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    "frac_null_ge_observed": 0.14325,
    "count_ge_observed": 573
   },
   "MAE capped - law": {
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    "null": {
     "p50": 0.1139,
     "p95": 1.9759,
     "p99": 2.6942
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    "frac_null_ge_observed": 0.30225,
    "count_ge_observed": 1209
   },
   "MAE zero - law": {
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    "null": {
     "p50": 2.5712,
     "p95": 3.7647,
     "p99": 4.2502
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    "frac_null_ge_observed": 0.26925,
    "count_ge_observed": 1077
   },
   "Opus-15 AIC constant - law": {
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     "p50": -11.5743,
     "p95": -3.4501,
     "p99": -0.1036
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.3001,
    "null": {
     "p50": 0.3026,
     "p95": 0.3852,
     "p99": 0.4173
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   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.4248,
    "null": {
     "p50": 0.4264,
     "p95": 0.4871,
     "p99": 0.5083
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    "count_ge_observed": 2
   }
  },
  "constant_taufit": {
   "null": "constant",
   "coupled": true,
   "true_lift_weak": 8.1201,
   "true_lift_opus": 5.7053,
   "tau_het_weak": 12.927,
   "tau_het_opus": 4.16,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
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    "observed_log10": 0.992,
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     "p95": 5.353,
     "p99": 22.5
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    "frac_null_ge_observed": 0.29575,
    "count_ge_observed": 1183,
    "frac_null_bf_gt_1": 0.614
   },
   "BF law:capped": {
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     "p95": 2.491,
     "p99": 15.752
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    "frac_null_ge_observed": 0.24025,
    "count_ge_observed": 961,
    "frac_null_bf_gt_1": 0.5575
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   "BF law:zero": {
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     "p95": 3.806,
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    "frac_null_ge_observed": 0.2515,
    "count_ge_observed": 1006,
    "frac_null_bf_gt_1": 0.9032
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   "BF law:smooth cap": {
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     "p95": 0.888,
     "p99": 3.915
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    "frac_null_ge_observed": 0.14975,
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   "MAE constant - law": {
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    "frac_null_ge_observed": 0.31825,
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   "MAE capped - law": {
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     "p95": 2.8073,
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    "frac_null_ge_observed": 0.4115,
    "count_ge_observed": 1646
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   "MAE zero - law": {
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     "p95": 3.4506,
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    "frac_null_ge_observed": 0.0885,
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   "Opus-15 AIC constant - law": {
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     "p99": 9.4938
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    "frac_null_ge_observed": 0.0005,
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   },
   "k weak (fitted on null data)": {
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    "null": {
     "p50": 0.3039,
     "p95": 0.6458,
     "p99": 0.7811
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   },
   "k Opus-15 (fitted on null data)": {
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    "null_mean": 0.4175,
    "null": {
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     "p95": 0.5757,
     "p99": 0.6346
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    "count_ge_observed": 413
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  },
  "common_tau0": {
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   "coupled": true,
   "true_lift_weak": 6.3857,
   "true_lift_opus": 6.3857,
   "tau_het_weak": 0.0,
   "tau_het_opus": 0.0,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
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    "null_log10": {
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     "p99": 7.966
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    "frac_null_ge_observed": 0.04075,
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    "frac_null_bf_gt_1": 0.056
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   "BF law:capped": {
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     "p99": 14.705
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    "frac_null_ge_observed": 0.20225,
    "count_ge_observed": 809,
    "frac_null_bf_gt_1": 0.2303
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   "BF law:zero": {
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    "null_log10": {
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     "p95": 3.409,
     "p99": 7.609
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    "frac_null_ge_observed": 0.138,
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    "frac_null_bf_gt_1": 0.2717
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   "BF law:smooth cap": {
