1{
 2  "idea": "Adaptive Ballistic-to-Diffusive Propagation Schedule",
 3  "prediction_checks": [
 4    {
 5      "prediction": "gamma=0 gives ballistic MSD proportional to t^2",
 6      "predicted": "exponent 2.0",
 7      "observed": 1.9999999999974571,
 8      "status": "confirmed"
 9    },
10    {
11      "prediction": "strong dephasing gives MSD slope 4 J^2/gamma",
12      "predicted": {"gamma=0.5": 8.0, "gamma=1": 4.0, "gamma=2": 2.0, "gamma=4": 1.0, "gamma=8": 0.5, "gamma=16": 0.25},
13      "observed": {"gamma=0.5": 7.7801, "gamma=1": 3.9960, "gamma=2": 2.0000, "gamma=4": 1.0000, "gamma=8": 0.5000, "gamma=16": 0.2500},
14      "status": "confirmed; relative errors 2.7%, 0.1%, and below 0.001% for gamma>=2"
15    },
16    {
17      "prediction": "dephasing suppresses coherent/high-frequency structure",
18      "predicted": "correlation and high-frequency proxy decrease with gamma",
19      "observed": "final correlation 0.2802 at gamma=0.5, 0.0810 at gamma=4, 0.0410 at gamma=16; high-frequency proxy is 4.76e-5 at gamma=0.5 and 8.08e-11 at gamma=4",
20      "status": "confirmed qualitatively"
21    },
22    {
23      "prediction": "crossover near gamma approximately 4J",
24      "predicted": 4.0,
25      "observed": "gamma=2 already has exponent 1.10 and gamma=4 has exponent 1.05; practical crossover is broad rather than sharp",
26      "status": "partially confirmed, not a sharp switch"
27    }
28  ],
29  "neural_comparison": {
30    "fixed_ballistic": {"loss": 0.09199984, "accuracy": 0.97265625},
31    "fixed_diffusive": {"loss": 0.09874058, "accuracy": 0.96875},
32    "adaptive": {"loss": 0.09449144, "accuracy": 0.970703125, "initial_gamma": 0.5, "final_gamma": 1.65498, "maximum_gamma": 23.1394}
33  },
34  "notes": "The controller uses detached neighboring correlation and clips gamma to [0.02,16] in the neural model; the toy controller used [0.02,32]."
35}