Spinor Corrections b-C & a-C and the Choptyuk Problem

Monograph: Spinor corrections b-C and a-C and the solution of the Choptyuk problem by Ishak Khamzatovich Isaev — Rigorous computation of spectral invariants on the Klein quartic curve with applications to LIGO/Virgo quasi-normal mode predictions.

Overview

This repository provides four independent implementations for the verification, simulation, and visualization of all results presented in the monograph:

Implementation	Language	Type	Directory
Full Verification & Simulation	Python 3.10+	CLI with interactive menu	`python/`
Full Verification & Simulation	Julia 1.9+	REPL with interactive menu	`julia/`
Web Application	Java 17+ (Spring Boot)	REST API + Web UI	`java-webapp/`
Interactive Visualization	Next.js 15 + React	Real-time dashboard	`interactive-viz/`

All implementations share:

Interactive parameter configuration (all values customizable, including arbitrary precision)
Hypothesis testing with custom spinor structures and group configurations
Multi-format report generation: DOCX, PDF, TXT, MD, CSV, HTML, JSON
High-resolution plots: 600 DPI PNG + vector PDF/SVG
Complete execution logs appended to every report
Structured output directory for all artifacts

Mathematical Background

The monograph establishes the following chain of results on the Klein quartic curve (genus 3, automorphism group PSL(2,7) of order 168):

Core Constants

Constant	Formula	Value
Spinor phase δ_A	π/2	1.570796
Spinor phase δ_B	π/3	1.047198
Spinor phase δ_C	π/7	0.448799
First eigenvalue λ₁(Δ)	Bourque–Strohmaier 2024	3.838
Trivial Dirac λ₁(D²_σ₀)	λ₁(Δ) + R/4	3.338

The Choptyuk Formula

b-C correction (1st order, Berry phase):

Δ_bC = λ₁(D²_σ₀) + δ_C²/2 = 3.438710

a-C correction (2nd order, braking):

δ_eff = δ_C⁵/22 ≈ 1/1200 = 0.000828

Unified Choptyuk formula (base):

Δ_Ch = λ₁(D²_σ₀) + δ_C²/2 − δ_C⁵/22 = 3.437883

With higher orders:

Δ_Ch = Δ_Ch(base) + δ_C⁴/8 + δ_C⁶/2 = 3.447040

Choptyuk constant:

b_Ch = 1 − cos(2π/7) = 2·sin²(π/7) ≈ 0.377

Applications

64 spinor structures on the Klein curve — full enumeration and spectral analysis
Bolza and Bring surfaces — comparative spectral invariants
LIGO/Virgo QNM predictions — quasi-normal mode corrections for GW150914, GW170104, GW170814, GW190521
Strong CP problem solution — the Choptuik–Strong CP operator framework, see docs/qcd_bridge/

Strong CP extension (v3.0)

The companion monograph docs/qcd_bridge/choptyuk_qcd_bridge.pdf extends the framework to the strong CP problem. The eight-step solution chain replaces QCD's free parameter $\bar\theta$ with a derived spectral quantity:

$$\bar\theta_{\mathrm{eff}} = \delta_C \cdot N\langle\lambda\rangle \cdot \mathcal{S}_{\mathrm{GUE}} = 0$$

because the Wigner semicircle is symmetric and forces $\langle\lambda\rangle = 0$ in the GUE regime (verified at framework BF ≥ 99 at the lattice-determined physical $\kappa_T > 2.62$, 95% CL). No new fields, scales, or symmetries are introduced. See docs/qcd_bridge/README.md for the full chain, the epistemic parity argument, and the falsification tests.

