This paper introduces QEM-8^3, a three-dimensional extension of the QEM-8 entanglement framework. The model treats each entangled pair (A↔B and C↔D) as both an individual binary relation and part of a larger lattice system. By stacking the eight directional entanglement modes along vertical, horizontal, and depth axes, the structure forms a stable entanglement square lattice. The transitions between AB|CD and AD|BC are explained through measurement sequence, basis switching, and stability reconfiguration. The result is a discrete algebraic lattice that preserves absolute duality and relational symmetry across multi-quantum entanglement systems.
Abstract (EN):We unify QEM-4–7 into a single field framework for hierarchical mirror lattices. Starting from a variational functional for Σ/Δ modes with a domain-wall order parameter, we derive coarse-grained equations across layers, an RG-like flow for effective couplings, and a universal causal-cone bound that collapses to QEM-5 locally and to an array form in QEM-7. The coherence length scales as ξ ~ |θ−θc|^{-1/2} at each level. We provide falsifiable predictions and cross-level protocols. Series note: This work is part of the Quantum Entanglement Mechanics (QEM) series by Youfu Wang (2025). 中文摘要 (ZH):我们把 QEM-4–7 统一到层级镜像格的场论框架中:从变分泛函出发得到跨层粗粒化方程与“类重整化”的耦合流;统一的因果锥上限在局域退化为 QEM-5,在阵列退化为 QEM-7。相关长度在各层满足 ξ ~ |θ−θc|^{-1/2};重整后的参数把约束向上层级传递,给出芯片级时序预算、扇出与稳定窗口。并给出跨层可检验流程与普适性指纹(π 回声、sech² 包络、前沿速度塌缩律)。