Resurgent asymptotics and Stokes phenomena in the Aether fractal family

The Aether fractal family z₍+₁ = K zₙ exp (Im (zₙ) ) + 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₍=₀^inf Dₙ (ln K) ^-n with coefficients Dₙ = (2n-1) !! / 2ⁿ. 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₍*| ≤ 2R D₍*+₁ (ln K) ^- (N*+1). The Stokes constant extracted via the Hankel contour is S₁ = 2√π, and the corresponding Stokes jump is purely imaginary and of order K^-1 (ln K) ^-1/2. Numerical experiments show that the three dynamical transition values Kcusp ≈ 11. 047, Kₐcc ≈ 14. 905, and K* ≈ 25 carry no signature in the Borel-plane structure of the area-law series: all are smooth points of A (K) and of the orbit-multiplier function λ₂ (K). A companion paper (doi: 10. 5281/zenodo. 19210343), released simultaneously, resolves the orbit-multiplier resurgence, the complex-K Stokes geometry, and the multi-instanton expansion, completing the resurgent analysis of the Aether fractal family.