The Sterile Vacuum and Topological Rarity: Entropy and Generation Formation in a Dynamical Graph Surrogate

We study whether the emergence of chiral fermion generations ($Q > 0$) is a generic thermodynamic feature of the QGEFT vacuum or a rare statistical anomaly. Following previous results that identified a stable $Q=5$ configuration on an $N=1024$ background, we perform an extensive Monte Carlo ensemble search across multiple independent replicas under identical thermal parameters ($T=0.3$, $N=1024$, 3d-local prior) and matter-backreaction scales. Across the current benchmark program, we find three linked results. First, in a controlled ensemble of 10 replicas, all configurations converged to a topologically trivial vacuum ($Q=0$) despite providing substantial thermalization time (up to 5,000 burn-in sweeps). Second, while the graphs exhibit high local connectivity ($b_{1} \approx 3390$), the smallest absolute eigenvalues of the Wilson-Dirac operator remain bounded away from zero, indicating a persistent mass gap in the typical thermal phase. Third, the comparison between these sterile ensembles and the previous $Q=5$ production run suggests that chiral generations are not a standard ground-state property but represent rare topological defects—effectively "topological instantons"—trapped during the graph’s thermal history. The narrow claim supported by the current data is that the QGEFT vacuum is predominantly sterile. We interpret the existence of fermion generations as a manifestation of topological rarity, providing a computational basis for an emergent anthropic principle: complex matter can only inhabit those rare, non-trivial fluctuations of the spacetime graph where the topological index spontaneously departs from zero.