{
  "math_check": {
    "predictions": [
      "Fixed tap ratios imply roots scale as 1/a because Phi(g,a*taps)=Phi(a*g,taps).",
      "A true periodic/antiperiodic bifurcation has det(Phi-sigma I)=0 and margin s_min=0.",
      "The sigma sign selects distinct modes; absence of a root is itself a negative result."
    ],
    "base_periodic_gain": 1.869158878505,
    "base_antiperiodic_gain": null,
    "periodic_margin_at_root": 2.9726491689180004e-13,
    "antiperiodic_root_margin": null,
    "antiperiodic_grid_min_gain": -1.3099999999999996,
    "antiperiodic_grid_min_margin": 0.41783691467025125,
    "scaling_rows": [
      {
        "tap_scale": 0.5,
        "predicted_signed_gain": 3.73831775701,
        "observed_signed_gain": 3.738317757009,
        "relative_error": 2.6752378090565786e-13,
        "method": "determinant_root"
      },
      {
        "tap_scale": 1.0,
        "predicted_signed_gain": 1.869158878505,
        "observed_signed_gain": 1.869158878505,
        "relative_error": 0.0,
        "method": "determinant_root"
      },
      {
        "tap_scale": 2.0,
        "predicted_signed_gain": 0.9345794392525,
        "observed_signed_gain": 0.934579439252,
        "relative_error": 5.349287679472516e-13,
        "method": "determinant_root"
      }
    ],
    "periodic_roots": [
      0.0,
      1.869158878505
    ],
    "antiperiodic_roots": []
  },
  "training": {
    "device": "cuda",
    "results": {
      "baseline": {
        "task_mse": 0.5452180504798889,
        "final_objective": 0.5452547669410706,
        "gain": 0.8768672943115234,
        "taps": [
          0.6636684536933899,
          -0.7438289523124695,
          0.04511900246143341
        ],
        "periodic_margin": 0.052992343253856516,
        "antiperiodic_margin": 0.6622874642097974
      },
      "idea": {
        "task_mse": 0.2027808278799057,
        "final_objective": 0.20314915478229523,
        "gain": 0.4715888500213623,
        "taps": [
          -0.004393601790070534,
          -0.0043095555156469345,
          0.7834413647651672
        ],
        "periodic_margin": 0.6211438517797099,
        "antiperiodic_margin": 0.9206322918109698
      }
    }
  }
}