1{
 2  "seed": 7,
 3  "T": 6.283185307179586,
 4  "omega": 1.0,
 5  "prediction_1_offset_scaling": {
 6    "predicted": "dominant Floquet exponent shifts as mu(gamma)=mu(0)+gamma; slope=1",
 7    "spectrum_filter": "discard eigenvectors with >20% mass in outer Fourier shell",
 8    "observed_exact_slope": 1.0000000000041032,
 9    "observed_hill_slope": 0.9999999999999957,
10    "max_exact_shift_error": 1.5461243396686086e-11,
11    "max_hill_vs_exact": 0.00816489667979614
12  },
13  "prediction_2_boundary": {
14    "predicted": "rho_F=1 exactly when max Re(mu)=0",
15    "exact_crossing_gamma": 0.0022506885014460937,
16    "hill_N8_crossing_gamma": -0.0059142081645997754,
17    "exact_rho_at_crossing": 1.0
18  },
19  "prediction_3_truncation": {
20    "predicted": "smooth periodic coefficients give improving Hill approximation; N=8 close to N=4",
21    "spectrum_filter": "discard edge-localized finite-section roots",
22    "monodromy_mu": -0.0022506885019959533,
23    "values": {
24      "1": {
25        "hill_mu": 0.008793599606706235,
26        "abs_error": 0.011044288108702189
27      },
28      "2": {
29        "hill_mu": 0.0058904564613814605,
30        "abs_error": 0.008141144963377414
31      },
32      "4": {
33        "hill_mu": 0.005914208164798997,
34        "abs_error": 0.00816489666679495
35      },
36      "8": {
37        "hill_mu": 0.005914208164604763,
38        "abs_error": 0.008164896666600717
39      },
40      "12": {
41        "hill_mu": 0.005914208164604317,
42        "abs_error": 0.00816489666660027
43      }
44    },
45    "N4_to_N8_relative_change": 3.2841993401983935e-11
46  },
47  "mini_optimization": {
48    "task_target_gamma": 0.2,
49    "baseline_gamma": 0.2,
50    "baseline_mu": 0.2059142081645971,
51    "regularized_gamma": 0.0627238612235988,
52    "regularized_mu": 0.06863806938821468,
53    "baseline_rho": 3.646606930940026,
54    "regularized_rho": 1.5392044762523813
55  }
56}