Universality in the Thermodynamic Limit of the EPPQ Vacuum: Why the Standard Model Parameters are dynamically selected within the universality class (O3 — Part V)

The Emergent Pre-Quantizable (EPPQ) framework has successfully derived quantum mechanics (O3 Parts I–IV) and the Standard Model flavor structure (O4) from a relational ontology based on the primordial distinction α: = (A ≠ ¬A) and the Principle of Absolute Historicity (PAH). However, the effective parameters that determine the Standard Model observables—the curvature exponent β, the spectral suppression γ, the gauge coupling α, and the overall mass scale ΛUV—have so far been treated as phenomenological inputs, previously estimated via finite-size numerical realizations. In this paper, we address the final open problem of the O3 program: universality in the thermodynamic limit. We show that, under the SOC scaling hypothesis, as the vacuum graph size N → ∞, the effective parameters converge to universal constants that depend only on the topological class of the graph (scale-free) and not on the microscopic details of the relational dynamics. The rigorous proof combines three mathematical frameworks: Theory of Graph Limits (Graphons): To define the continuum limit of the vacuum graph S*. Self-Organized Criticality (SOC): To show that the EPPQ dynamics drives the vacuum to a critical point where scale invariance emerges. Laplacian Renormalization Group (LRG) for Complex Networks: To demonstrate that the critical point is a universal attractor in the space of all possible relational configurations. The parameters β, γ, and ΛUV are shown to be universal constants determined by the critical exponents of the scale-free SOC fixed point. The gauge coupling α is shown to be an irrelevant parameter in the infrared, whose finite value at the electroweak scale is fixed by the ultraviolet boundary condition; its complete first-principles derivation is deferred to the O4 program. This result — conditional on the SOC scaling hypothesis and the spectral convergence of the vacuum graph — establishes a clear mechanism by which the EPPQ framework can be elevated from a theory with phenomenological parameters to a parameter-free fundamental theory, where the constants of nature are emergent consequences of the relational ontology.