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Choptyuk Spinor Corrections

PyPI version DOI Python

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
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

Citation

@book{isaev2024spinor,
  title     = {Spinor corrections b-C and a-C and the solution of the Choptyuk problem},
  author    = {Isaev, Ishak Khamzatovich},
  year      = {2024},
  address   = {Nalchik, Kabardino-Balkarian Republic},
  note      = {Monograph with verified computational implementations}
}