TITLE:
Global Stratified Reduction and Boundary Cohomology for Phase-Suppressed Covariant Field Theory
AUTHORS:
George Davey
KEYWORDS:
Covariant Phase Space, Stratified Presymplectic Reduction, Boundary Cohomology, Lie Algebra Cocycles, Finite-Action Admissibility, Phase Suppression
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.6,
June
18,
2026
ABSTRACT: In a complex scalar field theory with a divergent phase-stiffness functional, finite-action admissibility enforces the vanishing of phase variations on a high-stiffness stratum, with consequent enlargement of the presymplectic kernel and suppression of an explicitly-represented amplitude-phase boundary cocycle. This local mechanism leaves open four mathematical questions, which the present paper closes conditionally under explicit regularity, nondegeneracy, local-separation, and no-accidental-degeneracy hypotheses. We extend the finite-action selection theorem to admissible dynamical trigger functionals whose induced quadratic-form correction is subleading relative to the divergent stiffness-weighted admissibility form; we prove a global two-stratum presymplectic structure under a stratum-regularity assumption, with phase-sector reduction localised to the dense region; we give a sufficient cohomological non-triviality criterion for the boundary 2-cocycle using an abelian Hamiltonian amplitude-phase test subalgebra, and we construct such a subalgebra explicitly; and, after isolating the conditions excluding accidental degeneracies and imposing a local separating boundary test algebra, we prove a boundary-local converse direction of the Phase Boundary Characterisation Theorem. The combined result is that, within the class of pure stiffness-induced phase-sector mechanisms, the threshold hypersurface
?={
P=
P
?
}
is locally recoverable from the algebraic data of the augmented covariant phase space at boundary-accessible points.