The Doppler Parameter Distribution of Forest Lines: Thermal Widths, Turbulent Excess, and a Bounce Null

This study asks how much of the observed line width is thermal, how much must come from other broadening, and whether a bounce could supply the remainder. 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: b_thermal_at_10000K = 12.85; result = observed widths require non-thermal broadening; bounce supplies none (negative). Pure thermal broadening at ten thousand kelvin gives 12. All values are computed from the stated assumptions, not measured, and the computation is supplied so that every number can be reproduced.