This preprint develops a quantitative energy-dissipation framework for a class of dissipative dynamical systems. The de Bruijn–Newman heat flow of the RiemannXi-function appears as a special instance of this general analytic structure. The framework is organized into nine modules (R1–R9) that provide explicit constants,coercivity bounds, boundary estimates, and tail-control inequalities. Together these establish global regularity of the dissipative flow under a verified energy identity. When applied to the de Bruijn–Newman system, the analysis implies that the associated constant satisfies Lambda = 0. The manuscript was developed through a structured human–machine collaboration involving two large language models: one performing analytic exploration andderivation, and another carrying out independent symbolic verification and consistency checks. The resulting analytic program is modular, explicit, and suitable for external audit or formal verification. This preprint therefore presents both a quantitative analytic framework for dissipative systems and a reproducible methodology for collaborative inference in mathematical research.