{
  "seed": 2901,
  "predictions": {
    "threshold_tau_c": 1.5707963267948966,
    "estimated_threshold": 1.570796326794536,
    "threshold_relative_error": 2.295653690087445e-13,
    "beta_times_r_target": 1.0,
    "log_boundary_slope_target": 2.2222222222222223,
    "gumbel_vs_exponential_rule": "AIC_gumbel < AIC_exponential and KS p > 0.05"
  },
  "root_sweep": [
    {
      "tau": 1.2566370614359172,
      "real": -0.12573540609416542,
      "imag": 1.1644016526924585,
      "predicted_unstable": false
    },
    {
      "tau": 1.4922565104551517,
      "real": -0.02443200056302731,
      "imag": 1.036843769970623,
      "predicted_unstable": false
    },
    {
      "tau": 1.5707963267948966,
      "real": -7.10324548054366e-18,
      "imag": -1.0,
      "predicted_unstable": false
    },
    {
      "tau": 1.6493361431346414,
      "real": 0.021073068658481905,
      "imag": 0.9656105811341521,
      "predicted_unstable": true
    },
    {
      "tau": 1.8849555921538759,
      "real": 0.06910693847693873,
      "imag": -0.8751397397549342,
      "predicted_unstable": true
    }
  ],
  "gumbel_sweep": [
    {
      "mu": 22.899219004228403,
      "beta": 4.979128996981144,
      "ks_p": 0.6961633662172784,
      "aic_gumbel": 3249.9939809642065,
      "aic_exponential": 4350.834577675039,
      "beta_r": 0.9958257993962288,
      "r": 0.2
    },
    {
      "mu": 13.113619077378534,
      "beta": 2.872144791323946,
      "ks_p": 0.7805751088570765,
      "aic_gumbel": 2698.3098811361333,
      "aic_exponential": 3783.1005105542718,
      "beta_r": 1.005250676963381,
      "r": 0.35
    },
    {
      "mu": 7.6195036211472145,
      "beta": 1.6071664486991366,
      "ks_p": 0.37142651462846954,
      "aic_gumbel": 2106.5897575083072,
      "aic_exponential": 3223.4087309187253,
      "beta_r": 0.964299869219482,
      "r": 0.6
    },
    {
      "mu": 5.102563940438067,
      "beta": 1.1660907489370607,
      "ks_p": 0.7542920483477772,
      "aic_gumbel": 1788.701877180309,
      "aic_exponential": 2824.2163766962153,
      "beta_r": 1.0494816740433546,
      "r": 0.9
    }
  ],
  "log_boundary_scaling": {
    "points": [
      [
        2.995732273553991,
        7.850466447855373
      ],
      [
        4.605170185988092,
        11.34887567986559
      ],
      [
        6.214608098422191,
        15.142929000760951
      ],
      [
        7.824046010856292,
        18.646111215843536
      ]
    ],
    "slope": 2.2480511578194418,
    "predicted": 2.2222222222222223
  },
  "controller": [
    {
      "mu": 29.78152884994886,
      "beta": 7.029801797027441,
      "ks_p": 0.8051184263621931,
      "aic_gumbel": 228.82771118744037,
      "aic_exponential": 291.1914595015935,
      "beta_r": 1.1247682875243907,
      "r": 0.16,
      "accept": false,
      "validation_improves": false
    },
    {
      "mu": 13.011875538383624,
      "beta": 2.3302674340811835,
      "ks_p": 0.8498758477820716,
      "aic_gumbel": 163.70006701986068,
      "aic_exponential": 237.25571611542208,
      "beta_r": 0.8155936019284142,
      "r": 0.35,
      "accept": true,
      "validation_improves": true
    },
    {
      "mu": 8.681993437446744,
      "beta": 2.046282476565019,
      "ks_p": 0.7846338354682789,
      "aic_gumbel": 150.9698886271698,
      "aic_exponential": 212.52549041752806,
      "beta_r": 1.1254553621107606,
      "r": 0.55,
      "accept": true,
      "validation_improves": true
    }
  ],
  "notes": "Synthetic extreme-value seed tests the stated mechanism directly; ordinary Gaussian seeds are not claimed to be exactly Gumbel."
}