Dynamics of a Finite Cyclic Universe Using Time-Dependent Canonical Transformations in Complex Canonical Tensor Space: Complete Identification of Reverse-Time and Proof of Discrete Step Numbers to a Liouville Stable Point

The dynamics of a finite cyclic universe are structurally constructed via a complex canonical tensor transformation explicitly containing time, based on the BRST kernel processing of algebraic singularities in 16-dimensional sedenion algebra and the finite covering topology of compact spaces. By projecting the 8-dimensional covariant phase space (Omega_phase) after complexification onto a 4-dimensional complex canonical tensor space, the inversion of the metric sign in the singularity domain below the Planck limit (r < l_Planck) is completely identified and rigorously formalized as a non-Hermitian phase rotation on the complex time plane. Under the topological constraint that the number of patches (states) N of the finite covering is less than countably infinite, when the universe converges from the difference-driven Hamilton-Jacobi process to a Liouville measure-preserving stable point (Non-Equilibrium Steady State: NESS), the Banach fixed-point theorem topologically eliminates infinite loops and divergences, and uniquely determines the maximum number of discrete steps (n_max) deterministically. Furthermore, based on the unitarity of the kernel decomposition of the total Hamiltonian (H_+ + H_- = 0), the dynamical behavior of the Reverse-Time field transported to the white hole boundary while decreasing entropy according to Onsager's principle of minimum dissipation is deterministically determined by the algebraic closure.