{
  "normal_form": {
    "a": 2.0,
    "delta": 0.05
  },
  "prediction_1_boundary": {
    "predicted_mu": 0.0,
    "observed_mu_midpoint": 0.0025000000000000022,
    "last_stable_grid_mu": 0.0,
    "first_unstable_grid_mu": 0.0050000000000000044,
    "lambda_at_observed_midpoint": -1.0025
  },
  "prediction_2_sqrt_scaling": {
    "mu": [
      0.01,
      0.025454545454545452,
      0.04090909090909091,
      0.05636363636363636,
      0.07181818181818181,
      0.08727272727272727,
      0.10272727272727271,
      0.11818181818181817,
      0.13363636363636364,
      0.14909090909090908,
      0.16454545454545455,
      0.18
    ],
    "observed_amplitude": [
      0.07071067811865443,
      0.11281521496355304,
      0.1430193883868389,
      0.16787441193290348,
      0.18949694168796197,
      0.20889318714683716,
      0.22663547022396194,
      0.2430862174021988,
      0.25849213105659874,
      0.27303013486693095,
      0.28683222844151823,
      0.2999999999999999
    ],
    "predicted_amplitude": [
      0.07071067811865475,
      0.11281521496355323,
      0.14301938838683884,
      0.1678744119329035,
      0.18949694168796208,
      0.2088931871468374,
      0.22663547022396197,
      0.24308621740219885,
      0.25849213105659874,
      0.273030134866931,
      0.2868322284415182,
      0.3
    ],
    "mean_relative_error": 8.074276768344772e-16,
    "observed_sqrt_coefficient": 0.7071067811865474,
    "predicted_sqrt_coefficient": 0.7071067811865475
  },
  "prediction_3_cubic_scaling": {
    "a": [
      0.5,
      1.0,
      2.0,
      4.0
    ],
    "observed_amplitude": [
      0.4,
      0.28284271247461884,
      0.2,
      0.14142135623730942
    ],
    "predicted_amplitude": [
      0.4,
      0.282842712474619,
      0.2,
      0.1414213562373095
    ],
    "mean_relative_error": 2.9439233600320783e-16
  },
  "guard_training": {
    "target_mu": 0.15,
    "baseline_mu": 0.1499999933031802,
    "corrected_guard_mu": -0.05,
    "literal_formula_mu": 0.14999999457876492,
    "baseline_lambda": -1.1499999933031801,
    "corrected_guard_lambda": -0.95,
    "literal_formula_lambda": -1.149999994578765,
    "baseline_A_K": 0.0,
    "corrected_guard_A_K": 8.34484626490855e-49,
    "literal_formula_A_K": 0.0,
    "baseline_cycle_amplitude": 0.27386127263925086,
    "corrected_guard_cycle_amplitude": 7.724332055466626e-60,
    "literal_formula_cycle_amplitude": 0.273861273803695
  },
  "formula_sign_check": {
    "mu": 0.1,
    "lambda": -1.1,
    "displayed_penalty": 0.0,
    "corrected_lower_bound_penalty": 0.02250000000000004,
    "note": "The displayed formula penalizes lambda above -1+delta, rather than lambda below it; corrected results are reported separately."
  }
}