CPT-Coherence Theory: A Unified Framework for Recursive Identity, Mass and Collapse

We present a revised formulation of CPT-Coherence in which the -direction is restored as a genuine fifth structural dimension rather than treated as a numerical bookkeeping device or spectral spacing parameter. The theory is defined on a five-dimensional spectral-geometric arena whose admissible physical configurations are selected by a stationarity principle: stable states arise when geometric variation of tracked spectral branches vanishes. In this formulation, does not represent physical time. Instead, it parametrizes an internal structural direction along which localization, defect formation, boundary transport, and spectral relaxation are organized. This revision has four goals. First, it replaces the older recursion-constant-centered program with a stricter spectral-geometric framework. Second, it places the operator-theoretic Onto-Physical Entanglement (OPE) condition at the center of the theory and treats low-curvature Einstein dynamics as an emergent stationary limit rather than as an independent postulate. Third, it absorbs the strongest functional-analytic and ultraviolet/infrared control results of the recent Redux line into the primary theory paper. Fourth, it recasts flavor hierarchy and mixing as a localization problem in the -direction, with light generations supported by the bulk and the heavy generation realized as a topologically distinct asymmetric interior defect. Within this revised architecture, the theory does not claim a universal recursion constant, a one-number derivation of the Standard Model spectrum, or a completed nonperturbative quantum-gravity construction. What it does claim is narrower and stronger: the existence of a unified five-dimensional spectral-geometric framework in which gravity, state-selection structure, and flavor hierarchy are governed by a common variational logic. The main text develops the parent (4+1) -dimensional theory, the stationarity principle, the low-curvature gravitational limit, ultraviolet filtering and finite-rank dominance, and a constrained flavor realization. The appendices isolate assumptions, operator domains, theorem dependencies, variational closure, and the current computational ledger with referee-level explicitness.