This paper analyzes emergent spectral behavior in the Dual Incidence Graph (DIG), a discrete graph-theoretic model of spacetime developed within the Relational Blockworld (RBW) framework. The DIG operates using two distinct incidence relations: a directed, local-causal structure (I₁) and a symmetric, nonlocal structure (I₂) that encodes coherence. Through a large-scale Design of Experiments (DOE) using randomized input masks, we show that the DIG consistently produces structured probability spectra with a strong statistical affinity for the fine-structure constant alpha ≈ 1/137. High-density masks reveal near-zero sum-squared error (SSE) harmonic quantization, suggesting an intrinsic mechanism of projection-based renormalization arising from the metric tension between L1 and L2 norms. The findings point toward a novel mechanism of geometric frustration that reconciles discrete locality with emergent nonlocal coherence—proposing the DIG as a minimalist substrate for gauge-like behavior at the ontological boundary.