Transient Non-Perturbative Dynamics of Type-B Singularity Crossing: The Non-Disruptive Transition Region

Abstract

In the Order Parameter Spacetime Theory, the Type-B traversable singularity is a critical interface for information–geometry phase transitions. The series of papers has already proved that the information dissipation tensor is stabilized at an infrared fixed point in the strong-coupling region (the final state), and has axiomatically established the power-law constraints and the finiteness of the relaxation time for Type-B singularities. However, the transient process of the order-parameter field crossing a Type-B singularity — the complete dynamics of the information dissipation channel opening from zero — has not yet been rigorously formulated. This paper fills that gap. The core results include: establishing a time-dependent, non-equilibrium effective action framework for the transition region; introducing the "information emergence flux" F_Υ = (φ̇_c/φ_c)² as the geometric driving source term for the information dissipation tensor; deriving the evolution equation Υ̇ + (Υ−Υ_0)/τ = (φ̇_c/φ_c)² for the information dissipation tensor during singularity crossing; proving that under the Type-B singularity power-law constraints (α=0, β=1, γ=1), the relaxation time τ itself is the minimal dynamical time scale (ε=τ), and with this regularization scheme the solution of the evolution equation possesses strict C¹ smoothness, the information dissipation tensor opens smoothly, and the order-parameter gradient does not diverge; and providing observable predictions for the transition region, including the characteristic spectrum (~ e^{−ωτ} exponential decay) of gravitational-wave bursts during the exit from inflation, and systematically arguing their compatibility with CMB tensor-to-scalar ratio constraints. Together with the existing fixed-point analysis and mathematical axiomatization, this paper completes the dynamical skeleton of the Order Parameter Spacetime Theory from "birth" to "end."