Free-Fall Times Across the Cloud Density Hierarchy and Their Ratio to Every Shear Scale in the Problem

This paper addresses a single question: How long does gravity need to collapse each level of the cloud hierarchy if pressure support were removed, and how do the corresponding dynamical rates compare with the Galactic shear and with the critical shear of the torsion bound? Using published molecular-cloud and young-stellar-object measurements as inputs, and carrying the spin-torsion density bound of 9.72 x 10^57 kilograms per cubic metre and its critical shear of 8.56 x 10^32 per second as fixed comparison scales, the calculation finds that free-fall times fall from a few million years in cloud envelopes to about one hundred thousand years in dense cores, a hierarchy of a factor of several tens that organises the observed sequence of star formation activity; every dynamical rate in the hierarchy lies more than forty orders of magnitude below the critical shear, confirming that the shear bound is not a participant in cloud dynamics at any level - a negative result, quantified level by level rather than asserted once. The headline values are: tff core Myr = 0.11; tff envelope Myr = 3.4; rate ratio core = 3.47e-46. All values are computed from the stated formulae and inputs; this is a simulated and computed study, not a measurement. Where the comparison scales supplied by the torsion framework turn out to be too remote to influence the process, that outcome is reported as a negative result rather than passed over.