[
  {
    "local_id": "C1",
    "type": "theoretical",
    "core": true,
    "statement": "The area of the Mandelbrot set is greater than 1.50651.",
    "evidence": [
      {
        "result": "R1.area_lower_bound",
        "produced_by": "code/verify.py",
        "tolerance": 1e-09
      }
    ],
    "depends_on": [
      "C2"
    ],
    "falsified_if": "The area of the Mandelbrot set is shown to be at most 1.50651, or the components of C2 are shown not to be disjoint subsets of it.",
    "confidence": 0.99
  },
  {
    "local_id": "C2",
    "type": "theoretical",
    "core": true,
    "statement": "Ball arithmetic certifies a hyperbolic component of the Mandelbrot set at each of 617591 approximate centers, and these components with the mirror images of those off the real axis include 1234827 distinct components whose areas sum to more than 1.50651.",
    "evidence": [
      {
        "result": "R1.components_proven",
        "produced_by": "code/verify.py"
      },
      {
        "result": "R1.components_counted",
        "produced_by": "code/verify.py"
      },
      {
        "result": "R1.area_lower_bound",
        "produced_by": "code/verify.py",
        "tolerance": 1e-09
      }
    ],
    "depends_on": [],
    "falsified_if": "A correct ball-arithmetic check of the listed centers finds fewer hyperbolic components of the stated exact periods, finds two counted components to be one, or finds their areas to sum to 1.50651 or less.",
    "confidence": 0.99
  }
]