{
  "device": "cuda",
  "math_check": {
    "sorted_ot_cost": 0.14749999344348907,
    "random_coupling_cost": 2.112499952316284,
    "derivative_max_error": 0.00067901611328125
  },
  "locality_sweep": [
    {
      "epsilon": 0.06,
      "lambda": 0.0,
      "paired_R": 0.7111561298370361,
      "marginal_err": 4.0413811802864075e-05
    },
    {
      "epsilon": 0.06,
      "lambda": 0.5,
      "paired_R": 0.0283959973603487,
      "marginal_err": 1.2326985597610474e-05
    },
    {
      "epsilon": 0.06,
      "lambda": 2.0,
      "paired_R": 0.005961012560874224,
      "marginal_err": 6.226822733879089e-06
    },
    {
      "epsilon": 0.06,
      "lambda": 8.0,
      "paired_R": 0.0008196450653485954,
      "marginal_err": 2.3618340492248535e-06
    },
    {
      "epsilon": 0.16,
      "lambda": 0.0,
      "paired_R": 0.8314868211746216,
      "marginal_err": 1.30385160446167e-08
    },
    {
      "epsilon": 0.16,
      "lambda": 0.5,
      "paired_R": 0.10292951762676239,
      "marginal_err": 3.345310688018799e-06
    },
    {
      "epsilon": 0.16,
      "lambda": 2.0,
      "paired_R": 0.02393825724720955,
      "marginal_err": 7.588416337966919e-06
    },
    {
      "epsilon": 0.16,
      "lambda": 8.0,
      "paired_R": 0.004799625836312771,
      "marginal_err": 1.0259449481964111e-05
    },
    {
      "epsilon": 0.4,
      "lambda": 0.0,
      "paired_R": 0.9091153144836426,
      "marginal_err": 1.30385160446167e-08
    },
    {
      "epsilon": 0.4,
      "lambda": 0.5,
      "paired_R": 0.2552563548088074,
      "marginal_err": 9.313225746154785e-09
    },
    {
      "epsilon": 0.4,
      "lambda": 2.0,
      "paired_R": 0.07225342839956284,
      "marginal_err": 1.1175870895385742e-08
    },
    {
      "epsilon": 0.4,
      "lambda": 8.0,
      "paired_R": 0.01732504926621914,
      "marginal_err": 2.0343810319900513e-05
    }
  ],
  "comparison_lambda0": {
    "flow_w1": 0.4429539889097214,
    "mse_w1": 1.006102442741394,
    "flow_mode_coverage": 0.85107421875,
    "per_s_w1": [
      0.45495861768722534,
      0.29935240745544434,
      0.3903495669364929,
      0.6271553635597229
    ]
  },
  "comparison_lambda8": {
    "flow_w1": 0.17159544862806797,
    "mse_w1": 1.0032900869846344,
    "flow_mode_coverage": 0.908203125,
    "per_s_w1": [
      0.09672722965478897,
      0.20712798833847046,
      0.19947239756584167,
      0.18305417895317078
    ]
  },
  "predictions": {
    "lambda_effect_at_eps_0.16": "paired_R should decrease monotonically with lambda",
    "epsilon_effect_at_lambda_8": "paired_R should increase with epsilon",
    "flow_distributional_effect": "flow W1 should be lower than deterministic MSE W1 and mode coverage near 1"
  }
}