Result	Value	Status
Choptyuk critical exponent $\delta_C$	$\pi/7 \approx 0.4488$	derived
Spectrum size $N$	$22\ (K3) + 6\ (N_f) = 28$	structural
Lattice $\kappa_T$ (95% CL)	$> 2.62$	measured
Framework BF(GUE/Poi) at $\kappa_T > 2.62$	$\geq 99$ (strong)	interpolated
Framework BF(GUE/Poi) at best-fit $\hat\kappa_T = 8.45$	$510$ (decisive)	interpolated
Continuum $\bar\theta$	$0$ exactly	derived
Dynamic relaxation $\tau_{\mathrm{relax}}$	$\sim 5 \times 10^{-41}$ s	computed

Enhanced Verification (v2.0)

The enhanced monograph extends the theory to higher dimensions and broader applications:

Extension	Key Result	Status
4D spin manifold	δ_eff is conformally invariant; Seiberg-Witten compatible	✓ Verified
Kähler surfaces	Dolbeault correspondence; K3 hyperkähler (holonomy Sp(1)); I₇ elliptic fibration matches Klein	✓ Verified
Tyukovsky equations	δ_corr = δ₀ + δ_C²/2 − δ_C⁵/22; zero free parameters	✓ Verified
Einstein GR / QNM	ω^corr = ω·(1 − 1/(1200π²)) ≈ 0.999916·ω; shift ≈ 8.4×10⁻⁵	✓ Verified
Criticism response	b₂ = 22 unique (dev < 1%); non-coincidental (no better approx q < 1200); stable under deformation	✓ Verified

K3 Surface invariants:

Betti numbers: b₀ = 1, b₁ = 0, b₂ = 22, b₃ = 0, b₄ = 1
Hodge decomposition: b₂ = h^(1,1) + 2h^(2,0) = 20 + 2 = 22 ✓
Dirac index: Â(K3) = 2; b₂/Â = 11
Seiberg-Witten: b₂⁺ = 3 > 1 → SW-compatible ✓

QNM correction for LIGO events:

Event	f_QNM (Hz)	f^corr (Hz)	Δf (Hz)
GW150914	251.000	250.979	−0.0210
GW170104	293.000	292.975	−0.0246
GW170814	319.000	318.973	−0.0268
GW190521	110.000	109.991	−0.0092

Quick Start

Python (Recommended for quick verification)

cd python/
pip install -r requirements.txt
python run.py

Julia

cd julia/
julia --project=. -e 'using Pkg; Pkg.instantiate()'
julia --project=. run.jl

Java Web Application

cd java-webapp/
mvn clean package
java -jar target/choptyuk-webapp.jar
# Open http://localhost:8080

Interactive Visualization

cd interactive-viz/
npm install
npm run dev
# Open http://localhost:3000

Online demo: https://wild8highlander.github.io/choptuik_ac_bc/

Using Makefile (One Command)

make all          # Run verification + simulation + plots + reports
make verify       # Run verification only
make viz-dev      # Start interactive visualization
make setup        # Set up all environments
make docker-run   # Run via Docker

Using Docker

docker build -t choptyuk-verify -f docker/Dockerfile .
docker run --rm -v $(pwd)/output:/app/output choptyuk-verify

Using Dev Container

Open in VS Code with Dev Containers extension — all tools (Python, Julia, Java, Node.js) pre-installed.

Architecture

Mathematical Pipeline

flowchart LR
    subgraph Geometry["Riemannian Geometry"]
        direction TB
        KC["Klein Quartic<br/><b>x³y + y³z + z³x = 0</b><br/>genus 3, PSL(2,7)"]
        LAP["Laplacian Δ<br/><b>λ₁(Δ) = 3.838</b><br/>Bourque–Strohmaier 2024"]
        SC["Scalar Curvature<br/><b>R = −2</b><br/>hyperbolic metric"]
    end

    subgraph Spinors["Spinor Analysis"]
        direction TB
        PH["Spinor Phases<br/><b>δ_A=π/2  δ_B=π/3  δ_C=π/7</b>"]
        DIR["Dirac Operator D<br/><b>λ₁(D²_σ₀) = 3.338</b><br/>Lichnerowicz: λ₁(Δ)+R/4"]
        S64["64 Spinor Structures<br/><b>2^(2g) = 2⁶ = 64</b><br/>trivial σ₀ → minimum"]
    end

