{
  "seed": 1180,
  "math": {
    "continuum_scaling": [
      {
        "dimension": 1,
        "predicted_mass_slope": 1,
        "observed_mass_slope": 0.9971248067687789,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 1.0007235349778871
      },
      {
        "dimension": 2,
        "predicted_mass_slope": 2,
        "observed_mass_slope": 1.9798554639298027,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.9947957757026576
      },
      {
        "dimension": 3,
        "predicted_mass_slope": 3,
        "observed_mass_slope": 2.9885260298516685,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.9363492223759651
      },
      {
        "dimension": 4,
        "predicted_mass_slope": 4,
        "observed_mass_slope": 3.8208541061082606,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.7962891442726477
      },
      {
        "dimension": 5,
        "predicted_mass_slope": 5,
        "observed_mass_slope": 4.9862781093742665,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.5247419328173384
      }
    ],
    "dimension_scaling": [
      {
        "dimension": 1,
        "exponent_p": 0.0,
        "predicted_slope": 1.0,
        "observed_slope": 1.0003991033148736
      },
      {
        "dimension": 1,
        "exponent_p": 1.0,
        "predicted_slope": 0.0,
        "observed_slope": 0.00039910331487511745
      },
      {
        "dimension": 1,
        "exponent_p": 2.0,
        "predicted_slope": -1.0,
        "observed_slope": -0.9996008966851281
      },
      {
        "dimension": 2,
        "exponent_p": 0.0,
        "predicted_slope": 2.0,
        "observed_slope": 2.0035753041647397
      },
      {
        "dimension": 2,
        "exponent_p": 2.0,
        "predicted_slope": 0.0,
        "observed_slope": 0.003575304164734519
      },
      {
        "dimension": 2,
        "exponent_p": 3.0,
        "predicted_slope": -1.0,
        "observed_slope": -0.996424695835266
      },
      {
        "dimension": 3,
        "exponent_p": 0.0,
        "predicted_slope": 3.0,
        "observed_slope": 2.98619431718076
      },
      {
        "dimension": 3,
        "exponent_p": 3.0,
        "predicted_slope": 0.0,
        "observed_slope": -0.01380568281923986
      },
      {
        "dimension": 3,
        "exponent_p": 4.0,
        "predicted_slope": -1.0,
        "observed_slope": -1.013805682819245
      },
      {
        "dimension": 4,
        "exponent_p": 0.0,
        "predicted_slope": 4.0,
        "observed_slope": 3.966793589446673
      },
      {
        "dimension": 4,
        "exponent_p": 4.0,
        "predicted_slope": 0.0,
        "observed_slope": -0.03320641055332983
      },
      {
        "dimension": 4,
        "exponent_p": 5.0,
        "predicted_slope": -1.0,
        "observed_slope": -1.0332064105533332
      }
    ],
    "bandwidth_scaling": [
      {
        "dimension": 1,
        "predicted_effective_support_slope": 1,
        "observed_effective_support_slope": 1.0057431260587766,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.9910818976197515
      },
      {
        "dimension": 2,
        "predicted_effective_support_slope": 2,
        "observed_effective_support_slope": 2.0200210771108873,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.9912941705315172
      },
      {
        "dimension": 3,
        "predicted_effective_support_slope": 3,
        "observed_effective_support_slope": 2.9036358762022054,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.9645467671322842
      },
      {
        "dimension": 4,
        "predicted_effective_support_slope": 4,
        "observed_effective_support_slope": 3.3394918156719386,
        "predicted_radius_slope": 1.0,
        "observed_radius_slope": 0.803170442160515
      }
    ],
    "intrinsic_dimension_estimation": [
      {
        "dimension": 1,
        "m": 10,
        "predicted_mean_dimension": 1.0,
        "observed_mean_dimension": 1.1930547373369353,
        "observed_std": 0.3206530083341453
      },
      {
        "dimension": 1,
        "m": 20,
        "predicted_mean_dimension": 1.0,
        "observed_mean_dimension": 1.1236769846474124,
        "observed_std": 0.2070128236317298
      },
      {
        "dimension": 1,
        "m": 32,
        "predicted_mean_dimension": 1.0,
        "observed_mean_dimension": 1.0740733545723358,
        "observed_std": 0.1219649426055994
      },
      {
        "dimension": 2,
        "m": 10,
        "predicted_mean_dimension": 2.0,
        "observed_mean_dimension": 2.1422254616471923,
        "observed_std": 0.6032007869406106
      },
      {
        "dimension": 2,
        "m": 20,
        "predicted_mean_dimension": 2.0,
        "observed_mean_dimension": 2.217047668688947,
        "observed_std": 0.5220619949429813
      },
      {
        "dimension": 2,
        "m": 32,
        "predicted_mean_dimension": 2.0,
        "observed_mean_dimension": 2.141405328183512,
        "observed_std": 0.3895325311181988
      },
      {
        "dimension": 3,
        "m": 10,
        "predicted_mean_dimension": 3.0,
        "observed_mean_dimension": 3.6075804145453176,
        "observed_std": 1.5044792681813026
      },
      {
        "dimension": 3,
        "m": 20,
        "predicted_mean_dimension": 3.0,
        "observed_mean_dimension": 3.1470040002401376,
        "observed_std": 0.7306335578630023
      },
      {
        "dimension": 3,
        "m": 32,
        "predicted_mean_dimension": 3.0,
        "observed_mean_dimension": 3.052341310493895,
        "observed_std": 0.5332825592932924
      },
      {
        "dimension": 4,
        "m": 10,
        "predicted_mean_dimension": 4.0,
        "observed_mean_dimension": 4.204505020109922,
        "observed_std": 1.4172798495486385
      },
      {
        "dimension": 4,
        "m": 20,
        "predicted_mean_dimension": 4.0,
        "observed_mean_dimension": 4.016265770133284,
        "observed_std": 0.7818599086374509
      },
      {
        "dimension": 4,
        "m": 32,
        "predicted_mean_dimension": 4.0,
        "observed_mean_dimension": 4.1289600141042815,
        "observed_std": 0.8692914842607032
      }
    ]
  },
  "mini_experiment": {
    "kernel_mse": 0.6570898924640083,
    "dot_product_mse": 0.729866764651948,
    "uniform_mse": 0.707964917191898,
    "kernel_entropy": 3.986655666106431,
    "dot_product_entropy": 6.333542562177541,
    "kernel_mean_effective_neighbors": 40.662998207923934
  }
}