The Arithmetic Origin of Cosmic Evolution

This repository contains code to reproduce the core quantitative results from the manuscript "The Arithmetic Origin of Cosmic Evolution: From the Fine-Structure Constant to the Age of the Universe" submitted to Nature.

Overview

The code implements three key calculations:

1. α Evolution Analysis - Analysis of Webb et al. high-redshift quasar data showing the evolution of the fine-structure constant
2. Cosmic Age Calculation - Independent determination of universe age from α evolution
3. Golden Angle Verification - Numerical verification that α⁻¹ = 360°/φ² = 137.508

Installation

Requirements

• Python 3.7+
• NumPy
• SciPy
• Matplotlib

Setup

# Clone the repository
git clone https://github.com/JackZH26/The_Arithmetic_Origin_of_Cosmic_Evolution.git
cd The_Arithmetic_Origin_of_Cosmic_Evolution

# Install dependencies
pip install -r requirements.txt

Usage

1. Webb et al. α Evolution Analysis

Reproduces Figure 2 and the χ² = 0.69 result:

python webb_alpha_evolution.py

Expected Output:

• α⁻¹ at Planck epoch: 137.508 ± 0.xxx
• α⁻¹ today: 137.036 ± 0.xxx
• χ² ≈ 0.69 (8 degrees of freedom)
• Generates alpha_evolution.png

2. Cosmic Age Calculation

Calculates universe age from α evolution:

python cosmic_age_calculation.py

Expected Output:

• Universe age: 13.93 ± 1.5 Gyr
• Planck CMB comparison: 13.787 ± 0.020 Gyr
• Deviation: ~1.0%

3. Golden Angle Verification

Verifies the golden angle connection:

python golden_angle_verification.py

Expected Output:

• φ = 1.6180339887...
• 360°/φ² = 137.508°
• Matches α⁻¹ at Planck epoch

Results

All scripts reproduce the key quantitative claims from the manuscript:

Result	Calculated	Reference
α⁻¹ (Planck epoch)	137.508	Golden angle (360°/φ²)
α⁻¹ (today)	137.036	CODATA 2018
χ² (Webb data)	0.69	8 DOF
t₀ (universe age)	13.93 ± 1.5 Gyr	From α evolution
Planck CMB age	13.787 ± 0.020 Gyr	Planck 2018
Deviation	1.0%	Agreement

Data Sources

• Webb et al. quasar data: Phys. Rev. Lett. 107, 191101 (2011)
• Planck CMB data: Astron. Astrophys. 641, A6 (2020)
• CODATA constants: Rev. Mod. Phys. 93, 025010 (2021)

Citation

If you use this code, please cite:

Zhou, J. "The Arithmetic Origin of Cosmic Evolution: From the Fine-Structure 
Constant to the Age of the Universe." Submitted to Nature (2026).

License

MIT License - see LICENSE file for details.

Author

Jian Zhou
XD Inc., Shanghai, China
Email: jackzhou.sci@gmail.com
ORCID: 0009-0000-3536-9500

Acknowledgments

This work builds upon the foundational Bost-Connes framework established by Shaowu Hu. AI assistance (Wall-E, OpenClaw/Claude Opus 4.6) was used for numerical calculations and code development.