Relaxation Dynamics in Moduli Space: An Effective Mechanism for Compactification Selection (TSDC) V

This technical report consolidates the results of Phase 5 of the TSDC (Thermal Selection / Dissipative Cosmogenesis) research program. The study rigorously quantifies the structural robustness of the dissipative selection mechanism under metric deformations, parameter transitions, and adversarial initial conditions. Methodology followed a strict preregistered protocol (WP0) to prevent selection bias. Through extensive numerical integration and global sensitivity analysis (Sobol method), we established the following core findings: Universal Dissipation Floor: A robust operational threshold for the "Hot Big Bang" gate was identified at $\Gamma_{min} \approx 3.4 \times 10^{-4}$ (dimensionless), invariant under variations of the critical time scale $\tau_{crit} \in [50, 130]$. Geometric Robustness: The mechanism preserves its selection boundaries under metric deformations up to $\epsilon_G = 0.05$, validating its stability within an Effective Field Theory (EFT) context. Kinetic Dominance: Sensitivity analysis reveals that the failure boundary is primarily driven by the kinetic coupling parameter ($S_T^{kin} \approx 0.39$), with negligible dependence on the thermal exponent ($S_T^{inf} \approx 0.00$). Ignition Hysteresis: We successfully demonstrated the "Cold Start" (Ignition) scenario, quantifying a kinetic hysteresis cost of approximately $+50\%$ in the dissipation rate ($\Gamma_{ignition} \approx 6.0 \times 10^{-4}$) required to sustain the lock-in phase compared to the warm baseline. These results confirm that the TSDC mechanism functions as a robust dynamical attractor, independent of specific initial condition priors. This validation serves as the foundational basis for Phase 6, which will apply this framework to the "String Triad" problems: the Swampland Conjectures, Landscape selection, and Moduli stabilization. Keywords: Warm Inflation, Dissipative Cosmology, TSDC Mechanism, Structural Stability, Swampland Conjectures, Global Sensitivity Analysis, Numerical Relativity, Effective Field Theory.