Stability-Constrained Dynamics on Relational Manifolds: A Formal Framework

Coherence and persistence are formulated here as operator-level constraints on relational manifolds. A coherence field Ψ evolves under decay, alignment, and forcing, and persistence is defined by the finiteness of an instability functional I[Γ]. The framework generalizes invariant-constrained recurrence and provides a structural basis for directional dynamics compatible with measure-preserving flows. It is developed for relational Lorentzian manifolds and is connected explicitly to the Einstein–Rosen bridge and to Penrose’s global constraint structures in general relativity. The paper is a formal theoretical framework intended as a mathematical and conceptual bridge between recurrence, persistence, and constrained geometric dynamics.