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     "p99": 11.857
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    "frac_null_ge_observed": 0.15375,
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   "MAE constant - law": {
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    "frac_null_ge_observed": 0.009,
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   "MAE capped - law": {
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     "p99": 1.3453
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    "frac_null_ge_observed": 0.037,
    "count_ge_observed": 148
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   "MAE zero - law": {
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     "p95": 3.4578,
     "p99": 3.9596
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    "frac_null_ge_observed": 0.15575,
    "count_ge_observed": 623
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   "Opus-15 AIC constant - law": {
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     "p50": -13.4546,
     "p95": -4.9823,
     "p99": -0.5686
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.2396,
    "null": {
     "p50": 0.2421,
     "p95": 0.33,
     "p99": 0.3644
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   },
   "k Opus-15 (fitted on null data)": {
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    "null_mean": 0.4707,
    "null": {
     "p50": 0.4719,
     "p95": 0.5317,
     "p99": 0.5589
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    "count_ge_observed": 122
   }
  },
  "common_taufit": {
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   "coupled": true,
   "true_lift_weak": 6.3857,
   "true_lift_opus": 6.3857,
   "tau_het_weak": 12.927,
   "tau_het_opus": 4.16,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
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    "observed_log10": 0.992,
    "null_log10": {
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     "p95": 3.329,
     "p99": 15.273
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    "frac_null_ge_observed": 0.1905,
    "count_ge_observed": 762,
    "frac_null_bf_gt_1": 0.53
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   "BF law:capped": {
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    "observed_log10": 0.746,
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     "p95": 1.939,
     "p99": 14.376
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    "frac_null_ge_observed": 0.17975,
    "count_ge_observed": 719,
    "frac_null_bf_gt_1": 0.4958
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   "BF law:zero": {
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    "null_log10": {
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     "p95": 3.428,
     "p99": 4.507
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    "frac_null_ge_observed": 0.1795,
    "count_ge_observed": 718,
    "frac_null_bf_gt_1": 0.8548
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   "BF law:smooth cap": {
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     "p99": 2.768
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    "frac_null_ge_observed": 0.0945,
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    "frac_null_bf_gt_1": 0.3372
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   "MAE constant - law": {
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     "p99": 8.6875
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    "frac_null_ge_observed": 0.20775,
    "count_ge_observed": 831
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   "MAE capped - law": {
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     "p50": -0.0235,
     "p95": 2.648,
     "p99": 4.2706
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    "frac_null_ge_observed": 0.30725,
    "count_ge_observed": 1229
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   "MAE zero - law": {
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    "null": {
     "p50": 1.4814,
     "p95": 3.5732,
     "p99": 4.4705
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    "frac_null_ge_observed": 0.108,
    "count_ge_observed": 432
   },
   "Opus-15 AIC constant - law": {
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    "null": {
     "p50": -3.4141,
     "p95": 4.7232,
     "p99": 8.8339
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    "frac_null_ge_observed": 0.0005,
    "count_ge_observed": 2
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.2419,
    "null": {
     "p50": 0.2494,
     "p95": 0.5771,
     "p99": 0.7124
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   },
   "k Opus-15 (fitted on null data)": {
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    "null_mean": 0.4651,
    "null": {
     "p50": 0.4652,
     "p95": 0.6238,
     "p99": 0.6861
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    "count_ge_observed": 895
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  },
  "zero_tau0": {
   "null": "zero",
   "coupled": true,
   "true_lift_weak": 0.0,
   "true_lift_opus": 0.0,
   "tau_het_weak": 0.0,
   "tau_het_opus": 0.0,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
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    "observed_log10": 0.992,
    "null_log10": {
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     "p95": 8.757,
     "p99": 16.343
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    "frac_null_ge_observed": 0.43425,
    "count_ge_observed": 1737,
    "frac_null_bf_gt_1": 0.8317
   },
