Testing Structural Residuals in Early Galaxy Formation: A Multi-Regime Extension

We investigate the role of structural residuals in early galaxy formation using observationally motivated datasets. Building upon a minimal extension of the ΛCDM framework, we introduce the RDSS model as a localized correction to halo abundance and perform a quantitative comparison against observational data. We show that the RDSS model improves the fit relative to ΛCDM, and further extend the model by introducing a power-law tail motivated by regime-dependent scaling behavior. The extended model significantly improves agreement with observational data, reducing the χ² from 103.28 to 83.23. The improvement is particularly evident in the high-mass regime, where ΛCDM systematically underestimates the observed abundance. These results suggest that deviations in early galaxy formation may arise from a combination of localized structural residuals and scale-dependent regime effects, indicating the presence of multiple structural regimes.