1{
  2  "math_checks": {
  3    "3": {
  4      "fejer_p1_error": 0.0,
  5      "jackson_p1_error": 0.0,
  6      "jackson_degree": 2,
  7      "jackson_nonnegative_coeffs": true
  8    },
  9    "7": {
 10      "fejer_p1_error": 0.0,
 11      "jackson_p1_error": 0.0,
 12      "jackson_degree": 6,
 13      "jackson_nonnegative_coeffs": true
 14    },
 15    "15": {
 16      "fejer_p1_error": 0.0,
 17      "jackson_p1_error": 0.0,
 18      "jackson_degree": 14,
 19      "jackson_nonnegative_coeffs": true
 20    },
 21    "31": {
 22      "fejer_p1_error": 0.0,
 23      "jackson_p1_error": 0.0,
 24      "jackson_degree": 30,
 25      "jackson_nonnegative_coeffs": true
 26    },
 27    "iterate_identity_error": 5.389304540083722e-16
 28  },
 29  "critical_prediction": {
 30    "predicted": "Fejer residual*d0^{-1} = 1/(K+1)",
 31    "observed_Kplus1_residual": [
 32      0.9999999904172007,
 33      0.9999999840021145,
 34      0.9999999993205003,
 35      0.9999999480050258,
 36      0.9999999535213958
 37    ]
 38  },
 39  "gap_scaling_prediction": {
 40    "predicted": "Jackson residual proportional to 1/(K^2*s) at fixed sK large",
 41    "observed_K2s_at_sK8": [
 42      [
 43        7,
 44        3.3613056750000023
 45      ],
 46      [
 47        15,
 48        3.4053037260319416
 49      ],
 50      [
 51        31,
 52        3.3736351028840446
 53      ],
 54      [
 55        63,
 56        3.3926007200727635
 57      ],
 58      [
 59        127,
 60        3.410603409950107
 61      ]
 62    ]
 63  },
 64  "switch_prediction": {
 65    "predicted": "safe below sK=2; safeguard prevents >10% increase",
 66    "observed": [
 67      {
 68        "K": 15,
 69        "sK": 1,
 70        "jackson_over_fejer": 1.454378811497243,
 71        "accepted": false
 72      },
 73      {
 74        "K": 15,
 75        "sK": 2,
 76        "jackson_over_fejer": 1.4543790530845262,
 77        "accepted": false
 78      },
 79      {
 80        "K": 15,
 81        "sK": 4,
 82        "jackson_over_fejer": 0.648464227272687,
 83        "accepted": true
 84      },
 85      {
 86        "K": 15,
 87        "sK": 8,
 88        "jackson_over_fejer": 0.45404049942750047,
 89        "accepted": true
 90      },
 91      {
 92        "K": 31,
 93        "sK": 1,
 94        "jackson_over_fejer": 1.4505048115802315,
 95        "accepted": false
 96      },
 97      {
 98        "K": 31,
 99        "sK": 2,
100        "jackson_over_fejer": 1.4505048408369272,
101        "accepted": false
102      },
103      {
104        "K": 31,
105        "sK": 4,
106        "jackson_over_fejer": 0.746497942837081,
107        "accepted": true
108      },
109      {
110        "K": 31,
111        "sK": 8,
112        "jackson_over_fejer": 0.4353077576459635,
113        "accepted": true
114      },
115      {
116        "K": 63,
117        "sK": 1,
118        "jackson_over_fejer": 1.4495395492590513,
119        "accepted": false
120      },
121      {
122        "K": 63,
123        "sK": 2,
124        "jackson_over_fejer": 1.4495441716331054,
125        "accepted": false
126      },
127      {
128        "K": 63,
129        "sK": 4,
130        "jackson_over_fejer": 0.7885466004790886,
131        "accepted": true
132      },
133      {
134        "K": 63,
135        "sK": 8,
136        "jackson_over_fejer": 0.4308064447233301,
137        "accepted": true
138      },
139      {
140        "K": 127,
141        "sK": 1,
142        "jackson_over_fejer": 1.449296898784261,
143        "accepted": false
144      },
145      {
146        "K": 127,
147        "sK": 2,
148        "jackson_over_fejer": 1.4493027708944586,
149        "accepted": false
150      },
151      {
152        "K": 127,
153        "sK": 4,
154        "jackson_over_fejer": 0.8081212493197644,
155        "accepted": true
156      },
157      {
158        "K": 127,
159        "sK": 8,
160        "jackson_over_fejer": 0.4296823200383509,
161        "accepted": true
162      }
163    ]
164  },
165  "rows": []
166}