Boundary Time Geometry: Unified Theory of Time Scale, Resolution Hierarchy, and Interaction

Construct unified theoretical system with boundary as ontology and time as geometric scale. Basic assumption: physical reality first manifests as boundary observable algebra and its spectral data; bulk dynamics are extensions determined by boundary data. All observable time scales—scattering time, modular time, geometric time—belong to same equivalence class. Observer's finite resolution geometrically manifests as resolution fiber bundle with connection and curvature. Mathematically, introduce n