Function admit_analytic_path 

pub fn admit_analytic_path(
    stability: &StabilityClaim,
    realizability: &RealizabilityClaim,
) -> AnalyticPathVerdict

Admit or refuse the analytic path from a claim’s own constants.

Theorem 12.4 inherits Theorem 12.1’s step-size bounds 0 < η < min{2(α−β)/(L(α+β)²), 1/(2μ(α−β))} — the hypothesis that makes c > 0 and places the contraction factor in (1/2, 1). The runtime refuses the analytic path when it fails rather than reporting a floor computed from an inadmissible step size.