1{
  2  "pole_convention_sweep": [
  3    {
  4      "lambdaN_over_lambda2": 1,
  5      "paper_predicted_gamma": 0.6,
  6      "paper_measured_radius": 0.6000000000000001,
  7      "paper_abs_error": 1.1102230246251565e-16,
  8      "paper_worst_lambda": 1.0,
  9      "idea_predicted_gamma": 0.6,
 10      "idea_measured_radius": 0.6000000000000001,
 11      "idea_abs_error": 1.1102230246251565e-16,
 12      "idea_worst_lambda": 1.0
 13    },
 14    {
 15      "lambdaN_over_lambda2": 2,
 16      "paper_predicted_gamma": 0.7355040625237562,
 17      "paper_measured_radius": 0.7355040625237562,
 18      "paper_abs_error": 0.0,
 19      "paper_worst_lambda": 1.0,
 20      "idea_predicted_gamma": 0.447213595499958,
 21      "idea_measured_radius": 2.6271371873297307,
 22      "idea_abs_error": 2.179923591829773,
 23      "idea_worst_lambda": 2.0
 24    },
 25    {
 26      "lambdaN_over_lambda2": 5,
 27      "paper_predicted_gamma": 0.8639600347330562,
 28      "paper_measured_radius": 0.8639600347330562,
 29      "paper_abs_error": 0.0,
 30      "paper_worst_lambda": 1.0,
 31      "idea_predicted_gamma": 0.2609633613715236,
 32      "idea_measured_radius": 9.125956412175452,
 33      "idea_abs_error": 8.864993050803928,
 34      "idea_worst_lambda": 5.0
 35    },
 36    {
 37      "lambdaN_over_lambda2": 10,
 38      "paper_predicted_gamma": 0.9230769230769231,
 39      "paper_measured_radius": 0.9230769230769231,
 40      "paper_abs_error": 0.0,
 41      "paper_worst_lambda": 1.0,
 42      "idea_predicted_gamma": 0.15641015840158773,
 43      "idea_measured_radius": 20.089746039960303,
 44      "idea_abs_error": 19.933335881558715,
 45      "idea_worst_lambda": 10.0
 46    },
 47    {
 48      "lambdaN_over_lambda2": 30,
 49      "paper_predicted_gamma": 0.9711241737496669,
 50      "paper_measured_radius": 0.9711241737496669,
 51      "paper_abs_error": 0.0,
 52      "paper_worst_lambda": 1.0,
 53      "idea_predicted_gamma": 0.06076745372559669,
 54      "idea_measured_radius": 63.11397411398988,
 55      "idea_abs_error": 63.05320666026429,
 56      "idea_worst_lambda": 30.0
 57    },
 58    {
 59      "lambdaN_over_lambda2": 100,
 60      "paper_predicted_gamma": 0.9907257547496702,
 61      "paper_measured_radius": 0.9907257547496702,
 62      "paper_abs_error": 0.0,
 63      "paper_worst_lambda": 1.0,
 64      "idea_predicted_gamma": 0.019422899696788083,
 65      "idea_measured_radius": 209.4818274049749,
 66      "idea_abs_error": 209.4624045052781,
 67      "idea_worst_lambda": 100.0
 68    }
 69  ],
 70  "paper_endpoint_prediction": [
 71    {
 72      "ratio": 2,
 73      "predicted_gamma": 0.7355040625237562,
 74      "radius_lambda2": 0.7355040625237562,
 75      "radius_lambdaN": 0.7355040625237559
 76    },
 77    {
 78      "ratio": 5,
 79      "predicted_gamma": 0.8639600347330562,
 80      "radius_lambda2": 0.8639600347330562,
 81      "radius_lambdaN": 0.8639600347330558
 82    },
 83    {
 84      "ratio": 10,
 85      "predicted_gamma": 0.9230769230769231,
 86      "radius_lambda2": 0.9230769230769231,
 87      "radius_lambdaN": 0.9230769230769218
 88    },
 89    {
 90      "ratio": 30,
 91      "predicted_gamma": 0.9711241737496669,
 92      "radius_lambda2": 0.9711241737496669,
 93      "radius_lambdaN": 0.9711241737496661
 94    }
 95  ],
 96  "epsilon_scaling_prediction": [
 97    {
 98      "lambda2": 0.5,
 99      "lambdaN": 5,
100      "epsilon": 0.3076923076923075,
101      "epsilon_times_lambda2": 0.15384615384615374,
102      "alpha": 0.07692307692307687,
103      "gamma": 0.9230769230769231
104    },
105    {
106      "lambda2": 1,
107      "lambdaN": 10,
108      "epsilon": 0.15384615384615374,
109      "epsilon_times_lambda2": 0.15384615384615374,
110      "alpha": 0.07692307692307687,
111      "gamma": 0.9230769230769231
112    },
113    {
114      "lambda2": 2,
115      "lambdaN": 20,
116      "epsilon": 0.07692307692307687,
117      "epsilon_times_lambda2": 0.15384615384615374,
118      "alpha": 0.07692307692307687,
119      "gamma": 0.9230769230769231
120    },
121    {
122      "lambda2": 4,
123      "lambdaN": 40,
124      "epsilon": 0.038461538461538436,
125      "epsilon_times_lambda2": 0.15384615384615374,
126      "alpha": 0.07692307692307687,
127      "gamma": 0.9230769230769231
128    }
129  ],
130  "lower_bound_prediction": [
131    {
132      "epsilon_over_lower_bound": 0.5,
133      "radius": 0.9706179991346073,
134      "predicted_at_or_below_gamma": false,
135      "worst_lambda": 1.0
136    },
137    {
138      "epsilon_over_lower_bound": 0.8,
139      "radius": 0.9430882346825804,
140      "predicted_at_or_below_gamma": false,
141      "worst_lambda": 1.0
142    },
143    {
144      "epsilon_over_lower_bound": 1.0,
145      "radius": 0.9230769230769231,
146      "predicted_at_or_below_gamma": true,
147      "worst_lambda": 1.0
148    },
149    {
150      "epsilon_over_lower_bound": 1.2,
151      "radius": 1.263417607761387,
152      "predicted_at_or_below_gamma": false,
153      "worst_lambda": 10.0
154    }
155  ],
156  "quadratic_comparison": {
157    "graph_lambda2": 0.15224093497742652,
158    "graph_lambdaN": 3.847759065022573,
159    "baseline_final_loss": 0.20385561609981762,
160    "baseline_finite": true,
161    "paper_tuned_final_loss": 0.23949067010736508,
162    "paper_tuned_finite": true,
163    "idea_literal_final_loss": 1.2129031663279131e+101,
164    "idea_literal_finite": true
165  },
166  "conclusion": "The authoritative idea reverses the paper theorem kappa definition; literal gains are unstable for condition number > 1."
167}