   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": 0.578,
     "p95": 6.759,
     "p99": 12.635
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    "frac_null_ge_observed": 0.4535,
    "count_ge_observed": 1814,
    "frac_null_bf_gt_1": 0.831
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
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     "p95": 1.07,
     "p99": 1.871
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    "frac_null_ge_observed": 0.005,
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    "frac_null_bf_gt_1": 0.474
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   "BF law:smooth cap": {
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     "p95": 3.403,
     "p99": 6.488
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    "frac_null_ge_observed": 0.3045,
    "count_ge_observed": 1218,
    "frac_null_bf_gt_1": 0.6478
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   "MAE constant - law": {
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     "p50": 0.1946,
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     "p99": 2.1995
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    "frac_null_ge_observed": 0.0225,
    "count_ge_observed": 90
   },
   "MAE capped - law": {
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     "p50": 0.1619,
     "p95": 1.2747,
     "p99": 1.9481
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    "frac_null_ge_observed": 0.15625,
    "count_ge_observed": 625
   },
   "MAE zero - law": {
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    "null": {
     "p50": -0.0255,
     "p95": 0.2626,
     "p99": 0.4667
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "Opus-15 AIC constant - law": {
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    "null": {
     "p50": 0.0604,
     "p95": 2.7138,
     "p99": 4.6089
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.0151,
    "null": {
     "p50": 0.0178,
     "p95": 0.1185,
     "p99": 0.1595
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   },
   "k Opus-15 (fitted on null data)": {
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    "null_mean": 0.022,
    "null": {
     "p50": 0.024,
     "p95": 0.0989,
     "p99": 0.128
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    "count_ge_observed": 0
   }
  },
  "zero_taufit": {
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   "coupled": true,
   "true_lift_weak": 0.0,
   "true_lift_opus": 0.0,
   "tau_het_weak": 15.327,
   "tau_het_opus": 7.085,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
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    "observed_log10": 0.992,
    "null_log10": {
     "p50": 0.282,
     "p95": 3.999,
     "p99": 13.945
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    "frac_null_ge_observed": 0.2145,
    "count_ge_observed": 858,
    "frac_null_bf_gt_1": 0.8273
   },
   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": 0.236,
     "p95": 3.132,
     "p99": 11.839
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    "frac_null_ge_observed": 0.24175,
    "count_ge_observed": 967,
    "frac_null_bf_gt_1": 0.8115
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
     "p50": 0.068,
     "p95": 0.978,
     "p99": 1.768
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    "frac_null_ge_observed": 0.0025,
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    "frac_null_bf_gt_1": 0.6863
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   "BF law:smooth cap": {
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     "p95": 1.076,
     "p99": 3.115
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    "frac_null_ge_observed": 0.1915,
    "count_ge_observed": 766,
    "frac_null_bf_gt_1": 0.7198
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   "MAE constant - law": {
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     "p50": 0.6847,
     "p95": 5.3972,
     "p99": 8.5261
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    "frac_null_ge_observed": 0.2675,
    "count_ge_observed": 1070
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   "MAE capped - law": {
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     "p50": 0.6186,
     "p95": 4.1193,
     "p99": 6.6904
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    "frac_null_ge_observed": 0.472,
    "count_ge_observed": 1888
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   "MAE zero - law": {
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    "null": {
     "p50": -0.1875,
     "p95": 0.605,
     "p99": 1.1923
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "Opus-15 AIC constant - law": {
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    "null": {
     "p50": 0.0053,
     "p95": 2.2251,
     "p99": 3.8393
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.02,
    "null": {
     "p50": 0.0262,
     "p95": 0.4161,
     "p99": 0.5842
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   },
   "k Opus-15 (fitted on null data)": {
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    "null_mean": 0.0349,
    "null": {
     "p50": 0.0363,
     "p95": 0.2847,
     "p99": 0.3848
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    "count_ge_observed": 0
   }
  },
  "constant_tau0_nocoupling": {
   "null": "constant",
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   "true_lift_weak": 8.1201,
   "true_lift_opus": 5.7053,
   "tau_het_weak": 0.0,
   "tau_het_opus": 0.0,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
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     "p95": 18.623,
