{
  "scope": "Exact differential, count and weighted-form tests; conditional prescribed material ball, no self-support or causal claim.",
  "checks": 1254,
  "source_sha256": "b5d183ad185ebcfa99cb709f416534848f2a1d2dd48bbf611cf327a92e7722e9",
  "cases": [
    {
      "depth": 2,
      "squared_clock_polynomial": "(z + 2)**2/4",
      "spatial_derivative_order": 4,
      "examples": [
        {
          "angular_degree": 0,
          "radial_degree": 0,
          "total_degree": 0,
          "frequency_multiplier": 1
        },
        {
          "angular_degree": 0,
          "radial_degree": 1,
          "total_degree": 2,
          "frequency_multiplier": 6
        },
        {
          "angular_degree": 0,
          "radial_degree": 2,
          "total_degree": 4,
          "frequency_multiplier": 15
        },
        {
          "angular_degree": 0,
          "radial_degree": 3,
          "total_degree": 6,
          "frequency_multiplier": 28
        },
        {
          "angular_degree": 1,
          "radial_degree": 0,
          "total_degree": 1,
          "frequency_multiplier": 3
        },
        {
          "angular_degree": 1,
          "radial_degree": 1,
          "total_degree": 3,
          "frequency_multiplier": 10
        },
        {
          "angular_degree": 1,
          "radial_degree": 2,
          "total_degree": 5,
          "frequency_multiplier": 21
        },
        {
          "angular_degree": 1,
          "radial_degree": 3,
          "total_degree": 7,
          "frequency_multiplier": 36
        },
        {
          "angular_degree": 2,
          "radial_degree": 0,
          "total_degree": 2,
          "frequency_multiplier": 6
        },
        {
          "angular_degree": 2,
          "radial_degree": 1,
          "total_degree": 4,
          "frequency_multiplier": 15
        },
        {
          "angular_degree": 2,
          "radial_degree": 2,
          "total_degree": 6,
          "frequency_multiplier": 28
        },
        {
          "angular_degree": 2,
          "radial_degree": 3,
          "total_degree": 8,
          "frequency_multiplier": 45
        },
        {
          "angular_degree": 3,
          "radial_degree": 0,
          "total_degree": 3,
          "frequency_multiplier": 10
        },
        {
          "angular_degree": 3,
          "radial_degree": 1,
          "total_degree": 5,
          "frequency_multiplier": 21
        },
        {
          "angular_degree": 3,
          "radial_degree": 2,
          "total_degree": 7,
          "frequency_multiplier": 36
        },
        {
          "angular_degree": 3,
          "radial_degree": 3,
          "total_degree": 9,
          "frequency_multiplier": 55
        },
        {
          "angular_degree": 4,
          "radial_degree": 0,
          "total_degree": 4,
          "frequency_multiplier": 15
        },
        {
          "angular_degree": 4,
          "radial_degree": 1,
          "total_degree": 6,
          "frequency_multiplier": 28
        },
        {
          "angular_degree": 4,
          "radial_degree": 2,
          "total_degree": 8,
          "frequency_multiplier": 45
        },
        {
          "angular_degree": 4,
          "radial_degree": 3,
          "total_degree": 10,
          "frequency_multiplier": 66
        }
      ]
    },
    {
      "depth": 3,
      "squared_clock_polynomial": "(z + 3)**2*(z + 4)/36",
      "spatial_derivative_order": 6,
      "examples": [
        {
          "angular_degree": 0,
          "radial_degree": 0,
          "total_degree": 0,
          "frequency_multiplier": 1
        },
        {
          "angular_degree": 0,
          "radial_degree": 1,
          "total_degree": 2,
          "frequency_multiplier": 10
        },
        {
          "angular_degree": 0,
          "radial_degree": 2,
          "total_degree": 4,
          "frequency_multiplier": 35
        },
        {
          "angular_degree": 0,
          "radial_degree": 3,
          "total_degree": 6,
          "frequency_multiplier": 84
        },
        {
          "angular_degree": 1,
          "radial_degree": 0,
          "total_degree": 1,
          "frequency_multiplier": 4
        },
        {
          "angular_degree": 1,
          "radial_degree": 1,
          "total_degree": 3,
          "frequency_multiplier": 20
        },
        {
          "angular_degree": 1,
          "radial_degree": 2,
          "total_degree": 5,
          "frequency_multiplier": 56
        },
        {
          "angular_degree": 1,
          "radial_degree": 3,
          "total_degree": 7,
          "frequency_multiplier": 120
        },
        {
          "angular_degree": 2,
          "radial_degree": 0,
          "total_degree": 2,
