A Gradient-Inversion Null-Test Protocol for Constraining Frequency Shifts under Controlled Electromagnetic Energy-Density Gradients

This revised preprint presents a model-independent gradient-inversion null-test protocol for constraining possible frequency-shift contributions under controlled electromagnetic energy-density gradients. The standard gravitational-redshift relation is retained as the reference prediction. No deviation from general relativity is claimed. Instead, the manuscript introduces a phenomenological coupling parameter η and defines an experimentally testable antisymmetric signal channel under inversion of the applied electromagnetic energy-density gradient. Version 3.1 expands the related-work context, clarifies the null-test interpretation, improves the discussion of systematic effects and uncertainty treatment, and corrects layout and wording issues. In particular, the revised version gives a clearer explanation of Stark, Zeeman, thermal, mechanical, optical-link, and gradient-mismatch backgrounds, and emphasizes that a positive signal would require strict quantitative rejection of conventional systematic effects. A null result would also be scientifically useful, because it would provide an upper bound on the phenomenological parameter η for this clearly defined measurement channel.