{
 "label": "Case 1 analysis. TR rows: Chrono digital-twin recovery tests; physical reference: archived physical runs (Sim2Real). Rule: per-start rank.",
 "physical_order": {
  "P1_lateral": [
   "MPC",
   "NN-MPC",
   "PID",
   "NN-HD"
  ],
  "P1_heading": [
   "MPC",
   "NN-MPC",
   "NN-HD",
   "PID"
  ],
  "P2_lateral": [
   "MPC",
   "NN-MPC",
   "PID",
   "NN-HD"
  ],
  "P2_heading": [
   "MPC",
   "NN-MPC",
   "PID",
   "NN-HD"
  ],
  "P3_lateral": [
   "MPC",
   "PID",
   "NN-MPC",
   "NN-HD"
  ],
  "P3_heading": [
   "MPC",
   "PID",
   "NN-MPC",
   "NN-HD"
  ]
 },
 "physical_pairwise_tests": {
  "P1_lateral": [
   {
    "pair": "MPC vs NN-MPC",
    "mean_a": 0.1051,
    "mean_b": 0.2259,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs PID",
    "mean_a": 0.1051,
    "mean_b": 0.2673,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs NN-HD",
    "mean_a": 0.1051,
    "mean_b": 0.5113,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs PID",
    "mean_a": 0.2259,
    "mean_b": 0.2673,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs NN-HD",
    "mean_a": 0.2259,
    "mean_b": 0.5113,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "PID vs NN-HD",
    "mean_a": 0.2673,
    "mean_b": 0.5113,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   }
  ],
  "P1_heading": [
   {
    "pair": "MPC vs NN-MPC",
    "mean_a": 0.0851,
    "mean_b": 0.1665,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs PID",
    "mean_a": 0.0851,
    "mean_b": 0.2033,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs NN-HD",
    "mean_a": 0.0851,
    "mean_b": 0.1812,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs PID",
    "mean_a": 0.1665,
    "mean_b": 0.2033,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs NN-HD",
    "mean_a": 0.1665,
    "mean_b": 0.1812,
    "p_perm": 0.1349,
    "p_holm": 0.1349
   },
   {
    "pair": "PID vs NN-HD",
    "mean_a": 0.2033,
    "mean_b": 0.1812,
    "p_perm": 0.0238,
    "p_holm": 0.0476
   }
  ],
  "P2_lateral": [
   {
    "pair": "MPC vs NN-MPC",
    "mean_a": 0.1032,
    "mean_b": 0.2735,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs PID",
    "mean_a": 0.1032,
    "mean_b": 0.3171,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs NN-HD",
    "mean_a": 0.1032,
    "mean_b": 0.6626,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs PID",
    "mean_a": 0.2735,
    "mean_b": 0.3171,
    "p_perm": 0.0159,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs NN-HD",
    "mean_a": 0.2735,
    "mean_b": 0.6626,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "PID vs NN-HD",
    "mean_a": 0.3171,
    "mean_b": 0.6626,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   }
  ],
  "P2_heading": [
   {
    "pair": "MPC vs NN-MPC",
    "mean_a": 0.0659,
    "mean_b": 0.1284,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs PID",
    "mean_a": 0.0659,
    "mean_b": 0.1447,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs NN-HD",
    "mean_a": 0.0659,
    "mean_b": 0.1782,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs PID",
    "mean_a": 0.1284,
    "mean_b": 0.1447,
    "p_perm": 0.0556,
    "p_holm": 0.0556
   },
   {
    "pair": "NN-MPC vs NN-HD",
    "mean_a": 0.1284,
    "mean_b": 0.1782,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "PID vs NN-HD",
    "mean_a": 0.1447,
    "mean_b": 0.1782,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   }
  ],
  "P3_lateral": [
   {
    "pair": "MPC vs NN-MPC",
    "mean_a": 0.0891,
    "mean_b": 0.1635,
    "p_perm": 0.0159,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs PID",
    "mean_a": 0.0891,
    "mean_b": 0.1386,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs NN-HD",
    "mean_a": 0.0891,
    "mean_b": 0.4047,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs PID",
