{
  "checks": [
    {
      "name": "quarter-circle-controls",
      "passed": true,
      "scope": "99 exact distances at x=1/4; CK.3"
    },
    {
      "name": "normal-flow-angle-bound",
      "passed": true,
      "scope": "Exact rational angles imply cosine >=1/2; CK.6"
    },
    {
      "name": "exact-flow-margin",
      "passed": true,
      "scope": "Exact margin in CK.7"
    },
    {
      "name": "negative-fourier-coefficient",
      "passed": true,
      "scope": "64 exact Gaussian-rational Fourier polynomials; CK.8"
    },
    {
      "name": "exact-squared-distance-CND",
      "passed": true,
      "scope": "One exact zero-sum five-label Gram calculation; CK.2"
    },
    {
      "name": "phase-margin",
      "passed": true,
      "scope": "Exact bounded-phase lower margin; CK.8"
    }
  ],
  "count": 6,
  "epsilon": "1/8",
  "flow_margin": "17/64",
  "numerical_traces": [
    {
      "endpoint_sample": 1.3472172992911784,
      "n": 4,
      "t_exact": "1/18"
    },
    {
      "endpoint_sample": 1.3652144355900508,
      "n": 8,
      "t_exact": "1/34"
    },
    {
      "endpoint_sample": 1.3748025708715645,
      "n": 16,
      "t_exact": "1/66"
    },
    {
      "endpoint_sample": 1.3797505655858386,
      "n": 32,
      "t_exact": "1/130"
    }
  ],
  "phase_margin": "1/16",
  "proof_locators": [
    "CK.1\u2013CK.9",
    "SK.1\u2013SK.5"
  ],
  "result": "passed",
  "sample_base": "x=1/4 on R/Z",
  "samples": [
    {
      "cosine_angle_over_pi": "5/18",
      "derivative_over_pi": "9/2",
      "n": 4,
      "t": "1/18"
    },
    {
      "cosine_angle_over_pi": "9/34",
      "derivative_over_pi": "17/2",
      "n": 8,
      "t": "1/34"
    },
    {
      "cosine_angle_over_pi": "17/66",
      "derivative_over_pi": "33/2",
      "n": 16,
      "t": "1/66"
    },
    {
      "cosine_angle_over_pi": "33/130",
      "derivative_over_pi": "65/2",
      "n": 32,
      "t": "1/130"
    },
    {
      "cosine_angle_over_pi": "65/258",
      "derivative_over_pi": "129/2",
      "n": 64,
      "t": "1/258"
    }
  ],
  "schema": "smooth-labelled-kernel-finite-samples/v1",
  "scope": "Finite exact samples supplement CK.1\u2013CK.9; the infinite-label conclusions are proved in the lesson."
}