Time Geometrization of Manifold F: A Study on Temporalized Geometric Fixed Points Based on Solvable Models and Dynamical Selection Mechanisms

This paper, within the framework of the time geometrization program, systematically investigates the existence, stability, and dynamical selection mechanismsof temporalized geometric fixed points (TGPs) in the presence of multiple fixedpoints. By constructing a 1+1-dimensional integrable model (the SU(N) principalchiral model at the Wess-Zumino-Witten point), we rigorously prove the existenceof a TGP in the continuum limit and verify that it satisfies the geometric stability conditions of vanishing time curvature and a one-dimensional first-order timecohomology group. Furthermore, this paper reveals that when a theory possessesmultiple candidate TGPs, the system automatically selects the stable fixed pointwith a smaller effective cosmological constant (Λeff) through intrinsic dynamicalinstability. This mechanism provides a non-perturbative explanation for the natural selection of low-energy structures in quantum field theory, eliminating the needfor manual parameter tuning, thereby offering a new theoretical and numericalframework for understanding critical behavior in time-structured geometry.