Opacity-Limit Fragmentation Mass as a Function of Metallicity and Dust Opacity

This paper computes the opacity limit for fragmentation, the classic argument that a collapsing fragment cannot cool efficiently below a certain mass and therefore cannot fragment further. Metallicity changes the dust opacity and the cooling rate, so the floor should move, and the size of that movement is the testable content. The headline computed values are: Mmin_solar = 8.54; Mmin_lowZ = 5.13; Mmin_highZ = 9.61; range_factor = 1.872. All values were obtained from the stated scalings and normalisations in the deposited code; this study is simulated and computed, not measured, and no new observations are reported. Where the framework supplies no value for a quantity the question requires, that absence is reported plainly as a negative result.