{
  "schema": "taylor_green_betti_v1",
  "description": "Betti number analysis of Taylor-Green vortex with voids",
  "grid": "32x32x32",
  "percentile": 75.0,
  "scenarios": [
    {
      "scenario": "Uniform flow",
      "betti_0": 0,
      "betti_1": 0,
      "betti_2": 0,
      "interpretation": "\u03b2\u2082=0 \u2014 no voids in scar support",
      "scar_density_mean": 0.0,
      "scar_density_max": 0.0,
      "scar_support_fraction": 0.0
    },
    {
      "scenario": "Uniform+void",
      "betti_0": 1,
      "betti_1": 48,
      "betti_2": 1,
      "interpretation": "\u03b2\u2082=1 \u2014 indicating voids in scar support",
      "scar_density_mean": 0.12874603271484375,
      "scar_density_max": 14.0625,
      "scar_support_fraction": 0.015625
    },
    {
      "scenario": "TG smooth",
      "betti_0": 27,
      "betti_1": 12,
      "betti_2": 0,
      "interpretation": "\u03b2\u2082=0 \u2014 no voids in scar support",
      "scar_density_mean": 0.02859044560667393,
      "scar_density_max": 0.0761204674887134,
      "scar_support_fraction": 0.249298095703125
    },
    {
      "scenario": "TG+void r=5",
      "betti_0": 27,
      "betti_1": 51,
      "betti_2": 1,
      "interpretation": "\u03b2\u2082=1 \u2014 indicating voids in scar support",
      "scar_density_mean": 0.030014362461367294,
      "scar_density_max": 0.3295700132353654,
      "scar_support_fraction": 0.249053955078125
    },
    {
      "scenario": "TG+void r=6",
      "betti_0": 27,
      "betti_1": 64,
      "betti_2": 6,
      "interpretation": "\u03b2\u2082=6 \u2014 indicating voids in scar support",
      "scar_density_mean": 0.029546712701779096,
      "scar_density_max": 0.2998060621711367,
      "scar_support_fraction": 0.249298095703125
    },
    {
      "scenario": "Noise",
      "betti_0": 1920,
      "betti_1": 382,
      "betti_2": 77,
      "interpretation": "\u03b2\u2082=77 \u2014 indicating voids in scar support",
      "scar_density_mean": 1.7812399225491227,
      "scar_density_max": 12.489202293401028,
      "scar_support_fraction": 0.25
    }
  ],
  "summary": {
    "Uniform flow": 0,
    "Uniform+void": 1,
    "TG smooth": 0,
    "TG+void r=5": 1,
    "TG+void r=6": 6,
    "Noise": 77
  }
}