《量子引力扳手理论:一种自然实现面积律与全息原理的新框架》《Quantum Gravity Wrench Theory: A Novel Framework Naturally Realizing Area Law and Holographic Principle》

This dataset contains the numerical validation and supplementary materials for the paper **"Quantum Gravity Wrench Theory: A Natural Holographic Framework"**.

## Content Overview
- **Area Law Verification Data**: Raw numerical results confirming the area-law scaling of entanglement entropy ($S \sim A^{1/2}$) with high precision across varying coupling constants ($\lambda = 1.0, 2.0, 5.0$).
- **Scaling Analysis**: Data files documenting the extraction of scaling dimensions and critical exponents supporting the holographic principle.
- **Theory Summary**: Consolidated reports detailing the geometric "wrench" operator formalism and its application to black hole thermodynamics.

## Key Findings
The data robustly supports that the Quantum Gravity Wrench (QGW) framework naturally realizes:
1.  **Holographic Area Law**: Entanglement entropy scales with the boundary area, not the volume.
2.  **Dimensional Reduction**: Effective spatial dimension flows to $d=2$ in the infrared regime.
3.  **Black Hole Entropy**: A microscopic explanation for the Bekenstein-Hawking entropy formula.

Usage Notes
- **Formats**: Primary data is provided in plain text (.txt) for machine readability.
- **Relation**: This dataset is the companion to the preprint available on arXiv.
- **License**: Creative Commons Attribution 4.0 International (CC BY 4.0)

本数据集为论文《量子引力扳手理论:一种自然实现面积律与全息原理的新框架》的数值验证与补充材料。

## 内容概述
- **面积律验证数据**:不同耦合常数($\lambda = 1.0, 2.0, 5.0$)下精确验证纠缠熵满足面积律标度($S \sim A^{1/2}$)的原始数值结果。
- **标度分析**:提取标度维度和临界指数以支持全息原理的数据文件。
- **理论总结**:详细阐述几何“扳手”算子形式及其在黑洞热力学中应用的报告。

## 核心结论
数据强有力地支持量子引力扳手(QGW)框架自然实现了:
1.  **全息面积律**:纠缠熵随边界面积而非体积标度。
2.  **维度约化**:红外区域有效空间维度流向 $d=2$。
3.  **黑洞熵**:为Bekenstein-Hawking熵公式提供了微观解释。

使用说明
- **格式**:主要数据以纯文本(.txt)格式提供,便于机器读取。
- **关联**:本数据集是arXiv预印本论文的配套数据。
- **许可**:知识共享署名 4.0 国际许可协议 (CC BY 4.0)