Testing Weak Frequency-Dependent Residuals with Optical Atomic Clocks

This preprint develops a prospective experimental framework for testing weak frequency-dependent residual effects using high-precision optical atomic clocks. The study formulates the problem in terms of differential fractional-frequency measurements, sensitivity requirements, control strategies, reproducibility, and falsifiability. No detection of new physics is claimed. Origin of the experimental proposal: The atomic-clock test concept was introduced in the author's earlier QRUM-related work, Einstein–Quantum Resonance Spacetime Extension (2025), Zenodo DOI: 10.5281/zenodo.17620325. The present work develops that earlier proposal into a more explicit and independently testable precision-metrology framework. A predefined phenomenological test region is discussed to limit post-hoc frequency selection and the look-elsewhere effect. Any such region is treated strictly as a prospective search interval rather than evidence for a physical resonance or a fundamental constant. The proposed methodology is intended to permit independent experimental scrutiny regardless of the validity of QRUM as a broader theoretical framework. Null results obtained at sufficient sensitivity are scientifically informative because they constrain the tested phenomenological realization. Independent replication, alternative statistical treatments, and critical examination are encouraged.