{
  "experiment": "Experiment 12: Plasma as Geometric Phase Transition",
  "framework": "SUPERFLUID C = \u03c4/K applied to ballooning stability",
  "equation": "Connor-Hastie-Taylor (1978) s-\u03b1 model",
  "identification": {
    "tau": "magnetic shear s",
    "K": "pressure curvature alpha"
  },
  "geometry_results": {
    "Circular": {
      "geometry": "Circular",
      "kappa": 1.0,
      "delta": 0.0,
      "C_crit_mean": 1.345883,
      "C_crit_std": 0.3793,
      "CoV_pct": 28.18,
      "n_points": 10,
      "C_crit_high_s_mean": 1.655922,
      "C_crit_high_s_std": 0.028306,
      "CoV_high_s_pct": 1.71
    },
    "Elongated": {
      "geometry": "Elongated",
      "kappa": 1.7,
      "delta": 0.0,
      "C_crit_mean": 2.996509,
      "C_crit_std": 0.863461,
      "CoV_pct": 28.82,
      "n_points": 10,
      "C_crit_high_s_mean": 3.760045,
      "C_crit_high_s_std": 0.129789,
      "CoV_high_s_pct": 3.45
    },
    "D-shaped": {
      "geometry": "D-shaped",
      "kappa": 1.7,
      "delta": 0.33,
      "C_crit_mean": 3.11319,
      "C_crit_std": 0.920769,
      "CoV_pct": 29.58,
      "n_points": 10,
      "C_crit_high_s_mean": 3.93155,
      "C_crit_high_s_std": 0.153463,
      "CoV_high_s_pct": 3.9
    },
    "Neg-tri": {
      "geometry": "Neg-tri",
      "kappa": 1.7,
      "delta": -0.3,
      "C_crit_mean": 2.904535,
      "C_crit_std": 0.811432,
      "CoV_pct": 27.94,
      "n_points": 10,
      "C_crit_high_s_mean": 3.617678,
      "C_crit_high_s_std": 0.107413,
      "CoV_high_s_pct": 2.97
    }
  },
  "detailed_results": {
    "Circular": {
      "geometry": "Circular",
      "kappa": 1.0,
      "delta": 0.0,
      "C_crit_mean": 1.345883,
      "C_crit_std": 0.3793,
      "CoV_pct": 28.18,
      "n_points": 10,
      "details": [
        {
          "s": 0.2,
          "alpha_crit_1": 0.354117,
          "C_crit": 0.564785,
          "alpha_crit_2": 0.988975,
          "unstable_width": 0.6349
        },
        {
          "s": 0.3,
          "alpha_crit_1": 0.3535,
          "C_crit": 0.848656,
          "alpha_crit_2": 1.243436,
          "unstable_width": 0.8899
        },
        {
          "s": 0.4,
          "alpha_crit_1": 0.372683,
          "C_crit": 1.073299,
          "alpha_crit_2": 1.473776,
          "unstable_width": 1.1011
        },
        {
          "s": 0.5,
          "alpha_crit_1": 0.403096,
          "C_crit": 1.240399,
          "alpha_crit_2": 1.685895,
          "unstable_width": 1.2828
        },
        {
          "s": 0.7,
          "alpha_crit_1": 0.482067,
          "C_crit": 1.45208,
          "alpha_crit_2": 2.074823,
          "unstable_width": 1.5928
        },
        {
          "s": 1.0,
          "alpha_crit_1": 0.624495,
          "C_crit": 1.601294,
          "alpha_crit_2": 2.606629,
          "unstable_width": 1.9821
        },
        {
          "s": 1.3,
          "alpha_crit_1": 0.783181,
          "C_crit": 1.659898,
          "alpha_crit_2": 3.102509,
          "unstable_width": 2.3193
        },
        {
          "s": 1.5,
          "alpha_crit_1": 0.895132,
          "C_crit": 1.675731,
          "alpha_crit_2": 3.419911,
          "unstable_width": 2.5248
        },
        {
          "s": 2.0,
          "alpha_crit_1": 1.190722,
          "C_crit": 1.679653,
          "alpha_crit_2": 4.181769,
          "unstable_width": 2.991
        },
        {
          "s": 2.5,
          "alpha_crit_1": 1.503277,
          "C_crit": 1.663033,
          "alpha_crit_2": 4.911803,
          "unstable_width": 3.4085
        }
      ],
      "C_crit_high_s_mean": 1.655922,
      "C_crit_high_s_std": 0.028306,
      "CoV_high_s_pct": 1.71
    },
    "Elongated": {
      "geometry": "Elongated",
      "kappa": 1.7,
      "delta": 0.0,
      "C_crit_mean": 2.996509,
      "C_crit_std": 0.863461,
      "CoV_pct": 28.82,
      "n_points": 10,
      "details": [
        {
          "s": 0.2,
          "alpha_crit_1": 0.136652,
          "C_crit": 1.463568,
          "alpha_crit_2": 2.568786,
          "unstable_width": 2.4321
        },
        {
          "s": 0.3,
          "alpha_crit_1": 0.162113,