    "mean_a": 0.1635,
    "mean_b": 0.1386,
    "p_perm": 0.2937,
    "p_holm": 0.2937
   },
   {
    "pair": "NN-MPC vs NN-HD",
    "mean_a": 0.1635,
    "mean_b": 0.4047,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "PID vs NN-HD",
    "mean_a": 0.1386,
    "mean_b": 0.4047,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   }
  ],
  "P3_heading": [
   {
    "pair": "MPC vs NN-MPC",
    "mean_a": 0.0857,
    "mean_b": 0.1259,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "MPC vs PID",
    "mean_a": 0.0857,
    "mean_b": 0.0944,
    "p_perm": 0.0238,
    "p_holm": 0.0477
   },
   {
    "pair": "MPC vs NN-HD",
    "mean_a": 0.0857,
    "mean_b": 0.1352,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   },
   {
    "pair": "NN-MPC vs PID",
    "mean_a": 0.1259,
    "mean_b": 0.0944,
    "p_perm": 0.0159,
    "p_holm": 0.0477
   },
   {
    "pair": "NN-MPC vs NN-HD",
    "mean_a": 0.1259,
    "mean_b": 0.1352,
    "p_perm": 0.6111,
    "p_holm": 0.6111
   },
   {
    "pair": "PID vs NN-HD",
    "mean_a": 0.0944,
    "mean_b": 0.1352,
    "p_perm": 0.0079,
    "p_holm": 0.0474
   }
  ]
 },
 "method_comparison": {
  "TR (rank rule, S2)": {
   "order": {
    "P1_lateral": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "P1_heading": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "P2_lateral": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "P2_heading": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "P3_lateral": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "P3_heading": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ]
   },
   "tau": {
    "P1_lateral": 1.0,
    "P1_heading": 0.67,
    "P2_lateral": 1.0,
    "P2_heading": 1.0,
    "P3_lateral": 0.67,
    "P3_heading": 0.67
   },
   "tau_ci95": {
    "P1_lateral": [
     1.0,
     1.0
    ],
    "P1_heading": [
     0.67,
     0.67
    ],
    "P2_lateral": [
     1.0,
     1.0
    ],
    "P2_heading": [
     1.0,
     1.0
    ],
    "P3_lateral": [
     0.67,
     1.0
    ],
    "P3_heading": [
     0.33,
     0.67
    ]
   },
   "mean_tau": 0.83,
   "mean_tau_ci95": [
    0.78,
    0.89
   ],
   "exact_order_matches": 3,
   "best_selected": 6,
   "selected_error_ratio_to_best": {
    "P1_lateral": 1.0,
    "P1_heading": 1.0,
    "P2_lateral": 1.0,
    "P2_heading": 1.0,
    "P3_lateral": 1.0,
    "P3_heading": 1.0
   },
   "resolved_pairs_correct": [
    30,
    32
   ]
  },
  "Nominal simulation": {
   "order": {
    "P1_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P1_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P3_lateral": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "P3_heading": [
     "PID",
     "NN-MPC",
     "MPC",
     "NN-HD"
    ]
   },
   "tau": {
    "P1_lateral": 0.33,
    "P1_heading": 0.0,
    "P2_lateral": 0.33,
    "P2_heading": 0.33,
    "P3_lateral": 0.67,
    "P3_heading": 0.33
   },
   "tau_ci95": {
    "P1_lateral": [
     0.33,
     0.33
    ],
    "P1_heading": [
     0.0,
     0.0
    ],
    "P2_lateral": [
     0.33,
     0.33
    ],
    "P2_heading": [
     0.33,
     0.33
    ],
    "P3_lateral": [
     0.67,
     1.0
    ],
    "P3_heading": [
     0.0,
     0.33
    ]
   },
   "mean_tau": 0.33,
   "mean_tau_ci95": [
    0.28,
    0.39
   ],
   "exact_order_matches": 0,
   "best_selected": 1,
   "selected_error_ratio_to_best": {
    "P1_lateral": 2.15,
    "P1_heading": 1.96,
    "P2_lateral": 2.65,
    "P2_heading": 1.95,
    "P3_lateral": 1.0,
    "P3_heading": 1.1
   },
   "resolved_pairs_correct": [
    21,
    32
   ]
  },
  "Nominal simulation (2024 archive)": {
   "order": {
    "P1_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P1_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P3_lateral": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "P3_heading": [
     "PID",
     "NN-MPC",
