{
  "stability_boundary_prediction": "Euler rho=1 at h=damping/omega^2=0.20; semi-implicit should remain stable here",
  "rate_scaling_prediction": "pullback log-diameter slope and independent vector growth equal log(rho)/h; time scales as 1/abs(lambda)",
  "noise_replay_prediction": "shared replay contracts while independent noise produces a nonzero diameter floor",
  "noise_control": {
    "shared_initial": 1.394562978014576,
    "shared_final": 0.007589943676575483,
    "independent_initial": 1.394562978014576,
    "independent_final": 0.572402506418734,
    "shared_slope": -0.18387126628995323,
    "independent_slope": -0.12479348953160699
  },
  "stability_sweep": [
    {
      "method": "euler",
      "h": 0.1,
      "predicted_rho": 0.99498743710662,
      "measured_slope": -0.05058072756104425,
      "D0": 1.35946747710701,
      "D128": 0.712969501632517,
      "contracting_predicted": true,
      "contracting_observed": true
    },
    {
      "method": "euler",
      "h": 0.18,
      "predicted_rho": 0.9981983770774224,
      "measured_slope": -0.010023055165208376,
      "D0": 1.35946747710701,
      "D128": 1.082963880037245,
      "contracting_predicted": true,
      "contracting_observed": true
    },
    {
      "method": "euler",
      "h": 0.2,
      "predicted_rho": 1.0,
      "measured_slope": -8.691120684778637e-05,
      "D0": 1.35946747710701,
      "D128": 1.3560549726559297,
      "contracting_predicted": false,
      "contracting_observed": true
    },
    {
      "method": "euler",
      "h": 0.22,
      "predicted_rho": 1.0021975853094038,
      "measured_slope": 0.01003518124396238,
      "D0": 1.35946747710701,
      "D128": 1.8025327726780622,
      "contracting_predicted": false,
      "contracting_observed": false
    },
    {
      "method": "euler",
      "h": 0.4,
      "predicted_rho": 1.0392304845413265,
      "measured_slope": 0.09617872825922327,
      "D0": 1.35946747710701,
      "D128": 187.19553972109574,
      "contracting_predicted": false,
      "contracting_observed": false
    },
    {
      "method": "semi_implicit",
      "h": 0.1,
      "predicted_rho": 0.9901475429766744,
      "measured_slope": -0.09906108172109297,
      "D0": 1.35946747710701,
      "D128": 0.38255312060466884,
      "contracting_predicted": true,
      "contracting_observed": true
    },
    {
      "method": "semi_implicit",
      "h": 0.18,
      "predicted_rho": 0.9824718648648242,
      "measured_slope": -0.09825235988570194,
      "D0": 1.35946747710701,
      "D128": 0.14129191612575923,
      "contracting_predicted": true,
      "contracting_observed": true
    },
    {
      "method": "semi_implicit",
      "h": 0.2,
      "predicted_rho": 0.9805806756909202,
      "measured_slope": -0.09805178288320338,
      "D0": 1.35946747710701,
      "D128": 0.11046764794255905,
      "contracting_predicted": true,
      "contracting_observed": true
    },
    {
      "method": "semi_implicit",
      "h": 0.22,
      "predicted_rho": 0.9787003658578391,
      "measured_slope": -0.09786259042805054,
      "D0": 1.35946747710701,
      "D128": 0.0863643942309208,
      "contracting_predicted": true,
      "contracting_observed": true
    },
    {
      "method": "semi_implicit",
      "h": 0.4,
      "predicted_rho": 0.9622504486493764,
      "measured_slope": -0.0962081167968116,
      "D0": 1.35946747710701,
      "D128": 0.0098731530306816,
      "contracting_predicted": true,
      "contracting_observed": true
    }
  ],
  "rate_sweep": [
    {
      "damping": 0.05,
      "predicted_lambda": 0.0,
      "measured_pullback_slope": -3.3501163651821895e-05,
      "independent_vector_slope": 2.7991477937130204e-05,
      "predicted_time_to_0.1": null,
      "observed_time_to_0.1": null
    },
    {
      "damping": 0.1,
      "predicted_lambda": -0.025031302181185253,
      "measured_pullback_slope": -0.025154723045101888,
      "independent_vector_slope": -0.024973050269728285,
      "predicted_time_to_0.1": 91.98822643453128,
      "observed_time_to_0.1": null
    },
    {
      "damping": 0.2,
      "predicted_lambda": -0.07528266420791929,
      "measured_pullback_slope": -0.07575848245079597,
      "independent_vector_slope": -0.07508481466332806,
      "predicted_time_to_0.1": 30.58586086478894,
      "observed_time_to_0.1": null
    },
    {
      "damping": 0.4,
      "predicted_lambda": -0.17654935238720726,
      "measured_pullback_slope": -0.17854426894313524,
      "independent_vector_slope": -0.17446390057126537,
      "predicted_time_to_0.1": 13.042161083344142,
      "observed_time_to_0.1": 13.100000000000001
    },
    {
      "damping": 0.8,
      "predicted_lambda": -0.3822121282019786,
      "measured_pullback_slope": -0.39184775374925457,
      "independent_vector_slope": -0.3575591986290515,
      "predicted_time_to_0.1": 6.0243642812329945,
      "observed_time_to_0.1": 6.2
    }
  ]
}