This submission presents the core theoretical preprint of the Triple String-Dynamic Equilibrium Model (TSDEM), a novel cosmological framework designed to bridge the impasse between Quantum Field Theory and General Relativity. The model introduces a rigorous 3-Tiered Topology consisting of the sub-Planckian Universal Conductor (Bottom Layer), the dynamic String Matrix (Middle Layer), and the Observable Universe (Top Layer). By postulating a non-linear exponential damping mechanism within the intermediate String Matrix, TSDEM provides an elegant mathematical solution to the 120-orders-of-magnitude Cosmological Constant problem (Vacuum Catastrophe), deriving a precise geometric attenuation coefficient of \chi = 120 \cdot \ln(10) \approx 276.31. Furthermore, the framework replaces singular cosmological events with an eternal, cyclic Big Bounce driven by a synaptic-inspired mechanism. At the peak of the Big Crunch, the network undergoes complete functional fracture and subsequent Dynamic Rewiring, achieving a total thermodynamic reset of global entropy (S \to 0). This preprint details the emergent physics of mass, gravity, and topological solitons (Gordian Knots) within the model, establishing high compatibility with recent observational data regarding time-evolving Dark Energy profiles.