The Axis Model: A Unified Framework for Emergent Particle Structure, Cosmology, and Gravitational Phenomena

This repository contains the computational pipelines and empirical validation notebooks for the Axis Model framework—a geometric unification program in which fundamental particles and interactions emerge from scalar-stabilized configurations of quantized vector displacements (“mortons”). All notebooks are designed for direct reproducibility in Google Colab and mirror the figures, fits, and statistical tests reported in the companion manuscripts. Exploratory prototypes from early development are retained for archival comparison but superseded by preregistered and corrected pipelines. Domains covered Gravitational wave anomalies: frequency-scan pipelines with preregistered specifications and family-wise error control. Cosmological scaling: CMB large-angle suppression, dark-energy scaling, Hubble-tension diagnostics. Astrophysical structure: galactic rotation curves, lensing deviations, Einstein Cross modeling, dispersion relations. Particle benchmarks: electron finite-energy radius, muon decay, neutrino mass fits, chirality structure. Theoretical extensions: Statistical reproducibility and error-control formalism. Recursive dimensional growth into tri-vector geometry. Updated electron Morton benchmarks consistent with collider bounds and Planck cutoff. First-principles derivation of the fine-structure constant (Appendix AK) — including canonical EFT normalization, projection-geometry factors, one-loop RG flow, and ppm-level two-loop stability bounds. Minor clarifications and interpretive refinements.This version tightens the presentation of the cosmological sector by clarifying the role of effective scaling parameters, sharpening the separation between illustrative benchmarks and observational limits, and improving the explanatory linkage between low- and high-ℓ\ellℓ CMB treatments. No core derivations, model structure, or empirical inputs have been changed. This dataset supersedes prior releases. For questions, compatibility issues, or support with the Colab notebooks, contact: [e-mail]本仓库包含轴模型（Axis Model）框架所用的计算流程与实证验证笔记本。轴模型是一项几何统一框架，其中基本粒子与相互作用均由量化矢量位移（"mortons"）的标量稳定构型衍生而来。 所有笔记本均可在Google Colab平台直接复现结果，且与配套论文中的图表、拟合结果及统计检验完全匹配。早期开发阶段的探索性原型代码予以保留以供存档对比，但已由预先注册并修正后的计算流程所取代。 涵盖研究领域： 1. 引力波异常：包含预先注册规范与族错误率控制的频率扫描计算流程。 2. 宇宙学标度：宇宙微波背景（CMB）大角度抑制、暗能量标度、哈勃张力诊断。 3. 天体物理结构：星系旋转曲线、引力透镜偏差、爱因斯坦十字建模、色散关系。 4. 粒子物理基准：电子有限能量半径、μ子衰变、中微子质量拟合、手性结构。 5. 理论扩展： - 统计可复现性与误差控制形式体系。 - 递归维度生长至三矢量几何。 - 与对撞机边界及普朗克截断相符的更新版电子莫顿子基准。 - 精细结构常数的第一性原理推导（附录AK）——涵盖规范有效场论（Effective Field Theory, EFT）归一化、投影几何因子、单圈重整化群（Renormalization Group, RG）流，以及ppm级双圈稳定性边界。 本次版本包含细节阐释优化与解读精进。本版本针对宇宙学板块进行了优化：厘清了有效标度参数的作用，明确区分了示例基准与观测极限，并优化了低ℓ与高ℓ宇宙微波背景处理环节的解释关联性。核心推导、模型结构及实证输入均未发生改动。 本数据集已取代此前的所有发布版本。若有疑问、兼容性问题或需要对Google Colab笔记本提供技术支持，请联系：[e-mail]