Data · dataset · 2025
Dataset for Process Cyclicity Analysis of Mathematical Constants (π, e, √2, φ)
Listed in ScienceDB
Description
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 (numberworld.org/), computed using y-cruncher software.## Usage:Run `python precise_analysis.py` to reproduce all analyses.
Links
Where it is published
- DOI doi.org/10.57760/sciencedb.34455 ↗
DOI / persistent id · from scidb cn
Catalogue records · 1
- OAI-PMH record scidb.cn/oai?verb=GetRecord&metadataPrefix=oai_dc&identifier=10.57760%2… ↗
metadata API · from scidb cn
Topics
- From keywords
- Earth & Environmental Science · Engineering · Humanities · Life Sciences · Mathematics & Statistics · Social Science
- Inferred from text
- Numerical and computational mathematics 71%
Provenance · 1 source records, 12 field assertions
| Source | Key | Last seen | Raw |
|---|---|---|---|
| ScienceDB | 10.57760/sciencedb.34455 | 9 d ago | JSON v1 |
| Field | Assertion | Extractor | Evidence |
|---|---|---|---|
| access_level | source · scidb cn | connector:scidb_cn@1.0.0 | |
| concepts[field].anzsrc:group:4903 | enrichment · scidb cn | taxonomy-embedding@1.0.0 | title+keywords+description (71%) |
| concepts[field].local:field:earth-environmental | mapping · scidb cn | connector:scidb_cn@1.0.0 | |
| concepts[field].local:field:engineering | mapping · scidb cn | connector:scidb_cn@1.0.0 | |
| concepts[field].local:field:humanities | mapping · scidb cn | connector:scidb_cn@1.0.0 | |
| concepts[field].local:field:life-sciences | mapping · scidb cn | connector:scidb_cn@1.0.0 | |
| concepts[field].local:field:mathematics-statistics | mapping · scidb cn | connector:scidb_cn@1.0.0 | |
| concepts[field].local:field:social-science | mapping · scidb cn | connector:scidb_cn@1.0.0 | |
| description | source · scidb cn | connector:scidb_cn@1.0.0 | /metadata/dc/description |
| license | source · scidb cn | connector:scidb_cn@1.0.0 | /metadata/dc/rights |
| publication_date | source · scidb cn | connector:scidb_cn@1.0.0 | |
| title | source · scidb cn | connector:scidb_cn@1.0.0 | /metadata/dc/title |