1{
  2  "predictions": {
  3    "density_affine_bound": {
  4      "prediction": "safe high-pressure endpoints satisfy theta=(rho0-rhofloor)/(rho0-rhoraw)",
  5      "max_abs_error": 0.0,
  6      "rows": [
  7        [
  8          1e-09,
  9          0.9999990009999989,
 10          0.9999990009999989,
 11          0.0
 12        ],
 13        [
 14          2.6426195539300637e-09,
 15          0.9999990026426169,
 16          0.9999990026426169,
 17          0.0
 18        ],
 19        [
 20          6.983438106813499e-09,
 21          0.9999990069834312,
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 24        ],
 25        [
 26          1.8454570094725697e-08,
 27          0.999999018454552,
 28          0.999999018454552,
 29          0.0
 30        ],
 31        [
 32          4.876840779169491e-08,
 33          0.9999990487683613,
 34          0.9999990487683613,
 35          0.0
 36        ],
 37        [
 38          1.2887634804436826e-07,
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 41          0.0
 42        ],
 43        [
 44          3.4057115738114333e-07,
 45          0.9999993405709328,
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 47          0.0
 48        ],
 49        [
 50          9e-07,
 51          0.9999998999999099,
 52          0.9999998999999099,
 53          0.0
 54        ]
 55      ]
 56    },
 57    "pressure_root": {
 58      "prediction": "accepted theta equals the first pressure-floor crossing on a bad segment",
 59      "max_abs_error": 2.220446049250313e-16,
 60      "rows": [
 61        [
 62          2.0,
 63          0.9296590914081262,
 64          0.9296590914081262,
 65          0.0,
 66          -0.09999999999999998
 67        ],
 68        [
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 72          0.0,
 73          -0.09999999999999998
 74        ],
 75        [
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 78          0.991434338745937,
 79          1.1102230246251565e-16,
 80          -0.09999999999999998
 81        ],
 82        [
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 84          0.9979091577528039,
 85          0.9979091577528039,
 86          0.0,
 87          -0.09999999999999998
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 89        [
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 92          0.9994922428352966,
 93          2.220446049250313e-16,
 94          -0.09999999999999998
 95        ]
 96      ]
 97    },
 98    "inverse_strength_scaling": {
 99      "prediction": "for Lambda beyond the first crossing, Lambda*theta is constant",
100      "scales": [
101        1.0,
102        2.0,
103        4.0,
104        8.0,
105        16.0,
106        32.0
107      ],
108      "theta": [
109        0.9983463878300233,
110        0.49917319391501164,
111        0.24958659695750582,
112        0.12479329847875291,
113        0.062396649239376455,
114        0.031198324619688227
115      ],
116      "lambda_theta": [
117        0.9983463878300233,
118        0.9983463878300233,
119        0.9983463878300233,
120        0.9983463878300233,
121        0.9983463878300233,
122        0.9983463878300233
123      ],
124      "tail_ratio": 1.0
125    }
126  },
127  "comparison": {
128    "samples": 3000,
129    "raw_invalid_rate": 0.56,
130    "invariant_invalid_rate": 0.0,
131    "baseline_first_order_l2_to_raw": 3.3400666366809526,
132    "idea_l2_to_raw": 1.0645541551229296,
133    "idea_l2_to_cell": 2.2755124815580237,
134    "activation_rate": 0.56
135  }
136}