On Symmetry, Projection, and Noetherian Closure of Physical Invariants

Noether’s first theorem relates conserved currents and charges to continuous global symmetries of an action, while Noether’s second theorem yields identities and constraints associated with local gauge symmetries. This paper addresses a distinct closure problem that remains once equivalence has been fixed: which global normalizations, completions, and scale selections are admissible so that dimensionless quantities and global consistency constraints arise as invariants forced by structure rather than as independently specifiable inputs. We formulate this as an extension of Noether’s symmetry–invariant correspondence from dynamical laws to admissible normalization. The framework assumes a universal symmetry…