{
  "mechanism_checks": {
    "beta_zero_relative_error": 0.0,
    "L_convex_linearity_max_abs_error": 3.3306690738754696e-16,
    "beta_logit_sweep": [
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        "beta": 0.0,
        "predicted_logit_shift_max": 0.0,
        "observed_minus_predicted_relative": 0.0
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      {
        "beta": 0.1,
        "predicted_logit_shift_max": 0.5282469816229073,
        "observed_minus_predicted_relative": 0.0
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      {
        "beta": 0.3,
        "predicted_logit_shift_max": 1.584740944868722,
        "observed_minus_predicted_relative": 0.0
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      {
        "beta": 1.0,
        "predicted_logit_shift_max": 5.282469816229073,
        "observed_minus_predicted_relative": 0.0
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      {
        "beta": 2.0,
        "predicted_logit_shift_max": 10.564939632458145,
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      {
        "beta": 4.0,
        "predicted_logit_shift_max": 21.12987926491629,
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    ],
    "feasibility_sweep": [
      {
        "shape": [
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          4
        ],
        "max_row_excess": 0.0,
        "max_col_excess": 0.0
      },
      {
        "shape": [
          5,
          7
        ],
        "max_row_excess": 0.0,
        "max_col_excess": 0.0
      },
      {
        "shape": [
          12,
          20
        ],
        "max_row_excess": 0.0,
        "max_col_excess": 0.0
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    ]
  },
  "beta_sweep": [
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      "matched_mass_fraction": 0.7167839841434622,
      "distractor_mass_fraction": 0.15107894218325763,
      "transported_mass": 0.7042068460449659,
      "entropy": 3.6497481639520686
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      "distractor_mass_fraction": 0.14760159540731255,
      "transported_mass": 0.7015904474266927,
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    {
      "beta": 0.3,
      "accuracy": 1.0,
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      "distractor_mass_fraction": 0.14120391349252584,
      "transported_mass": 0.6968991081465781,
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    {
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      "accuracy": 1.0000000000000002,
      "matched_mass_fraction": 0.7996902908245576,
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      "matched_mass_fraction": 0.8820189408463366,
      "distractor_mass_fraction": 0.0897639006616261,
      "transported_mass": 0.6591696378951832,
      "entropy": 3.208341054558804
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  ],
  "epsilon_sweep": [
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      "epsilon": 0.04,
      "accuracy": 1.0,
      "matched_mass_fraction": 0.9596130897984609,
      "distractor_mass_fraction": 0.03775141613906143,
      "transported_mass": 0.6235394991100452,
      "entropy": 3.065345410069695
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    {
      "epsilon": 0.06,
      "accuracy": 1.0000000000000002,
      "matched_mass_fraction": 0.9239846875233899,
      "distractor_mass_fraction": 0.06344221254832429,
      "transported_mass": 0.6406438642003803,
      "entropy": 3.128820558591908
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    {
      "epsilon": 0.1,
      "accuracy": 1.0,
      "matched_mass_fraction": 0.842856728464204,
      "distractor_mass_fraction": 0.10495021575308063,
      "transported_mass": 0.6703537731198164,
      "entropy": 3.3083484359773268
    },
    {
      "epsilon": 0.16,
      "accuracy": 1.0,
      "matched_mass_fraction": 0.7115833886822865,
      "distractor_mass_fraction": 0.1585894747410327,
      "transported_mass": 0.7099810030079368,
      "entropy": 3.6523909467204354
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    {
      "epsilon": 0.25,
      "accuracy": 1.0,
      "matched_mass_fraction": 0.5340271158908982,
      "distractor_mass_fraction": 0.2318628888237309,
      "transported_mass": 0.774757257309588,
      "entropy": 4.144728995351831
    },
    {
      "epsilon": 0.4,
      "accuracy": 1.0000000000000002,
      "matched_mass_fraction": 0.3417922383713152,
      "distractor_mass_fraction": 0.3094730777126748,
      "transported_mass": 0.8621593811847469,
      "entropy": 4.698616168843879
    }
  ],
  "comparison": {
    "softmax": {
      "accuracy": 1.0,
      "matched_mass_fraction": 0.7480652976071648,
      "distractor_mass_fraction": 0.10639082537868162,
      "transported_mass": 12.0,
      "entropy": 0.7691446324167127
    },
    "balanced_sinkhorn": {
      "accuracy": 0.8333333512187313,
      "matched_mass_fraction": 0.47700466754422394,
      "distractor_mass_fraction": 0.4,
      "transported_mass": 1.0,
      "entropy": 3.8223186000359064
    },
    "partial_gw": {
      "accuracy": 1.0000000000000002,
      "matched_mass_fraction": 0.7996902908245576,
      "distractor_mass_fraction": 0.12303111941184133,
      "transported_mass": 0.6841747903273336,
      "entropy": 3.4155788099393543
    }
  },
  "notes": "Uniform upper bounds are used; the MVP does not optimize transported mass with a learned dustbin penalty."
}