     "NN-HD",
     "MPC"
    ]
   },
   "tau": {
    "P1_lateral": 0.33,
    "P1_heading": 0.0,
    "P2_lateral": 0.33,
    "P2_heading": 0.33,
    "P3_lateral": 0.67,
    "P3_heading": 0.0
   },
   "tau_ci95": {
    "P1_lateral": [
     0.33,
     0.33
    ],
    "P1_heading": [
     0.0,
     0.0
    ],
    "P2_lateral": [
     0.33,
     0.33
    ],
    "P2_heading": [
     0.33,
     0.33
    ],
    "P3_lateral": [
     0.67,
     1.0
    ],
    "P3_heading": [
     -0.33,
     0.0
    ]
   },
   "mean_tau": 0.28,
   "mean_tau_ci95": [
    0.22,
    0.33
   ],
   "exact_order_matches": 0,
   "best_selected": 1,
   "selected_error_ratio_to_best": {
    "P1_lateral": 2.15,
    "P1_heading": 1.96,
    "P2_lateral": 2.65,
    "P2_heading": 1.95,
    "P3_lateral": 1.0,
    "P3_heading": 1.1
   },
   "resolved_pairs_correct": [
    20,
    32
   ]
  },
  "Monte Carlo, start jitter (RF-A)": {
   "order": {
    "P1_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P1_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P3_lateral": [
     "NN-MPC",
     "MPC",
     "PID",
     "NN-HD"
    ],
    "P3_heading": [
     "PID",
     "NN-MPC",
     "NN-HD",
     "MPC"
    ]
   },
   "tau": {
    "P1_lateral": 0.33,
    "P1_heading": 0.0,
    "P2_lateral": 0.33,
    "P2_heading": 0.33,
    "P3_lateral": 0.33,
    "P3_heading": 0.0
   },
   "tau_ci95": {
    "P1_lateral": [
     0.33,
     0.33
    ],
    "P1_heading": [
     0.0,
     0.0
    ],
    "P2_lateral": [
     0.33,
     0.33
    ],
    "P2_heading": [
     0.33,
     0.33
    ],
    "P3_lateral": [
     0.33,
     0.67
    ],
    "P3_heading": [
     -0.33,
     0.0
    ]
   },
   "mean_tau": 0.22,
   "mean_tau_ci95": [
    0.17,
    0.28
   ],
   "exact_order_matches": 0,
   "best_selected": 0,
   "selected_error_ratio_to_best": {
    "P1_lateral": 2.15,
    "P1_heading": 1.96,
    "P2_lateral": 2.65,
    "P2_heading": 1.95,
    "P3_lateral": 1.84,
    "P3_heading": 1.1
   },
   "resolved_pairs_correct": [
    19,
    32
   ]
  },
  "Monte Carlo, jitter + disturbances (RF-B)": {
   "order": {
    "P1_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P1_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_lateral": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P2_heading": [
     "NN-MPC",
     "PID",
     "MPC",
     "NN-HD"
    ],
    "P3_lateral": [
     "PID",
     "MPC",
     "NN-HD",
     "NN-MPC"
    ],
    "P3_heading": [
     "PID",
     "NN-HD",
     "MPC",
     "NN-MPC"
    ]
   },
   "tau": {
    "P1_lateral": 0.33,
    "P1_heading": 0.0,
    "P2_lateral": 0.33,
    "P2_heading": 0.33,
    "P3_lateral": 0.33,
    "P3_heading": 0.0
   },
   "tau_ci95": {
    "P1_lateral": [
     0.33,
     0.33
    ],
    "P1_heading": [
     0.0,
     0.0
    ],
    "P2_lateral": [
     0.33,
     0.33
    ],
    "P2_heading": [
     0.33,
     0.33
    ],
    "P3_lateral": [
     0.0,
     0.33
    ],
    "P3_heading": [
     0.0,
     0.33
    ]
   },
   "mean_tau": 0.22,
   "mean_tau_ci95": [
    0.17,
    0.28
   ],
   "exact_order_matches": 0,
   "best_selected": 0,
   "selected_error_ratio_to_best": {
    "P1_lateral": 2.15,
    "P1_heading": 1.96,
    "P2_lateral": 2.65,
    "P2_heading": 1.95,
    "P3_lateral": 1.56,
    "P3_heading": 1.1
   },
   "resolved_pairs_correct": [
    19,
    32
   ]
  }
 },
 "tr_minus_nominal": {
  "TR minus nominal, mean tau": 0.5,
  "ci95": [
   0.5,
   0.5
  ]
 },
 "tr_minus_nominal_tables_II_III": {
  "TR minus nominal (Tables II-III), mean tau": 0.56,
  "ci95": [
   0.56,
   0.56
  ],
  "min": 0.56,
  "share_of_replicates_gt_0": 1.0
 },
 "offset_sweep": [
  {
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.42,
    "NN-MPC": 2.28,
    "PID": 3.03,
    "NN-HD": 3.27
   },
   "rank_pct": {
    "MPC": [
     75.8,
     11.5,
     7.5,
     5.2
