{
  "seed": 7,
  "T": 6.283185307179586,
  "omega": 1.0,
  "prediction_1_offset_scaling": {
    "predicted": "dominant Floquet exponent shifts as mu(gamma)=mu(0)+gamma; slope=1",
    "spectrum_filter": "discard eigenvectors with >20% mass in outer Fourier shell",
    "observed_exact_slope": 1.0000000000041032,
    "observed_hill_slope": 0.9999999999999957,
    "max_exact_shift_error": 1.5461243396686086e-11,
    "max_hill_vs_exact": 0.00816489667979614
  },
  "prediction_2_boundary": {
    "predicted": "rho_F=1 exactly when max Re(mu)=0",
    "exact_crossing_gamma": 0.0022506885014460937,
    "hill_N8_crossing_gamma": -0.0059142081645997754,
    "exact_rho_at_crossing": 1.0
  },
  "prediction_3_truncation": {
    "predicted": "smooth periodic coefficients give improving Hill approximation; N=8 close to N=4",
    "spectrum_filter": "discard edge-localized finite-section roots",
    "monodromy_mu": -0.0022506885019959533,
    "values": {
      "1": {
        "hill_mu": 0.008793599606706235,
        "abs_error": 0.011044288108702189
      },
      "2": {
        "hill_mu": 0.0058904564613814605,
        "abs_error": 0.008141144963377414
      },
      "4": {
        "hill_mu": 0.005914208164798997,
        "abs_error": 0.00816489666679495
      },
      "8": {
        "hill_mu": 0.005914208164604763,
        "abs_error": 0.008164896666600717
      },
      "12": {
        "hill_mu": 0.005914208164604317,
        "abs_error": 0.00816489666660027
      }
    },
    "N4_to_N8_relative_change": 3.2841993401983935e-11
  },
  "mini_optimization": {
    "task_target_gamma": 0.2,
    "baseline_gamma": 0.2,
    "baseline_mu": 0.2059142081645971,
    "regularized_gamma": 0.0627238612235988,
    "regularized_mu": 0.06863806938821468,
    "baseline_rho": 3.646606930940026,
    "regularized_rho": 1.5392044762523813
  }
}