          "frequency_multiplier": 10
        },
        {
          "angular_degree": 2,
          "radial_degree": 1,
          "total_degree": 4,
          "frequency_multiplier": 35
        },
        {
          "angular_degree": 2,
          "radial_degree": 2,
          "total_degree": 6,
          "frequency_multiplier": 84
        },
        {
          "angular_degree": 2,
          "radial_degree": 3,
          "total_degree": 8,
          "frequency_multiplier": 165
        },
        {
          "angular_degree": 3,
          "radial_degree": 0,
          "total_degree": 3,
          "frequency_multiplier": 20
        },
        {
          "angular_degree": 3,
          "radial_degree": 1,
          "total_degree": 5,
          "frequency_multiplier": 56
        },
        {
          "angular_degree": 3,
          "radial_degree": 2,
          "total_degree": 7,
          "frequency_multiplier": 120
        },
        {
          "angular_degree": 3,
          "radial_degree": 3,
          "total_degree": 9,
          "frequency_multiplier": 220
        },
        {
          "angular_degree": 4,
          "radial_degree": 0,
          "total_degree": 4,
          "frequency_multiplier": 35
        },
        {
          "angular_degree": 4,
          "radial_degree": 1,
          "total_degree": 6,
          "frequency_multiplier": 84
        },
        {
          "angular_degree": 4,
          "radial_degree": 2,
          "total_degree": 8,
          "frequency_multiplier": 165
        },
        {
          "angular_degree": 4,
          "radial_degree": 3,
          "total_degree": 10,
          "frequency_multiplier": 286
        }
      ]
    },
    {
      "depth": 4,
      "squared_clock_polynomial": "(z + 4)**2*(z + 6)**2/576",
      "spatial_derivative_order": 8,
      "examples": [
        {
          "angular_degree": 0,
          "radial_degree": 0,
          "total_degree": 0,
          "frequency_multiplier": 1
        },
        {
          "angular_degree": 0,
          "radial_degree": 1,
          "total_degree": 2,
          "frequency_multiplier": 15
        },
        {
          "angular_degree": 0,
          "radial_degree": 2,
          "total_degree": 4,
          "frequency_multiplier": 70
        },
        {
          "angular_degree": 0,
          "radial_degree": 3,
          "total_degree": 6,
          "frequency_multiplier": 210
        },
        {
          "angular_degree": 1,
          "radial_degree": 0,
          "total_degree": 1,
          "frequency_multiplier": 5
        },
        {
          "angular_degree": 1,
          "radial_degree": 1,
          "total_degree": 3,
          "frequency_multiplier": 35
        },
        {
          "angular_degree": 1,
          "radial_degree": 2,
          "total_degree": 5,
          "frequency_multiplier": 126
        },
        {
          "angular_degree": 1,
          "radial_degree": 3,
          "total_degree": 7,
          "frequency_multiplier": 330
        },
        {
          "angular_degree": 2,
          "radial_degree": 0,
          "total_degree": 2,
          "frequency_multiplier": 15
        },
        {
          "angular_degree": 2,
          "radial_degree": 1,
          "total_degree": 4,
          "frequency_multiplier": 70
        },
        {
          "angular_degree": 2,
          "radial_degree": 2,
          "total_degree": 6,
          "frequency_multiplier": 210
        },
        {
          "angular_degree": 2,
          "radial_degree": 3,
          "total_degree": 8,
          "frequency_multiplier": 495
        },
        {
          "angular_degree": 3,
          "radial_degree": 0,
          "total_degree": 3,
          "frequency_multiplier": 35
        },
        {
          "angular_degree": 3,
          "radial_degree": 1,
          "total_degree": 5,
          "frequency_multiplier": 126
        },
        {
          "angular_degree": 3,
          "radial_degree": 2,
          "total_degree": 7,
          "frequency_multiplier": 330
        },
        {
          "angular_degree": 3,
          "radial_degree": 3,
          "total_degree": 9,
          "frequency_multiplier": 715
        },
        {
          "angular_degree": 4,
          "radial_degree": 0,
          "total_degree": 4,
          "frequency_multiplier": 70
        },
        {
          "angular_degree": 4,
          "radial_degree": 1,
          "total_degree": 6,
          "frequency_multiplier": 210
        },
        {
          "angular_degree": 4,
          "radial_degree": 2,
          "total_degree": 8,
          "frequency_multiplier": 495
        },
        {
          "angular_degree": 4,
          "radial_degree": 3,
          "total_degree": 10,
