[
  {
    "local_id": "C1",
    "type": "empirical",
    "core": true,
    "statement": "In negative binomial branching processes with reproduction number R0 = 2.50, increasing transmission overdispersion from the Poisson limit (k -> inf) to geometric variance (k = 1.00) to SARS-like superspreading (k = 0.10) increases the single-case extinction probability from 0.107355 to 0.400000 to 0.860685, expanding the critical introduction threshold for 95% epidemic certainty from 2 to 4 to 20 independent introductions.",
    "evidence": [
      {
        "result": "R1.sars_q1",
        "produced_by": "code/analyze.py",
        "tolerance": 0.00001
      },
      {
        "result": "R1.geometric_q1",
        "produced_by": "code/analyze.py",
        "tolerance": 0.00001
      },
      {
        "result": "R1.sars_j_star_95",
        "produced_by": "code/analyze.py"
      }
    ],
    "depends_on": [],
    "falsified_if": "Independent solution of the negative binomial probability generating function fixed point yields an extinction probability differing by more than 0.0001.",
    "confidence": 1.0
  },
  {
    "local_id": "C2",
    "type": "resource",
    "core": true,
    "statement": "For SARS-like superspreading dynamics (R0 = 2.50, k = 0.10), closed-form Otter-Dwass evaluation establishes that solitary index cases without secondary spread account for 0.721943 extinction probability (83.88% of all extinctions), and cumulative summation over finite cluster sizes s from 1 through 500 recovers the complete extinction probability with an absolute residual under 1.0e-6, verified across 50000 independent branching process simulations.",
    "evidence": [
      {
        "result": "R1.sars_p_s1",
        "produced_by": "code/analyze.py",
        "tolerance": 0.00001
      },
      {
        "result": "R1.sars_sum_500_residual",
        "produced_by": "code/analyze.py",
        "tolerance": 0.00001
      }
    ],
    "depends_on": [],
    "falsified_if": "The Otter-Dwass cluster size summation contradicts the generating function fixed point or deviates from Monte Carlo simulation beyond statistical error.",
    "confidence": 1.0
  }
]