The Phase-Coordination Principle: From Fundamental Theorem to Quantum Network Implementation

Release label: v2.0 alignment release (tick-canonical interoperability; corrected bounded-skew statement). This paper formalizes the Phase-Coordination Principle as an operational coordination method for distributed systems with autonomous local clocks. It recalls a fundamental limitation: without continuous physical coupling, inter-node clock-offset uncertainty grows without bound over long horizons, so absolute timestamp targeting cannot provide time-uniform, fixed-tolerance guarantees. The proposed solution is to replace absolute-time targets with a shared cyclic phase convention and to execute actions when a node’s locally estimated phase enters a wrap-around-safe acceptance window on \( \mathbb{S}^1 \), explicitly anchored to an intended cycle index to avoid “same phase / wrong cycle” ambiguity. Bounded coordination (operational statement). Under explicit short-horizon phase estimation error bounds (and a non-straddling condition), the inter-node execution skew is bounded by the chosen window duration plus short-horizon estimation terms, and does not scale with time since initialization. Implementation-facing interoperability. The paper includes a minimal, tick-canonical view compatible with Q-Address-style macro window + micro slot addressing. It also clarifies that human-facing displays (HS degrees, HS index, SWT labels) are derived-only and must not be used for verification or boundary checks. Security scope. Phase-window coordination is not security by itself. Security requires authenticated messaging, nonces, anti-replay policy, and explicit threat models, as defined by external security profiles. Timeverse/Q-Address fields are treated as public context, not secrets. Normative dependencies (DOIs): Phase-Coordination Series Conventions (canonical \(t_0, T_{\mathrm{cycle}}, n(t), \phi(t)\); modulo; wrap-safe windows; ticks):https://doi.org/10.5281/zenodo.18068999 Q-Address (tick-canonical execution primitive): https://doi.org/10.5281/zenodo.18068997 Timeverse Security Profile (signatures, nonces, anti-replay, suite identifiers): https://doi.org/10.5281/zenodo.18069423 Keywords: phase coordination, cyclic phase, distributed systems, clock drift, window triggering, bounded coordination, interoperability, ticks, Q-Address, quantum networks.