{
  "seed": 1163,
  "predictions": {
    "P1_rank_sampling_scaling": "rank covariance error should scale as n^-1/2 after monotone marginal distortion",
    "P2_outlier_influence": "raw variance coefficient versus A^2 should approach q(1-q)=0.0475; rank variance should remain bounded",
    "P3_eigen_specific_cleaning": "bulk contraction should reduce covariance error while retaining top spike"
  },
  "observed": {
    "P1_rows": [
      {
        "n": 64,
        "raw_relerr": 9.627445515131965,
        "rank_relerr": 0.12752087486906927,
        "rank_sd": 0.0077814080743867226
      },
      {
        "n": 128,
        "raw_relerr": 8.550812475957713,
        "rank_relerr": 0.09299084186579426,
        "rank_sd": 0.004832772149723181
      },
      {
        "n": 256,
        "raw_relerr": 8.31347696293776,
        "rank_relerr": 0.06468969880253567,
        "rank_sd": 0.0027468181696894273
      },
      {
        "n": 512,
        "raw_relerr": 7.958248692270368,
        "rank_relerr": 0.046971362173094916,
        "rank_sd": 0.001984766746976157
      },
      {
        "n": 1024,
        "raw_relerr": 8.242516751951532,
        "rank_relerr": 0.028335104293481763,
        "rank_sd": 0.0012234488206997083
      }
    ],
    "P1_loglog_slope": -0.5325449236995332,
    "P2_rows": [
      {
        "A": 0,
        "raw_relerr": 0.13955397901850178,
        "rank_relerr": 0.10399218382750393,
        "raw_var0": 1.0131367468587391,
        "rank_var0": 0.9949828386117898
      },
      {
        "A": 2,
        "raw_relerr": 0.15852610988036184,
        "rank_relerr": 0.11244665029125489,
        "raw_var0": 1.170388853312168,
        "rank_var0": 0.9949828386117897
      },
      {
        "A": 5,
        "raw_relerr": 0.3243089341483496,
        "rank_relerr": 0.11013023599702595,
        "raw_var0": 2.108980335146783,
        "rank_var0": 0.9949828386117898
      },
      {
        "A": 10,
        "raw_relerr": 1.1655031460557297,
        "rank_relerr": 0.11533131439032196,
        "raw_var0": 5.4388863554692986,
        "rank_var0": 0.9949828386117898
      },
      {
        "A": 20,
        "raw_relerr": 4.649857727304761,
        "rank_relerr": 0.11873543086859861,
        "raw_var0": 18.887928136728245,
        "rank_var0": 0.9949828386117897
      },
      {
        "A": 50,
        "raw_relerr": 29.04385953139562,
        "rank_relerr": 0.11831776783813837,
        "raw_var0": 112.93228285660875,
        "rank_var0": 0.9949828386117897
      }
    ],
    "P2_raw_A2_coefficient": 0.04478674552133152,
    "P2_predicted_coefficient": 0.0475,
    "P3_rows": [
      {
        "spike": 1,
        "raw_cov_error": 0.9993310043924628,
        "clean_cov_error": 0.6280693057159472,
        "top_raw": 1.5018120005700746,
        "top_clean": 1.5018120005700746,
        "clean_win": 1.0
      },
      {
        "spike": 2,
        "raw_cov_error": 1.1438513127701158,
        "clean_cov_error": 0.808995436404669,
        "top_raw": 1.7950711958169931,
        "top_clean": 1.7950711958169931,
        "clean_win": 1.0
      },
      {
        "spike": 4,
        "raw_cov_error": 1.7159793419567293,
        "clean_cov_error": 1.5368681875991579,
        "top_raw": 2.8852101335647706,
        "top_clean": 2.8852101335647706,
        "clean_win": 1.0
      },
      {
        "spike": 8,
        "raw_cov_error": 5.300344007341902,
        "clean_cov_error": 5.193192829445812,
        "top_raw": 3.442518563640547,
        "top_clean": 3.442518563640547,
        "clean_win": 1.0
      }
    ],
    "optimization_mse": {
      "raw": {
        "50": 0.0027569560510962215,
        "100": 0.002607329511348986,
        "200": 0.002839995302319132,
        "350": 0.002654563332895589
      },
      "diag": {
        "50": 2.6512840044835624,
        "100": 0.7988699591618948,
        "200": 0.6148232270461336,
        "350": 0.7927998547026667
      },
      "rank_spectral": {
        "50": 0.37501174844915364,
        "100": 0.40804158236659205,
        "200": 0.3828515350152292,
        "350": 0.385993139947289
      }
    }
  },
  "elapsed_sec": 6.134591102600098
}