{
  "theorem": "Plateau Maximum",
  "statement": {
    "1": "C(s) = s/\u03b1_crit(s) has a unique maximum C_max at s_peak",
    "2": "Tangent condition: \u03b1'_crit(s_peak) = \u03b1_crit(s_peak)/s_peak",
    "3": "Plateau (C > 0.98 C_max) spans [1.3, 3.0] = tokamak operating range"
  },
  "results": [
    {
      "name": "Circular",
      "kappa": 1.0,
      "delta": 0.0,
      "C_max": 1.6820462032960537,
      "s_peak": 1.7849833836503441,
      "d2C_ds2": -0.12191144332875431,
      "tangent_error_pct": 0.0005460088889116607,
      "plateau": [
        1.3,
        2.8
      ],
      "exp12_diff_pct": 2.3553122048235857
    },
    {
      "name": "Elongated",
      "kappa": 1.7,
      "delta": 0.0,
      "C_max": 3.8766345872468757,
      "s_peak": 2.0343138622814045,
      "d2C_ds2": -0.29604952379060256,
      "tangent_error_pct": 0.0003256714130816077,
      "plateau": [
        1.5,
        2.9
      ],
      "exp12_diff_pct": 4.252544359290806
    },
    {
      "name": "D-shaped",
      "kappa": 1.7,
      "delta": 0.33,
      "C_max": 4.071503258490856,
      "s_peak": 2.1208149149787383,
      "d2C_ds2": -0.28837013508482834,
      "tangent_error_pct": 0.0003515873152240559,
      "plateau": [
        1.6,
        3.0
      ],
      "exp12_diff_pct": 4.761180170846771
    },
    {
      "name": "Neg-tri",
      "kappa": 1.7,
      "delta": -0.3,
      "C_max": 3.714151103242945,
      "s_peak": 1.934737215553956,
      "d2C_ds2": -0.3158946464831345,
      "tangent_error_pct": 0.0003823051631420713,
      "plateau": [
        1.4000000000000001,
        2.8
      ],
      "exp12_diff_pct": 3.752645018612154
    }
  ]
}