The AVIO Wave Equation: Coupling Constants β, γ, C. From Determinism to Probability and the Emergent Born Rule in the Alpha Void Information Ontology Paper 11

Abstract

This paper derives the three key coupling constants of the nonlinear wave equation — β (magnetic threading), γ (nonlinear self-interaction strength), and C (fine-structure prefactor) — directly from geometric primitives and the preferred eccentricity e₀ = 1/√2. These derivations show that the wave equation flows parameter-free from a single topological defect. It then demonstrates how blackbody radiation (Planck spectrum, Stefan–Boltzmann law, Wien’s and Rayleigh–Jeans limits) emerges from collective persistence-cost leakage and mismatch radiation across networks of locked configurations. Finally, a deterministic derivation of the emergent Born rule is presented, arising from constructive interference of external deviation waves that enable threshold crossing in a multi-node environment. The framework remains strictly deterministic while recovering the statistical phenomenology of quantum mechanics. All results follow from a small set of geometric and dynamical primitives with minimal or no tuning.