Free-Streaming and Thermal Cutoffs in the Forest: Separating Particle Mass Limits from Gas Temperature

This study asks how a free-streaming cutoff from warm dark matter differs, in scale and in redshift behaviour, from the thermal cutoff of the gas. 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: k_hm_at_3p3keV = 12.0; result = particle cutoff and thermal cutoff overlap in scale; joint fitting required; bounce adds no cutoff. A 3. All values are computed from the stated assumptions, not measured, and the computation is supplied so that every number can be reproduced.