1{
  2  "stability_boundary_prediction": "Euler rho=1 at h=damping/omega^2=0.20; semi-implicit should remain stable here",
  3  "rate_scaling_prediction": "pullback log-diameter slope and independent vector growth equal log(rho)/h; time scales as 1/abs(lambda)",
  4  "noise_replay_prediction": "shared replay contracts while independent noise produces a nonzero diameter floor",
  5  "noise_control": {
  6    "shared_initial": 1.394562978014576,
  7    "shared_final": 0.007589943676575483,
  8    "independent_initial": 1.394562978014576,
  9    "independent_final": 0.572402506418734,
 10    "shared_slope": -0.18387126628995323,
 11    "independent_slope": -0.12479348953160699
 12  },
 13  "stability_sweep": [
 14    {
 15      "method": "euler",
 16      "h": 0.1,
 17      "predicted_rho": 0.99498743710662,
 18      "measured_slope": -0.05058072756104425,
 19      "D0": 1.35946747710701,
 20      "D128": 0.712969501632517,
 21      "contracting_predicted": true,
 22      "contracting_observed": true
 23    },
 24    {
 25      "method": "euler",
 26      "h": 0.18,
 27      "predicted_rho": 0.9981983770774224,
 28      "measured_slope": -0.010023055165208376,
 29      "D0": 1.35946747710701,
 30      "D128": 1.082963880037245,
 31      "contracting_predicted": true,
 32      "contracting_observed": true
 33    },
 34    {
 35      "method": "euler",
 36      "h": 0.2,
 37      "predicted_rho": 1.0,
 38      "measured_slope": -8.691120684778637e-05,
 39      "D0": 1.35946747710701,
 40      "D128": 1.3560549726559297,
 41      "contracting_predicted": false,
 42      "contracting_observed": true
 43    },
 44    {
 45      "method": "euler",
 46      "h": 0.22,
 47      "predicted_rho": 1.0021975853094038,
 48      "measured_slope": 0.01003518124396238,
 49      "D0": 1.35946747710701,
 50      "D128": 1.8025327726780622,
 51      "contracting_predicted": false,
 52      "contracting_observed": false
 53    },
 54    {
 55      "method": "euler",
 56      "h": 0.4,
 57      "predicted_rho": 1.0392304845413265,
 58      "measured_slope": 0.09617872825922327,
 59      "D0": 1.35946747710701,
 60      "D128": 187.19553972109574,
 61      "contracting_predicted": false,
 62      "contracting_observed": false
 63    },
 64    {
 65      "method": "semi_implicit",
 66      "h": 0.1,
 67      "predicted_rho": 0.9901475429766744,
 68      "measured_slope": -0.09906108172109297,
 69      "D0": 1.35946747710701,
 70      "D128": 0.38255312060466884,
 71      "contracting_predicted": true,
 72      "contracting_observed": true
 73    },
 74    {
 75      "method": "semi_implicit",
 76      "h": 0.18,
 77      "predicted_rho": 0.9824718648648242,
 78      "measured_slope": -0.09825235988570194,
 79      "D0": 1.35946747710701,
 80      "D128": 0.14129191612575923,
 81      "contracting_predicted": true,
 82      "contracting_observed": true
 83    },
 84    {
 85      "method": "semi_implicit",
 86      "h": 0.2,
 87      "predicted_rho": 0.9805806756909202,
 88      "measured_slope": -0.09805178288320338,
 89      "D0": 1.35946747710701,
 90      "D128": 0.11046764794255905,
 91      "contracting_predicted": true,
 92      "contracting_observed": true
 93    },
 94    {
 95      "method": "semi_implicit",
 96      "h": 0.22,
 97      "predicted_rho": 0.9787003658578391,
 98      "measured_slope": -0.09786259042805054,
 99      "D0": 1.35946747710701,
100      "D128": 0.0863643942309208,
101      "contracting_predicted": true,
102      "contracting_observed": true
103    },
104    {
105      "method": "semi_implicit",
106      "h": 0.4,
107      "predicted_rho": 0.9622504486493764,
108      "measured_slope": -0.0962081167968116,
109      "D0": 1.35946747710701,
110      "D128": 0.0098731530306816,
111      "contracting_predicted": true,
112      "contracting_observed": true
113    }
114  ],
115  "rate_sweep": [
116    {
117      "damping": 0.05,
118      "predicted_lambda": 0.0,
119      "measured_pullback_slope": -3.3501163651821895e-05,
120      "independent_vector_slope": 2.7991477937130204e-05,
121      "predicted_time_to_0.1": null,
122      "observed_time_to_0.1": null
123    },
124    {
125      "damping": 0.1,
126      "predicted_lambda": -0.025031302181185253,
127      "measured_pullback_slope": -0.025154723045101888,
128      "independent_vector_slope": -0.024973050269728285,
129      "predicted_time_to_0.1": 91.98822643453128,
130      "observed_time_to_0.1": null
131    },
132    {
133      "damping": 0.2,
134      "predicted_lambda": -0.07528266420791929,
135      "measured_pullback_slope": -0.07575848245079597,
136      "independent_vector_slope": -0.07508481466332806,
137      "predicted_time_to_0.1": 30.58586086478894,
138      "observed_time_to_0.1": null
139    },
140    {
141      "damping": 0.4,
142      "predicted_lambda": -0.17654935238720726,
143      "measured_pullback_slope": -0.17854426894313524,
144      "independent_vector_slope": -0.17446390057126537,
145      "predicted_time_to_0.1": 13.042161083344142,
146      "observed_time_to_0.1": 13.100000000000001
147    },
148    {
149      "damping": 0.8,
150      "predicted_lambda": -0.3822121282019786,
151      "measured_pullback_slope": -0.39184775374925457,
152      "independent_vector_slope": -0.3575591986290515,
153      "predicted_time_to_0.1": 6.0243642812329945,
154      "observed_time_to_0.1": 6.2
155    }
156  ]
157}