    subgraph Choptyuk["Choptyuk Formula"]
        direction TB
        BC["b-C Correction<br/><b>Δ_bC = 3.438710</b><br/>Berry phase, 1st order"]
        AC["a-C Braking<br/><b>δ_eff ≈ 1/1200</b><br/>2nd order, δ_C⁵/22"]
        CH["Unified Formula<br/><b>Δ_Ch = 3.447040</b><br/>base + δ_C⁴/8 + δ_C⁶/2"]
    end

    subgraph Physics["Physical Predictions"]
        direction TB
        BCH["Choptyuk Constant<br/><b>b_Ch = 0.376510</b><br/>1 − cos(2π/7)"]
        QNM["QNM Frequencies<br/><b>LIGO/Virgo</b><br/>GW150914 GW170104<br/>GW170814 GW190521"]
    end

    KC --> LAP & SC
    LAP --> DIR
    SC --> DIR
    PH --> BC
    DIR --> BC & AC
    BC --> CH
    AC --> CH
    CH --> BCH --> QNM
    KC -.-> S64
    DIR -.-> S64

Implementation & CI/CD

flowchart TB
    subgraph Core["Mathematical Engine"]
        M["Core computations<br/>Klein curve · Dirac · Choptyuk"]
    end

    subgraph Impl["Four Independent Implementations"]
        direction LR
        PY["<b>Python 3.10+</b><br/>CLI + Interactive Menu<br/>NumPy · SciPy · mpmath"]
        JL["<b>Julia 1.9+</b><br/>REPL + Interactive Menu<br/>LinearAlgebra · Plots"]
        JV["<b>Java 17+</b><br/>Spring Boot REST API<br/>Commons Math · JFreeChart"]
        NX["<b>Next.js 15 + React 19</b><br/>Real-time Dashboard<br/>Recharts · MathJS · Tailwind"]
    end

    subgraph Out["Outputs"]
        direction LR
        RPT["<b>7 Report Formats</b><br/>DOCX · PDF · TXT · MD<br/>CSV · HTML · JSON"]
        PLT["<b>Publication Plots</b><br/>600 DPI PNG<br/>PDF · SVG vectors"]
        LOG["<b>Execution Logs</b><br/>Timestamped records<br/>Full provenance"]
    end

    subgraph CI["CI/CD & Reproducibility"]
        direction LR
        GHA["<b>GitHub Actions</b><br/>CI · Lint · Release<br/>Pages · Scorecard · Stale"]
        DOC["<b>Docker + Dev Container</b><br/>One-command setup<br/>Full toolchain"]
        HKS["<b>Pre-commit Hooks</b><br/>ruff · mypy · format<br/>YAML/JSON validation"]
        ZEN["<b>Zenodo DOI</b><br/>Permanent archive<br/>Versioned snapshots"]
    end

    M --> PY & JL & JV & NX
    PY & JL & JV & NX --> RPT & PLT & LOG
    M -.-> CI

    style Core fill:#2c3e50,stroke:#1a252f,color:#fff
    style Impl fill:#ecf0f1,stroke:#bdc3c7
    style Out fill:#e8f8f5,stroke:#1abc9c
    style CI fill:#fef9e7,stroke:#f1c40f

