This is Version 2 of the paper. This version incorporates clarifications of the volume-constrained variationalproblem, a refined spectral non-collapse argument, a streamlined blow-upclassification, and an explicit elimination of all admissible alternativegeometric limits. The main results and conclusions remain unchanged. In particular, the roundsphere remains the unique compact, simply connected, dynamically stable criticalpoint of the zeta-regularized Dirac determinant flow. This version supersedes v1. Related work:Monotonicity methods, blow-up analysis, and elimination of geometric alternativesare inspired by Perelman’s work on Ricci flow. The convergence mechanism is basedon the Lojasiewicz–Simon inequality for analytic gradient flows. Zeta-regularizeddeterminants and Dirac-type operators have been studied by Atiyah, Patodi, Singer,Bär, Hijazi, and others in the context of spectral geometry. The present paperdiffers in that it provides a complete closure: global existence, non-collapse,blow-up classification, rigidity, and global convergence for a single spectralflow.