    ],
    "NN-MPC": [
     8.8,
     62.0,
     21.5,
     7.8
    ],
    "PID": [
     6.5,
     15.0,
     47.8,
     30.8
    ],
    "NN-HD": [
     9.0,
     11.5,
     23.2,
     56.2
    ]
   },
   "fail_pct": {
    "MPC": 0.0,
    "NN-MPC": 0.0,
    "PID": 0.0,
    "NN-HD": 0.0
   },
   "n_all_recover": 200,
   "mean_st_all_recover": {
    "MPC": 1.28,
    "NN-MPC": 1.58,
    "PID": 1.77,
    "NN-HD": 2.27
   },
   "pairwise_win_rate_ci95": {
    "MPC beats NN-MPC": [
     0.86,
     [
      0.818,
      0.9
     ]
    ],
    "MPC beats PID": [
     0.858,
     [
      0.815,
      0.897
     ]
    ],
    "MPC beats NN-HD": [
     0.86,
     [
      0.815,
      0.897
     ]
    ],
    "NN-MPC beats PID": [
     0.782,
     [
      0.735,
      0.83
     ]
    ],
    "NN-MPC beats NN-HD": [
     0.795,
     [
      0.745,
      0.845
     ]
    ],
    "PID beats NN-HD": [
     0.612,
     [
      0.552,
      0.675
     ]
    ]
   },
   "range": "S0",
   "mean_tau_vs_physical": 0.83
  },
  {
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.14,
    "NN-MPC": 1.92,
    "PID": 2.96,
    "NN-HD": 3.98
   },
   "rank_pct": {
    "MPC": [
     89.5,
     8.5,
     0.5,
     1.5
    ],
    "NN-MPC": [
     9.8,
     88.2,
     2.0,
     0.0
    ],
    "PID": [
     0.8,
     3.2,
     95.0,
     1.0
    ],
    "NN-HD": [
     0.0,
     0.0,
     2.5,
     97.5
    ]
   },
   "fail_pct": {
    "MPC": 0.5,
    "NN-MPC": 0.0,
    "PID": 0.0,
    "NN-HD": 0.0
   },
   "n_all_recover": 199,
   "mean_st_all_recover": {
    "MPC": 4.7,
    "NN-MPC": 4.88,
    "PID": 5.25,
    "NN-HD": 7.98
   },
   "pairwise_win_rate_ci95": {
    "MPC beats NN-MPC": [
     0.898,
     [
      0.855,
      0.94
     ]
    ],
    "MPC beats PID": [
     0.978,
     [
      0.955,
      0.995
     ]
    ],
    "MPC beats NN-HD": [
     0.985,
     [
      0.965,
      1.0
     ]
    ],
    "NN-MPC beats PID": [
     0.975,
     [
      0.95,
      0.995
     ]
    ],
    "NN-MPC beats NN-HD": [
     1.0,
     [
      1.0,
      1.0
     ]
    ],
    "PID beats NN-HD": [
     0.99,
     [
      0.975,
      1.0
     ]
    ]
   },
   "range": "S1",
   "mean_tau_vs_physical": 0.83
  },
  {
   "n": 400,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.27,
    "NN-MPC": 2.17,
    "PID": 2.68,
    "NN-HD": 3.88
   },
   "rank_pct": {
    "MPC": [
     90.2,
     0.9,
     0.1,
     8.8
    ],
    "NN-MPC": [
     9.0,
     66.9,
     22.8,
     1.4
    ],
    "PID": [
     0.8,
     31.8,
     66.6,
     0.9
    ],
    "NN-HD": [
     0.0,
     0.5,
     10.5,
     89.0
    ]
   },
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "n_all_recover": 361,
   "mean_st_all_recover": {
    "MPC": 6.1,
    "NN-MPC": 6.54,
    "PID": 6.64,
    "NN-HD": 10.09
   },
   "pairwise_win_rate_ci95": {
    "MPC beats NN-MPC": [
     0.902,
     [
      0.875,
      0.93
     ]
    ],
    "MPC beats PID": [
     0.911,
     [
      0.884,
      0.938
     ]
    ],
    "MPC beats NN-HD": [
     0.912,
     [
      0.885,
      0.94
     ]
    ],
    "NN-MPC beats PID": [
     0.752,
     [
      0.713,
      0.796
     ]
    ],
    "NN-MPC beats NN-HD": [
     0.985,
     [
      0.973,
      0.995
     ]
    ],
    "PID beats NN-HD": [
     0.988,
     [
      0.977,
      0.998
     ]
    ]
   },
   "range": "S2",
   "mean_tau_vs_physical": 0.83
  },
  {
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.31,
    "NN-MPC": 1.99,
    "PID": 2.92,
    "NN-HD": 3.77
   },
   "rank_pct": {
    "MPC": [
     83.9,
     6.9,
     3.4,
     5.9
    ],
    "NN-MPC": [
     11.9,
     79.1,
     7.1,
     1.9
    ],
    "PID": [
     1.1,
     12.4,
     79.4,
     7.1
    ],
    "NN-HD": [
     3.1,
     1.6,
     10.1,
     85.1
    ]
   },
   "fail_pct": {
    "MPC": 4.0,
    "NN-MPC": 0.5,
