1{
  2  "normal_form": {
  3    "a": 2.0,
  4    "delta": 0.05
  5  },
  6  "prediction_1_boundary": {
  7    "predicted_mu": 0.0,
  8    "observed_mu_midpoint": 0.0025000000000000022,
  9    "last_stable_grid_mu": 0.0,
 10    "first_unstable_grid_mu": 0.0050000000000000044,
 11    "lambda_at_observed_midpoint": -1.0025
 12  },
 13  "prediction_2_sqrt_scaling": {
 14    "mu": [
 15      0.01,
 16      0.025454545454545452,
 17      0.04090909090909091,
 18      0.05636363636363636,
 19      0.07181818181818181,
 20      0.08727272727272727,
 21      0.10272727272727271,
 22      0.11818181818181817,
 23      0.13363636363636364,
 24      0.14909090909090908,
 25      0.16454545454545455,
 26      0.18
 27    ],
 28    "observed_amplitude": [
 29      0.07071067811865443,
 30      0.11281521496355304,
 31      0.1430193883868389,
 32      0.16787441193290348,
 33      0.18949694168796197,
 34      0.20889318714683716,
 35      0.22663547022396194,
 36      0.2430862174021988,
 37      0.25849213105659874,
 38      0.27303013486693095,
 39      0.28683222844151823,
 40      0.2999999999999999
 41    ],
 42    "predicted_amplitude": [
 43      0.07071067811865475,
 44      0.11281521496355323,
 45      0.14301938838683884,
 46      0.1678744119329035,
 47      0.18949694168796208,
 48      0.2088931871468374,
 49      0.22663547022396197,
 50      0.24308621740219885,
 51      0.25849213105659874,
 52      0.273030134866931,
 53      0.2868322284415182,
 54      0.3
 55    ],
 56    "mean_relative_error": 8.074276768344772e-16,
 57    "observed_sqrt_coefficient": 0.7071067811865474,
 58    "predicted_sqrt_coefficient": 0.7071067811865475
 59  },
 60  "prediction_3_cubic_scaling": {
 61    "a": [
 62      0.5,
 63      1.0,
 64      2.0,
 65      4.0
 66    ],
 67    "observed_amplitude": [
 68      0.4,
 69      0.28284271247461884,
 70      0.2,
 71      0.14142135623730942
 72    ],
 73    "predicted_amplitude": [
 74      0.4,
 75      0.282842712474619,
 76      0.2,
 77      0.1414213562373095
 78    ],
 79    "mean_relative_error": 2.9439233600320783e-16
 80  },
 81  "guard_training": {
 82    "target_mu": 0.15,
 83    "baseline_mu": 0.1499999933031802,
 84    "corrected_guard_mu": -0.05,
 85    "literal_formula_mu": 0.14999999457876492,
 86    "baseline_lambda": -1.1499999933031801,
 87    "corrected_guard_lambda": -0.95,
 88    "literal_formula_lambda": -1.149999994578765,
 89    "baseline_A_K": 0.0,
 90    "corrected_guard_A_K": 8.34484626490855e-49,
 91    "literal_formula_A_K": 0.0,
 92    "baseline_cycle_amplitude": 0.27386127263925086,
 93    "corrected_guard_cycle_amplitude": 7.724332055466626e-60,
 94    "literal_formula_cycle_amplitude": 0.273861273803695
 95  },
 96  "formula_sign_check": {
 97    "mu": 0.1,
 98    "lambda": -1.1,
 99    "displayed_penalty": 0.0,
100    "corrected_lower_bound_penalty": 0.02250000000000004,
101    "note": "The displayed formula penalizes lambda above -1+delta, rather than lambda below it; corrected results are reported separately."
102  }
103}