvature": "4/289"
      },
      {
        "k": "2/11",
        "radius": 2,
        "curvature": "4/289"
      },
      {
        "k": "3/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "4/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "5/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "6/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "7/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "8/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "9/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "10/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "1",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "12/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "13/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "14/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "15/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "16/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "17/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "18/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "19/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "20/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "21/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "2",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "23/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "24/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "25/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "26/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "27/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "28/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "29/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "30/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "31/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "32/11",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "3",
        "radius": 1,
        "curvature": "4/25"
      },
      {
        "k": "1/10",
        "radius": 2,
        "curvature": "4/289"
      },
      {
        "k": "1/100",
        "radius": 4,
        "curvature": "4/4225"
      },
      {
        "k": "1/1000",
        "radius": 4,
        "curvature": "4/4225"
      },
      {
        "k": "1/10000",
        "radius": 8,
        "curvature": "4/66049"
      },
      {
        "k": "1/100000",
        "radius": 16,
        "curvature": "4/1050625"
      },
      {
        "k": "1/1000000",
        "radius": 32,
        "curvature": "4/16785409"
      },
      {
        "k": "1/10000000",
        "radius": 64,
        "curvature": "4/268468225"
      },
      {
        "k": "1/100000000",
        "radius": 128,
        "curvature": "4/4295098369"
      },
      {
        "k": "1/1000000000",
        "radius": 128,
        "curvature": "4/4295098369"
      },
      {
        "k": "1/10000000000",
        "radius": 256,
        "curvature": "4/68720001025"
      },
      {
        "k": "1/100000000000",
        "radius": 512,
        "curvature": "4/1099513724929"
      },
      {
        "k": "1/1000000000000",
        "radius": 1024,
        "curvature": "4/17592194433025"
      },
      {
        "k": "1/10000000000000",
        "radius": 2048,
        "curvature": "4/281475010265089"
      },
      {
        "k": "1/100000000000000",
        "radius": 4096,
        "curvature": "4/4503599761588225"
      },
      {
        "k": "1/1000000000000000",
        "radius": 4096,
        "curvature": "4/4503599761588225"
      },
      {
        "k": "1/10000000000000000",
        "radius": 8192,
        "curvature": "4/72057594574798849"
      },
      {
        "k": "1/100000000000000000",
        "radius": 16384,
        "curvature": "4/1152921506754330625"
      },
      {
        "k": "1/1000000000000000000",
        "radius": 32768,
        "curvature": "4/18446744082299486209"
      },
      {
        "k": "1/10000000000000000000",
        "radius": 65536,
        "curvature": "4/295147905213712564225"
      },
      {
        "k": "1/100000000000000000000",
        "radius": 131072,
        "curvature": "4/4722366483007084167169"
      },
      {
        "k": "1/1000000000000000000000",
        "radius": 131072,
        "curvature": "4/4722366483007084167169"
      },
      {
        "k": "1/10000000000000000000000",
        "radius": 262144,
        "curvature": "4/75557863726464079233025"
      },
      {
        "k": "1/100000000000000000000000",
        "radius": 524288,
        "curvature": "4/1208925819616828197961729"
      },
      {
        "k": "1/1000000000000000000000000",
        "radius": 1048576,
        "curvature": "4/19342813113842862888321025"
      }
    ]
  },
  "floating_diagnostics": {
    "sphere_vector_cases": 512,
    "max_gauss_absolute_error": "1.421e-14",
    "max_central_difference_absolute_error": "1.290e-09",
    "max_integral_absolute_error": "7.105e-15",
    "projective_sample_distance": "0.927295218002",
    "note": "Tolerance diagnostics only; exact identities and global conclusions are proved in the text."
  }
}