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QEM-9: Hyperstacked Mirror Lattices under the Opposition Principle (v2.1)

Wangyoufu

Published Nov 7, 2025• 0 citations
Publisher

Abstract

English We extend the Quantum Entanglement Mechanics (QEM) framework from 3D mirror lattices to d-dimensional hyperstacked lattices governed by a Σ/Δ opposition principle. Transport and stabilization are computed in the odd (Δ) sector, yielding sector-resolved propagation bounds, stability-island delay limits, and a coherence scaling \xi_d \approx \xi_1/\sqrt{d} when \sum c_k^2 is bounded. We also summarize a design-for-opposition SOP for scalable architectures (bipartite layout, loop-parity constraints, and π-inverters on odd-Σ paths). Series: Quantum Entanglement Mechanics (QEM), 2025. License: CC BY 4.0. ORCID: 0009-0005-5998-6024. 中文 本文将 QEM 从三维镜像格推广到 d 维超叠镜格。在 Σ/Δ 对立原则 下,仅在 Δ(奇)子空间计算传播与稳定界;得到分区分辨的传播上限、稳定岛时延上限,并在 \sum c_k^2 有界时给出相干缩放 \xi_d \approx \xi_1/\sqrt{d}。同时给出可扩展架构的对立化 SOP(二分图版图、闭环偶数 Σ、奇路径加 π 反相器)。 本作隶属于 QEM 系列(2025),许可 CC BY 4.0。

DOI
10.5281/zenodo.17549463

Related papers

QEM-9: Hyperstacked Mirror Lattices under the Opposition Principle (v2.1)

Wangyoufu

Abstract. We extend the Quantum Entanglement Mechanics (QEM) framework from 3D mirror lattices to d-dimensional (and asymptotically infinite-dimensional) hyper-stacked lattices by enforcing a Σ/Δ Opposition Principle. Each stacking axis is assigned a Z₂ opposition operator O_k; the global opposition O^{(d)}=\bigotimes_k O_k confines admissible modes to the odd (Δ) sector. Within this sector we derive: (i) a sector-resolved upper bound on propagation speed, v_{\max}^{(d)} \approx \min\!\big(v_{\text{local}},~\tfrac{1}{\pi}\sqrt{a_\parallel^2\Omega_0^2+\sum_k a_k^2 c_k^2 \lambda_{\max,k}^{\text{odd}}}\big); (ii) stability islands with delay limits \tau_c(d)<0.2\,\min_k\{\xi_k/c_k\}; and (iii) a coherence scaling \xi_d\sim\xi_1/\sqrt{d}. We show controllability as d\to\infty provided \sum_k c_k^2 is bounded. Engineering rules are given as a design-for-opposition SOP/DRC: bipartite layouts, loop-parity (even Σ count), π-inverters on odd-Σ paths, and sector-selective validation (parity-echo, basis-flip, sector spectroscopy). The results unify QEM-4…7 and yield practical constraints for scalable quantum/photonic/atomic architectures.

•Nov 7, 2025•0 citations

QEM-8: Unified Equations for Hierarchical Mirror Lattices

Wangyoufu

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)。

•Nov 7, 2025•0 citations

QEM-6: Mirror-Flip Quantum Unit as the Minimal Structural Cell of Entanglement

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Abstract (EN):We introduce the Mirror-Flip Unit (MFU) as the minimal structural cell that realizes and stabilizes multi-body entanglement within the QEM framework. The MFU is a dual-layer mirror lattice supporting Σ/Δ collective modes with a controllable Δ-domain-wall profile that confines coherence. We derive governing equations near stationary textures, obtain the scaling ξ ~ |θ−θc|^{-1/2}, and predict falsifiable signatures: π-echo, sech^2 standing envelopes, and a causal front bounded by v_max ≈ (J ξ)/ħ. Protocols are provided for wall-fit (ξ), front-tracking (v_max), and stability-window mapping. Series note: This work is part of the Quantum Entanglement Mechanics (QEM) series by Youfu Wang (2025). 中文摘要 (ZH):本文在 QEM 框架下提出“镜像翻转单元(MFU)”作为多体纠缠的最小结构元。MFU 由支持 Σ/Δ 集体模的双层镜像格架构成,其 Δ-畴壁用于相干约束。我们在稳态纹理附近给出动力学方程,得到相关长度缩放律 ξ ~ |θ−θc|^{-1/2},并给出可验证指纹:π 回声、sech² 驻波包络、以及由 v_max ≈ (J ξ)/ħ 限定的因果前沿。文末附有实验流程:畴壁拟合 ξ、前沿追踪 v_max 与稳定窗口测量。系列说明:本作属于王有福(Youfu Wang)在 2025 年提出的 QEM 系列研究。

