2026-10-12T09:11:20Z https://www.scidb.cn/oai

10.57760/sciencedb.34455 2025-12-29T12:45:40Z

2025-12-29 Dataset for Process Cyclicity Analysis of Mathematical Constants (π, e, √2, φ) doi:10.57760/sciencedb.34455 en This dataset provides comprehensive materials for studying the "Process Cyclicity" theory through analysis of four mathematical constants: π (pi), e (Euler's number), √2 (square root of 2), and φ (golden ratio).## Contents:1. **Digit sequences**:  - π: 10,000,000 decimal digits  - e: 1,000,000 decimal digits    - √2: 1,000,000 decimal digits  - φ: 1,000,000 decimal digits2. **Analysis results**:  - Six-dimensional metrics: Hurst exponent, self-similarity, uniformity, inclusiveness, alternation, hierarchy, and nesting  - Key finding: All constants show Hurst exponents significantly greater than 0.5 (range: 0.5266-0.5325), indicating long-term memory3. **Reproducible code**:  - Complete Python scripts for all analyses  - Simplified version for quick verification4. **Manuscript**:  - LaTeX source of the accompanying paper  - Key visualization figure## Scientific significance:Demonstrates that mathematical constants exhibit weak but systematic periodic structures ("process cyclicity") while maintaining statistical randomness in digit distribution.## Data source:Digit sequences extracted from Alexander Yee's number library (http://www.numberworld.org/), computed using y-cruncher software.## Usage:Run `python precise_analysis.py` to reproduce all analyses. mathematical constants; process cyclicity; Hurst exponent; self-similarity; decimal expansion; number theory; computational mathematics Wenju Fu PUBLIC https://creativecommons.org/licenses/by/4.0/ dataset Science Data Bank