    "PID": 0.5,
    "NN-HD": 0.0
   },
   "n_all_recover": 191,
   "mean_st_all_recover": {
    "MPC": 4.46,
    "NN-MPC": 4.79,
    "PID": 5.08,
    "NN-HD": 7.61
   },
   "pairwise_win_rate_ci95": {
    "MPC beats NN-MPC": [
     0.855,
     [
      0.807,
      0.902
     ]
    ],
    "MPC beats PID": [
     0.915,
     [
      0.875,
      0.95
     ]
    ],
    "MPC beats NN-HD": [
     0.918,
     [
      0.877,
      0.953
     ]
    ],
    "NN-MPC beats PID": [
     0.918,
     [
      0.877,
      0.953
     ]
    ],
    "NN-MPC beats NN-HD": [
     0.948,
     [
      0.915,
      0.975
     ]
    ],
    "PID beats NN-HD": [
     0.908,
     [
      0.868,
      0.945
     ]
    ]
   },
   "range": "S3",
   "mean_tau_vs_physical": 0.83
  },
  {
   "n": 200,
   "order": [
    "MPC",
    "PID",
    "NN-MPC",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.7,
    "NN-MPC": 2.48,
    "PID": 2.05,
    "NN-HD": 3.77
   },
   "rank_pct": {
    "MPC": [
     73.6,
     0.6,
     8.4,
     17.4
    ],
    "NN-MPC": [
     18.6,
     16.4,
     63.4,
     1.6
    ],
    "PID": [
     7.1,
     81.9,
     9.9,
     1.1
    ],
    "NN-HD": [
     0.6,
     1.1,
     18.4,
     79.9
    ]
   },
   "fail_pct": {
    "MPC": 27.0,
    "NN-MPC": 3.5,
    "PID": 3.0,
    "NN-HD": 18.0
   },
   "n_all_recover": 143,
   "mean_st_all_recover": {
    "MPC": 7.13,
    "NN-MPC": 7.75,
    "PID": 7.59,
    "NN-HD": 11.31
   },
   "pairwise_win_rate_ci95": {
    "MPC beats NN-MPC": [
     0.742,
     [
      0.682,
      0.8
     ]
    ],
    "MPC beats PID": [
     0.742,
     [
      0.682,
      0.802
     ]
    ],
    "MPC beats NN-HD": [
     0.82,
     [
      0.775,
      0.863
     ]
    ],
    "NN-MPC beats PID": [
     0.29,
     [
      0.23,
      0.352
     ]
    ],
    "NN-MPC beats NN-HD": [
     0.972,
     [
      0.95,
      0.99
     ]
    ],
    "PID beats NN-HD": [
     0.982,
     [
      0.968,
      0.995
     ]
    ]
   },
   "range": "S4",
   "mean_tau_vs_physical": 0.72
  }
 ],
 "tube_horizon_sensitivity": [
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.05,
   "H_s": 15.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 69.8,
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 29.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.05,
   "H_s": 25.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 69.8,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.05,
   "H_s": 40.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 69.8,
   "fail_pct": {
    "MPC": 8.0,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.1,
   "H_s": 15.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 30.5,
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 29.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.1,
   "H_s": 25.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 30.5,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.1,
   "H_s": 40.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 30.5,
   "fail_pct": {
    "MPC": 7.8,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.2,
   "H_s": 15.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 30.5,
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 29.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.2,
   "H_s": 25.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 30.5,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.05,
   "tube_head_rad": 0.2,
   "H_s": 40.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 30.5,
   "fail_pct": {
    "MPC": 7.8,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.05,
   "H_s": 15.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 79.0,
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 1.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.05,
