{
  "seed": 1729,
  "A": 1.0,
  "D": 1.0,
  "alpha": 0.08,
  "kappa": 0.2,
  "trials": 30000,
  "note": "pair_kicks uses the paper's exact effective marginal diffusivity; cross-label covariance is not time-discretely simulated",
  "regimes": {
    "independent": {
      "name": "independent",
      "means": [
        0.42253894176368184,
        0.2107921429898502,
        0.13693478000308715,
        0.10075924386041893,
        0.07980809411341716,
        0.06590948047273837,
        0.05616555490094398
      ],
      "loglog_slope": -0.45954959461169564,
      "loglog_slope_highN": -0.2805513074027317,
      "loglogN_slope": -1.444649625220236
    },
    "normalized_bounded": {
      "name": "normalized_bounded",
      "means": [
        0.3932620151418388,
        0.20300097780069984,
        0.13380758597783116,
        0.09901389403254895,
        0.07904632939113884,
        0.06547432824263939,
        0.05576683560976021
      ],
      "loglog_slope": -0.44565696276790673,
      "loglog_slope_highN": -0.27564398404268725,
      "loglogN_slope": -1.398965348369097
    },
    "unnormalized_coherent": {
      "name": "unnormalized_coherent",
      "means": [
        0.3459021833925929,
        0.17127850184246834,
        0.10529312962500585,
        0.06998823840352987,
        0.047471768198628625,
        0.03155364537487639,
        0.02023671113402679
      ],
      "loglog_slope": -0.654148310892,
      "loglog_slope_highN": -0.5959676059068667,
      "loglogN_slope": -1.9856413795556467
    },
    "pair_kicks": {
      "name": "pair_kicks",
      "means": [
        0.27021409723253004,
        0.08797414612786875,
        0.034083848308068605,
        0.014007904478775583,
        0.00586722189453608,
        0.0024985308785933683,
        0.0010810920483939341
      ],
      "loglog_slope": -1.3110929780271239,
      "loglog_slope_highN": -1.2318637149652265,
      "loglogN_slope": -3.9455293732435415
    }
  },
  "checks": {
    "log_extreme_prediction": {
      "predicted": "slope of log(E[T]) vs log(log N) approximately -1",
      "independent_observed": -1.444649625220236,
      "normalized_observed": -1.398965348369097
    },
    "coherent_prediction": {
      "predicted": "E[T] approximately A/(alpha*(N-1)); high-N log-log slope -1",
      "observed_highN_slope": -0.5959676059068667,
      "alpha_values": [
        0.8,
        1.6,
        3.2,
        6.4
      ],
      "alpha_times_mean": [
        0.005445948080164498,
        0.00606907215932431,
        0.006551472584187587,
        0.006917004397847707
      ],
      "target_alpha_times_mean": 0.007874015748031496,
      "zero_noise_alpha_times_mean": [
        0.007874015748031496,
        0.007874015748031496,
        0.007874015748031496,
        0.007874015748031496
      ]
    },
    "pair_kick_prediction": {
      "predicted": "N*log(N)*E[T] tends to A^2/(4*kappa)=1.2500",
      "observed_highN_NlogN_mean": [
        1.5616697525442296,
        1.5517372720989047,
        1.5346808939930243
      ],
      "observed_highN_loglog_slope": -1.2318637149652265,
      "kappa_values": [
        0.05,
        0.1,
        0.2,
        0.4
      ],
      "kappa_times_NlogN_mean": [
        0.2787529543701529,
        0.2990522241554367,
        0.3105261900812297,
        0.31682236880126247
      ],
      "target_kappa_times_NlogN_mean": 0.25
    }
  }
}