Cosmological Fabric Displacement: A Non-Dark Matter Alternative to Galactic Rotation Curves

Modern physics is currently gridlocked by three foundational discrepancies: the missing mass problem (Dark Matter), the cosmic acceleration mechanism (Dark Energy), and the catastrophic $120$-orders-of-magnitude discrepancy in the Cosmological Constant problem. In this paper, we demonstrate that the **Fabric Displacement Model (FDM)** serves as a rigorous mathematical bridge capable of resolving these crises simultaneously. By treating the spacetime continuum as a conserved fluid medium displaced outwardly by baryonic matter, we eliminate the singular behaviors of gravitational cores, derive the accelerated expansion of the universe as a localized back-reaction flux, and regularize the vacuum energy density. This framework successfully circumvents the necessity for arbitrary dark sectors, offering a clean, unified geometric paradigm for cosmology.