The Aether iteration z₍+₁ = K zₙ exp (Im (zₙ) ) + c admits a period-doubling cascade with bifurcation points K₁₈₅, ₂䂞 converging to K^1Dacc = 14. 7666 at the Feigenbaum rate δF = 4. 6692…. In the companion paper (Bird 2026, Paper 6), the Stokes line |λ₂ (K) | = 1 in the complex-K plane was proved to be a closed curve whose unique real-axis terminus is exactly Kbif, 2 = 12. 509. Here we prove that the analogous Stokes lines for periods 2ⁿ, n = 1, 2, 3, 4, form a nested family of closed curves whose real-axis termini Tₙ satisfy (Tₙ − K^1Dacc) / (Tn−1 − K^1D₀₂₂) → δF^−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 δF. 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.
Michael Bird (Tue,) studied this question.