Emergence of the Historical Inertia Parameter from Self-Organized Criticality in the EPPQ Framework

This work derives the historical inertia parameter λ within the Emergent Pre-Quantizable (EPPQ) framework as a consequence of self-organized criticality (SOC). Building on the Principle of Minimal Historical Action (PMAH) and the SOC-Θ series, we show that the criticality condition R₀ = 1 imposes a balance between tension accumulation and dissipation, yielding the scaling relation: λ = K · β · ⟨d⟩ where β is the curvature exponent, ⟨d⟩ the mean degree of the vacuum graph, and K a universal dimensionless constant. The theoretical derivation is complemented by a computational study contrasting: - a non-critical MCMC baseline (local equilibrium)- a self-organized critical (SOC) dynamical regime The results demonstrate that λ does not emerge in equilibrium-like dynamics, but is dynamically selected in the critical regime via feedback stabilization toward R₀ = 1. This establishes λ as an emergent thermodynamic parameter rather than a free input, completing the parameter closure of the EPPQ framework. --- Related works: - O2 (PMAH dynamics): https://doi.org/10.5281/zenodo.19585980 - SOC-Θ 1: https://doi.org/10.5281/zenodo.19596783 - SOC-Θ 2: https://doi.org/10.5281/zenodo.19598463 Code and reproducibility: - SOC implementation: https://doi.org/10.5281/zenodo.19585617 - MDMC baseline: https://doi.org/10.5281/zenodo.19599300