   "H_s": 25.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 79.0,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.05,
   "H_s": 40.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 79.0,
   "fail_pct": {
    "MPC": 7.5,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.1,
   "H_s": 15.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 90.2,
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 1.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.1,
   "H_s": 25.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 90.2,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.1,
   "H_s": 40.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 90.2,
   "fail_pct": {
    "MPC": 7.5,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.2,
   "H_s": 15.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 46.5,
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 1.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.2,
   "H_s": 25.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 46.5,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.1,
   "tube_head_rad": 0.2,
   "H_s": 40.0,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 46.5,
   "fail_pct": {
    "MPC": 7.5,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.5
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.05,
   "H_s": 15.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 79.0,
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 0.5
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.05,
   "H_s": 25.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 79.0,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.05,
   "H_s": 40.0,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mpc_first_pct": 79.0,
   "fail_pct": {
    "MPC": 7.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.83
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.1,
   "H_s": 15.0,
   "order": [
    "MPC",
    "PID",
    "NN-MPC",
    "NN-HD"
   ],
   "mpc_first_pct": 87.0,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.72
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.1,
   "H_s": 25.0,
   "order": [
    "MPC",
    "PID",
    "NN-MPC",
    "NN-HD"
   ],
   "mpc_first_pct": 87.0,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.72
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.1,
   "H_s": 40.0,
   "order": [
    "MPC",
    "PID",
    "NN-MPC",
    "NN-HD"
   ],
   "mpc_first_pct": 87.0,
   "fail_pct": {
    "MPC": 7.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.72
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.2,
   "H_s": 15.0,
   "order": [
    "MPC",
    "PID",
    "NN-MPC",
    "NN-HD"
   ],
   "mpc_first_pct": 89.8,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.2,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.72
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.2,
   "H_s": 25.0,
   "order": [
    "MPC",
    "PID",
    "NN-MPC",
    "NN-HD"
   ],
   "mpc_first_pct": 89.8,
   "fail_pct": {
    "MPC": 8.2,
    "NN-MPC": 1.0,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.72
  },
  {
   "tube_lat_m": 0.2,
   "tube_head_rad": 0.2,
   "H_s": 40.0,
   "order": [
    "MPC",
    "PID",
    "NN-MPC",
    "NN-HD"
   ],
   "mpc_first_pct": 89.8,
   "fail_pct": {
    "MPC": 7.2,
    "NN-MPC": 0.8,
    "PID": 0.8,
    "NN-HD": 0.0
   },
   "mean_tau_vs_physical": 0.72
  }
 ],
 "trial_number_sensitivity": [
  {
   "N": 10,
   "p_same_order_as_400": 0.942,
   "p_mpc_first": 0.974
  },
  {
   "N": 25,
   "p_same_order_as_400": 0.999,
   "p_mpc_first": 0.999
  },
  {
   "N": 50,
   "p_same_order_as_400": 1.0,
   "p_mpc_first": 1.0
  },
  {
   "N": 100,
   "p_same_order_as_400": 1.0,
   "p_mpc_first": 1.0
  },
  {
   "N": 200,
   "p_same_order_as_400": 1.0,
   "p_mpc_first": 1.0
  },
  {
   "N": 400,
   "p_same_order_as_400": 1.0,
   "p_mpc_first": 1.0
