Choptyuk Spinor Corrections¶
Welcome to the documentation for Choptyuk Spinor Corrections — a computational framework for the verification, simulation, and visualization of spinor corrections b-C and a-C on the Klein quartic curve, with applications to gravitational wave physics.
Overview¶
This project implements the mathematical results from the monograph "Spinor corrections b-C and a-C and the solution of the Choptyuk problem" by Ishak Khamzatovich Isaev.
The core result is the Choptyuk formula:
\[
\Delta_{\mathrm{Ch}} = \lambda_1(D^2_{\sigma_0}) + \frac{\delta_C^2}{2} - \frac{\delta_C^5}{22} + \frac{\delta_C^4}{8} + \frac{\delta_C^6}{2} \approx 3.447040
\]
where \(\delta_C = \pi/7\) is the spinor phase of the Klein quartic curve, and \(\lambda_1(D^2_{\sigma_0}) = 3.338\) is the first eigenvalue of the squared Dirac operator on the trivial spinor structure.
Features¶
- Full verification of all monograph results (25+ tests)
- Interactive visualization via Next.js dashboard
- 7 report formats: DOCX, PDF, TXT, MD, CSV, HTML, JSON
- Publication-quality plots: 600 DPI PNG + vector PDF/SVG
- Four implementations: Python, Julia, Java, Next.js
- Web API: Spring Boot REST API with web UI
- LIGO/Virgo QNM predictions: gravitational wave frequency corrections
Quick Links¶
| Section | Description |
|---|---|
| Tutorials | Step-by-step guides for running verification, simulations, and analysis |
| Mathematics | Mathematical background: Klein quartic, Dirac operator, Choptyuk formula |
| API Reference | Auto-generated Python API documentation from docstrings |
| Development | Contributing, testing, CI/CD, and release process |
Implementations¶
| Language | Directory | Type |
|---|---|---|
| Python 3.10+ | python/ |
CLI + Interactive Menu |
| Julia 1.9+ | julia/ |
REPL + Interactive Menu |
| Java 17+ | java-webapp/ |
Spring Boot REST API |
| Next.js 15 | interactive-viz/ |
Real-time Dashboard |
Installation¶
# Python (recommended for quick verification)
cd python/
pip install -r requirements.txt
python run.py
# Or use the Makefile
make all