Spacetime Dispersive Membrane Theory with Volatility and Matter-Wave Dynamics in Asymmetric Geometric Reservoirs (SDM-V Theory v3.0)

**Abstract:** This paper proposes the mathematical foundation of **Spacetime Dispersive Membrane Theory with Volatility and Matter-Wave Dynamics in Asymmetric Geometric Reservoirs (SDM-V Theory v3.0)**. Returning to Occam's razor, the theory redefines the universe as a self-organizing dynamic information field to address macroscopic gravitational anomalies without assuming dark matter elementary particle halo parameters. In version 3.0, the framework derives the Baryonic Tully-Fisher Relation ($M_{b}\\propto v_{f}^{4}$) and galaxy rotation curve flattening from first principles by integrating the Unruh effect in quantum field theory, Euclidean de Sitter horizon periodicity, and local thermodynamic phase transitions of geometric entropy density. By establishing phase-locking conditions between local accelerated systems and holographic screen boundaries, the critical acceleration $a_{0} = \\frac{cH_{0}}{2\\pi}$ is algebraically extracted with zero tuned degrees of freedom ($N_{\\text{params}} = 0$). Proof of Concept (PoC) simulations using empirical observational data demonstrate successful velocity profile flattening in bulge-dominated galaxies (M31, $\\chi^2_{\\text{red}} = 4.10$). Crucially, the transparent exposure of velocity deficits in bulgeless galaxies (NGC 3198, $\\chi^2_{\\text{red}} = 13.38$) pinpoints the physical limitation of 1st-order local acceleration gradient approximations, setting a clear theoretical roadmap toward non-local integral formulations and JWST high-redshift empirical verification.