Project Structure

choptuik_ac_bc/
├── README.md                    # This file
├── LICENSE                      # Isaev Proprietary License
├── CITATION.cff                 # Citation metadata (v2.0.0)
├── CONTRIBUTING.md              # Contribution guidelines
├── CHANGELOG.md                 # Version history
├── .gitignore                   # Git ignore rules
├── .github/                     # GitHub templates & CI
│   ├── workflows/               # GitHub Actions CI/CD (enhanced verification)
│   └── ISSUE_TEMPLATE/          # Issue templates
├── docs/                        # Documentation
│   ├── monograph/               # Monograph files (EN/RU, DOCX/PDF/LaTeX)
│   │   ├── figures/             # Publication-quality visualizations (2D/3D/4D)
│   │   ├── verification_results_enhanced.json
│   │   └── ...                  # Original + Enhanced monographs
│   └── qcd_bridge/              # Strong-CP extension (v3.0)
│       ├── README.md            # Section overview + 8-step CP solution
│       ├── choptyuk_qcd_bridge.{tex,pdf}  # 40-page companion monograph
│       ├── figures/             # 12 figures @ 600 DPI PNG + vector PDF
│       ├── ochi_eigenvalues.json          # 28×28 O_chi spectrum
│       ├── ochi_lattice_results.json      # K3 vs chGUE comparison
│       ├── qcd_vs_framework_params.json   # epistemic parity accounting
│       └── honesty_results.json           # Monte Carlo + Cabibbo audits
├── python/                      # Python implementation (v2.0.0)
│   ├── run.py                   # Entry point with interactive menu
│   ├── requirements.txt         # Dependencies
│   ├── setup.py                 # Package setup
│   ├── config/                  # Default configurations
│   ├── presets/                 # Preset parameter sets
│   ├── src/                     # Source modules
│   │   ├── core/                # Core computations + enhanced_verification
│   │   ├── verification/        # Verification + verify_enhanced
│   │   ├── simulation/          # Simulation engine
│   │   ├── visualization/       # Plot generation (enhanced)
│   │   ├── reporting/           # Report generation (7 formats)
│   │   └── ui/                  # Interactive CLI menu
│   └── tests/                   # Unit tests (25+ tests incl. enhanced)
├── julia/                       # Julia implementation
│   ├── run.jl                   # Entry point
│   ├── Project.toml             # Julia project
│   ├── config/                  # Configurations
│   ├── presets/                 # Presets
│   ├── src/                     # Source modules (incl. enhanced_verification.jl)
│   └── test/                    # Tests (incl. 9 enhanced test sets)
├── java-webapp/                 # Java Spring Boot web application
│   ├── pom.xml                  # Maven configuration
│   └── src/                     # Source (incl. K3Surface, TyukovskyEquation, EinsteinQNMCorrection, EnhancedController)
├── interactive-viz/             # Next.js real-time visualization
│   ├── package.json             # NPM configuration
│   └── src/                     # Source (incl. /enhanced page, new types & compute functions)
├── scripts/                     # Utility scripts
│   ├── run_all.sh, run_verify.sh, build_java.sh, run_viz.sh
│   └── qcd_bridge/              # Strong-CP extension (v3.0)
│       ├── generate_figures.py            # 12 figures @ 600 DPI PNG + vector PDF
│       ├── ochi_explicit_construction.py  # K3+M_F+V_T, N=28, kappa_T sweep
│       ├── ochi_lattice_firstprinciples.py  # K3 vs chGUE first-principles upgrade
│       ├── kappa_T_physical_estimate.py   # physical kappa_T from lattice Dirac data
│       ├── cp_solution_spectral.py        # spectral CP solution audit
│       └── honesty_calculations.py        # Monte Carlo, Cabibbo, scaling audits

QCD Bridge Suite (v3.1, added 2026-08-10)

In addition to the original four-implementation monograph suite above, this release adds a self-contained QCD-bridge package under qcd_bridge/ and code/, with a parallel bilingual monograph and dynamic 4D visualizations.

What is added

Artifact	Path	Description
Bilingual monograph (DOCX)	`monograph/`	EN + RU, 11 sections, 18 embedded 3D/4D figures (~22 MB each)
600 DPI figures	`qcd_bridge/figures/`	54 files: 18 PNG @ 600 dpi + 18 PDF + 18 SVG, English labels, 9 sections × 3D + 4D variants
Dynamic 4D animations	`qcd_bridge/animations/`	18 files: 9 MP4 + 9 GIF, 60 frames each, replacing static surfaces with frame-based 4D evolution
Verification configs	`qcd_bridge/configs/`	`verify_all.json`, `verify_section_3_8.json`, `verify_custom.json` (arbitrary precision, N → ∞, any matrices)
Sample 7-format reports	`qcd_bridge/reports/` + `reports_java/`	TXT, CSV, MD, PDF, HTML, DOCX, JSON — results first, then execution log

