{
  "seed": 2716,
  "depths": [
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    64,
    128,
    256,
    512,
    1024,
    2048,
    4096,
    8192,
    16384,
    32768
  ],
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      "s1_slope_observed": 0.7055120547793522,
      "s1_slope_predicted": 0.7,
      "s2_slope_observed": 0.4259993229498566,
      "s2_slope_predicted": 0.4,
      "s1_at_final": 2067.9099490388685,
      "s2_at_final": 158.0483151112958,
      "s1_tail_slope_observed": 0.7008663230515949,
      "s2_tail_slope_observed": 0.40906193432470234,
      "s2_normalized_final": 2.4695049236139965,
      "gaussian_q2_empirical_L128": 21493.061717758712,
      "gaussian_q2_exact_L128": 21558.605545692786,
      "gaussian_excess_per_2L": 19.213302912862446
    },
    {
      "gamma": 0.5,
      "s1_slope_observed": 0.5160477810910512,
      "s1_slope_predicted": 0.5,
      "s2_slope_observed": 0.14037684743002116,
      "s2_slope_predicted": 0.0,
      "s1_at_final": 360.58107958754226,
      "s2_at_final": 10.974438632012166,
      "s1_tail_slope_observed": 0.504317063981964,
      "s2_tail_slope_observed": 0.10491115550690087,
      "s2_normalized_final": null,
      "gaussian_q2_empirical_L128": 18297.134124307093,
      "gaussian_q2_exact_L128": 18419.503899776013,
      "gaussian_excess_per_2L": 6.951187108500051
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    {
      "gamma": 0.75,
      "s1_slope_observed": 0.30145542420151533,
      "s1_slope_predicted": 0.25,
      "s2_slope_observed": 0.017733224648378922,
      "s2_slope_predicted": 0.0,
      "s1_at_final": 50.37629048548575,
      "s2_at_final": 2.6013268895225026,
      "s1_tail_slope_observed": 0.27539738774215705,
      "s2_tail_slope_observed": 0.004570156281511213,
      "s2_normalized_final": null,
      "gaussian_q2_empirical_L128": 17273.024169617125,
      "gaussian_q2_exact_L128": 17300.10180338721,
      "gaussian_excess_per_2L": 2.5785226694812877
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    {
      "gamma": 1.0,
      "s1_slope_observed": 0.1403768474300212,
      "s1_slope_predicted": 0.0,
      "s2_slope_observed": 0.001985491711703831,
      "s2_slope_predicted": 0.0,
      "s1_at_final": 10.974438632012166,
      "s2_at_final": 1.6449035497357587,
      "s1_tail_slope_observed": 0.10491115550690087,
      "s2_tail_slope_observed": 9.634683849950251e-05,
      "s2_normalized_final": null,
      "gaussian_q2_empirical_L128": 16891.13941232137,
      "gaussian_q2_exact_L128": 16951.037846186147,
      "gaussian_excess_per_2L": 1.2149915866646381
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    {
      "gamma": 1.25,
      "s1_slope_observed": 0.052641441487315116,
      "s1_slope_predicted": 0.0,
      "s2_slope_observed": 0.00024345211321796616,
      "s2_slope_predicted": 0.0,
      "s1_at_final": 4.297811181201336,
      "s2_at_final": 1.341487144861894,
      "s1_tail_slope_observed": 0.02574985464263504,
      "s2_tail_slope_observed": 1.761675772098138e-06,
      "s2_normalized_final": null,
      "gaussian_q2_empirical_L128": 16934.23825275766,
      "gaussian_q2_exact_L128": 16810.227495399868,
      "gaussian_excess_per_2L": 0.6649511539057329
    }
  ],
  "critical_log_checks": [
    {
      "gamma": 0.5,
      "quantity": "S2",
      "log_fit_slope": 0.14037684743002116,
      "endpoints": [
        4.05849519543652,
        10.974438632012166
      ],
      "log_ratio_start": 1.1710341783855904,
      "log_ratio_end": 1.055517879396281
    },
    {
      "gamma": 1.0,
      "quantity": "S1",
      "log_fit_slope": 0.1403768474300212,
      "endpoints": [
        4.05849519543652,
        10.974438632012166
      ],
      "log_ratio_start": 1.1710341783855904,
      "log_ratio_end": 1.055517879396281
    }
  ],
  "network_jacobian_sanity": [
    {
      "depth": 16,
      "iid": {
        "median_sv": 0.9992318380178953,
        "max_sv": 1.3548490695423971,
        "normalized_gradient_fourth": 1.0062354085612784
      },
      "powerlaw_gamma_0.3": {
        "median_sv": 1.0124693364158148,
        "max_sv": 2.5138964582934546,
        "normalized_gradient_fourth": 1.0827352203586673
      }
    },
    {
      "depth": 32,
      "iid": {
        "median_sv": 0.9982063276567298,
        "max_sv": 1.3644839170724725,
        "normalized_gradient_fourth": 1.0070338422749523
      },
      "powerlaw_gamma_0.3": {
        "median_sv": 0.9877556861745743,
        "max_sv": 2.888992305970983,
        "normalized_gradient_fourth": 1.1146772071572455
      }
    },
    {
      "depth": 64,
      "iid": {
        "median_sv": 0.9949002849902472,
        "max_sv": 1.3586440681930814,
        "normalized_gradient_fourth": 1.007257281950197
      },
      "powerlaw_gamma_0.3": {
        "median_sv": 0.9839729015509657,
        "max_sv": 3.967246737588677,
        "normalized_gradient_fourth": 1.1691086453482293
      }
    },
    {
      "depth": 128,
      "iid": {
        "median_sv": 0.9938653952485531,
        "max_sv": 1.3566726344044833,
        "normalized_gradient_fourth": 1.007058792334494
      },
      "powerlaw_gamma_0.3": {
        "median_sv": 1.0114593042006408,
        "max_sv": 5.327694756783201,
        "normalized_gradient_fourth": 1.2286738627508607
      }
    }
  ],
  "notes": "S1=sum_{t=1}^L t^(-gamma), S2=sum c_t^2. Slopes use finite-depth log-log regression. Gaussian check uses exact Wick formula."
}