{
  "analytic_model": "two_covering_zeros_hyperbolic_jung",
  "source_credit": "Classical Schwarz factorization and hyperbolic Jung; Wikstrom moment-duality criterion arXiv:2607.17748",
  "c": "54/125",
  "R": "999/1000",
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  "second_tail_t0": "4999/5000",
  "second_tail_t1": "9999/10000",
  "second_tail_k": 24000,
  "certificate_format": "exact rational hypotheses for the documented geometric lemma"
}