1{
  2  "seed": 1645,
  3  "predictions": [
  4    "Floquet multiplier from the analytic one-cycle Jacobian equals finite-difference cycle response.",
  5    "The decay/growth transition occurs at spectral radius rho=1.",
  6    "Stable noisy response increases with the predicted resolvent scale 1/(1-rho)."
  7  ],
  8  "floquet_check": [
  9    {
 10      "amp": 0.0,
 11      "rho_analytic": 0.17495396743299985,
 12      "rho_finite_difference": 0.17495396743299982,
 13      "relative_error": 1.5864501973216558e-16
 14    },
 15    {
 16      "amp": 0.2,
 17      "rho_analytic": 0.17495396743299982,
 18      "rho_finite_difference": 0.17495396743299985,
 19      "relative_error": 1.586450197321656e-16
 20    },
 21    {
 22      "amp": 0.5,
 23      "rho_analytic": 0.1749539674329998,
 24      "rho_finite_difference": 0.17495396743299987,
 25      "relative_error": 4.759350591964969e-16
 26    },
 27    {
 28      "amp": 0.8,
 29      "rho_analytic": 0.17495396743299976,
 30      "rho_finite_difference": 0.1749539674329998,
 31      "relative_error": 1.5864501973216566e-16
 32    }
 33  ],
 34  "stability_boundary_sweep": [
 35    {
 36      "eta0": 2.272385272905983,
 37      "rho": 0.1732640312499973,
 38      "predicted_log_multiplier": -1.7529386557355395,
 39      "observed_log_decay_per_cycle": -1.5358878749975107,
 40      "decays": true
 41    },
 42    {
 43      "eta0": 2.312385272905983,
 44      "rho": 0.842380279273987,
 45      "predicted_log_multiplier": -0.17152372860497506,
 46      "observed_log_decay_per_cycle": -0.16104313646968826,
 47      "decays": true
 48    },
 49    {
 50      "eta0": 2.3323852729059826,
 51      "rho": 1.1630990087380746,
 52      "predicted_log_multiplier": 0.15108800210393783,
 53      "observed_log_decay_per_cycle": 0.15628348168299627,
 54      "decays": false
 55    },
 56    {
 57      "eta0": 2.3723852729059827,
 58      "rho": 1.8692285268219169,
 59      "predicted_log_multiplier": 0.6255257932416506,
 60      "observed_log_decay_per_cycle": 0.6256390313498245,
 61      "decays": false
 62    }
 63  ],
 64  "noise_scaling": [
 65    {
 66      "mu0": 0.1,
 67      "rho": 0.0007941861768760064,
 68      "noise_rms": 2.2965943150654663e-05,
 69      "predicted_resolvent": 1.000794817409876
 70    },
 71    {
 72      "mu0": 0.25,
 73      "rho": 0.0002441406249999999,
 74      "noise_rms": 2.3374997234630756e-05,
 75      "predicted_resolvent": 1.0002442002442002
 76    },
 77    {
 78      "mu0": 0.4,
 79      "rho": 0.004096000000000001,
 80      "noise_rms": 2.4641354404038522e-05,
 81      "predicted_resolvent": 1.0041128462181093
 82    },
 83    {
 84      "mu0": 0.55,
 85      "rho": 0.027680640625000013,
 86      "noise_rms": 2.7392842290497347e-05,
 87      "predicted_resolvent": 1.0284686716952678
 88    },
 89    {
 90      "mu0": 0.7,
 91      "rho": 0.11764899999999995,
 92      "noise_rms": 3.337198731939529e-05,
 93      "predicted_resolvent": 1.1333358266721518
 94    },
 95    {
 96      "mu0": 0.82,
 97      "rho": 0.30400667142399984,
 98      "noise_rms": 4.3817529675946784e-05,
 99      "predicted_resolvent": 1.4367953814241243
100    }
101  ],
102  "summary": {
103    "predicted_eta_boundary_rho1": 2.322385272905983,
104    "noise_monotone_with_rho": false
105  },
106  "mlp_comparison": {
107    "constant_average_momentum_test_mse": 0.004579042865205034,
108    "cyclic_test_mse": 0.004434701990241929
109  }
110}