The Transition Lives Where the Freeze Puts It: The Sigmoid Dark Energy Fit, Priced at Its Two Frozen Inputs

Prices the sigmoid dark-energy fit of Torres-Arzayus et al. (2311.05510) at its frozen Omega_m = 0.3153 and frozen width r = 0.125: instrument recovers inputs exactly; across Omega_m 0.285-0.345 all refits stay within chi2 0.72 while z_a runs 0.08-1.80, and r = 0.50 moves z_a to 0.24 -- the transition redshift is carried by the freezes, while H0 is comparatively robust (freeing Omega_m inflates its error only x1.16).