Resurgent asymptotics and Stokes phenomena in the Aether fractal family

The Aether fractal family z_{n+1} = K z_n exp(Im(z_n)) + c produces a Class C stable-area law A(K) ~ C K^{-2} whose subleading corrections are captured by an explicit Poincaré asymptotic series sum_{n=0}^{inf} D_n (ln K)^{-n} with coefficients D_n = (2n-1)!! / 2^n. We analyse this series via resurgence theory. The Borel transform is computed in closed form: Â(s) = (1-s)^{-1/2}, a function analytic on C \ [1,∞) with a square-root branch point at s* = 1. The optimal truncation depth is N* = floor(ln K), and the remainder satisfies the next-term bound |R_{N*}| ≤ 2R D_{N*+1} (ln K)^{-(N*+1)}. The Stokes constant extracted via the Hankel contour is S_1 = 2√π, and the corresponding Stokes jump is purely imaginary…