{
  "seed": 1645,
  "predictions": [
    "Floquet multiplier from the analytic one-cycle Jacobian equals finite-difference cycle response.",
    "The decay/growth transition occurs at spectral radius rho=1.",
    "Stable noisy response increases with the predicted resolvent scale 1/(1-rho)."
  ],
  "floquet_check": [
    {
      "amp": 0.0,
      "rho_analytic": 0.17495396743299985,
      "rho_finite_difference": 0.17495396743299982,
      "relative_error": 1.5864501973216558e-16
    },
    {
      "amp": 0.2,
      "rho_analytic": 0.17495396743299982,
      "rho_finite_difference": 0.17495396743299985,
      "relative_error": 1.586450197321656e-16
    },
    {
      "amp": 0.5,
      "rho_analytic": 0.1749539674329998,
      "rho_finite_difference": 0.17495396743299987,
      "relative_error": 4.759350591964969e-16
    },
    {
      "amp": 0.8,
      "rho_analytic": 0.17495396743299976,
      "rho_finite_difference": 0.1749539674329998,
      "relative_error": 1.5864501973216566e-16
    }
  ],
  "stability_boundary_sweep": [
    {
      "eta0": 2.272385272905983,
      "rho": 0.1732640312499973,
      "predicted_log_multiplier": -1.7529386557355395,
      "observed_log_decay_per_cycle": -1.5358878749975107,
      "decays": true
    },
    {
      "eta0": 2.312385272905983,
      "rho": 0.842380279273987,
      "predicted_log_multiplier": -0.17152372860497506,
      "observed_log_decay_per_cycle": -0.16104313646968826,
      "decays": true
    },
    {
      "eta0": 2.3323852729059826,
      "rho": 1.1630990087380746,
      "predicted_log_multiplier": 0.15108800210393783,
      "observed_log_decay_per_cycle": 0.15628348168299627,
      "decays": false
    },
    {
      "eta0": 2.3723852729059827,
      "rho": 1.8692285268219169,
      "predicted_log_multiplier": 0.6255257932416506,
      "observed_log_decay_per_cycle": 0.6256390313498245,
      "decays": false
    }
  ],
  "noise_scaling": [
    {
      "mu0": 0.1,
      "rho": 0.0007941861768760064,
      "noise_rms": 2.2965943150654663e-05,
      "predicted_resolvent": 1.000794817409876
    },
    {
      "mu0": 0.25,
      "rho": 0.0002441406249999999,
      "noise_rms": 2.3374997234630756e-05,
      "predicted_resolvent": 1.0002442002442002
    },
    {
      "mu0": 0.4,
      "rho": 0.004096000000000001,
      "noise_rms": 2.4641354404038522e-05,
      "predicted_resolvent": 1.0041128462181093
    },
    {
      "mu0": 0.55,
      "rho": 0.027680640625000013,
      "noise_rms": 2.7392842290497347e-05,
      "predicted_resolvent": 1.0284686716952678
    },
    {
      "mu0": 0.7,
      "rho": 0.11764899999999995,
      "noise_rms": 3.337198731939529e-05,
      "predicted_resolvent": 1.1333358266721518
    },
    {
      "mu0": 0.82,
      "rho": 0.30400667142399984,
      "noise_rms": 4.3817529675946784e-05,
      "predicted_resolvent": 1.4367953814241243
    }
  ],
  "summary": {
    "predicted_eta_boundary_rho1": 2.322385272905983,
    "noise_monotone_with_rho": false
  },
  "mlp_comparison": {
    "constant_average_momentum_test_mse": 0.004579042865205034,
    "cyclic_test_mse": 0.004434701990241929
  }
}