Regime map for transmission through a hydrodynamic planetary wind, shown in the plane of the absorption cross section, σ(λ), and mass-loss rate, Ṁ, for HD 209458 b. The color scale represents the dimensionless saturation parameter S ≡ σ(λ) Ṁ/C_sat, where C_sat = 2e^1/2τ_∗µm_pc_sr_s. The dashed black curve marks the analytic validity boundary σ(λ) Ṁ = C_sat, separating the opacity-limited regime (S ≪ 1), in which the transmission depth scales linearly with σ Ṁ, from the saturation-limited regime (S ≫ 1), in which the effective transit radius is set primarily by geometry. The shaded light gray region indicates cross sections of σ ≲ σ_obs,base ∼ 4 × 10⁻²⁰ cm², for which absorption becomes optically thin above the XUV heating base and the observed signal is expected to probe below the wind launch region. This figure illustrates the sharp, quantitative boundary between invertible and non-invertible transmission regimes predicted by the analytic model.