Pi as a Structural Irrational Number: Complete Evidence Package for Six Mathematical Properties (Final Integrated Version)

This dataset constitutes the final and integrated evidence package for the study titled "Pi as a Structural Irrational Number: Empirical Discovery of Six Mathematical Properties."**Core Content:**It contains the complete computational evidence verifying six inherent properties in the decimal expansion of π: Processuality, Randomness, Inclusiveness, Alternation, Hierarchy, and Nesting. The analysis is based on the first 100 million decimal digits.**Key Evidence Includes:**1. Statistical proof of long-range memory (Hurst exponent analysis).2. Results from a full battery of randomness tests.3. Complete coverage tables for 2, 3, and 4-digit patterns.4. Symmetry analysis of the digit transition matrix.5. Scaling law analysis revealing anomalous hierarchy.6. Detection of nested periodic structures.**Version Statement:**This dataset is the definitive, curated version.

It integrates and supersedes the preliminary findings archived in earlier datasets (see "Related Datasets").**Structure:**The main archive `Pi_Six_Properties_Evidence_Complete.tar` contains logically organized folders for results, summary charts, and processed data files.