          "frequency_multiplier": 1001
        }
      ]
    },
    {
      "depth": 5,
      "squared_clock_polynomial": "(z + 5)**2*(z + 8)**2*(z + 9)/14400",
      "spatial_derivative_order": 10,
      "examples": [
        {
          "angular_degree": 0,
          "radial_degree": 0,
          "total_degree": 0,
          "frequency_multiplier": 1
        },
        {
          "angular_degree": 0,
          "radial_degree": 1,
          "total_degree": 2,
          "frequency_multiplier": 21
        },
        {
          "angular_degree": 0,
          "radial_degree": 2,
          "total_degree": 4,
          "frequency_multiplier": 126
        },
        {
          "angular_degree": 0,
          "radial_degree": 3,
          "total_degree": 6,
          "frequency_multiplier": 462
        },
        {
          "angular_degree": 1,
          "radial_degree": 0,
          "total_degree": 1,
          "frequency_multiplier": 6
        },
        {
          "angular_degree": 1,
          "radial_degree": 1,
          "total_degree": 3,
          "frequency_multiplier": 56
        },
        {
          "angular_degree": 1,
          "radial_degree": 2,
          "total_degree": 5,
          "frequency_multiplier": 252
        },
        {
          "angular_degree": 1,
          "radial_degree": 3,
          "total_degree": 7,
          "frequency_multiplier": 792
        },
        {
          "angular_degree": 2,
          "radial_degree": 0,
          "total_degree": 2,
          "frequency_multiplier": 21
        },
        {
          "angular_degree": 2,
          "radial_degree": 1,
          "total_degree": 4,
          "frequency_multiplier": 126
        },
        {
          "angular_degree": 2,
          "radial_degree": 2,
          "total_degree": 6,
          "frequency_multiplier": 462
        },
        {
          "angular_degree": 2,
          "radial_degree": 3,
          "total_degree": 8,
          "frequency_multiplier": 1287
        },
        {
          "angular_degree": 3,
          "radial_degree": 0,
          "total_degree": 3,
          "frequency_multiplier": 56
        },
        {
          "angular_degree": 3,
          "radial_degree": 1,
          "total_degree": 5,
          "frequency_multiplier": 252
        },
        {
          "angular_degree": 3,
          "radial_degree": 2,
          "total_degree": 7,
          "frequency_multiplier": 792
        },
        {
          "angular_degree": 3,
          "radial_degree": 3,
          "total_degree": 9,
          "frequency_multiplier": 2002
        },
        {
          "angular_degree": 4,
          "radial_degree": 0,
          "total_degree": 4,
          "frequency_multiplier": 126
        },
        {
          "angular_degree": 4,
          "radial_degree": 1,
          "total_degree": 6,
          "frequency_multiplier": 462
        },
        {
          "angular_degree": 4,
          "radial_degree": 2,
          "total_degree": 8,
          "frequency_multiplier": 1287
        },
        {
          "angular_degree": 4,
          "radial_degree": 3,
          "total_degree": 10,
          "frequency_multiplier": 3003
        }
      ]
    },
    {
      "depth": 6,
      "squared_clock_polynomial": "(z + 6)**2*(z + 10)**2*(z + 12)**2/518400",
      "spatial_derivative_order": 12,
      "examples": [
        {
          "angular_degree": 0,
          "radial_degree": 0,
          "total_degree": 0,
          "frequency_multiplier": 1
        },
        {
          "angular_degree": 0,
          "radial_degree": 1,
          "total_degree": 2,
          "frequency_multiplier": 28
        },
        {
          "angular_degree": 0,
          "radial_degree": 2,
          "total_degree": 4,
          "frequency_multiplier": 210
        },
        {
          "angular_degree": 0,
          "radial_degree": 3,
          "total_degree": 6,
          "frequency_multiplier": 924
        },
        {
          "angular_degree": 1,
          "radial_degree": 0,
          "total_degree": 1,
          "frequency_multiplier": 7
        },
        {
          "angular_degree": 1,
          "radial_degree": 1,
          "total_degree": 3,
          "frequency_multiplier": 84
        },
        {
          "angular_degree": 1,
          "radial_degree": 2,
          "total_degree": 5,
          "frequency_multiplier": 462
        },
        {
          "angular_degree": 1,
          "radial_degree": 3,
          "total_degree": 7,
          "frequency_multiplier": 1716
        },
        {
          "angular_degree": 2,
          "radial_degree": 0,
          "total_degree": 2,
          "frequency_multiplier": 28
        },
        {
          "angular_degree": 2,
          "radial_degree": 1,
          "total_degree": 4,
