Mathematical Formalism and Statistical Derivations of the Inversion Coherence Law (ICL)

This paper introduces a formal engineering framework for the analysis of the Quranic text, treated as a multidimensional information system. By applying a "Coordinate Inversion" methodology, the research explores the structural relationship between chapter and verse numbers, revealing a highly non-linear and symmetrical architecture. The study moves beyond traditional literary analysis to propose a model of "Textual Relativity," where the physical placement of information within the corpus acts as a governing law for its thematic content. The author demonstrates that the distribution of data within the text follows a predictable mathematical pattern, suggesting a deliberate information design. Included in this submission are two critical appendices: Appendix A: Mathematical FormalismProvides the rigorous mathematical definitions for the Coordinate Inversion Operator, the Coherence Identity Function, and the statistical validation models (including Z-score analysis) used to reject the possibility of random distribution. Appendix B: Data Sets and EvidenceContains the raw data tables mapping the flipped coordinates, categorized by their thematic coherence and boundary conditions (Single and Double Exceptions). This work aims to provide a bridge between ancient scriptural structures and modern information theory, establishing the Quranic corpus as a "Governed Information System" that exhibits a level of structural integrity statistically inconsistent with manual composition.