Environment-Dependent Distance Residuals in the Cosmicflows-4 Compendium: A Multi-Method Detection

We report the detection of a statistically significant correlation between local galaxy density and distance modulus residuals across multiple photon-based distance indicators in the Cosmicflows-4 (CF4) compendium. Among 12,141 spiral galaxies with Tully-Fisher (TF) measurements, we find a Spearman rank correlation ρ = −0.092 (10.2σ) between 5th-nearest-neighbor angular density and distance residual. The correlation is absent in 22,696 elliptical galaxies measured via the Fundamental Plane (FP): ρ = +0.003 (0.5σ).Critically, the same analysis applied to 880 Type Ia supernovae in CF4 yields ρ = −0.129 (3.8σ, permutation p = 0.0001), confirming the signal in an independent photon-based distance indicator with an independent calibration chain. Five of six photon-based methods in CF4 show a negative density-residual correlation, while the one method containing a geometric observable (FP) shows none. The TF signal survives all robustness tests including redshift subdivision (19/20 fine bins negative, p = 2 × 10⁻⁵), sky-region jackknife (minimum 6.6σ), density-scale independence (k = 3 through 15), bootstrap resampling, permutation testing, and a two-sample KS test (p = 8.3 × 10⁻²⁰). A mock-observer test using the IllustrisTNG TNG300-1 simulation confirms that ΛCDM does not reproduce the observed signal. We parameterize the effect as a modified redshift-scale factor mapping 1 + z_eff = (1 + z_FLRW)(1 + βδ) and measure β_TF = −2.8 × 10⁻⁵ ± 0.8 × 10⁻⁵. The concordance between TF and SN Ia — two completely independent distance indicators — in both sign and magnitude substantially constrains the calibration-systematic interpretation and is consistent with an environment-dependent effect on photon-derived distance indicators.