{
  "math_checks": {
    "3": {
      "fejer_p1_error": 0.0,
      "jackson_p1_error": 0.0,
      "jackson_degree": 2,
      "jackson_nonnegative_coeffs": true
    },
    "7": {
      "fejer_p1_error": 0.0,
      "jackson_p1_error": 0.0,
      "jackson_degree": 6,
      "jackson_nonnegative_coeffs": true
    },
    "15": {
      "fejer_p1_error": 0.0,
      "jackson_p1_error": 0.0,
      "jackson_degree": 14,
      "jackson_nonnegative_coeffs": true
    },
    "31": {
      "fejer_p1_error": 0.0,
      "jackson_p1_error": 0.0,
      "jackson_degree": 30,
      "jackson_nonnegative_coeffs": true
    },
    "iterate_identity_error": 5.389304540083722e-16
  },
  "critical_prediction": {
    "predicted": "Fejer residual*d0^{-1} = 1/(K+1)",
    "observed_Kplus1_residual": [
      0.9999999904172007,
      0.9999999840021145,
      0.9999999993205003,
      0.9999999480050258,
      0.9999999535213958
    ]
  },
  "gap_scaling_prediction": {
    "predicted": "Jackson residual proportional to 1/(K^2*s) at fixed sK large",
    "observed_K2s_at_sK8": [
      [
        7,
        3.3613056750000023
      ],
      [
        15,
        3.4053037260319416
      ],
      [
        31,
        3.3736351028840446
      ],
      [
        63,
        3.3926007200727635
      ],
      [
        127,
        3.410603409950107
      ]
    ]
  },
  "switch_prediction": {
    "predicted": "safe below sK=2; safeguard prevents >10% increase",
    "observed": [
      {
        "K": 15,
        "sK": 1,
        "jackson_over_fejer": 1.454378811497243,
        "accepted": false
      },
      {
        "K": 15,
        "sK": 2,
        "jackson_over_fejer": 1.4543790530845262,
        "accepted": false
      },
      {
        "K": 15,
        "sK": 4,
        "jackson_over_fejer": 0.648464227272687,
        "accepted": true
      },
      {
        "K": 15,
        "sK": 8,
        "jackson_over_fejer": 0.45404049942750047,
        "accepted": true
      },
      {
        "K": 31,
        "sK": 1,
        "jackson_over_fejer": 1.4505048115802315,
        "accepted": false
      },
      {
        "K": 31,
        "sK": 2,
        "jackson_over_fejer": 1.4505048408369272,
        "accepted": false
      },
      {
        "K": 31,
        "sK": 4,
        "jackson_over_fejer": 0.746497942837081,
        "accepted": true
      },
      {
        "K": 31,
        "sK": 8,
        "jackson_over_fejer": 0.4353077576459635,
        "accepted": true
      },
      {
        "K": 63,
        "sK": 1,
        "jackson_over_fejer": 1.4495395492590513,
        "accepted": false
      },
      {
        "K": 63,
        "sK": 2,
        "jackson_over_fejer": 1.4495441716331054,
        "accepted": false
      },
      {
        "K": 63,
        "sK": 4,
        "jackson_over_fejer": 0.7885466004790886,
        "accepted": true
      },
      {
        "K": 63,
        "sK": 8,
        "jackson_over_fejer": 0.4308064447233301,
        "accepted": true
      },
      {
        "K": 127,
        "sK": 1,
        "jackson_over_fejer": 1.449296898784261,
        "accepted": false
      },
      {
        "K": 127,
        "sK": 2,
        "jackson_over_fejer": 1.4493027708944586,
        "accepted": false
      },
      {
        "K": 127,
        "sK": 4,
        "jackson_over_fejer": 0.8081212493197644,
        "accepted": true
      },
      {
        "K": 127,
        "sK": 8,
        "jackson_over_fejer": 0.4296823200383509,
        "accepted": true
      }
    ]
  },
  "rows": []
}