Star Formation Dust Recycling and Closure Gated Collapse: A ψ₀-OCM Extension of the Standard Star Formation Model

Standard star-formation theory successfully models gravitational collapse, magnetohydrodynamics (MHD), and radiative cooling. However, several key observed outcomes—such as low star-formation efficiency, intermittency of collapse, the ubiquity of disks and jets, and the robustness of the stellar initial mass function (IMF)—are typically incorporated through empirical prescriptions rather than determinant-level mechanisms. This work introduces a ψ₀–OCM (Osborne Cosmological Model) extension in which collapse is governed by closure-gated redistribution: gravitational collapse proceeds only where redistribution leakage is sufficiently suppressed across coupled channels (turbulent, magnetic, radiative, and rotational). A modified dispersion relation is derived to demonstrate how leakage alters collapse thresholds while preserving standard limits. In the closure limit, classical Jeans instability and ideal-MHD behavior are fully recovered. The framework provides unified, mechanism-level interpretations of: Turbulence regulation of collapse Magnetic criticality and mass-to-flux thresholds Angular momentum transport and jet formation Star-formation efficiency per free-fall time Dust shielding thresholds for collapse Robustness of the stellar initial mass function (IMF) Testable predictions link collapse suppression to observable leakage proxies, including turbulence linewidth–size scaling, magnetic criticality, and shielding column density. The formulation remains explicitly compatible with standard astrophysical practice and reduces to established star-formation models in the appropriate limits, positioning ψ₀–OCM as a mechanism-layer extension rather than a replacement.