Noether Balance and Weyl Gauge Projection in a Dynamical Torsion Geometry

This work presents a theoretical framework in which torsion provides a dynamical channel for momentum storage, propagation, and exchange between matter and geometry. Starting from a tetrad–spin connection formulation with independent variation, we derive the full Noether balance identities associated with diffeomorphism and local Lorentz invariance in a torsionful spacetime. These identities show that the conserved quantity is a combined matter–geometric current, rather than the matter energy-momentum alone. We then construct a controlled effective field theory (EFT) truncation based on the irreducible decomposition of the torsion tensor. In the infrared regime, the vector-trace mode is identified as the dominant propagating degree of freedom. Its effective action is derived from the geometric sector, yielding a Weyl-type vector field with parameters fixed by the underlying torsion couplings. The resulting field satisfies a causal wave equation and is sourced by a projected Noether current. This provides a dynamical realization of a geometric “storage-and-return” mechanism, in which momentum is temporarily stored in the geometric sector and subsequently fed back into the metric evolution. The framework is constructed to interface directly with numerical relativity. A 3+1 decomposition compatible with the BSSN formalism is provided, together with a mapping between the action-derived variables and effective quantities used in numerical simulations. General Relativity is recovered as a limiting case in which the torsion channel decouples. This version is a working draft. Certain aspects—such as a fully explicit derivation of the effective action at all orders and the coupling to particle dynamics (inertia/geodesics)—remain under development. An alternative geometry-intrinsic sourcing of torsion is outlined as an open research direction.