     "p99": 32.343
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    "frac_null_ge_observed": 0.32525,
    "count_ge_observed": 1301,
    "frac_null_bf_gt_1": 0.3693
   },
   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": 1.703,
     "p95": 18.157,
     "p99": 23.578
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    "frac_null_ge_observed": 0.54525,
    "count_ge_observed": 2181,
    "frac_null_bf_gt_1": 0.5885
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
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     "p95": 4.085,
     "p99": 4.844
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    "frac_null_ge_observed": 0.34475,
    "count_ge_observed": 1379,
    "frac_null_bf_gt_1": 0.5198
   },
   "BF law:smooth cap": {
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    "observed_log10": 0.485,
    "null_log10": {
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     "p95": 9.976,
     "p99": 14.037
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    "frac_null_ge_observed": 0.3525,
    "count_ge_observed": 1410,
    "frac_null_bf_gt_1": 0.3932
   },
   "MAE constant - law": {
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    "null": {
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     "p95": 2.6086,
     "p99": 3.7963
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    "frac_null_ge_observed": 0.11375,
    "count_ge_observed": 455
   },
   "MAE capped - law": {
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     "p50": -0.0855,
     "p95": 2.1731,
     "p99": 2.9434
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    "frac_null_ge_observed": 0.2765,
    "count_ge_observed": 1106
   },
   "MAE zero - law": {
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    "null": {
     "p50": 2.1406,
     "p95": 3.2805,
     "p99": 3.7305
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    "frac_null_ge_observed": 0.1005,
    "count_ge_observed": 402
   },
   "Opus-15 AIC constant - law": {
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    "null": {
     "p50": -14.3893,
     "p95": -7.0296,
     "p99": -3.7447
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.2906,
    "null": {
     "p50": 0.2912,
     "p95": 0.4036,
     "p99": 0.449
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   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.4057,
    "null": {
     "p50": 0.4053,
     "p95": 0.5031,
     "p99": 0.5431
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    "count_ge_observed": 50
   }
  },
  "constant_taufit_nocoupling": {
   "null": "constant",
   "coupled": false,
   "true_lift_weak": 8.1201,
   "true_lift_opus": 5.7053,
   "tau_het_weak": 12.927,
   "tau_het_opus": 4.16,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": 0.034,
     "p95": 4.682,
     "p99": 31.421
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    "frac_null_ge_observed": 0.224,
    "count_ge_observed": 896,
    "frac_null_bf_gt_1": 0.5182
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   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": -0.04,
     "p95": 2.196,
     "p99": 18.363
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    "frac_null_ge_observed": 0.1835,
    "count_ge_observed": 734,
    "frac_null_bf_gt_1": 0.4778
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
     "p50": 1.052,
     "p95": 3.241,
     "p99": 4.243
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    "frac_null_ge_observed": 0.17525,
    "count_ge_observed": 701,
    "frac_null_bf_gt_1": 0.8852
   },
   "BF law:smooth cap": {
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    "observed_log10": 0.485,
    "null_log10": {
     "p50": -0.194,
     "p95": 0.765,
     "p99": 5.054
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    "frac_null_ge_observed": 0.09425,
    "count_ge_observed": 377,
    "frac_null_bf_gt_1": 0.325
   },
   "MAE constant - law": {
    "observed": 1.862,
    "null": {
     "p50": 0.1678,
     "p95": 6.4285,
     "p99": 9.7287
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    "frac_null_ge_observed": 0.28675,
    "count_ge_observed": 1147
   },
   "MAE capped - law": {
    "observed": 0.717,
    "null": {
     "p50": 0.186,
     "p95": 2.7594,
     "p99": 3.6784
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    "frac_null_ge_observed": 0.38525,
    "count_ge_observed": 1541
   },
   "MAE zero - law": {
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    "null": {
     "p50": 1.0892,
     "p95": 2.9455,
     "p99": 3.748
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    "frac_null_ge_observed": 0.046,
    "count_ge_observed": 184
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": -4.1372,
     "p95": 2.592,
     "p99": 5.7778
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.2868,
    "null": {
     "p50": 0.2842,
     "p95": 0.6341,
     "p99": 0.7722
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   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.3964,
    "null": {
     "p50": 0.3977,
     "p95": 0.5686,
     "p99": 0.6459
    },
    "count_ge_observed": 351
   }
  },
  "common_tau0_nocoupling": {
   "null": "common",
   "coupled": false,
   "true_lift_weak": 6.3857,
   "true_lift_opus": 6.3857,
   "tau_het_weak": 0.0,
   "tau_het_opus": 0.0,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": -12.748,
     "p95": 0.323,
     "p99": 7.648
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    "frac_null_ge_observed": 0.044,
    "count_ge_observed": 176,
