Covariance among the Rydberg constant, fine-structure constant, electron mass and electron g−2 on a finite-domain standing-wave eigenmedium

We study covariance among the Rydberg constant, fine-structure constant, electron mass, and electron g−2 on a finite-domain standing-wave medium described equivalently by a classical substrate and a frame-independent operator picture. Three generators (including transport, phase, and scale) act on this medium, linking effective constants (ℏ, α, m_e) to precision observables and predicting a sign-fixed covariance among R_∞, α, m_e and g−2 while organizing mode families. Being Lorentz-invariant in band, the target is not LIV but a pattern of covariance, which may already be latent in public datasets. We test it using a hierarchical meta-analysis of optical-clock ratios and spectroscopy with geometry-motivated sign priors, and a one-parameter dispersion fit to GRB/FRB arrival times; analyses may be preregistered for transparency. As calibration for the latter, TeV-photon timing from LHAASO’s GRB 221009A sets strong null bounds on energy-dependent lags, treated as model-agnostic dispersion constraints (no Lorentz violation). Any deviations, if present, are constrained as few-parameter, beyond-band dispersion. Each test enables falsification (e.g., R_∞ versus g−2 at >3σ). We will present predicted signs, a public-data demonstration or bound, and open scripts and schema.