Projection-Covariant Dynamics in Coherence Geometry: Presymplectic Reduction, Mapping-Space Evolution, and Observable Descent

This paper develops a projection-covariant framework for separating complete Source dynamics from the dynamics of selected observables in Coherence Geometry. A complete Source is represented by a map into coherence-state space, while physical or informational observables arise through selected projections or differential readouts. The paper develops the presymplectic geometry induced by such readouts, identifies the corresponding observable-active quotient, and shows how complete Source transport constrains the projected dynamics without requiring the selected realization to represent the entire Source. The work also develops the metric counterpart of this reduction. Projection-induced horizontal metrics, connections, and stiffness operators are constructed so that spatial refinement descends consistently to the observable level. The resulting architecture provides a general mathematical layer for generator descent, hidden Source directions, observable closure, and projection-covariant evolution across fluid, reactive, electromagnetic, informational, thermodynamic, and other coherence-geometric systems. Coherence Geometry Institute reference: CGI-RSR-000040. This work is released as an archival research preprint and has not undergone external peer review.