Phase and Holonomy Discretization Tightening

This paper shows that if phase-like and holonomy-like parameters are required to preserve standing under admissible transport and redescription, then continuous phase freedom cannot be retained without loss of admissibility. When such parameters are transported around closed redescription loops, continuous variation produces non-equivalent outcomes at re-identification boundaries, yielding representational instability. Preserving standing therefore forces collapse of admissible phase structure into discrete transport-closed equivalence classes or quotient identifications, with any non-forced residual freedom explicitly deferred.

The result is conditional and eliminative. It does not introduce geometric, dynamical, probabilistic, or empirical interpretations of phases or holonomies, nor does it claim completeness of the tightening. Instead, it excludes continuously tunable phase parameters as standing-preserving descriptors wherever transport coherence and redescription stability are required. Admissible phase structure is thereby restricted to discrete holonomy classes, quotient spaces, or envelope-deferred parameters under the stated conditions.