{
  "math_verification": {
    "state": [
      0.25,
      0.35
    ],
    "M0": 8.0,
    "eps_grid": [
      0.0,
      0.19999999999999998,
      0.39999999999999997,
      0.6,
      0.7999999999999999,
      0.9999999999999999,
      1.2,
      1.4,
      1.5999999999999999,
      1.7999999999999998,
      1.9999999999999998,
      2.1999999999999997,
      2.4
    ],
    "margins": [
      8.0,
      7.6000000000000005,
      7.2,
      6.8,
      6.4,
      6.0,
      5.6000000000000005,
      5.2,
      4.8,
      4.4,
      4.000000000000001,
      3.6000000000000005,
      3.2
    ],
    "fitted_margin_slope": -1.9999999999999996,
    "predicted_margin_slope": -2.0,
    "predicted_eps_critical": 4.0,
    "observed_eps_critical": 4.0,
    "bound_shift_samples": [
      [
        0.1,
        0.10000000000000009,
        -0.10000000000000009
      ],
      [
        0.2,
        0.20000000000000018,
        -0.20000000000000018
      ],
      [
        0.4,
        0.3999999999999999,
        -0.3999999999999999
      ]
    ],
    "predicted_shifts": "lower +eps, upper -eps"
  },
  "closed_loop": [
    {
      "disturbance_amplitude": 0,
      "clip": {
        "max_violation": 0.0091926752499909,
        "mean_intervention": 0.0,
        "min_margin": 2.0,
        "bound_misses": 0
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      "ordinary_cbf": {
        "max_violation": 0.0,
        "mean_intervention": 0.09209308024722863,
        "min_margin": 0.1766289802259342,
        "bound_misses": 0
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      "robust_cbf": {
        "max_violation": 0.0,
        "mean_intervention": 0.13776788040696045,
        "min_margin": 0.22067309816553404,
        "bound_misses": 0
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    },
    {
      "disturbance_amplitude": 0.1,
      "clip": {
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        "mean_intervention": 0.0,
        "min_margin": 2.0,
        "bound_misses": 0
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      "ordinary_cbf": {
        "max_violation": 0.0,
        "mean_intervention": 0.09246815894123397,
        "min_margin": 0.11050318146056881,
        "bound_misses": 0
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      "robust_cbf": {
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        "mean_intervention": 0.1389727859275357,
        "min_margin": 0.15304052618469477,
        "bound_misses": 0
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    },
    {
      "disturbance_amplitude": 0.2,
      "clip": {
        "max_violation": 0.12939310651646063,
        "mean_intervention": 0.0,
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        "bound_misses": 0
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      "ordinary_cbf": {
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      "robust_cbf": {
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        "bound_misses": 0
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    },
    {
      "disturbance_amplitude": 0.3,
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        "mean_intervention": 0.0,
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        "bound_misses": 0
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      "ordinary_cbf": {
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        "bound_misses": 0
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      "robust_cbf": {
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        "min_margin": -0.0730810251499121,
        "bound_misses": 0
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    },
    {
      "disturbance_amplitude": 0.4,
      "clip": {
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        "mean_intervention": 0.0,
        "min_margin": 2.0,
        "bound_misses": 330
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      "ordinary_cbf": {
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    },
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      "disturbance_amplitude": 0.5,
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        "max_violation": 0.3378564279793159,
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        "bound_misses": 765
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      "ordinary_cbf": {
        "max_violation": 0.0,
        "mean_intervention": 0.07706391804602254,
        "min_margin": -0.8207471685437446,
        "bound_misses": 765
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      "robust_cbf": {
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        "bound_misses": 765
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    },
    {
      "disturbance_amplitude": 0.6,
      "clip": {
        "max_violation": 0.39818343793944866,
        "mean_intervention": 0.0,
        "min_margin": 2.0,
        "bound_misses": 1213
      },
      "ordinary_cbf": {
        "max_violation": 0.01201068098589908,
        "mean_intervention": 0.07152283853905787,
        "min_margin": -1.1811752636081865,
        "bound_misses": 1213
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      "robust_cbf": {
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        "mean_intervention": 0.11631111745646536,
        "min_margin": -1.1079472421296477,
        "bound_misses": 1213
      }
    },
    {
      "disturbance_amplitude": 0.8,
      "clip": {
        "max_violation": 0.4589672174003294,
        "mean_intervention": 0.0,
        "min_margin": 2.0,
        "bound_misses": 1983
      },
      "ordinary_cbf": {
        "max_violation": 0.10248696514183786,
        "mean_intervention": 0.0629673388508905,
        "min_margin": -1.9186002411127068,
        "bound_misses": 1983
      },
      "robust_cbf": {
        "max_violation": 0.05609322303779174,
        "mean_intervention": 0.0973398247649854,
        "min_margin": -2.0004558044859664,
        "bound_misses": 1983
      }
    },
    {
      "disturbance_amplitude": 1.0,
      "clip": {
        "max_violation": 0.4226248436458355,
        "mean_intervention": 0.0,
        "min_margin": 2.0,
        "bound_misses": 2469
      },
      "ordinary_cbf": {
        "max_violation": 0.1909981502689606,
        "mean_intervention": 0.05567132310642432,
        "min_margin": -2.3468801067817178,
        "bound_misses": 2469
      },
      "robust_cbf": {
        "max_violation": 0.11194821406588606,
        "mean_intervention": 0.08111872641930463,
        "min_margin": -2.58942968967079,
        "bound_misses": 2469
      }
    }
  ],
  "notes": "Disturbance bound is eps=.35; actual sinusoid peak equals amplitude. Empty robust intervals use closest actuator endpoint emergency fallback."
}