NON-PERTURBATIVE STRUCTURE OF THE CLASS A WATSON INTEGRAL: CLASS B BOREL SINGULARITY, FULL BOUNDARY-LAYER SERIES, AND THE STOKES CONSTANT

We resolve the three open problems stated in Paper 10 (Bird 2026, DOI:10.5281/zenodo.19228226), §6.2. (1) Class B Borel singularity. The Class B iterated-logarithm series Σ Pₙ(ln ln K)/(ln K)ⁿ is not a Gevrey-1 series of any fixed order in v = 1/ln K: its Borel-transform radius of convergence satisfies ρ(K) ~ 1/ln ln K → 0 as K → ∞, so no Borel–Laplace re-summation exists in the standard sense. The obstruction is the non-Gevrey growth aₙ ~ (ln ln K)ⁿ, consistent with Écalle-type doubly-iterated resurgence (Costin 2008). (2) Full boundary-layer series. All higher-order coefficients dₖ of the Class A boundary-layer series Σₖ dₖ W^(k+3/2)/(k+3/2) are computed analytically via a direct binomial convolution and confirmed numerically to relative error 7.2×10⁻¹⁵ at K = 10⁹ for k ≤ 10, all three benchmark α-values. (3) Stokes constant amplitude. Via the convergent amplitude ratio |S₁^A| = lim_{|K|→∞} |A_NP(K)| / (C_A |K|^{−γ_A}) along the Stokes ray arg K = π/(1+α), we establish |S₁^A| to five significant figures for α ∈ {1/4, 1/2, 3/4}. The sign of S₁^A is identified as an open problem requiring Picard–Lefschetz orientation analysis.