Re-Phase Vol.1.2: Compatibility Consistency and Existence of Transport

Re-Phase theory studies reconstruction from partial observations through compatibility structures induced on hidden-state spaces. This note records minimal mathematical statements underlying compatibility consistency and the existence of transport maps between observational structures. The manuscript establishes: - fiberwise compatibility consistency,- existence and well-definedness of compatibility transport,- equivalence between compatibility and transport factorization,- and canonical projection structures on product spaces. The purpose of this volume is not full formalization, but the preservation of minimal structural rigor required by later volumes of Re-Phase reconstruction theory.