Hyper-Phase Time Framework (HPTF): Global Network Detection of Ultralight Scalar Dark Matter

We introduce the Hyper-Phase Time Framework (HPTF), a theoretical and experimental protocol for detecting ultralight scalar dark matter using global networks of optical lattice clocks. By establishing a correspondence between proper time and scalar phase evolution, the framework predicts a globally coherent fractional frequency modulation observable across spatially separated precision clocks. We show that a network of N clocks achieves a detection significance scaling as √(N T) through zero-lag cross-correlation, enabling sensitivity to signals far below the noise floor of individual sensors. The framework leverages existing clock infrastructure and requires no modification of experimental hardware. Additionally, relativistic redshift effects induce measurable phase gradients across gravitational potentials, providing a secondary consistency signature within standard General Relativity. This work presents a concrete, falsifiable detection strategy for probing the wave-like nature of ultralight scalar dark matter using current quantum metrology platforms.