{
  "geometry": [
    {
      "grass_cells": 1620,
      "clusters": 312,
      "largest_cluster": 115,
      "forest_grass_edges": 3465,
      "grass_weighted_perimeter": 40.598148148148155,
      "expected_grass_burn_cells": 22.729629629629628,
      "expected_forest_loss_cells": 1.9817163734567913,
      "first_order_forest_loss_cells": 2.029907407407408,
      "pf": 0.05,
      "case": "随机分散"
    },
    {
      "grass_cells": 1620,
      "clusters": 1,
      "largest_cluster": 1620,
      "forest_grass_edges": 60,
      "grass_weighted_perimeter": 60.0,
      "expected_grass_burn_cells": 1620.0,
      "expected_forest_loss_cells": 2.9999999999999982,
      "first_order_forest_loss_cells": 3.0,
      "pf": 0.05,
      "case": "连成一片"
    }
  ],
  "front_checks": {
    "coarse": [
      {
        "a": 0.3,
        "measured_speed": 0.28265966820671107,
        "analytic_speed": 0.282842712474619
      },
      {
        "a": 0.5,
        "measured_speed": -9.909040585495122e-17,
        "analytic_speed": 0.0
      },
      {
        "a": 0.7,
        "measured_speed": -0.28265966820671096,
        "analytic_speed": -0.28284271247461895
      }
    ],
    "fine_speed_a03": 0.2827970225857732,
    "fine_dx": 0.1,
    "fine_dt": 0.0025,
    "parameters": "D=r=1; cubic reaction prescribed; no map to actual rainfall, distance or years"
  },
  "spatial_mixture": {
    "sites": 2000,
    "within_class_ranges": [
      [
        0.17,
        0.33
      ],
      [
        0.67,
        0.83
      ]
    ],
    "unique_local_equilibria": true,
    "KDE_bandwidth": 0.035,
    "meaning": "Every location du/dt=m(x)-u; pooling spatially different m creates bimodality without a second equilibrium at any location."
  },
  "published_transformation_examples": [
    {
      "biome": "forest",
      "frequency_increment_per_year": 0.2,
      "baseline_cover_percent": 25.0,
      "fitted_sqrt_cover_increment": 0.974,
      "back_transformed_cover_percent": 35.688676,
      "over_100_percent": false
    },
    {
      "biome": "forest",
      "frequency_increment_per_year": 0.2,
      "baseline_cover_percent": 50.0,
      "fitted_sqrt_cover_increment": 0.974,
      "back_transformed_cover_percent": 64.72311609751395,
      "over_100_percent": false
    },
    {
      "biome": "forest",
      "frequency_increment_per_year": 0.2,
      "baseline_cover_percent": 75.0,
      "fitted_sqrt_cover_increment": 0.974,
      "back_transformed_cover_percent": 92.81885086572089,
      "over_100_percent": false
    },
    {
      "biome": "savanna",
      "frequency_increment_per_year": 0.2,
      "baseline_cover_percent": 25.0,
      "fitted_sqrt_cover_increment": 1.4,
      "back_transformed_cover_percent": 40.96000000000001,
      "over_100_percent": false
    },
    {
      "biome": "savanna",
      "frequency_increment_per_year": 0.2,
      "baseline_cover_percent": 50.0,
      "fitted_sqrt_cover_increment": 1.4,
      "back_transformed_cover_percent": 71.75898987322334,
      "over_100_percent": false
    },
    {
      "biome": "savanna",
      "frequency_increment_per_year": 0.2,
      "baseline_cover_percent": 75.0,
      "fitted_sqrt_cover_increment": 1.4,
      "back_transformed_cover_percent": 101.2087113059643,
      "over_100_percent": true
    }
  ],
  "limits": [
    "No full FGBA Gillespie process, long-term stochastic stationarity proof or satellite inversion rerun.",
    "Connectivity example burns connected grass with certainty and allows only direct forest-edge loss; wind, moisture and further forest burning omitted.",
    "Front equation assumes a bistable reaction to examine spatial consequences, not to derive ecological feedback.",
    "Fire study raw data download API required authentication; only public paper and dataset metadata obtained.",
    "India figure data API returned403; classification/potential argument checked in original text/SI, not recalculated."
  ]
}