{
  "predictions": {
    "density_affine_bound": {
      "prediction": "safe high-pressure endpoints satisfy theta=(rho0-rhofloor)/(rho0-rhoraw)",
      "max_abs_error": 0.0,
      "rows": [
        [
          1e-09,
          0.9999990009999989,
          0.9999990009999989,
          0.0
        ],
        [
          2.6426195539300637e-09,
          0.9999990026426169,
          0.9999990026426169,
          0.0
        ],
        [
          6.983438106813499e-09,
          0.9999990069834312,
          0.9999990069834312,
          0.0
        ],
        [
          1.8454570094725697e-08,
          0.999999018454552,
          0.999999018454552,
          0.0
        ],
        [
          4.876840779169491e-08,
          0.9999990487683613,
          0.9999990487683613,
          0.0
        ],
        [
          1.2887634804436826e-07,
          0.9999991288762358,
          0.9999991288762358,
          0.0
        ],
        [
          3.4057115738114333e-07,
          0.9999993405709328,
          0.9999993405709328,
          0.0
        ],
        [
          9e-07,
          0.9999998999999099,
          0.9999998999999099,
          0.0
        ]
      ]
    },
    "pressure_root": {
      "prediction": "accepted theta equals the first pressure-floor crossing on a bad segment",
      "max_abs_error": 2.220446049250313e-16,
      "rows": [
        [
          2.0,
          0.9296590914081262,
          0.9296590914081262,
          0.0,
          -0.09999999999999998
        ],
        [
          4.0,
          0.9689251672318285,
          0.9689251672318285,
          0.0,
          -0.09999999999999998
        ],
        [
          8.0,
          0.9914343387459369,
          0.991434338745937,
          1.1102230246251565e-16,
          -0.09999999999999998
        ],
        [
          16.0,
          0.9979091577528039,
          0.9979091577528039,
          0.0,
          -0.09999999999999998
        ],
        [
          32.0,
          0.9994922428352964,
          0.9994922428352966,
          2.220446049250313e-16,
          -0.09999999999999998
        ]
      ]
    },
    "inverse_strength_scaling": {
      "prediction": "for Lambda beyond the first crossing, Lambda*theta is constant",
      "scales": [
        1.0,
        2.0,
        4.0,
        8.0,
        16.0,
        32.0
      ],
      "theta": [
        0.9983463878300233,
        0.49917319391501164,
        0.24958659695750582,
        0.12479329847875291,
        0.062396649239376455,
        0.031198324619688227
      ],
      "lambda_theta": [
        0.9983463878300233,
        0.9983463878300233,
        0.9983463878300233,
        0.9983463878300233,
        0.9983463878300233,
        0.9983463878300233
      ],
      "tail_ratio": 1.0
    }
  },
  "comparison": {
    "samples": 3000,
    "raw_invalid_rate": 0.56,
    "invariant_invalid_rate": 0.0,
    "baseline_first_order_l2_to_raw": 3.3400666366809526,
    "idea_l2_to_raw": 1.0645541551229296,
    "idea_l2_to_cell": 2.2755124815580237,
    "activation_rate": 0.56
  }
}