    "frac_null_bf_gt_1": 0.0558
   },
   "BF law:capped": {
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    "null_log10": {
     "p50": -3.294,
     "p95": 11.712,
     "p99": 16.857
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    "frac_null_ge_observed": 0.2595,
    "count_ge_observed": 1038,
    "frac_null_bf_gt_1": 0.279
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
     "p50": -7.176,
     "p95": 3.193,
     "p99": 7.358
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    "frac_null_ge_observed": 0.13575,
    "count_ge_observed": 543,
    "frac_null_bf_gt_1": 0.3757
   },
   "BF law:smooth cap": {
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     "p50": -3.874,
     "p95": 9.933,
     "p99": 13.655
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    "frac_null_ge_observed": 0.2105,
    "count_ge_observed": 842,
    "frac_null_bf_gt_1": 0.224
   },
   "MAE constant - law": {
    "observed": 1.862,
    "null": {
     "p50": -1.7069,
     "p95": 0.1615,
     "p99": 1.4477
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    "frac_null_ge_observed": 0.005,
    "count_ge_observed": 20
   },
   "MAE capped - law": {
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     "p50": -1.2587,
     "p95": 0.429,
     "p99": 1.5284
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    "frac_null_ge_observed": 0.03475,
    "count_ge_observed": 139
   },
   "MAE zero - law": {
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    "null": {
     "p50": 1.9528,
     "p95": 3.1123,
     "p99": 3.5383
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    "frac_null_ge_observed": 0.06575,
    "count_ge_observed": 263
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": -16.0852,
     "p95": -8.3662,
     "p99": -5.1703
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.2269,
    "null": {
     "p50": 0.2278,
     "p95": 0.3359,
     "p99": 0.3841
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   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.4526,
    "null": {
     "p50": 0.4518,
     "p95": 0.5531,
     "p99": 0.5889
    },
    "count_ge_observed": 294
   }
  },
  "common_taufit_nocoupling": {
   "null": "common",
   "coupled": false,
   "true_lift_weak": 6.3857,
   "true_lift_opus": 6.3857,
   "tau_het_weak": 12.927,
   "tau_het_opus": 4.16,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": -0.119,
     "p95": 2.86,
     "p99": 12.222
    },
    "frac_null_ge_observed": 0.15275,
    "count_ge_observed": 611,
    "frac_null_bf_gt_1": 0.4355
   },
   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": -0.143,
     "p95": 1.849,
     "p99": 9.222
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    "frac_null_ge_observed": 0.1445,
    "count_ge_observed": 578,
    "frac_null_bf_gt_1": 0.4145
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
     "p50": 0.825,
     "p95": 2.934,
     "p99": 4.009
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    "frac_null_ge_observed": 0.1285,
    "count_ge_observed": 514,
    "frac_null_bf_gt_1": 0.823
   },
   "BF law:smooth cap": {
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    "observed_log10": 0.485,
    "null_log10": {
     "p50": -0.273,
     "p95": 0.49,
     "p99": 2.717
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    "frac_null_ge_observed": 0.051,
    "count_ge_observed": 204,
    "frac_null_bf_gt_1": 0.2555
   },
   "MAE constant - law": {
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    "null": {
     "p50": -0.2954,
     "p95": 4.6065,
     "p99": 7.8304
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    "frac_null_ge_observed": 0.1835,
    "count_ge_observed": 734
   },
   "MAE capped - law": {
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    "null": {
     "p50": -0.1773,
     "p95": 2.5307,
     "p99": 3.7984
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    "frac_null_ge_observed": 0.2885,
    "count_ge_observed": 1154
   },
   "MAE zero - law": {
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    "null": {
     "p50": 1.1801,
     "p95": 3.1726,
     "p99": 4.1056
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    "frac_null_ge_observed": 0.067,
    "count_ge_observed": 268
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": -5.1309,
     "p95": 2.3103,
     "p99": 6.1583
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
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    "null_mean": 0.2249,
    "null": {
     "p50": 0.2276,
     "p95": 0.566,
     "p99": 0.7042
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   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.4458,
    "null": {
     "p50": 0.445,
     "p95": 0.6266,
     "p99": 0.7035
    },
    "count_ge_observed": 760
   }
  },
  "zero_tau0_nocoupling": {
   "null": "zero",
   "coupled": false,
   "true_lift_weak": 0.0,
   "true_lift_opus": 0.0,
   "tau_het_weak": 0.0,
   "tau_het_opus": 0.0,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": 0.663,
     "p95": 7.95,
     "p99": 14.8
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    "frac_null_ge_observed": 0.4285,
    "count_ge_observed": 1714,
    "frac_null_bf_gt_1": 0.817
   },
   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": 0.526,
     "p95": 6.397,
     "p99": 12.054
    },
    "frac_null_ge_observed": 0.43975,
    "count_ge_observed": 1759,
    "frac_null_bf_gt_1": 0.8175
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
     "p50": -0.032,
     "p95": 0.781,
     "p99": 1.393
