[
  {
    "local_id": "C1",
    "type": "theoretical",
    "core": true,
    "statement": "For every binary significand precision p >= 3, the exactly representable parameter c_p = 1/4 + 2^(-(p+1)) has an unbounded exact critical orbit, while both nearest-even recurrences RN_p(RN_p(x_n^2)+c_p) and RN_p(x_n^2+c_p), starting at zero, stay in [0,1/2] for every iterate, with 1/2 absorbing.",
    "evidence": [],
    "depends_on": [],
    "falsified_if": "A stated rounding map is not monotone, the midpoint rounds above 1/2 under nearest-even, or an exact critical orbit fails the positive-increment identity.",
    "confidence": 0.99
  },
  {
    "local_id": "C2",
    "type": "resource",
    "core": false,
    "statement": "For all 22 precisions p from 3 through 24, the supplied exact-dyadic benchmark reaches the stationary value 1/2 under both rounding models and certifies finite exact first escapes, with first stationary transitions 8999 and 9532 and exact first escape 18196 at p=24.",
    "evidence": [
      {
        "result": "R1.cases",
        "produced_by": "code/verify.py",
        "tolerance": 0
      },
      {
        "result": "R1.boundary_cases",
        "produced_by": "code/verify.py",
        "tolerance": 0
      },
      {
        "result": "R1.native",
        "produced_by": "code/verify.py",
        "tolerance": 0
      },
      {
        "result": "R1.exhaustive_transition_comparisons",
        "produced_by": "code/verify.py",
        "tolerance": 0
      }
    ],
    "depends_on": [],
    "falsified_if": "A fresh run differs on a stationarity or certified escape count, or fails a native comparison or invariant assertion.",
    "confidence": 0.99
  }
]