Yukawa-Induced Fermion Mass Generation and Wilson Criticality in a Dynamical Graph Surrogate

We study whether a background-free graph surrogate supports a Higgs-sensitive fermion mass response once its geometry and Higgs sector are frozen from a stabilized electroweak-like branch. Using Wilson fermions and a graph-adapted propagator, we test if the fermion sector exhibits a heavy-mass regime and if the effective mass responds to the Yukawa coupling near the Wilson critical region. We find four linked results. First, at bare mass $m_{0}=5.0$, the shell-averaged propagator decays sharply between radii $r=0$ and $r=1$, yielding an effective mass proxy $m_{eff}\approx2.43$ via the ratio $\log[G(0)/G(1)]$, confirming a heavy fermion branch. Second, scanning the bare mass reveals a near-chiral critical region around $m_{0}\approx1.0$, consistent with additive mass renormalization. Third, scanning the Yukawa coupling at $m_{0}=1.0$ reveals a nontrivial mass response and narrow critical band: over $y\in[0.50,0.60]$, the mass proxy rises rapidly from 0.069 to 1.368. Fourth, a long-run validation on a larger $N=1024$ background shows that both the Dirac gap and graph-local propagator gap increase monotonically with Yukawa coupling over $y\in[0,2]$, with near-linear fits $R^{2}\approx0.99998$ and $R^{2}\approx0.992$, respectively. The narrow claim is that the QGEFT surrogate supports a Higgs-sensitive fermion mass response, a Wilson-like critical band on a fluctuating graph, and is effectively probed by a graph-local observable resolving both the critical onset and heavy branches.