Vortical Constraint Algebra (VCA): An Effective Cross-Scale Gauge Framework for Geometrodynamic Phase Invariants and Covariant Saturation

We propose a phenomenological framework termed Vortical Constraint Algebra (VCA), intended as an effective cross-scale gauge approach for analyzing geometrodynamic phase invariants and covariant saturation. This framework explores a potential mechanism to account for the non-dissipative harmonic phase invariants observed across disparate astrophysical scales, particularly in the gravitational lensing system Q2237+0305 (Huchra’s Lens) and core-collapse supernovae orientations. Rather than extending the dark sector with ad hoc particles, VCA models high-density angular momentum environments via a constrained 5-dimensional spacetime-frequency manifold M x F. By deforming the canonical commutation relations with a non-zero Vorticity Tensor Ωμν , we derive an algebraic metric-stiffening effect attributed to a microphysical substrate of Primordial Elementary Whirlings (PEWs). VCA is presented as a framework that recovers General Relativity in low-vorticity regimes, maintaining consistency with standard Einsteinian dynamics and local energy-momentum conservation laws. This work serves as the theoretical companion to the study Cross-Scale Astrophysical Phase Invariants and Metric Anchoring via the Vortical Constraint Algebra (VCA), which discusses the implementation of these algebraic constraints in modeling observed galactic and stellar phase locks.