Stokes Line Hierarchy and the Feigenbaum Renormalization Spectrum in Aether Fractals

The Aether iteration z_{n+1} = K z_n exp(Im(z_n)) + c admits a period-doubling cascade with bifurcation points K_{bif,2^n} converging to K^{1D}{acc} = 14.7666 at the Feigenbaum rate δ_F = 4.6692…. In the companion paper (Bird 2026, Paper 6), the Stokes line {|λ_2(K)| = 1} in the complex-K plane was proved to be a closed curve whose unique real-axis terminus is exactly K{bif,2} = 12.509. Here we prove that the analogous Stokes lines for periods 2^n, n = 1, 2, 3, 4, form a nested family of closed curves whose real-axis termini T_n satisfy (T_n − K^{1D}{acc}) / (T{n−1} − K^{1D}_{acc}) → δ_F^{−1} = 0.2142, confirmed numerically to 0.38% at n = 4. We prove analytically that this convergence rate is a direct consequence of the linearised Feigenbaum renormalization-group (RG) operator, whose unstable eigenvalue is δ_F. The Stokes lines therefore provide a novel geometric imprint of the RG spectrum: the same universal constant that governs the period-doubling cascade also governs the convergence of the Stokes line family in the complex-K plane. The result links resurgence geometry, dynamical systems theory, and the Feigenbaum universality class in a single theorem.