Four-language engine (each with interactive menu + 7-format reports)

Implementation	Path	Stack	Notes
Python (canonical)	`code/python/`	Python 3.10+, NumPy, Matplotlib, ReportLab, python-docx	9 sections, ReportEngine, CLI with 5 modes, web_runner bridge
Julia	`code/julia/`	Julia 1.9+, LinearAlgebra, Statistics	Full mirror of Python engine, hand-rolled PDF 1.4 + OOXML DOCX (stdlib has no zlib)
Java	`code/java/`	Pure Java 17+, no external deps	Jacobi eigensolver from scratch, hand-rolled PDF + DOCX via `java.util.zip`
Web app	`code/web/`	Next.js 16 + React 19 + TypeScript + Tailwind 4 + Plotly.js	Real-time 3D/4D viz, interactive dashboard with section-specific sliders for all 9 sections, EN/RU i18n, API routes for Python backend

The 9 QCD-bridge sections

O_χ random matrix theory — GUE-vs-Poisson spacing, Bayes factor
RMT sweep — κ_T scan over N and ensemble
K3 spectral staircase — 22×22 intersection form, E₈⊕E₈⊕U⊕U⊕U
N-scaling test — ⟨λ⟩ → 0 trend, θ̄_artifact ~ 1/√N
τ-relaxation dynamics — physical time-scale estimate
κ_T lattice physical estimate — Cabibbo-angle coincidence
Cabibbo angle coincidence — δ_C = π/7
CP 8-step solution chain — spectral CP solution audit
Jet wake bridge — CMS HIN-25-012 connection

Quick start (QCD bridge)

# Python — verify all 9 sections, generate 7-format reports + 600 dpi figures + 4D animations
cd code/python
python3 run.py --config ../../qcd_bridge/configs/verify_all.json

# Python — custom config (any N, any matrices, arbitrary precision)
python3 run.py --config ../../qcd_bridge/configs/verify_custom.json

# Python — single section
python3 run.py --section 3,6,8

# Julia — same 9 sections, 7 report formats
cd code/julia
julia qcd_bridge_engine.jl --section 1,2,3

# Java — same 9 sections, 7 report formats (no external deps)
cd code/java
javac qcd_bridge_engine.java && java qcd_bridge_engine --section 1,2,3

# Web app — interactive dashboard with sliders for all 9 sections
cd code/web
bun install && bun run dev   # → http://localhost:3000

Authorship (QCD bridge suite)

Same as the main monograph: Ishak Khamzatovich Isaev (ORCID 0009-0003-7299-0701). Embedded in both DOCX monographs, all 7-format reports, the web app header/footer/About page, and CITATION.cff.

Report Formats

Every implementation generates reports in all of the following formats:

Format	Extension	Description
Microsoft Word	`.docx`	Formatted document with tables and figures
Portable Document	`.pdf`	Publication-ready PDF
Plain Text	`.txt`	Human-readable text report
Markdown	`.md`	GitHub-compatible markdown
Comma-Separated	`.csv`	Tabular data for analysis
HTML	`.html`	Styled web report
JSON	`.json`	Machine-readable structured data

Each report contains:

Results section — computed constants, deviations, comparison tables
Execution log — complete timestamped log of all computations

Visualization Output

All plots are generated in two high-resolution formats:

PNG at 600 DPI — for screen display and documents
PDF/SVG — vector format for publication

Plot types include:

Spinor phase diagrams
Spectral eigenvalue landscapes
64 spinor structure heatmaps
QNM frequency comparison charts
Deviation analysis plots
Convergence diagrams

Verification Results (Reference)

Constant	Computed	Observed	Deviation
Δ_bC	3.438710	3.443	0.125%
Δ_Ch (base)	3.437883	3.443	0.149%
Δ_Ch (full)	3.447040	3.443	0.117%
b_Ch	0.376510	0.377	0.130%

Citation

If you use this code in your research, please cite:

@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}
}

Zenodo Archive

A permanent DOI-backed archive of this software is available on Zenodo. When a new release is published on GitHub, Zenodo automatically creates a snapshot with a versioned DOI for exact reproducibility.

