Graph Theoretic Probability Distributions and the Fine Structure Constant

This work investigates the emergence of structured probability distributions within a discrete, events-only formulation of the Relational Block World (RBW) framework. Using a dual-incidence graph—where a local causal incidence enforces Minkowski-like constraints and a nonlocal incidence captures quantum entanglement—we analyze the distribution of event probabilities across the network. Unexpectedly, numerical results reveal a persistent affinity not only to the fine-structure constant (α ≈ 0.007297) but also to its integer multiples and structured periodic behavior. The probability distribution exhibits quasi-fractal organization, suggesting that discrete causal networks may naturally encode fundamental physical constants through structured probability redistribution. These findings motivate further study of discrete event-based models of spacetime, particularly in understanding how fundamental constants may emerge from nonlocal incidence relations.