EET Mathematical Foundations: Dimensional Analysis, Scaling Laws and Cross-Document Invariants

This document establishes the complete mathematical foundations of Energy-Efficiency Theory (EET), fully aligned with Core Rules v5. 2 and the companion ontologies. It provides the dimensional analysis of all core parameters across the mother texts, formalizes the capacity geometry and unified action quantum, develops the graph-theoretic mathematics (Laplacian, spectral gap, Ollivier-Ricci curvature, spectral embedding), derives the hierarchical scaling laws from the universal exponent 0. 6, and presents the response pool dynamics and variational principle. Version 2. 3 integrates all variables from the cognitive constitution—including consciousness indices (I₂₀ₔₒ₀₋, Iₓ₇ₑ₄ₒ₇₎₋₃), spirit indices (M, d, (t) ), cross-level dynamics (ₗ), and cognitive inverse entropy (Ṡ₈₍ₕ^cog) —with full dimensional verification and bridge declarations. The core equations quick reference now includes the complete coupled dynamics of the consciousness-spirit cycle.