Picard–Lefschetz Stokes Constant Law for Class A: Watson–Borel–Alien Extraction and the α^1/3 K (1−α) ^δ Universality (Paper 16 in the Non-Holomorphic Fractal Series)

Paper 16 in the Non-Holomorphic Fractal Series. Papers 12–15 fixed the sign, exact exponent, and Picard–Lefschetz definition of the Class A Stokes constant S₁ᴬ (α) but left its normalized magnitude and α-dependence as open numerical questions. In this paper we compute the Picard–Lefschetz normalized magnitude |S₁ᴬ|PL (α) on a 13-point α-grid using the Watson–Borel–alien route: we build the Watson generating function GA (s; α) = ₂F₁ (1/2, p; p + 1/2; s) with p = 1 − α/2, evaluate its branch-cut discontinuity at the first Borel singularity s = 1 via high-precision Padé approximants and direct ₂F₁ evaluation, and convert the jump to a Stokes magnitude via the Picard–Lefschetz bridge equation |S₁ᴬ|PL = |Δω|/ (2π). All 13 values satisfy arg S₁ᴬ = π (real negative), confirming Paper 12 at every grid point. After factoring out α^1/3, the residual f (α) = |S₁ᴬ|PL (α) /α^1/3 is smooth and strongly suppressed as α → 1. On the high-α slice 0. 80, 0. 99 the data obey the two-parameter universality law |S₁ᴬ|PL (α) ≈ α^1/3 K (1−α) ^δ, K ≈ 4. 49 × 10⁻⁸, δ ≈ 1. 05, with relative error below 3% at every fitted point. This Picard–Lefschetz Stokes constant law is the numerical capstone of the Class A programme.