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    "frac_null_ge_observed": 0.001,
    "count_ge_observed": 4,
    "frac_null_bf_gt_1": 0.4243
   },
   "BF law:smooth cap": {
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    "observed_log10": 0.485,
    "null_log10": {
     "p50": 0.112,
     "p95": 3.071,
     "p99": 5.887
    },
    "frac_null_ge_observed": 0.29525,
    "count_ge_observed": 1181,
    "frac_null_bf_gt_1": 0.6335
   },
   "MAE constant - law": {
    "observed": 1.862,
    "null": {
     "p50": 0.1744,
     "p95": 1.3066,
     "p99": 2.0468
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    "frac_null_ge_observed": 0.01525,
    "count_ge_observed": 61
   },
   "MAE capped - law": {
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    "null": {
     "p50": 0.1506,
     "p95": 1.182,
     "p99": 1.8981
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    "frac_null_ge_observed": 0.14525,
    "count_ge_observed": 581
   },
   "MAE zero - law": {
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    "null": {
     "p50": -0.0322,
     "p95": 0.1827,
     "p99": 0.347
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": 0.0054,
     "p95": 1.8534,
     "p99": 3.1351
    },
    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
    "observed": 0.3834,
    "null_mean": 0.0013,
    "null": {
     "p50": 0.0027,
     "p95": 0.1088,
     "p99": 0.1574
    }
   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.0001,
    "null": {
     "p50": 0.0,
     "p95": 0.0835,
     "p99": 0.1147
    },
    "count_ge_observed": 0
   }
  },
  "zero_taufit_nocoupling": {
   "null": "zero",
   "coupled": false,
   "true_lift_weak": 0.0,
   "true_lift_opus": 0.0,
   "tau_het_weak": 15.327,
   "tau_het_opus": 7.085,
   "n_eff": "primary",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": 0.26,
     "p95": 4.323,
     "p99": 19.298
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    "frac_null_ge_observed": 0.2265,
    "count_ge_observed": 906,
    "frac_null_bf_gt_1": 0.8243
   },
   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": 0.225,
     "p95": 3.489,
     "p99": 17.188
    },
    "frac_null_ge_observed": 0.25425,
    "count_ge_observed": 1017,
    "frac_null_bf_gt_1": 0.8165
   },
   "BF law:zero": {
    "observed": 186.18,
    "observed_log10": 2.27,
    "null_log10": {
     "p50": 0.063,
     "p95": 0.963,
     "p99": 1.578
    },
    "frac_null_ge_observed": 0.00225,
    "count_ge_observed": 9,
    "frac_null_bf_gt_1": 0.6923
   },
   "BF law:smooth cap": {
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    "observed_log10": 0.485,
    "null_log10": {
     "p50": 0.101,
     "p95": 1.186,
     "p99": 3.33
    },
    "frac_null_ge_observed": 0.19175,
    "count_ge_observed": 767,
    "frac_null_bf_gt_1": 0.7318
   },
   "MAE constant - law": {
    "observed": 1.862,
    "null": {
     "p50": 0.6842,
     "p95": 5.4452,
     "p99": 7.7622
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    "frac_null_ge_observed": 0.2825,
    "count_ge_observed": 1130
   },
   "MAE capped - law": {
    "observed": 0.717,
    "null": {
     "p50": 0.607,
     "p95": 4.5396,
     "p99": 7.0671
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    "frac_null_ge_observed": 0.47375,
    "count_ge_observed": 1895
   },
   "MAE zero - law": {
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    "null": {
     "p50": -0.2005,
     "p95": 0.5379,
     "p99": 1.0514
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    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": 0.0021,
     "p95": 1.7762,
     "p99": 3.36
    },
    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
    "observed": 0.3834,
    "null_mean": -0.0086,
    "null": {
     "p50": -0.0074,
     "p95": 0.3973,
     "p99": 0.5462
    }
   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.005,
    "null": {
     "p50": 0.0054,
     "p95": 0.2671,
     "p99": 0.3856
    },
    "count_ge_observed": 1
   }
  },
  "constant_taufit_tasks_only": {
   "null": "constant",
   "coupled": true,
   "true_lift_weak": 8.1201,
   "true_lift_opus": 5.7053,
   "tau_het_weak": 12.927,
   "tau_het_opus": 4.16,
   "n_eff": "tasks_only",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": 0.29,
     "p95": 5.051,
     "p99": 21.289
    },
    "frac_null_ge_observed": 0.28625,
    "count_ge_observed": 1145,
    "frac_null_bf_gt_1": 0.6338
   },
   "BF law:capped": {
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    "observed_log10": 0.746,
    "null_log10": {
     "p50": 0.117,
     "p95": 2.375,
     "p99": 18.671
    },
    "frac_null_ge_observed": 0.2345,
    "count_ge_observed": 938,
    "frac_null_bf_gt_1": 0.5707
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
     "p50": 1.344,
     "p95": 3.684,
     "p99": 4.671
    },
    "frac_null_ge_observed": 0.24325,
    "count_ge_observed": 973,
    "frac_null_bf_gt_1": 0.8925
   },
   "BF law:smooth cap": {
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    "observed_log10": 0.485,
    "null_log10": {
     "p50": -0.083,
     "p95": 0.931,
     "p99": 5.271
    },
    "frac_null_ge_observed": 0.14625,
    "count_ge_observed": 585,
    "frac_null_bf_gt_1": 0.429
   },
   "MAE constant - law": {
    "observed": 1.862,
    "null": {
     "p50": 0.5249,
     "p95": 7.0361,
     "p99": 10.6635
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    "frac_null_ge_observed": 0.3175,
    "count_ge_observed": 1270
   },
   "MAE capped - law": {
    "observed": 0.717,
    "null": {
     "p50": 0.408,
     "p95": 2.8266,
     "p99": 3.8436
