Difference Hierarchy Theory: A Unified Framework for Quantum–Gravity Dynamics Based on the Ψ-Layer Reference Structure

This work proposes a unified framework for quantum and gravitational phenomena by reformulating the universe as a hierarchy of differences, termed the Difference Hierarchy Theory. The model introduces a reference structure, the Ψ-layer, which functions not as an initial condition or physical background but as a structural origin that defines all higher-order differences. The universe is classified into four layers—Ψ-layer (zero difference), white layer (first-order difference), gray layer (first- plus second-order differences), and black layer (difference extinction)—each corresponding to distinct physical regimes. A single update equation, Snext=S+αΔS+βΔ2S, governs the evolution of the state variable S, naturally reproducing first-order quantum behavior and second-order gravitational curvature in the continuous limit. Singularities, such as black hole cores, emerge not as divergences but as zero-difference regions where updates cease. The framework predicts observable signatures including neutrino mass fluctuations, gravitational-wave dissipation, large-scale structure patterns, and quantum–gravity interference at the white–gray boundary. This theory provides a structural language that unifies quantum mechanics, general relativity, and cosmological evolution within a single difference-based hierarchy.