Scaling of the instellation at which the chaotic fraction is maximized for stabilizing fourth feedbacks near the freezing point (263 K < T_f < 283 K). Left: instellation corresponding to the maximum fraction of chaotic climates, S_peak, as a function of the normalized volcanic outgassing rate (V/W₀), with a logarithmic fit. Right: fraction of chaotic climates as a function of shifted instellation, showing that the curves exhibit similar profiles after accounting for the dependence of S_peak on V/W₀. Increasing normalized volcanic outgassing shifts the peak of the chaotic regime to lower instellation while preserving the overall shape of the chaotic-fraction curve.