Stellar Fate as Basin Architecture: Coupling, Flat-Region Failure, and the Population Distribution of Remnants

This paper applies the basin architecture framework to stellar populations, arguing that stellar fate is a coupling geometry problem rather than a mass threshold problem. The Chandrasekhar limit is reframed as a commit-radius condition in mass coordinate space; binary accretion is external coupling pressure; and the Type Ia supernova is the threshold-crossing event that results when coupling geometry is sufficient. Two structurally distinct failure modes govern remnants that do not reach their commit radius: Failure Mode 1 (diffuse optionality) characterizes low-mass stars whose gradient dissipates across distributed pathways; Failure Mode 2 (dominant mass isolation) characterizes systems whose well depth exceeds the matching capacity of their environment. A third structural channel - the minor exit event - describes asymmetric coupling between non-equivalent systems, with IRAS 00500+6713 (an ONe and CO white dwarf merger product embedded in a putative SN Iax remnant) providing direct empirical evidence. A permeability-probability phase space maps the full remnant distribution from white dwarfs through neutron stars to black holes, connecting to black hole spin inversion as the high-mass terminus of the same geometric logic. The primary falsifiable prediction - Type Ia rate correlates with binary companion frequency as the mechanistic variable, supported by APOGEE, SDSS, and Gaia data - distinguishes the basin account from purely mass-based stellar evolution models. This paper is the fourth in the basin architecture tetraptych.