III.T55 — S-Duality Transport

S-duality transport for Eisenstein series at τ = iι_τ. The modular transformation E_{2k}(−1/τ) = τ^{2k}E_{2k}(τ) with i⁴=+1 and i⁶=−1 gives E₄·ι⁴ = 1+240q' (2.4 ppm) and E₆·ι⁶ = −(1−504q') (5.1 ppm). Closes OQ.09 (E₄/E₆ fixed point). The S-dual nome q' = e^{−2π/ι_τ} < e^{−18} is exponentially suppressed.