An Exploratory Correlation Test of Luminosity and a Local-Expansion Proxy in Cosmicflows-3 Galaxy Groups

A directional radiation-matter conversion hypothesis predicts a minimal catalog-level sign: after major nuisance trends are controlled, more luminous systems may show larger redshift-distance residuals. We tested this prediction in 858 Cosmicflows-3 galaxy groups using Hₗₒc = v_CMB/D and total Kₛ-band luminosity. Hₗₒc is an observer-frame proxy derived from redshift and distance; it is not a direct covariant expansion scalar and retains peculiar-motion contamination. A multivariable model adjusted for velocity trend, selection correction, richness, distance quality, and sky direction. The residual correlation was weak (ρ = 0.0850, p = 0.0128), but the adjusted slope was positive: β = 0.0384 dex per luminosity dex (95% CI 0.0068–0.0700; p = 0.0176), equivalent to 9.2% higher Hₗₒc per luminosity decade. The strict subset remained positive, whereas the SN Ia-only subset was null. CF3 therefore provides preliminary sign-level consistency evidence that justifies continued testing; it does not establish causation, a specific response function, or a value of κ.