(Math4/GQR34) Geometry, Constraint, and Governance: Why Stability, Catalysis, and Memory Are Time-Structured Problems.

Traditional descriptions of dynamical systems emphasise static structure, energetic opti-misation, or equilibrium statistics. While successful in many contexts, such descriptions failto capture regimes in which function depends on geometry, time structure, and recoverabilityunder repeated perturbation. Here we develop a geometry-first, implementation-agnostic frame-work in which persistence, directionality, and effective irreversibility arise from two structuralconstraints: phase closure and mode suppression. These constraints govern which trajectoriessurvive under noise, coupling, and finite regulatory capacity, independent of microscopic carrier.We show how this perspective unifies time-gated catalysis, capacity-limited governance, hystere-sis, and burnout across adaptive systems, while leaving biological, chemical, and technologicalinstantiations as downstream applications rather than axioms. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.