{
  "seed": 2094,
  "predictions": {
    "threshold_q_equals_1": [
      {
        "q": 0.8,
        "observed_gain": 0.0012379400392853821,
        "predicted_gain": 0.0012379400392853823,
        "observed_log_rate": -0.2231435513142097,
        "predicted_log_rate": -0.2231435513142097
      },
      {
        "q": 0.95,
        "observed_gain": 0.21463876394293724,
        "predicted_gain": 0.21463876394293727,
        "observed_log_rate": -0.051293294387550585,
        "predicted_log_rate": -0.05129329438755058
      },
      {
        "q": 1.0,
        "observed_gain": 1.0,
        "predicted_gain": 1.0,
        "observed_log_rate": 0.0,
        "predicted_log_rate": 0.0
      },
      {
        "q": 1.05,
        "observed_gain": 4.321942375150669,
        "predicted_gain": 4.321942375150668,
        "observed_log_rate": 0.048790164169432056,
        "predicted_log_rate": 0.04879016416943205
      },
      {
        "q": 1.2,
        "observed_gain": 237.37631379976955,
        "predicted_gain": 237.37631379976955,
        "observed_log_rate": 0.1823215567939546,
        "predicted_log_rate": 0.1823215567939546
      }
    ],
    "defect_floor": [
      {
        "delta": 0.001,
        "observed_floor": 0.004999999999999999,
        "predicted_floor": 0.005000000000000001,
        "relative_error": 3.4694469519536137e-16
      },
      {
        "delta": 0.003,
        "observed_floor": 0.014999999999999996,
        "predicted_floor": 0.015000000000000003,
        "relative_error": 4.625929269271485e-16
      },
      {
        "delta": 0.01,
        "observed_floor": 0.05000000000000001,
        "predicted_floor": 0.05000000000000001,
        "relative_error": 0.0
      },
      {
        "delta": 0.03,
        "observed_floor": 0.14999999999999997,
        "predicted_floor": 0.15000000000000002,
        "relative_error": 3.700743415417188e-16
      }
    ],
    "phase_invariant_vs_pointwise": {
      "q": 0.85,
      "shear": 2.5,
      "initial_transverse": 0.15,
      "orbital_error_at_80": 3.385363568138043e-07,
      "orbital_predicted_at_80": 3.3853635681380424e-07,
      "pointwise_error_at_80": 1.747147831935192,
      "pointwise_peak": 1.747147831935192,
      "orbital_max": 0.15,
      "interpretation": "phase shear leaves transverse contraction intact but increases phase-sensitive error"
    }
  },
  "comparison": {
    "baseline_unconstrained": {
      "q": 1.02,
      "cycles": 1000,
      "defect_sigma": 0.004,
      "median_orbital_error": 40241576.84723182,
      "p95_orbital_error": 52864613.14784893,
      "median_pointwise_error": 40241577.53474505,
      "fraction_orbital_inside_0.05": 0.0,
      "qhat_max_over_trials": 1.0200000000003757
    },
    "contractive_idea": {
      "q": 0.8,
      "cycles": 1000,
      "defect_sigma": 0.004,
      "median_orbital_error": 0.004281468992204954,
      "p95_orbital_error": 0.012927978968120656,
      "median_pointwise_error": 0.7177862139003627,
      "fraction_orbital_inside_0.05": 1.0,
      "qhat_max_over_trials": 0.8000000000000932
    }
  },
  "checks": {
    "threshold_relative_errors": [
      1.7516230804060184e-16,
      1.2931296801079168e-16,
      0.0,
      2.055044567014067e-16,
      0.0
    ],
    "max_defect_relative_error": 4.625929269271485e-16,
    "empirical_q_contractive": true,
    "empirical_q_baseline_noncontractive": true
  }
}