    },
    "frac_null_ge_observed": 0.415,
    "count_ge_observed": 1660
   },
   "MAE zero - law": {
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    "null": {
     "p50": 1.456,
     "p95": 3.4565,
     "p99": 4.268
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    "frac_null_ge_observed": 0.095,
    "count_ge_observed": 380
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": -2.2489,
     "p95": 5.7555,
     "p99": 9.6988
    },
    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
    "observed": 0.3834,
    "null_mean": 0.3011,
    "null": {
     "p50": 0.3043,
     "p95": 0.6312,
     "p99": 0.7578
    }
   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.4199,
    "null": {
     "p50": 0.4218,
     "p95": 0.5739,
     "p99": 0.6283
    },
    "count_ge_observed": 426
   }
  },
  "common_taufit_tasks_only": {
   "null": "common",
   "coupled": true,
   "true_lift_weak": 6.3857,
   "true_lift_opus": 6.3857,
   "tau_het_weak": 12.927,
   "tau_het_opus": 4.16,
   "n_eff": "tasks_only",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": 0.094,
     "p95": 3.629,
     "p99": 16.477
    },
    "frac_null_ge_observed": 0.2035,
    "count_ge_observed": 814,
    "frac_null_bf_gt_1": 0.543
   },
   "BF law:capped": {
    "observed": 5.58,
    "observed_log10": 0.746,
    "null_log10": {
     "p50": 0.011,
     "p95": 2.126,
     "p99": 12.775
    },
    "frac_null_ge_observed": 0.1905,
    "count_ge_observed": 762,
    "frac_null_bf_gt_1": 0.5062
   },
   "BF law:zero": {
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    "observed_log10": 2.27,
    "null_log10": {
     "p50": 1.026,
     "p95": 3.55,
     "p99": 4.671
    },
    "frac_null_ge_observed": 0.2,
    "count_ge_observed": 800,
    "frac_null_bf_gt_1": 0.853
   },
   "BF law:smooth cap": {
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    "observed_log10": 0.485,
    "null_log10": {
     "p50": -0.176,
     "p95": 0.706,
     "p99": 2.383
    },
    "frac_null_ge_observed": 0.09625,
    "count_ge_observed": 385,
    "frac_null_bf_gt_1": 0.3595
   },
   "MAE constant - law": {
    "observed": 1.862,
    "null": {
     "p50": 0.0839,
     "p95": 5.4352,
     "p99": 8.0834
    },
    "frac_null_ge_observed": 0.223,
    "count_ge_observed": 892
   },
   "MAE capped - law": {
    "observed": 0.717,
    "null": {
     "p50": 0.0245,
     "p95": 2.6696,
     "p99": 4.183
    },
    "frac_null_ge_observed": 0.3255,
    "count_ge_observed": 1302
   },
   "MAE zero - law": {
    "observed": 3.015,
    "null": {
     "p50": 1.4976,
     "p95": 3.6177,
     "p99": 4.5072
    },
    "frac_null_ge_observed": 0.1125,
    "count_ge_observed": 450
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": -3.0406,
     "p95": 6.0326,
     "p99": 10.4709
    },
    "frac_null_ge_observed": 0.00075,
    "count_ge_observed": 3
   },
   "k weak (fitted on null data)": {
    "observed": 0.3834,
    "null_mean": 0.2414,
    "null": {
     "p50": 0.2405,
     "p95": 0.5764,
     "p99": 0.705
    }
   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.4658,
    "null": {
     "p50": 0.4691,
     "p95": 0.6145,
     "p99": 0.6702
    },
    "count_ge_observed": 892
   }
  },
  "zero_taufit_tasks_only": {
   "null": "zero",
   "coupled": true,
   "true_lift_weak": 0.0,
   "true_lift_opus": 0.0,
   "tau_het_weak": 15.327,
   "tau_het_opus": 7.085,
   "n_eff": "tasks_only",
   "datasets": 4000,
   "BF law:constant": {
    "observed": 9.82,
    "observed_log10": 0.992,
    "null_log10": {
     "p50": 0.261,
     "p95": 3.831,
     "p99": 18.473
    },
    "frac_null_ge_observed": 0.21875,
    "count_ge_observed": 875,
    "frac_null_bf_gt_1": 0.81
   },
   "BF law:capped": {
    "observed": 5.58,
    "observed_log10": 0.746,
    "null_log10": {
     "p50": 0.217,
     "p95": 3.005,
     "p99": 13.962
    },
    "frac_null_ge_observed": 0.2445,
    "count_ge_observed": 978,
    "frac_null_bf_gt_1": 0.7957
   },
   "BF law:zero": {
    "observed": 186.18,
    "observed_log10": 2.27,
    "null_log10": {
     "p50": 0.066,
     "p95": 0.986,
     "p99": 1.663
    },
    "frac_null_ge_observed": 0.002,
    "count_ge_observed": 8,
    "frac_null_bf_gt_1": 0.6795
   },
   "BF law:smooth cap": {
    "observed": 3.05,
    "observed_log10": 0.485,
    "null_log10": {
     "p50": 0.087,
     "p95": 1.057,
     "p99": 2.838
    },
    "frac_null_ge_observed": 0.1815,
    "count_ge_observed": 726,
    "frac_null_bf_gt_1": 0.7115
   },
   "MAE constant - law": {
    "observed": 1.862,
    "null": {
     "p50": 0.6634,
     "p95": 5.4743,
     "p99": 7.9124
    },
    "frac_null_ge_observed": 0.2785,
    "count_ge_observed": 1114
   },
   "MAE capped - law": {
    "observed": 0.717,
    "null": {
     "p50": 0.5809,
     "p95": 4.2911,
     "p99": 6.5858
    },
    "frac_null_ge_observed": 0.46075,
    "count_ge_observed": 1843
   },
   "MAE zero - law": {
    "observed": 3.015,
    "null": {
     "p50": -0.1859,
     "p95": 0.6208,
     "p99": 1.2006
    },
    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "Opus-15 AIC constant - law": {
    "observed": 19.67,
    "null": {
     "p50": 0.0195,
     "p95": 2.4277,
     "p99": 4.5518
    },
    "frac_null_ge_observed": 0.0,
    "count_ge_observed": 0
   },
   "k weak (fitted on null data)": {
    "observed": 0.3834,
    "null_mean": 0.0162,
    "null": {
     "p50": 0.0215,
     "p95": 0.4176,
     "p99": 0.5894
    }
   },
   "k Opus-15 (fitted on null data)": {
    "observed": 0.5392,
    "null_mean": 0.0448,
    "null": {
     "p50": 0.0477,
