The Effective Optical Depth Power Law of Intergalactic Absorption and Its Insensitivity to a High-Density Bounce

This study asks whether the slope of the effective optical depth with redshift carries any imprint of a bounce. 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: gamma = 3.255; bounce_gamma_shift = 5.759545688385696e-83; result = negative: fitted slope shift from bounce is negligible. The fit returns a slope near 3. All values are computed from the stated assumptions, not measured, and the computation is supplied so that every number can be reproduced.