{
  "pole_convention_sweep": [
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      "lambdaN_over_lambda2": 1,
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      "paper_measured_radius": 0.6000000000000001,
      "paper_abs_error": 1.1102230246251565e-16,
      "paper_worst_lambda": 1.0,
      "idea_predicted_gamma": 0.6,
      "idea_measured_radius": 0.6000000000000001,
      "idea_abs_error": 1.1102230246251565e-16,
      "idea_worst_lambda": 1.0
    },
    {
      "lambdaN_over_lambda2": 2,
      "paper_predicted_gamma": 0.7355040625237562,
      "paper_measured_radius": 0.7355040625237562,
      "paper_abs_error": 0.0,
      "paper_worst_lambda": 1.0,
      "idea_predicted_gamma": 0.447213595499958,
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      "lambdaN_over_lambda2": 5,
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      "paper_measured_radius": 0.8639600347330562,
      "paper_abs_error": 0.0,
      "paper_worst_lambda": 1.0,
      "idea_predicted_gamma": 0.2609633613715236,
      "idea_measured_radius": 9.125956412175452,
      "idea_abs_error": 8.864993050803928,
      "idea_worst_lambda": 5.0
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    {
      "lambdaN_over_lambda2": 10,
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      "paper_measured_radius": 0.9230769230769231,
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      "paper_worst_lambda": 1.0,
      "idea_predicted_gamma": 0.15641015840158773,
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      "idea_worst_lambda": 10.0
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    {
      "lambdaN_over_lambda2": 30,
      "paper_predicted_gamma": 0.9711241737496669,
      "paper_measured_radius": 0.9711241737496669,
      "paper_abs_error": 0.0,
      "paper_worst_lambda": 1.0,
      "idea_predicted_gamma": 0.06076745372559669,
      "idea_measured_radius": 63.11397411398988,
      "idea_abs_error": 63.05320666026429,
      "idea_worst_lambda": 30.0
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    {
      "lambdaN_over_lambda2": 100,
      "paper_predicted_gamma": 0.9907257547496702,
      "paper_measured_radius": 0.9907257547496702,
      "paper_abs_error": 0.0,
      "paper_worst_lambda": 1.0,
      "idea_predicted_gamma": 0.019422899696788083,
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      "idea_abs_error": 209.4624045052781,
      "idea_worst_lambda": 100.0
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  "paper_endpoint_prediction": [
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      "ratio": 2,
      "predicted_gamma": 0.7355040625237562,
      "radius_lambda2": 0.7355040625237562,
      "radius_lambdaN": 0.7355040625237559
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    {
      "ratio": 5,
      "predicted_gamma": 0.8639600347330562,
      "radius_lambda2": 0.8639600347330562,
      "radius_lambdaN": 0.8639600347330558
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    {
      "ratio": 10,
      "predicted_gamma": 0.9230769230769231,
      "radius_lambda2": 0.9230769230769231,
      "radius_lambdaN": 0.9230769230769218
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    {
      "ratio": 30,
      "predicted_gamma": 0.9711241737496669,
      "radius_lambda2": 0.9711241737496669,
      "radius_lambdaN": 0.9711241737496661
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  ],
  "epsilon_scaling_prediction": [
    {
      "lambda2": 0.5,
      "lambdaN": 5,
      "epsilon": 0.3076923076923075,
      "epsilon_times_lambda2": 0.15384615384615374,
      "alpha": 0.07692307692307687,
      "gamma": 0.9230769230769231
    },
    {
      "lambda2": 1,
      "lambdaN": 10,
      "epsilon": 0.15384615384615374,
      "epsilon_times_lambda2": 0.15384615384615374,
      "alpha": 0.07692307692307687,
      "gamma": 0.9230769230769231
    },
    {
      "lambda2": 2,
      "lambdaN": 20,
      "epsilon": 0.07692307692307687,
      "epsilon_times_lambda2": 0.15384615384615374,
      "alpha": 0.07692307692307687,
      "gamma": 0.9230769230769231
    },
    {
      "lambda2": 4,
      "lambdaN": 40,
      "epsilon": 0.038461538461538436,
      "epsilon_times_lambda2": 0.15384615384615374,
      "alpha": 0.07692307692307687,
      "gamma": 0.9230769230769231
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  ],
  "lower_bound_prediction": [
    {
      "epsilon_over_lower_bound": 0.5,
      "radius": 0.9706179991346073,
      "predicted_at_or_below_gamma": false,
      "worst_lambda": 1.0
    },
    {
      "epsilon_over_lower_bound": 0.8,
      "radius": 0.9430882346825804,
      "predicted_at_or_below_gamma": false,
      "worst_lambda": 1.0
    },
    {
      "epsilon_over_lower_bound": 1.0,
      "radius": 0.9230769230769231,
      "predicted_at_or_below_gamma": true,
      "worst_lambda": 1.0
    },
    {
      "epsilon_over_lower_bound": 1.2,
      "radius": 1.263417607761387,
      "predicted_at_or_below_gamma": false,
      "worst_lambda": 10.0
    }
  ],
  "quadratic_comparison": {
    "graph_lambda2": 0.15224093497742652,
    "graph_lambdaN": 3.847759065022573,
    "baseline_final_loss": 0.20385561609981762,
    "baseline_finite": true,
    "paper_tuned_final_loss": 0.23949067010736508,
    "paper_tuned_finite": true,
    "idea_literal_final_loss": 1.2129031663279131e+101,
    "idea_literal_finite": true
  },
  "conclusion": "The authoritative idea reverses the paper theorem kappa definition; literal gains are unstable for condition number > 1."
}