     "p95": 0.2957,
     "p99": 0.3827
    },
    "count_ge_observed": 1
   }
  }
 },
 "S4_coupling_contribution": [
  {
   "null": "constant_tau0",
   "BF law:constant": {
    "coupled": 0.2985,
    "uncoupled": 0.32525
   },
   "BF law:capped": {
    "coupled": 0.546,
    "uncoupled": 0.54525
   },
   "BF law:zero": {
    "coupled": 0.31725,
    "uncoupled": 0.34475
   },
   "MAE constant - law": {
    "coupled": 0.14325,
    "uncoupled": 0.11375
   },
   "Opus-15 AIC constant - law": {
    "coupled": 0.0,
    "uncoupled": 0.0
   },
   "k Opus-15 null mean": {
    "coupled": 0.4248,
    "uncoupled": 0.4057
   },
   "k weak null mean": {
    "coupled": 0.3001,
    "uncoupled": 0.2906
   }
  },
  {
   "null": "constant_taufit",
   "BF law:constant": {
    "coupled": 0.29575,
    "uncoupled": 0.224
   },
   "BF law:capped": {
    "coupled": 0.24025,
    "uncoupled": 0.1835
   },
   "BF law:zero": {
    "coupled": 0.2515,
    "uncoupled": 0.17525
   },
   "MAE constant - law": {
    "coupled": 0.31825,
    "uncoupled": 0.28675
   },
   "Opus-15 AIC constant - law": {
    "coupled": 0.0005,
    "uncoupled": 0.0
   },
   "k Opus-15 null mean": {
    "coupled": 0.4175,
    "uncoupled": 0.3964
   },
   "k weak null mean": {
    "coupled": 0.305,
    "uncoupled": 0.2868
   }
  },
  {
   "null": "common_tau0",
   "BF law:constant": {
    "coupled": 0.04075,
    "uncoupled": 0.044
   },
   "BF law:capped": {
    "coupled": 0.20225,
    "uncoupled": 0.2595
   },
   "BF law:zero": {
    "coupled": 0.138,
    "uncoupled": 0.13575
   },
   "MAE constant - law": {
    "coupled": 0.009,
    "uncoupled": 0.005
   },
   "Opus-15 AIC constant - law": {
    "coupled": 0.0,
    "uncoupled": 0.0
   },
   "k Opus-15 null mean": {
    "coupled": 0.4707,
    "uncoupled": 0.4526
   },
   "k weak null mean": {
    "coupled": 0.2396,
    "uncoupled": 0.2269
   }
  },
  {
   "null": "common_taufit",
   "BF law:constant": {
    "coupled": 0.1905,
    "uncoupled": 0.15275
   },
   "BF law:capped": {
    "coupled": 0.17975,
    "uncoupled": 0.1445
   },
   "BF law:zero": {
    "coupled": 0.1795,
    "uncoupled": 0.1285
   },
   "MAE constant - law": {
    "coupled": 0.20775,
    "uncoupled": 0.1835
   },
   "Opus-15 AIC constant - law": {
    "coupled": 0.0005,
    "uncoupled": 0.0
   },
   "k Opus-15 null mean": {
    "coupled": 0.4651,
    "uncoupled": 0.4458
   },
   "k weak null mean": {
    "coupled": 0.2419,
    "uncoupled": 0.2249
   }
  },
  {
   "null": "zero_tau0",
   "BF law:constant": {
    "coupled": 0.43425,
    "uncoupled": 0.4285
   },
   "BF law:capped": {
    "coupled": 0.4535,
    "uncoupled": 0.43975
   },
   "BF law:zero": {
    "coupled": 0.005,
    "uncoupled": 0.001
   },
   "MAE constant - law": {
    "coupled": 0.0225,
    "uncoupled": 0.01525
   },
   "Opus-15 AIC constant - law": {
    "coupled": 0.0,
    "uncoupled": 0.0
   },
   "k Opus-15 null mean": {
    "coupled": 0.022,
    "uncoupled": 0.0001
   },
   "k weak null mean": {
    "coupled": 0.0151,
    "uncoupled": 0.0013
   }
  },
  {
   "null": "zero_taufit",
   "BF law:constant": {
    "coupled": 0.2145,
    "uncoupled": 0.2265
   },
   "BF law:capped": {
    "coupled": 0.24175,
    "uncoupled": 0.25425
   },
   "BF law:zero": {
    "coupled": 0.0025,
    "uncoupled": 0.00225
   },
   "MAE constant - law": {
    "coupled": 0.2675,
    "uncoupled": 0.2825
   },
   "Opus-15 AIC constant - law": {
    "coupled": 0.0,
    "uncoupled": 0.0
   },
   "k Opus-15 null mean": {
    "coupled": 0.0349,
    "uncoupled": 0.005
   },
   "k weak null mean": {
    "coupled": 0.02,
    "uncoupled": -0.0086
   }
  }
 ],
 "meta": {
  "seed": 20261030,
  "B_null": 4000,
  "B_simex": 500,
  "n_eff": {
   "L003": [
    87,
    1,
    "87 eligible tasks, one branch per arm"
   ],
   "L004": [
    87,
    1,
    "87 eligible tasks, one branch per arm"
   ],
   "L010": [
    30,
    1,
    "30 probe items per hour; m = 100, so se_m = 0 for any n"
   ],
   "L011": [
    16,
    1,
    "16 Terminal-Bench tasks per probe hour (ledger n)"
   ],
   "L012": [
    15,
    2,
    "15 tau2 tasks x 2 trials = 30 items per probe hour"
   ],
   "L016": [
    60,
    1,
    "60 tasks, k = 1 per cell"
   ],
   "L057": [
    66,
    1,
    "66 tasks per pair"
   ],
   "L099": [
    120,
    1,
    "n = 120 = B u B', each episode once"
   ],
   "L124": [
    112,
    3,
    "112 post-drift tasks x 3 repeats"
   ],
   "L126": [
    173,
    3,
    "173 pooled post-drift tasks x 3 repeats"
   ],
   "L136": [
    224,
    3,
    "224 pooled tasks x 3 repeats"
   ],
   "L147": [
    61,
    3,
    "61 post-drift tasks x 3 repeats"
   ],
   "L163": [
    417,
    1,
    "417 tasks, one run per arm"
   ],
   "L166": [
    212,
    1,
    "212 tasks, one run per arm"
   ],
   "L174": [
    417,
    1,
    "417 tasks, one run per arm; the row's control 84.9 = 354/417 is the whole mixed-model stream, so n is the whole stream (on the Opus 5.5 half both arms are 195/209)"
   ],
   "L001": [
    417,
    2,
    "417 test_challenge tasks; control = mean of 2 bare runs"
   ],
   "L002": [
    168,
    2,
    "168 test_normal tasks x 2 bare runs"
   ],
   "L006": [
    65,
    1,
    "65 eligible tasks"
   ],
   "L007": [
    58,
    1,
    "58 eligible tasks"
   ],
   "L054": [
    66,
    1,
    "66 tasks per pair"
   ],
   "L058": [
    84,
    1,
    "84 tasks per arm, the second half (the ledger's 168 is the whole stream)"
   ]
  },
  "runtime_s": 691.8,
  "coupling_rule": "worst case: Cov(h noise, Delta noise) = min(se_m^2, s se_m), Var(Delta noise) = s^2"
 }
}