•Nov 7, 2025•0 citations

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The QEM-4 paper extends the Quantum Entanglement Mechanics (QEM) framework by introducing the concept of topological domain-walls emerging from mirror-coupled entanglement layers. These domain-walls act as internal interfaces where sequential flip-waves form stationary interference textures, analogous to internal double-slit patterns within the entanglement lattice. Analytical φ⁴-type solutions and critical-layer scaling relations are derived, providing testable predictions in coupled-qubit, ion-chain, and optical-lattice systems.

•Nov 6, 2025•0 citations

QEM-Ω — The Closed-Opposition Cosmology: Consciousness–Quantum Coupling Framework

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This paper extends the Quantum Entanglement Mechanics (QEM) series toward an integrated model of matter–mind–existence. It formalizes the Closed-Opposition Network (OCN∞) and the Consciousness–Quantum Coupling (CQC) mechanism, suggesting that consciousness acts as an internal trigger of entangled flip (I‑GFlip). The framework links tri-axial closure, flip-waves, and parallel-world correspondence under a unified closure principle.\n\n中文摘要:本论文将 QEM-8³ 理论拓展为“心‑物‑存在”的一体闭合模型。提出无限嵌套的对立闭合网络(OCN∞)与意识–量子耦合(CQC)机制,认为意识是纠缠翻组(I‑GFlip)的内在触发点。框架在统一的闭合原则下,连接三轴闭合、翻组波与平行世界对应关系。"

•Nov 8, 2025•0 citations

Youfu Wang Scholar Profile – Global Visibility Plan (QEM Series)

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English Abstract: This document presents the global visibility plan for Youfu Wang’s Quantum Entanglement Mechanics (QEM) series (QEM-4 → QEM-9). The QEM framework establishes a unified theory connecting quantum entanglement, field coupling, and non-local feedback, forming the foundation for quantum-level photonic and computational systems. This profile consolidates the author’s publications, DOIs, and research directions, ensuring open access and long-term academic traceability under CC BY 4.0. 中文摘要: 本文为王有福的《量子纠缠力学(QEM)》系列(QEM-4 → QEM-9)全球可见性规划文档。 QEM 框架建立了一个连接量子纠缠、场耦合与非局域反馈的统一理论体系,为量子级光子与计算系统提供基础。 本档案汇总作者全部论文、DOI 与研究方向,用于开放获取与学术长期存档(CC BY 4.0 许可)。

