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 Kcusp ≈ 11. 047, Kₐcc ≈ 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䂞 (K) along the period-doubling cascade and prove: (i) The imaginary orbit map admits a period-doubling cascade accumulating at Kₐcc^1D ≈ 14. 7666, distinct from the 2D parameter-space accumulation Kₐcc^2D ≈ 14. 9048, with Feigenbaum ratios converging to δF = 4. 6692 within 0. 11%. (ii) The slopes μₙ = dλ₂䂞/dK|₊_₁₈₅, ₍ grow as C δFⁿ, confirming Feigenbaum universality in the orbit-multiplier series. (iii) The slope generating series has a simple pole at s* = 1/δF ≈ 0. 2142 with Stokes constant S₁^orb ≈ 0. 0618. (iv) The Stokes line |λ₂ (K) | = 1 in the complex K-plane is a closed curve whose unique real-axis intersection is K₁₈₅, ₂ ≈ 12. 509; all dynamical transition values lie strictly outside. (v) The multi-instanton trans-series has a geometric resurgence ratio S₁ 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.