We present a framework for detecting and reconstructing ultralight scalar fields through their coupling to Standard Model sectors using precision atomic clock networks. Scalar fields induce oscillatory variations in fundamental constants, producing measurable phase evolution across distributed clocks. We derive the forward mapping from scalar field dynamics to observables and construct an inversion formalism for recovering the full coupling vector. The method connects effective field theory with measurement by expressing scalar interactions in terms of clock frequency shifts and network phase observables. The framework defines a coupling vector spanning electromagnetic, electron mass, and gluonic sectors and provides a systematic approach for reconstructing these couplings using network data and Fisher information analysis. This establishes a direct operational bridge between field theory and precision measurement, enabling both detection and parameter-space tomography of ultralight scalar fields.
John Strother (Mon,) studied this question.