Quantum HS°: A Resource Theory of Temporal Alignment

This document introduces HS° (Harmony Segment Degree) as a minimal and implementation-agnostic quantum resource for temporal alignment. By defining a cyclic angular temporal basis and a corresponding resource theory, it formalizes temporal coherence as a consumable quantity required for deterministic synchronization tasks. The framework is compatible with standard quantum mechanics, avoids the use of time operators, and positions temporal coherence alongside entanglement and asymmetry as a first-class informational resource. This paper is intended as a foundational reference for subsequent theoretical and applied work on phase-based coordination in quantum systems.