Thermodynamic Bounds and Topological Dimensional Reduction in Chiral Manifolds

This manuscript investigates the thermodynamic and topological evolution of geometrically constrained state spaces. We propose a purely axiomatic framework where intrinsic geometric stability and entropy gradients act as the primary drivers for systemic state generation. Specifically, we examine the mechanism of topological dimensional reduction, detailing how a theoretical 64-dimensional unconstrained state space undergoes a spontaneous constraint collapse into a 32-dimensional stable configuration. This dimensional reduction is strictly mediated by the formation of 1/2-chiral topological knots and their associated backflow constraints. Furthermore, the study structurally distinguishes between steady-state knot formation (analogous to stable local configurations) and critical topological collapse events (high-density systemic instability and phase transitions). The boundary conditions of these manifolds are defined not by rigid limits, but by the maximum diffusion range of information entropy, expressed via an energetic-entropic identity bounds. Finally, to satisfy global topological closure and entropy conservation, the framework introduces a conjugate topological manifold. This conjugate space is characterized by an inverted 1/2-chiral constraint and a reversed entropy gradient (time-reversal symmetry). It exists not as orthogonal extra matter, but as a strictly anti-directional topological knot system, ensuring perfect global symmetry and structural completeness of the constrained manifold pair.