Author

Ishak Khamzatovich Isaev

ORCID: 0009-0003-7299-0701
Email: aslan08_05@mail.ru
GitHub: @wild8highlander
Location: Nalchik, Kabardino-Balkarian Republic

License

This project is licensed under the Isaev Proprietary License — see the LICENSE file for details.

Summary: This is a proprietary license. You may view and cite the work for academic reference, but you may NOT copy, modify, distribute, or use it commercially without the author's written permission. All intellectual property rights are retained by Ishak Khamzatovich Isaev.

Reproducibility

This project is designed for full computational reproducibility:

Docker: One-command reproducible environment (make docker-run)
Dev Containers: VS Code one-click setup with all tools pre-installed
Makefile: Unified build system (make all)
Pre-commit hooks: Automated code quality enforcement
CI/CD: Every push is automatically verified across Python 3.10-3.12, Julia 1.9-1.10, Java 17, and Node 20
Cross-implementation consistency: CI verifies that all implementations produce matching results
Version pinning: All dependencies are version-pinned in requirements.txt, Project.toml, pom.xml, package.json
Zenodo DOI: Permanent archived snapshots for each release

Contributing

See CONTRIBUTING.md for detailed guidelines. Quick workflow:

Fork → Branch → Commit → PR
CI runs automatically (Python + Julia + Java + Viz)
All verification tests must pass
Deviations from reference values must remain within tolerance
New features require corresponding tests

Acknowledgments

Bourque & Strohmaier (2024) for the rigorous computation of λ₁(Δ) on the Klein quartic
LIGO/Virgo Collaboration for gravitational wave observational data
The PSL(2,7) symmetry group and its role in the spinor structure classification

Name		Name	Last commit message	Last commit date
.devcontainer		.devcontainer
.github		.github
code		code
docker		docker
docs-site		docs-site
docs		docs
interactive-viz		interactive-viz
java-webapp		java-webapp
julia		julia
monograph		monograph
notebooks		notebooks
python		python
qcd_bridge		qcd_bridge
scripts		scripts
.editorconfig		.editorconfig
.gitignore		.gitignore
.pre-commit-config.yaml		.pre-commit-config.yaml
.readthedocs.yaml		.readthedocs.yaml
.zenodo.json		.zenodo.json
CHANGELOG.md		CHANGELOG.md
CITATION.cff		CITATION.cff
CODE_OF_CONDUCT.md		CODE_OF_CONDUCT.md
CONTRIBUTING.md		CONTRIBUTING.md
LICENSE		LICENSE
Makefile		Makefile
README.md		README.md
SECURITY.md		SECURITY.md
codecov.yml		codecov.yml
worklog.md		worklog.md

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Spinor Corrections b-C & a-C and the Choptyuk Problem

Overview

Mathematical Background

Core Constants

The Choptyuk Formula

Applications

Strong CP extension (v3.0)

Enhanced Verification (v2.0)

Quick Start

Python (Recommended for quick verification)

Julia

Java Web Application

Interactive Visualization

Using Makefile (One Command)

Using Docker

Using Dev Container

Architecture

Mathematical Pipeline

Implementation & CI/CD

Project Structure

QCD Bridge Suite (v3.1, added 2026-08-10)

What is added

Four-language engine (each with interactive menu + 7-format reports)

The 9 QCD-bridge sections

Quick start (QCD bridge)

Authorship (QCD bridge suite)

Report Formats

Visualization Output

Verification Results (Reference)

Citation

Zenodo Archive

Author

License

Reproducibility

Contributing

Acknowledgments

About

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Resources

Code of conduct

Contributing

Security policy

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