Hierarchical Structure and Chi-Square Decomposition in Twin Prime Residue Classes Modulo Primorials: Data and Reproducibility Package

This repository contains the complete reproducibility package accompanying the research article: "Hierarchical Structure and Chi-Square Decomposition in Twin Prime Residue Classes Modulo Primorials" The project investigates the distribution of twin primes across admissible residue classes modulo successive primorials and studies the hierarchical structure induced by the Chinese Remainder Theorem (CRT). The repository includes all materials required to reproduce the results reported in the manuscript, including datasets, source code, statistical analyses, Monte Carlo simulations, generated figures, and the final PDF version of the paper. Repository Contents Manuscript The repository contains: Complete LaTeX source files. Bibliographic database (.bib). Final compiled PDF manuscript. Figures used in the article. Dataset The dataset consists of approximately 10 million verified twin prime pairs used throughout the analysis. The data were employed to compute: admissible residue-class frequencies, Pearson chi-square statistics, hierarchical CRT decompositions, conditional within-family statistics, Monte Carlo validation results. Source Code The repository includes all Python scripts required to reproduce the analysis, including: residue-class counting, primorial hierarchy construction, chi-square decomposition calculations, conditional multinomial simulations, Monte Carlo validation procedures, figure generation scripts. All scripts are provided in fully editable form and can be executed independently. Statistical Analysis The analysis presented in the paper includes: Construction of admissible residue systems modulo successive primorials. Exact CRT-based hierarchical decomposition of the Pearson chi-square statistic. Verification of the decomposition across multiple primorial levels. Definition of a conditional within-family statistic. Monte Carlo simulations preserving observed family totals. Comparison between empirical fluctuations and conditional multinomial expectations. Main Result The principal theoretical result is an exact decomposition of the Pearson chi-square statistic across successive primorial levels into: between-family contributions, within-family contributions. The decomposition reveals a recursive propagation law through the CRT hierarchy. Empirically, the observed fluctuations are consistently smaller than those predicted by both unconditional and conditional multinomial reference models, indicating the presence of additional statistical structure within admissible residue classes. Reproducibility All tables and figures appearing in the manuscript can be regenerated directly from the provided data and source code. The repository is intended to provide complete computational transparency and allow independent verification of every numerical result reported in the paper. Author Victor Eduardo Morales Córdoba Independent Researcher Heredia, Costa Rica ORCID: 0009-0000-8787-6141 Email: [email protected] DOI DOI: 10.5281/zenodo.20682313