The Column-Density Distribution of Forest Absorbers: Slope Recovery and a Bounce Null

This study asks whether the slope of the absorber column-density distribution responds to the background expansion in a way a bounce could exploit. 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: beta_recovered = 1.5; expected_beta_input = 1.5; bounce_beta_shift = 1.769185185185185e-83; result = slope recovered; bounce contributes no measurable tilt (negative). The recovered slope is 1. All values are computed from the stated assumptions, not measured, and the computation is supplied so that every number can be reproduced.