Algebraic Chrono–Dynamics: Stratified Covariant Phase Space and Boundary Algebra

We construct a fully self-contained covariant phase-space formulation of a complex scalar field theory whose canonical structure becomes stratified under a diffeomorphism-invariant local trigger condition. Beginning from a well-posed variational principle on a globally hyperbolic spacetime with boundary, we derive the presymplectic current, establish hypersurface independence through explicit boundary symplectic augmentation, and perform presymplectic reduction to obtain the physical phase space. We then construct integrable boundary charges and prove that their algebra is represented up to a cocycle determined by the boundary symplectic structure. A local invariant functional partitions spacetime into regular and dense strata. In the dense stratum, admissible variations are restricted, enlarging the presymplectic kernel and suppressing the boundary cocycle. The resulting theory exhibits a mathematically controlled transition in algebraic structure without modification of Euler-Lagrange dynamics. Quantization is shown to preserve consistency on both strata. The work provides a complete algebraic closure independent of prior physical interpretation.