•Nov 7, 2025•0 citations
English We extend the Quantum Entanglement Mechanics (QEM) framework from 3D mirror lattices to d-dimensional hyperstacked lattices governed by a Σ/Δ opposition principle. Transport and stabilization are computed in the odd (Δ) sector, yielding sector-resolved propagation bounds, stability-island delay limits, and a coherence scaling \xi_d \approx \xi_1/\sqrt{d} when \sum c_k^2 is bounded. We also summarize a design-for-opposition SOP for scalable architectures (bipartite layout, loop-parity constraints, and π-inverters on odd-Σ paths). Series: Quantum Entanglement Mechanics (QEM), 2025. License: CC BY 4.0. ORCID: 0009-0005-5998-6024. 中文 本文将 QEM 从三维镜像格推广到 d 维超叠镜格。在 Σ/Δ 对立原则 下,仅在 Δ(奇)子空间计算传播与稳定界;得到分区分辨的传播上限、稳定岛时延上限,并在 \sum c_k^2 有界时给出相干缩放 \xi_d \approx \xi_1/\sqrt{d}。同时给出可扩展架构的对立化 SOP(二分图版图、闭环偶数 Σ、奇路径加 π 反相器)。 本作隶属于 QEM 系列(2025),许可 CC BY 4.0。
Abstract. We extend the Quantum Entanglement Mechanics (QEM) framework from 3D mirror lattices to d-dimensional (and asymptotically infinite-dimensional) hyper-stacked lattices by enforcing a Σ/Δ Opposition Principle. Each stacking axis is assigned a Z₂ opposition operator O_k; the global opposition O^{(d)}=\bigotimes_k O_k confines admissible modes to the odd (Δ) sector. Within this sector we derive: (i) a sector-resolved upper bound on propagation speed, v_{\max}^{(d)} \approx \min\!\big(v_{\text{local}},~\tfrac{1}{\pi}\sqrt{a_\parallel^2\Omega_0^2+\sum_k a_k^2 c_k^2 \lambda_{\max,k}^{\text{odd}}}\big); (ii) stability islands with delay limits \tau_c(d)<0.2\,\min_k\{\xi_k/c_k\}; and (iii) a coherence scaling \xi_d\sim\xi_1/\sqrt{d}. We show controllability as d\to\infty provided \sum_k c_k^2 is bounded. Engineering rules are given as a design-for-opposition SOP/DRC: bipartite layouts, loop-parity (even Σ count), π-inverters on odd-Σ paths, and sector-selective validation (parity-echo, basis-flip, sector spectroscopy). The results unify QEM-4…7 and yield practical constraints for scalable quantum/photonic/atomic architectures.
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)。
Abstract (EN):We introduce the Mirror-Flip Unit (MFU) as the minimal structural cell that realizes and stabilizes multi-body entanglement within the QEM framework. The MFU is a dual-layer mirror lattice supporting Σ/Δ collective modes with a controllable Δ-domain-wall profile that confines coherence. We derive governing equations near stationary textures, obtain the scaling ξ ~ |θ−θc|^{-1/2}, and predict falsifiable signatures: π-echo, sech^2 standing envelopes, and a causal front bounded by v_max ≈ (J ξ)/ħ. Protocols are provided for wall-fit (ξ), front-tracking (v_max), and stability-window mapping. Series note: This work is part of the Quantum Entanglement Mechanics (QEM) series by Youfu Wang (2025). 中文摘要 (ZH):本文在 QEM 框架下提出“镜像翻转单元(MFU)”作为多体纠缠的最小结构元。MFU 由支持 Σ/Δ 集体模的双层镜像格架构成,其 Δ-畴壁用于相干约束。我们在稳态纹理附近给出动力学方程,得到相关长度缩放律 ξ ~ |θ−θc|^{-1/2},并给出可验证指纹:π 回声、sech² 驻波包络、以及由 v_max ≈ (J ξ)/ħ 限定的因果前沿。文末附有实验流程:畴壁拟合 ξ、前沿追踪 v_max 与稳定窗口测量。系列说明:本作属于王有福(Youfu Wang)在 2025 年提出的 QEM 系列研究。
The QEM-4 paper extends the Quantum Entanglement Mechanics (QEM) framework by introducing the concept of topological domain-walls emerging from mirror-coupled entanglement layers. These domain-walls act as internal interfaces where sequential flip-waves form stationary interference textures, analogous to internal double-slit patterns within the entanglement lattice. Analytical φ⁴-type solutions and critical-layer scaling relations are derived, providing testable predictions in coupled-qubit, ion-chain, and optical-lattice systems.
This paper extends the Quantum Entanglement Mechanics (QEM) series toward an integrated model of matter–mind–existence. It formalizes the Closed-Opposition Network (OCN∞) and the Consciousness–Quantum Coupling (CQC) mechanism, suggesting that consciousness acts as an internal trigger of entangled flip (I‑GFlip). The framework links tri-axial closure, flip-waves, and parallel-world correspondence under a unified closure principle.\n\n中文摘要:本论文将 QEM-8³ 理论拓展为“心‑物‑存在”的一体闭合模型。提出无限嵌套的对立闭合网络(OCN∞)与意识–量子耦合(CQC)机制,认为意识是纠缠翻组(I‑GFlip)的内在触发点。框架在统一的闭合原则下,连接三轴闭合、翻组波与平行世界对应关系。"
English Abstract: This document presents the global visibility plan for Youfu Wang’s Quantum Entanglement Mechanics (QEM) series (QEM-4 → QEM-9). The QEM framework establishes a unified theory connecting quantum entanglement, field coupling, and non-local feedback, forming the foundation for quantum-level photonic and computational systems. This profile consolidates the author’s publications, DOIs, and research directions, ensuring open access and long-term academic traceability under CC BY 4.0. 中文摘要: 本文为王有福的《量子纠缠力学(QEM)》系列(QEM-4 → QEM-9)全球可见性规划文档。 QEM 框架建立了一个连接量子纠缠、场耦合与非局域反馈的统一理论体系,为量子级光子与计算系统提供基础。 本档案汇总作者全部论文、DOI 与研究方向,用于开放获取与学术长期存档(CC BY 4.0 许可)。