          "C_crit": 1.850564,
          "alpha_crit_2": 3.091776,
          "unstable_width": 2.9297
        },
        {
          "s": 0.4,
          "alpha_crit_1": 0.179812,
          "C_crit": 2.224541,
          "alpha_crit_2": 3.690718,
          "unstable_width": 3.5109
        },
        {
          "s": 0.5,
          "alpha_crit_1": 0.195467,
          "C_crit": 2.557976,
          "alpha_crit_2": 4.338889,
          "unstable_width": 4.1434
        },
        {
          "s": 0.7,
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          "C_crit": 3.068215,
          "alpha_crit_2": 3.844859,
          "unstable_width": 3.6167
        },
        {
          "s": 1.0,
          "alpha_crit_1": 0.284271,
          "C_crit": 3.51777,
          "alpha_crit_2": 4.966088,
          "unstable_width": 4.6818
        },
        {
          "s": 1.3,
          "alpha_crit_1": 0.347703,
          "C_crit": 3.738821
        },
        {
          "s": 1.5,
          "alpha_crit_1": 0.393211,
          "C_crit": 3.814747,
          "alpha_crit_2": 3.824563,
          "unstable_width": 3.4314
        },
        {
          "s": 2.0,
          "alpha_crit_1": 0.515935,
          "C_crit": 3.876457,
          "alpha_crit_2": 4.35848,
          "unstable_width": 3.8425
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        {
          "s": 2.5,
          "alpha_crit_1": 0.648941,
          "C_crit": 3.852428,
          "alpha_crit_2": 4.869617,
          "unstable_width": 4.2207
        }
      ],
      "C_crit_high_s_mean": 3.760045,
      "C_crit_high_s_std": 0.129789,
      "CoV_high_s_pct": 3.45
    },
    "D-shaped": {
      "geometry": "D-shaped",
      "kappa": 1.7,
      "delta": 0.33,
      "C_crit_mean": 3.11319,
      "C_crit_std": 0.920769,
      "CoV_pct": 29.58,
      "n_points": 10,
      "details": [
        {
          "s": 0.2,
          "alpha_crit_1": 0.13351,
          "C_crit": 1.498019,
          "alpha_crit_2": 2.829356,
          "unstable_width": 2.6958
        },
        {
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          "alpha_crit_1": 0.15812,
          "C_crit": 1.897295,
          "alpha_crit_2": 3.185092,
          "unstable_width": 3.027
        },
        {
          "s": 0.4,
          "alpha_crit_1": 0.175159,
          "C_crit": 2.283637,
          "alpha_crit_2": 3.609473,
          "unstable_width": 3.4343
        },
        {
          "s": 0.5,
          "alpha_crit_1": 0.190136,
          "C_crit": 2.629703,
          "alpha_crit_2": 4.064018,
          "unstable_width": 3.8739
        },
        {
          "s": 0.7,
          "alpha_crit_1": 0.221135,
          "C_crit": 3.165494,
          "alpha_crit_2": 3.897057,
          "unstable_width": 3.6759
        },
        {
          "s": 1.0,
          "alpha_crit_1": 0.27399,
          "C_crit": 3.649764,
          "alpha_crit_2": 4.816732,
          "unstable_width": 4.5427
        },
        {
          "s": 1.3,
          "alpha_crit_1": 0.333557,
          "C_crit": 3.89738,
          "alpha_crit_2": 5.819676,
          "unstable_width": 5.4861
        },
        {
          "s": 1.5,
          "alpha_crit_1": 0.376269,
          "C_crit": 3.986505,
          "alpha_crit_2": 4.310718,
          "unstable_width": 3.9344
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        {
          "s": 2.0,
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          "C_crit": 4.06924,
          "alpha_crit_2": 4.862266,
          "unstable_width": 4.3708
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        {
          "s": 2.5,
          "alpha_crit_1": 0.616544,
          "C_crit": 4.05486,
          "alpha_crit_2": 5.390739,
          "unstable_width": 4.7742
        }
      ],
      "C_crit_high_s_mean": 3.93155,
      "C_crit_high_s_std": 0.153463,
      "CoV_high_s_pct": 3.9
    },
    "Neg-tri": {
      "geometry": "Neg-tri",
      "kappa": 1.7,
      "delta": -0.3,
      "C_crit_mean": 2.904535,
      "C_crit_std": 0.811432,
      "CoV_pct": 27.94,
      "n_points": 10,
      "details": [
        {
          "s": 0.2,
          "alpha_crit_1": 0.138398,
