GFD Essentials: Tetrads, Field Closure, and the Inverse Pipeline (A Gentle Walk-Through for General Relativists)

Most general relativists picture spacetime as a smooth manifold. Yet the tetrad formalism and gravitational wave observations already imply a definite local structure: tetrahedral field chambers coupled through exactly four active channels. This note walks from tetrads and non-degeneracy to that structure, then to field closure and the constitutive law that determines the scalar-tensor action of Gravity Field Dynamics Nelson2026. The framework comprises the standard Poisson equation and the spherical limit of the scalar-tensor theory (SST), in which the constitutive law fixes the kinetic term. The inverse pipeline uses the SST and Poisson to decode observed velocity to effective mass Mdec (r), not Poisson alone. The aim is to close the gap between "what every GR textbook already implies" and the effective mass Mdec (r) and the vortex picture. The foundations are tetrad gravity (Misner, Thorne & Wheeler 1973), ghost-free bimetric gravity (Hassan & Rosen 2012), simplex geometry (Ziegler 1995), and Plateau's laws (Taylor 1976). The framework and its application to galaxy rotation curves are presented in "Gravity Field Dynamics: Decoding mass from observed rotation curves" (Nelson 2026).