Dual-Topology Emergent Gravity (DTEG): A Unified Framework of Thermodynamic Emergent Gravity, Information Dynamics, and Lagrangian Mechanics.

This paper establishes the formal ontological and mathematical foundation for the Dual-Topology Emergent Gravity (DTEG) Theory, providing a resolution to the quantum gravity problem via an information-gating function, Σ(S). By abandoning the paradigm of a single unified spacetime, we model the universe as a bipartite topological structure: a discrete Quantum Information Lattice (QIL) and a continuous Emergent Gravitational Manifold (EGM). Through the Principle of Least Action, we demonstrate that Einstein’s General Relativity is a macroscopic asymptote reached only when the quantum information threshold is breached. This model naturally derives the mass defect phenomenon in bound systems, resolves Tolman’s Paradox regarding the gravitation of light, and defines time ontologically as the processing rate of entropy. Furthermore, by applying the Margolus-Levitin limit, we derive gravitational time dilation directly from quantum thermodynamics and formulate a non-linear Schrodinger equation that solves the measurement problem. Ultimately, the framework models cyclic cosmological evolution via a complexified entropy variable on a Riemann surface, replacing the singular ’Heat Death’ with smooth transitions between multidimensional beta-versions of the universe