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

We provide a coordinate-free characterisation of phase boundaries in field theory by proving that a complex scalar field on a globally hyperbolic spacetime with boundary admits a stratified covariant phase space. The stratification is governed by a diffeomorphism-invariant functional $P$ partitioning spacetime into strata, together with a finite-energy selection rule: in the dense stratum $\{P \geq P_\star\}$, a diverging phase-stiffness functional $\kappa(P)$ forces any finite-action tangent vector to satisfy $\delta\theta = 0$, reducing the admissible variation class to amplitude fluctuations alone. We show that this selection rule simultaneously enlarges the presymplectic kernel of the augmented symplectic form $\Omega^{\mathrm{aug}}_\Sigma$ and suppresses the central extension of the boundary charge algebra: $K_{dens} = 0$. The Phase Boundary Characterisation Theorem establishes that these two effects are algebraically equivalent, identifying $\mathcal{H}$ as the unique degeneracy locus of $\Omega^{\mathrm{aug}}_\Sigma$ --- a purely coordinate-free characterisation independent of the specific trigger functional. The Iyer--Wald--Zoupas ambiguity in the boundary symplectic density is resolved by explicit mixed boundary conditions, and the algebraic structure on each stratum is compatible with standard quantization procedures applied independently per stratum.