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  2  "seed": 2454,
  3  "n": 64,
  4  "m": 16,
  5  "trials": 500,
  6  "predictions": {
  7    "P1": "orthogonality defect remains at floating-point roundoff for every T",
  8    "P2": "scaled quadratic norm has mean near 1",
  9    "P3": "quadratic-statistic spread moves toward the Haar reference as T increases"
 10  },
 11  "haar_reference": {
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 16    "mse": 0.09218868094388902
 17  },
 18  "sweep": [
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 27      "mse": 0.025999307840035166,
 28      "std_over_haar_std": 0.0,
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 30    },
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 66    },
 67    {
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 90    },
 91    {
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100      "std_over_haar_std": 1.00193692607272,
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103    {
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111      "mse": 0.09630950543854609,
112      "std_over_haar_std": 1.0229003033902562,
113      "orthogonality_max_abs": 1.3322676295501878e-15
114    }
115  ],
116  "prediction_checks": {
117    "P1_max_defect_all_T": 1.3322676295501878e-15,
118    "P2_mean_range": [
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120      1.0001193975028697
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122    "P2_max_abs_error_vs_analytic_mean": 0.01593885670077888,
123    "P3_std_ratio_T0": 0.0,
124    "P3_std_ratio_T8n": 1.00193692607272,
125    "P3_std_ratio_T16n": 1.0229003033902562
126  },
127  "distortion": {
128    "Kac": {
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131      "std": 0.316543062652471,
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133      "mse": 0.10248153996079176
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135    "Gaussian": {
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140      "mse": 0.1180153034068356
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142    "Haar": {
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147      "mse": 0.12040944984865364
148    }
149  },
150  "timing_seconds_per_batch": {
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152    "Gaussian_dense": 4.3902997276745737e-05,
153    "Haar_dense_not_timed": 5.9994999901391566e-05
154  },
155  "storage": {
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157    "Kac_explicit_i_j_theta_bytes": 8192,
158    "dense_projection_bytes": 8192,
159    "dense_full_orthogonal_bytes": 32768,
160    "dense_full_over_explicit_triples": 4.0,
161    "dense_projection_over_runtime_arrays": 0.6666666666666666
162  }
163}