Geometric Flavor Dynamics: Emergent Mass Hierarchy and Topological Localization in a Background-Free Graph Surrogate

We study whether a background-free graph surrogate can natively generate a mass hierarchy among fermion generations without explicitly tuning distinct Yukawa couplings. Building on the previous identification of a structurally stable topological vacuum with nontrivial Wilson spectral flow on a thermal QGEFT background, we investigate the local geometric environment of the low Wilson-Dirac modes. Across the current benchmark, we find three linked results. First, the dominant localization centers exhibit a universal geometric signature: in all `3/3` valid multi-center configurations currently resolved by the batch scan, both leading centers are triangle-free and carry negative Ollivier-Ricci proxy curvature, indicating localization on sparse saddle-like defects rather than dense clique cores. Second, in the stabilized `N=1024` Einstein branch, the low-mode family splits into a broader component with `IPR \sim 0.13` and a sharply localized component with `IPR \sim 0.46`, showing that the topological generations do not occupy identical graph environments. Third, this geometric splitting translates into a Higgs-weighted mass hierarchy: the local scalar amplitude is `|\phi(885)| \sim 0.670` versus `|\phi(509)| \sim 0.282`, and the resulting overlap ratio reaches `M_max/M_min \sim 1.94` at fixed microscopic Yukawa coupling. The narrow claim supported by these data is that the QGEFT surrogate provides a concrete fine-tuning-free mechanism for partial fermion mass hierarchy generation, where flavor is determined by the local topological density and condensate geography of the emergent spacetime graph.