1{
  2  "seed": 1729,
  3  "A": 1.0,
  4  "D": 1.0,
  5  "alpha": 1.0,
  6  "kappa": 0.2,
  7  "trials": 30000,
  8  "note": "pair_kicks uses the paper's exact effective marginal diffusivity; cross-label covariance is not time-discretely simulated",
  9  "regimes": {
 10    "independent": {
 11      "name": "independent",
 12      "means": [
 13        0.42253894176368184,
 14        0.2107921429898502,
 15        0.13693478000308715,
 16        0.10075924386041893,
 17        0.07980809411341716,
 18        0.06590948047273837,
 19        0.05616555490094398
 20      ],
 21      "loglog_slope": -0.45954959461169564,
 22      "loglog_slope_highN": -0.2805513074027317,
 23      "loglogN_slope": -1.444649625220236
 24    },
 25    "normalized_bounded": {
 26      "name": "normalized_bounded",
 27      "means": [
 28        0.2310074483353142,
 29        0.15036768531643363,
 30        0.10894657681329084,
 31        0.08480774036700674,
 32        0.06969384519674375,
 33        0.05887319241512188,
 34        0.05090114544538722
 35      ],
 36      "loglog_slope": -0.3534517613899999,
 37      "loglog_slope_highN": -0.24529138626942237,
 38      "loglogN_slope": -1.0953699400799208
 39    },
 40    "unnormalized_coherent": {
 41      "name": "unnormalized_coherent",
 42      "means": [
 43        0.13648583007508497,
 44        0.06470609355542804,
 45        0.03428429257899801,
 46        0.018829134885680405,
 47        0.010376984083494412,
 48        0.005662504081455707,
 49        0.0030455763280417933
 50      ],
 51      "loglog_slope": -0.9003791375033156,
 52      "loglog_slope_highN": -0.8758413764715667,
 53      "loglogN_slope": -2.7006819555090438
 54    },
 55    "pair_kicks": {
 56      "name": "pair_kicks",
 57      "means": [
 58        0.27021409723253004,
 59        0.08797414612786875,
 60        0.034083848308068605,
 61        0.014007904478775583,
 62        0.00586722189453608,
 63        0.0024985308785933683,
 64        0.0010810920483939341
 65      ],
 66      "loglog_slope": -1.3110929780271239,
 67      "loglog_slope_highN": -1.2318637149652265,
 68      "loglogN_slope": -3.9455293732435415
 69    }
 70  },
 71  "checks": {
 72    "log_extreme_prediction": {
 73      "predicted": "slope of log(E[T]) vs log(log N) approximately -1",
 74      "independent_observed": -1.444649625220236,
 75      "normalized_observed": -1.0953699400799208
 76    },
 77    "coherent_prediction": {
 78      "predicted": "E[T] approximately A/(alpha*(N-1)); high-N log-log slope -1",
 79      "observed_highN_slope": -0.8758413764715667,
 80      "alpha_values": [
 81        0.8,
 82        1.6,
 83        3.2,
 84        6.4
 85      ],
 86      "alpha_times_mean": [
 87        0.005445948080164498,
 88        0.00606907215932431,
 89        0.006551472584187587,
 90        0.006917004397847707
 91      ],
 92      "target_alpha_times_mean": 0.007874015748031496,
 93      "zero_noise_alpha_times_mean": [
 94        0.007874015748031496,
 95        0.007874015748031496,
 96        0.007874015748031496,
 97        0.007874015748031496
 98      ]
 99    },
100    "pair_kick_prediction": {
101      "predicted": "N*log(N)*E[T] tends to A^2/(4*kappa)=1.2500",
102      "observed_highN_NlogN_mean": [
103        1.5616697525442296,
104        1.5517372720989047,
105        1.5346808939930243
106      ],
107      "observed_highN_loglog_slope": -1.2318637149652265,
108      "kappa_values": [
109        0.05,
110        0.1,
111        0.2,
112        0.4
113      ],
114      "kappa_times_NlogN_mean": [
115        0.2787529543701529,
116        0.2990522241554367,
117        0.3105261900812297,
118        0.31682236880126247
119      ],
120      "target_kappa_times_NlogN_mean": 0.25
121    }
122  }
123}