  }
 ],
 "hoeffding": {
  "loss": "per-start rank, bounded in [1, 4] (B = 3)",
  "K": 4,
  "alpha": 0.05,
  "smallest_adjacent_mean_rank_gap_at_N400": 0.511,
  "n_bound": 350
 },
 "ablation_by_channel": [
  {
   "condition": "D1a",
   "channel": "actuation: +0.10 s delay",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.43,
    "NN-MPC": 2.03,
    "PID": 2.69,
    "NN-HD": 3.85
   },
   "fail_pct": {
    "MPC": 10.5,
    "NN-MPC": 1.5,
    "PID": 1.5,
    "NN-HD": 0.0
   },
   "mpc_first_pct": 80.5,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
  {
   "condition": "D1b",
   "channel": "actuation: +0.20 s delay",
   "n": 200,
   "order": [
    "NN-MPC",
    "MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.88,
    "NN-MPC": 1.73,
    "PID": 2.52,
    "NN-HD": 3.87
   },
   "fail_pct": {
    "MPC": 9.0,
    "NN-MPC": 1.5,
    "PID": 2.0,
    "NN-HD": 0.0
   },
   "mpc_first_pct": 51.8,
   "mean_tau_vs_physical": 0.5,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
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   "condition": "D2a",
   "channel": "actuation: steering bias 0.013",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.37,
    "NN-MPC": 2.24,
    "PID": 2.51,
    "NN-HD": 3.88
   },
   "fail_pct": {
    "MPC": 10.0,
    "NN-MPC": 0.5,
    "PID": 0.5,
    "NN-HD": 0.0
   },
   "mpc_first_pct": 84.8,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
  {
   "condition": "D2b",
   "channel": "actuation: steering bias 0.026",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.38,
    "NN-MPC": 2.17,
    "PID": 2.56,
    "NN-HD": 3.89
   },
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 0.5,
    "PID": 1.0,
    "NN-HD": 0.5
   },
   "mpc_first_pct": 81.2,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
  {
   "condition": "D3a",
   "channel": "observation: pose noise 0.02 m / 0.01 rad",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.29,
    "NN-MPC": 2.14,
    "PID": 2.66,
    "NN-HD": 3.9
   },
   "fail_pct": {
    "MPC": 8.5,
    "NN-MPC": 0.5,
    "PID": 0.5,
    "NN-HD": 0.0
   },
   "mpc_first_pct": 88.5,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
  {
   "condition": "D3b",
   "channel": "observation: pose noise 0.05 m / 0.03 rad",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.61,
    "NN-MPC": 2.04,
    "PID": 2.5,
    "NN-HD": 3.85
   },
   "fail_pct": {
    "MPC": 9.5,
    "NN-MPC": 1.0,
    "PID": 2.5,
    "NN-HD": 0.0
   },
   "mpc_first_pct": 71.2,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
  {
   "condition": "D4a",
   "channel": "plant: friction 0.6",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.34,
    "NN-MPC": 2.19,
    "PID": 2.61,
    "NN-HD": 3.85
   },
   "fail_pct": {
    "MPC": 9.0,
    "NN-MPC": 0.5,
    "PID": 0.0,
    "NN-HD": 1.0
   },
   "mpc_first_pct": 85.5,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
  {
   "condition": "D4b",
   "channel": "plant: friction 0.4",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.72,
    "NN-MPC": 2.22,
    "PID": 2.56,
    "NN-HD": 3.51
   },
   "fail_pct": {
    "MPC": 9.5,
    "NN-MPC": 0.5,
    "PID": 0.0,
    "NN-HD": 0.0
   },
   "mpc_first_pct": 67.5,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  },
  {
   "condition": "D5",
   "channel": "combined D1a + D2a + D3a",
   "n": 200,
   "order": [
    "MPC",
    "NN-MPC",
    "PID",
    "NN-HD"
   ],
   "mean_rank": {
    "MPC": 1.64,
    "NN-MPC": 1.94,
    "PID": 2.54,
    "NN-HD": 3.88
   },
   "fail_pct": {
    "MPC": 10.5,
    "NN-MPC": 0.5,
    "PID": 0.5,
    "NN-HD": 0.5
   },
   "mpc_first_pct": 71.2,
   "mean_tau_vs_physical": 0.83,
   "same_starts_no_disturbance": {
    "order": [
     "MPC",
     "NN-MPC",
     "PID",
     "NN-HD"
    ],
    "mean_tau_vs_physical": 0.83
   }
  }
 ],
 "bootstrap_B": 2000
}