The Larson Relations Revisited as a Test: Line Width, Size and Surface Density Against Any Shear Ceiling

This paper addresses a single question: Do the empirical size-line width and size-mass relations obeyed by molecular clouds approach any ceiling set by the maximum shear of the torsion framework, or are they fully explained without it? 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 the velocity gradient implied by the Larson size-line width relation is of order 10^-13 to 10^-14 per second across the cloud size range, roughly forty-seven orders of magnitude below the critical shear, so the relations neither approach nor test that ceiling; their near-constant surface density is instead the informative content, and it follows from clouds being close to virial balance at a common external pressure - the frame supplies no number for this system, a negative result stated plainly. The headline values are: sigma 10pc km s = 2.6; gradient 10pc per s = 8.55e-15; gradient ratio to bound = 9.99e-48. 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.