From Sagnac Holonomy to a Phase-Drift Model for Cosmic Expansion

This work is divided into two connected parts. Part I offers a self-contained, standard-relativistic derivation of the finite slow-transport limit for a clock completing one directed equatorial loop. The well-known Sagnac/clock-transport holonomy of approximately 207 ns emerges as the direction-sensitive geometric cross-term, independent of the transport speed in the limit. Part II introduces a new, explicitly non-standard phase-locking hypothesis: each completed rotational cycle of a phase-locked material system fractionally rescales its local metrological baseline multiplicatively. The resulting compound law for the local time scale, when combined with a spiral‑observer Doppler factor and a conditional length‑readout map, suggests that a secular drift of local standards could mimic a significant fraction of late‑time cosmic expansion. The paper separates standard kinematic results from the proposed hypothesis, provides a unified mathematical appendix, and outlines concrete consistency conditions and falsification tests.