CP like Phases as Admissible Holonomy Classes

This paper shows that if CP-like phase distinctions are retained under admissible local redescription, then they must be representable as holonomy classes rather than as freely specifiable parameters. When phase differences are treated as continuously adjustable quantities, admissible transport around closed representational paths produces inconsistencies at boundary re-identification, resulting in loss of standing. Treating such phases as holonomy classes avoids this failure by constraining phase distinctions to path-dependent but admissibly stable equivalence classes. The result is conditional and eliminative. It does not posit a specific geometric or physical mechanism for CP-like phases, nor does it claim completeness or uniqueness of the holonomy classification. Instead, it excludes representations in which CP-like phases are treated as locally tunable degrees of freedom while standing is preserved. CP-like phases are therefore constrained to admissible holonomy classes whenever boundary consistency is retained.