1{
 2  "math_check": {
 3    "predictions": [
 4      "Fixed tap ratios imply roots scale as 1/a because Phi(g,a*taps)=Phi(a*g,taps).",
 5      "A true periodic/antiperiodic bifurcation has det(Phi-sigma I)=0 and margin s_min=0.",
 6      "The sigma sign selects distinct modes; absence of a root is itself a negative result."
 7    ],
 8    "base_periodic_gain": 1.869158878505,
 9    "base_antiperiodic_gain": null,
10    "periodic_margin_at_root": 2.9726491689180004e-13,
11    "antiperiodic_root_margin": null,
12    "antiperiodic_grid_min_gain": -1.3099999999999996,
13    "antiperiodic_grid_min_margin": 0.41783691467025125,
14    "scaling_rows": [
15      {
16        "tap_scale": 0.5,
17        "predicted_signed_gain": 3.73831775701,
18        "observed_signed_gain": 3.738317757009,
19        "relative_error": 2.6752378090565786e-13,
20        "method": "determinant_root"
21      },
22      {
23        "tap_scale": 1.0,
24        "predicted_signed_gain": 1.869158878505,
25        "observed_signed_gain": 1.869158878505,
26        "relative_error": 0.0,
27        "method": "determinant_root"
28      },
29      {
30        "tap_scale": 2.0,
31        "predicted_signed_gain": 0.9345794392525,
32        "observed_signed_gain": 0.934579439252,
33        "relative_error": 5.349287679472516e-13,
34        "method": "determinant_root"
35      }
36    ],
37    "periodic_roots": [
38      0.0,
39      1.869158878505
40    ],
41    "antiperiodic_roots": []
42  },
43  "training": {
44    "device": "cuda",
45    "results": {
46      "baseline": {
47        "task_mse": 0.5452180504798889,
48        "final_objective": 0.5452547669410706,
49        "gain": 0.8768672943115234,
50        "taps": [
51          0.6636684536933899,
52          -0.7438289523124695,
53          0.04511900246143341
54        ],
55        "periodic_margin": 0.052992343253856516,
56        "antiperiodic_margin": 0.6622874642097974
57      },
58      "idea": {
59        "task_mse": 0.2027808278799057,
60        "final_objective": 0.20314915478229523,
61        "gain": 0.4715888500213623,
62        "taps": [
63          -0.004393601790070534,
64          -0.0043095555156469345,
65          0.7834413647651672
66        ],
67        "periodic_margin": 0.6211438517797099,
68        "antiperiodic_margin": 0.9206322918109698
69      }
70    }
71  }
72}