The Arc Law: A Unified Geometric Framework for Transformation

The Arc Theorem: A Geometric Theory of Transformation Rates This repository contains the complete formal derivation, validation record, and supporting evidence for the Arc Theorem — a theorem establishing that observed scaling exponents in rate laws are geometric invariants arising from traversal through imaginary space. The theorem states: α=dT+dC×ϕ2π\alpha = d_T + d_C \times \frac{\phi}{2\pi}α=dT+dC×2πϕ where: α\alphaα is the observed scaling exponent dTd_TdT is the terminal (mode-counting) dimension dCd_CdC is the cycling dimension ϕ\phiϕ is the traversal angle in imaginary space The Arc Theorem demonstrates that historically empirical laws across physics, chemistry, biology, and dynamical systems are projections of trajectories through structured imaginary space. This release (v4) establishes theorem status through: Independent derivations from Wigner threshold theory Instanton and Euclidean action formalism Classical evanescent wave analysis (Maxwell-only) Cross-domain validation and preregistered tests The repository includes formal proofs, derivation manuscripts, empirical validation figures, preregistration documents, reproducibility code, and interactive visualizers. All results are fully reproducible using included data and scripts. This is an archival scientific release. No files are reorganized or rewritten. See README_V4.md and CHANGELOG.md for full version details.弧定理：变换速率的几何理论 本仓库收录弧定理的完整形式化推导、验证记录与支撑佐证。该定理证明，速率定律中观测到的标度指数（scaling exponent），实为穿行于虚空间所产生的几何不变量。 该定理表述如下： $$alpha = d_T + d_C imes frac{phi}{2pi}$$ 其中： - $alpha$：观测得到的标度指数（scaling exponent） - $d_T$：终端（模式计数）维度（terminal (mode-counting) dimension） - $d_C$：循环维度（cycling dimension） - $phi$：虚空间穿行角（traversal angle in imaginary space） 弧定理表明，物理学、化学、生物学与动力学系统领域中诸多既往经验定律，均为结构化虚空间内轨迹的投影。 本版本（v4）通过以下路径确立该定理的正式学术地位： 1. 基于维格纳阈值理论（Wigner threshold theory）的独立推导 2. 瞬子（Instanton）与欧几里得作用量（Euclidean action）形式体系 3. 经典倏逝波（evanescent wave）分析（仅基于麦克斯韦理论） 4. 跨领域验证与预注册（preregistered）测试 本仓库包含形式化证明文档、推导手稿、经验验证图表、预注册文件、可复现代码与交互式可视化工具。所有结果均可通过附带的数据与脚本实现完全复现。 本次发布为存档级科学版本，未对任何文件进行重组或重写。 完整版本详情请参阅README_V4.md与CHANGELOG.md文件。