Statistical Evidence for Multi-Population Structure in ISP Blazars: Limitations of SED-Based Classification

Preprint version. Not yet peer-reviewed. We investigate the luminosity distribution of ISP blazars in the Fermi-LAT 4LAC-DR3 catalog (N=246). After accounting for redshift-dependent effects via luminosity-bin normalization, the ISP luminosity distribution exhibits statistically significant non-Gaussianity (skewness=-0.908, Anderson-Darling p<0.001) that persists after accounting for several commonly used physical proxies (variability index, nu_syn, PL_Index), and remains after both linear and non-linear regression approaches (including Random Forest). GMM decomposition (k=3, selected via BIC minimization) identifies three statistically distinct sub-populations with significant differences in beaming and luminosity (Kruskal-Wallis p<0.001), but no difference in nu_syn (p=0.961) — the defining parameter of ISP classification. These results suggest that ISP blazars may represent a physically heterogeneous transition region, and that nu_syn-based SED classification may have limited discriminating power within the ISP regime.