          "C_crit": 1.445105,
          "alpha_crit_2": 2.454969,
          "unstable_width": 2.3166
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        {
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          "alpha_crit_1": 0.164644,
          "C_crit": 1.822117,
          "alpha_crit_2": 3.115969,
          "unstable_width": 2.9513
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        {
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          "C_crit": 2.185689,
          "alpha_crit_2": 3.83188,
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          "C_crit": 2.508257,
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        {
          "s": 1.0,
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          "alpha_crit_2": 5.146764,
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        {
          "s": 1.3,
          "alpha_crit_1": 0.360148,
          "C_crit": 3.609623
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        {
          "s": 1.5,
          "alpha_crit_1": 0.408408,
          "C_crit": 3.672794,
          "alpha_crit_2": 3.445489,
          "unstable_width": 3.0371
        },
        {
          "s": 2.0,
          "alpha_crit_1": 0.538574,
          "C_crit": 3.713508,
          "alpha_crit_2": 3.960086,
          "unstable_width": 3.4215
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        {
          "s": 2.5,
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          "C_crit": 3.678883,
          "alpha_crit_2": 4.452662,
          "unstable_width": 3.7731
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      ],
      "C_crit_high_s_mean": 3.617678,
      "C_crit_high_s_std": 0.107413,
      "CoV_high_s_pct": 2.97
    }
  },
  "stability_boundary": {
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    "second": [
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  },
  "topology": {
    "pi1": "Z x Z (torus)",
    "davis_types": [
      "Type I: irrational (good)",
      "Type II: rational (islands possible)",
      "Type III: overlap (stochastic)"
    ],
    "rational_surfaces": [
      {
        "m": 5,
        "n": 4,
        "q": 1.25,
        "r_over_a": 0.2673,
        "davis_type": "II-high",
        "risk": "LOW (high-order, weak coupling)"
      },
      {
        "m": 4,
        "n": 3,
        "q": 1.3333,
        "r_over_a": 0.3086,
        "davis_type": "II-high",
        "risk": "LOW (high-order, weak coupling)"
      },
      {
        "m": 3,
        "n": 2,
        "q": 1.5,
        "r_over_a": 0.378,
        "davis_type": "II-mid",
        "risk": "MODERATE"
      },
      {
        "m": 5,
        "n": 3,
        "q": 1.6667,
        "r_over_a": 0.4364,
        "davis_type": "II-high",
        "risk": "LOW (high-order, weak coupling)"
      },
      {
        "m": 7,
        "n": 4,
        "q": 1.75,
        "r_over_a": 0.4629,
        "davis_type": "II-high",
        "risk": "LOW (high-order, weak coupling)"
      },
      {
        "m": 2,
        "n": 1,
        "q": 2.0,
        "r_over_a": 0.5345,
        "davis_type": "II-low",
        "risk": "HIGH (low-order resonance)"
      },
      {
        "m": 7,
        "n": 3,
        "q": 2.3333,
        "r_over_a": 0.6172,
        "davis_type": "II-high",
        "risk": "LOW (high-order, weak coupling)"
      },
      {
        "m": 5,
        "n": 2,
        "q": 2.5,
        "r_over_a": 0.6547,
        "davis_type": "II-high",
        "risk": "LOW (high-order, weak coupling)"
      },
      {
        "m": 3,
        "n": 1,
        "q": 3.0,
        "r_over_a": 0.7559,
        "davis_type": "II-mid",
        "risk": "MODERATE"
      },
      {
        "m": 7,
        "n": 2,
        "q": 3.5,
        "r_over_a": 0.8452,
        "davis_type": "II-high",
        "risk": "LOW (high-order, weak coupling)"
      },
      {
        "m": 4,
        "n": 1,
        "q": 4.0,
        "r_over_a": 0.9258,
        "davis_type": "II-mid",
        "risk": "MODERATE"
      }
    ]
  },
  "bec_comparison": {
    "beta_hard": 0.425,
    "beta_soft": 0.486,
    "beta_ratio": 0.8745
  },
  "runtime_seconds": 102.5
}