          "frequency_multiplier": 210
        },
        {
          "angular_degree": 2,
          "radial_degree": 2,
          "total_degree": 6,
          "frequency_multiplier": 924
        },
        {
          "angular_degree": 2,
          "radial_degree": 3,
          "total_degree": 8,
          "frequency_multiplier": 3003
        },
        {
          "angular_degree": 3,
          "radial_degree": 0,
          "total_degree": 3,
          "frequency_multiplier": 84
        },
        {
          "angular_degree": 3,
          "radial_degree": 1,
          "total_degree": 5,
          "frequency_multiplier": 462
        },
        {
          "angular_degree": 3,
          "radial_degree": 2,
          "total_degree": 7,
          "frequency_multiplier": 1716
        },
        {
          "angular_degree": 3,
          "radial_degree": 3,
          "total_degree": 9,
          "frequency_multiplier": 5005
        },
        {
          "angular_degree": 4,
          "radial_degree": 0,
          "total_degree": 4,
          "frequency_multiplier": 210
        },
        {
          "angular_degree": 4,
          "radial_degree": 1,
          "total_degree": 6,
          "frequency_multiplier": 924
        },
        {
          "angular_degree": 4,
          "radial_degree": 2,
          "total_degree": 8,
          "frequency_multiplier": 3003
        },
        {
          "angular_degree": 4,
          "radial_degree": 3,
          "total_degree": 10,
          "frequency_multiplier": 8008
        }
      ]
    },
    {
      "depth": 10,
      "squared_clock_polynomial": "(z + 10)**2*(z + 18)**2*(z + 24)**2*(z + 28)**2*(z + 30)**2/13168189440000",
      "spatial_derivative_order": 20,
      "examples": [
        {
          "angular_degree": 0,
          "radial_degree": 0,
          "total_degree": 0,
          "frequency_multiplier": 1
        },
        {
          "angular_degree": 0,
          "radial_degree": 1,
          "total_degree": 2,
          "frequency_multiplier": 66
        },
        {
          "angular_degree": 0,
          "radial_degree": 2,
          "total_degree": 4,
          "frequency_multiplier": 1001
        },
        {
          "angular_degree": 0,
          "radial_degree": 3,
          "total_degree": 6,
          "frequency_multiplier": 8008
        },
        {
          "angular_degree": 1,
          "radial_degree": 0,
          "total_degree": 1,
          "frequency_multiplier": 11
        },
        {
          "angular_degree": 1,
          "radial_degree": 1,
          "total_degree": 3,
          "frequency_multiplier": 286
        },
        {
          "angular_degree": 1,
          "radial_degree": 2,
          "total_degree": 5,
          "frequency_multiplier": 3003
        },
        {
          "angular_degree": 1,
          "radial_degree": 3,
          "total_degree": 7,
          "frequency_multiplier": 19448
        },
        {
          "angular_degree": 2,
          "radial_degree": 0,
          "total_degree": 2,
          "frequency_multiplier": 66
        },
        {
          "angular_degree": 2,
          "radial_degree": 1,
          "total_degree": 4,
          "frequency_multiplier": 1001
        },
        {
          "angular_degree": 2,
          "radial_degree": 2,
          "total_degree": 6,
          "frequency_multiplier": 8008
        },
        {
          "angular_degree": 2,
          "radial_degree": 3,
          "total_degree": 8,
          "frequency_multiplier": 43758
        },
        {
          "angular_degree": 3,
          "radial_degree": 0,
          "total_degree": 3,
          "frequency_multiplier": 286
        },
        {
          "angular_degree": 3,
          "radial_degree": 1,
          "total_degree": 5,
          "frequency_multiplier": 3003
        },
        {
          "angular_degree": 3,
          "radial_degree": 2,
          "total_degree": 7,
          "frequency_multiplier": 19448
        },
        {
          "angular_degree": 3,
          "radial_degree": 3,
          "total_degree": 9,
          "frequency_multiplier": 92378
        },
        {
          "angular_degree": 4,
          "radial_degree": 0,
          "total_degree": 4,
          "frequency_multiplier": 1001
        },
        {
          "angular_degree": 4,
          "radial_degree": 1,
          "total_degree": 6,
          "frequency_multiplier": 8008
        },
        {
          "angular_degree": 4,
          "radial_degree": 2,
          "total_degree": 8,
          "frequency_multiplier": 43758
        },
        {
          "angular_degree": 4,
          "radial_degree": 3,
          "total_degree": 10,
          "frequency_multiplier": 184756
        }
      ]
    }
  ]
}
