Resurgent asymptotics and Stokes phenomena in the Aether fractal family

The Aether fractal family zₙ₊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 sumₙ₌₀ⁱⁿᶠ 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 |RN*| ≤ 2R DN*+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 and of order K⁻¹(ln K)-1/2. Numerical experiments show that the three dynamical transition values K_cusp ≈ 11.047, K_acc ≈ 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 λ_2(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.