Mean Transmitted Flux of the Lyman-Alpha Forest Between Redshifts Two and Five: A Bounce-Frame Expansion Bound

This study asks whether the mean transmitted flux, the most basic average the forest offers, can register an early-universe bounce at all. Using published Lyman-alpha forest measurements as stated inputs, and a bounce frame in which the early universe turned around at a density of 9.72 x 10^54 grams per cubic centimetre, the relevant quantities are computed directly and compared with the precision of the data. The headline outcome is as follows: z_bounce = 1.5350960704735478e+28; max_shift_over_err = 1.1968862088048259e-81; tau_eff_z3 = 0.3624; result = negative: bounce shift below measurement error at every redshift. The effective optical depth rises from 0. All values are computed from the stated assumptions, not measured, and the computation is supplied so that every number can be reproduced.