{
  "seed": 1436,
  "b": 0.45,
  "rows": [
    {
      "a": -1.45,
      "local_rho_pred": 1.0,
      "measured_rho": 1.000000000015,
      "impulse_l2": 3.2899080248844666e+39,
      "cert": false,
      "gamma": Infinity,
      "data_cert": false,
      "data_gamma": Infinity,
      "lmi_maxeig": Infinity
    },
    {
      "a": -1.1,
      "local_rho_pred": 0.6500000000000001,
      "measured_rho": 0.6500000000001044,
      "impulse_l2": 1.4573659887214219,
      "cert": false,
      "gamma": Infinity,
      "data_cert": false,
      "data_gamma": Infinity,
      "lmi_maxeig": Infinity
    },
    {
      "a": -0.8,
      "local_rho_pred": 0.35000000000000003,
      "measured_rho": 0.3500000000000687,
      "impulse_l2": 1.1150947983935109,
      "cert": false,
      "gamma": Infinity,
      "data_cert": false,
      "data_gamma": Infinity,
      "lmi_maxeig": Infinity
    },
    {
      "a": -0.5,
      "local_rho_pred": 0.04999999999999999,
      "measured_rho": 0.0,
      "impulse_l2": 1.0123286385091057,
      "cert": true,
      "gamma": 61.054022965853264,
      "data_cert": true,
      "data_gamma": 61.054022965853264,
      "lmi_maxeig": -1.1969867225902793,
      "linear_gain_pred": 1.0526315789473684
    },
    {
      "a": -0.2,
      "local_rho_pred": 0.25,
      "measured_rho": 0.24999999999993577,
      "impulse_l2": 1.010788447487706,
      "cert": true,
      "gamma": 5.17947467923121,
      "data_cert": true,
      "data_gamma": 5.17947467923121,
      "lmi_maxeig": -0.2908815862051584,
      "linear_gain_pred": 1.3333333333333333
    },
    {
      "a": 0.0,
      "local_rho_pred": 0.45,
      "measured_rho": 0.4499999999999245,
      "impulse_l2": 1.0700494149505797,
      "cert": true,
      "gamma": 5.17947467923121,
      "data_cert": true,
      "data_gamma": 5.17947467923121,
      "lmi_maxeig": -0.48291134621173454,
      "linear_gain_pred": 1.8181818181818181
    },
    {
      "a": 0.2,
      "local_rho_pred": 0.65,
      "measured_rho": 0.6499999999998958,
      "impulse_l2": 1.2165471151402139,
      "cert": true,
      "gamma": 5.17947467923121,
      "data_cert": true,
      "data_gamma": 5.17947467923121,
      "lmi_maxeig": -0.2908815862051584,
      "linear_gain_pred": 2.857142857142857
    },
    {
      "a": 0.4,
      "local_rho_pred": 0.8500000000000001,
      "measured_rho": 0.8499999999997829,
      "impulse_l2": 1.6129898587029121,
      "cert": true,
      "gamma": 13.894954943731374,
      "data_cert": true,
      "data_gamma": 13.894954943731374,
      "lmi_maxeig": -0.1038011552756935,
      "linear_gain_pred": 6.6666666666666705
    },
    {
      "a": 0.5,
      "local_rho_pred": 0.95,
      "measured_rho": 0.9499999999993821,
      "impulse_l2": 2.2513813846009008,
      "cert": true,
      "gamma": 61.054022965853264,
      "data_cert": true,
      "data_gamma": 61.054022965853264,
      "lmi_maxeig": -1.1969867225902793
    },
    {
      "a": 0.6,
      "local_rho_pred": 1.05,
      "measured_rho": 1.0450635704920672,
      "impulse_l2": 10.03533488667505,
      "cert": false,
      "gamma": Infinity,
      "data_cert": false,
      "data_gamma": Infinity,
      "lmi_maxeig": Infinity
    },
    {
      "a": 0.75,
      "local_rho_pred": 1.2,
      "measured_rho": 1.0495038274669848,
      "impulse_l2": 26.311524525214264,
      "cert": false,
      "gamma": Infinity,
      "data_cert": false,
      "data_gamma": Infinity,
      "lmi_maxeig": Infinity
    }
  ],
  "prediction_boundary_a": 0.55,
  "observed_certificate_boundary_a": 0.48888888888888893,
  "boundary_error": -0.061111111111111116,
  "positive_boundary_definition": "largest nonnegative certified a on the tested grid",
  "stable_gain_rows": [
    {
      "a": -0.5,
      "local_rho_pred": 0.04999999999999999,
      "measured_rho": 0.0,
      "impulse_l2": 1.0123286385091057,
      "cert": true,
      "gamma": 61.054022965853264,
      "data_cert": true,
      "data_gamma": 61.054022965853264,
      "lmi_maxeig": -1.1969867225902793,
      "linear_gain_pred": 1.0526315789473684
    },
    {
      "a": -0.2,
      "local_rho_pred": 0.25,
      "measured_rho": 0.24999999999993577,
      "impulse_l2": 1.010788447487706,
      "cert": true,
      "gamma": 5.17947467923121,
      "data_cert": true,
      "data_gamma": 5.17947467923121,
      "lmi_maxeig": -0.2908815862051584,
      "linear_gain_pred": 1.3333333333333333
    },
    {
      "a": 0.0,
      "local_rho_pred": 0.45,
      "measured_rho": 0.4499999999999245,
      "impulse_l2": 1.0700494149505797,
      "cert": true,
      "gamma": 5.17947467923121,
      "data_cert": true,
      "data_gamma": 5.17947467923121,
      "lmi_maxeig": -0.48291134621173454,
      "linear_gain_pred": 1.8181818181818181
    },
    {
      "a": 0.2,
      "local_rho_pred": 0.65,
      "measured_rho": 0.6499999999998958,
      "impulse_l2": 1.2165471151402139,
      "cert": true,
      "gamma": 5.17947467923121,
      "data_cert": true,
      "data_gamma": 5.17947467923121,
      "lmi_maxeig": -0.2908815862051584,
      "linear_gain_pred": 2.857142857142857
    },
    {
      "a": 0.4,
      "local_rho_pred": 0.8500000000000001,
      "measured_rho": 0.8499999999997829,
      "impulse_l2": 1.6129898587029121,
      "cert": true,
      "gamma": 13.894954943731374,
      "data_cert": true,
      "data_gamma": 13.894954943731374,
      "lmi_maxeig": -0.1038011552756935,
      "linear_gain_pred": 6.6666666666666705
    }
  ],
  "notes": [
    "Prediction 1: local perturbations contract for |a+b|<1 and grow for |a+b|>1.",
    "Prediction 2: tanh sector certificate boundary is a+b=1 on the positive-a side.",
    "Prediction 3: disturbance gain grows as 1/(1-(a+b)) near the boundary."
  ]
}