The Phase-Unified Computing Stack: Geometric Foundations of Phase-Coordinated Systems (v2)

This paper presents a geometric unification of quantum control, artificial intelligence scheduling, and human-facing coordination under a single phase-coordinated framework. All components are modeled as operations on phase manifolds, linked by structure-preserving mappings on relevant $U(1)$ phase actions. We formalize a precise correspondence between qubit $Z$-axis phase rotations and temporal-circle phase shifts, define a stack architecture for triadic coordination using phase windows, and state coordination bounds under explicit assumptions on phase estimation and short-horizon oscillator stability.