Orbit-multiplier resurgence and the Borel geometry of the Feigenbaum cascade in Aether fractals

The companion paper (doi:10.5281/zenodo.19210339) established that the Borel structure of the Class C stable-area law A(K) ~ C K⁻² for the Aether fractal family is entirely determined by a single square-root singularity at s* = 1, and that the three dynamical transition values K_cusp ≈ 11.047, K_acc ≈ 14.905, and K* ≈ 25 are smooth points of that structure. The present paper resolves the three questions raised in the companion paper, §6.4. We study the orbit-multiplier sequence λ2^n(K) along the period-doubling cascade and prove: (i) The imaginary orbit map admits a period-doubling cascade accumulating at K_acc1D ≈ 14.7666, distinct from the 2D parameter-space accumulation K_acc2D ≈ 14.9048, with Feigenbaum ratios converging to δ_F = 4.6692 within 0.11%. (ii) The slopes μ_n = dλ2^n/dK|_{Kbif,n} grow as C δ_F^n, confirming Feigenbaum universality in the orbit-multiplier series. (iii) The slope generating series has a simple pole at s* = 1/δ_F ≈ 0.2142 with Stokes constant S_1ᵒʳᵇ ≈ 0.0618. (iv) The Stokes line |λ_2(K)| = 1 in the complex K-plane is a closed curve whose unique real-axis intersection is Kbif,2 ≈ 12.509; all dynamical transition values lie strictly outside. (v) The multi-instanton trans-series has a geometric resurgence ratio S_1 K⁻¹ (π ln K)-1/2, confirmed to 10⁻¹² relative error. Together with the companion paper, these results constitute a complete resurgent analysis of the Aether fractal family.