1{
  2  "seed": 2901,
  3  "predictions": {
  4    "threshold_tau_c": 1.5707963267948966,
  5    "estimated_threshold": 1.570796326794536,
  6    "threshold_relative_error": 2.295653690087445e-13,
  7    "beta_times_r_target": 1.0,
  8    "log_boundary_slope_target": 2.2222222222222223,
  9    "gumbel_vs_exponential_rule": "AIC_gumbel < AIC_exponential and KS p > 0.05"
 10  },
 11  "root_sweep": [
 12    {
 13      "tau": 1.2566370614359172,
 14      "real": -0.12573540609416542,
 15      "imag": 1.1644016526924585,
 16      "predicted_unstable": false
 17    },
 18    {
 19      "tau": 1.4922565104551517,
 20      "real": -0.02443200056302731,
 21      "imag": 1.036843769970623,
 22      "predicted_unstable": false
 23    },
 24    {
 25      "tau": 1.5707963267948966,
 26      "real": -7.10324548054366e-18,
 27      "imag": -1.0,
 28      "predicted_unstable": false
 29    },
 30    {
 31      "tau": 1.6493361431346414,
 32      "real": 0.021073068658481905,
 33      "imag": 0.9656105811341521,
 34      "predicted_unstable": true
 35    },
 36    {
 37      "tau": 1.8849555921538759,
 38      "real": 0.06910693847693873,
 39      "imag": -0.8751397397549342,
 40      "predicted_unstable": true
 41    }
 42  ],
 43  "gumbel_sweep": [
 44    {
 45      "mu": 22.899219004228403,
 46      "beta": 4.979128996981144,
 47      "ks_p": 0.6961633662172784,
 48      "aic_gumbel": 3249.9939809642065,
 49      "aic_exponential": 4350.834577675039,
 50      "beta_r": 0.9958257993962288,
 51      "r": 0.2
 52    },
 53    {
 54      "mu": 13.113619077378534,
 55      "beta": 2.872144791323946,
 56      "ks_p": 0.7805751088570765,
 57      "aic_gumbel": 2698.3098811361333,
 58      "aic_exponential": 3783.1005105542718,
 59      "beta_r": 1.005250676963381,
 60      "r": 0.35
 61    },
 62    {
 63      "mu": 7.6195036211472145,
 64      "beta": 1.6071664486991366,
 65      "ks_p": 0.37142651462846954,
 66      "aic_gumbel": 2106.5897575083072,
 67      "aic_exponential": 3223.4087309187253,
 68      "beta_r": 0.964299869219482,
 69      "r": 0.6
 70    },
 71    {
 72      "mu": 5.102563940438067,
 73      "beta": 1.1660907489370607,
 74      "ks_p": 0.7542920483477772,
 75      "aic_gumbel": 1788.701877180309,
 76      "aic_exponential": 2824.2163766962153,
 77      "beta_r": 1.0494816740433546,
 78      "r": 0.9
 79    }
 80  ],
 81  "log_boundary_scaling": {
 82    "points": [
 83      [
 84        2.995732273553991,
 85        7.850466447855373
 86      ],
 87      [
 88        4.605170185988092,
 89        11.34887567986559
 90      ],
 91      [
 92        6.214608098422191,
 93        15.142929000760951
 94      ],
 95      [
 96        7.824046010856292,
 97        18.646111215843536
 98      ]
 99    ],
100    "slope": 2.2480511578194418,
101    "predicted": 2.2222222222222223
102  },
103  "controller": [
104    {
105      "mu": 29.78152884994886,
106      "beta": 7.029801797027441,
107      "ks_p": 0.8051184263621931,
108      "aic_gumbel": 228.82771118744037,
109      "aic_exponential": 291.1914595015935,
110      "beta_r": 1.1247682875243907,
111      "r": 0.16,
112      "accept": false,
113      "validation_improves": false
114    },
115    {
116      "mu": 13.011875538383624,
117      "beta": 2.3302674340811835,
118      "ks_p": 0.8498758477820716,
119      "aic_gumbel": 163.70006701986068,
120      "aic_exponential": 237.25571611542208,
121      "beta_r": 0.8155936019284142,
122      "r": 0.35,
123      "accept": true,
124      "validation_improves": true
125    },
126    {
127      "mu": 8.681993437446744,
128      "beta": 2.046282476565019,
129      "ks_p": 0.7846338354682789,
130      "aic_gumbel": 150.9698886271698,
131      "aic_exponential": 212.52549041752806,
132      "beta_r": 1.1254553621107606,
133      "r": 0.55,
134      "accept": true,
135      "validation_improves": true
136    }
137  ],
138  "notes": "Synthetic extreme-value seed tests the stated mechanism directly; ordinary Gaussian seeds are not claimed to be exactly Gumbel."
139}