# A Closed-Form Hypergeometric Product Formula for General SU(2) 3nj Recoupling Coefficients — Research Paper

This repository hosts the LaTeX source, published PDF, and analysis scripts accompanying a research paper describing a closed-form hypergeometric product expression for SU(2) 3nj recoupling coefficients. The materials are intended for reproducibility and independent verification by researchers in mathematical physics.

**Paper (rendered):** https://arcticoder.github.io/su2-3nj-closedform/

## Abstract (concise)

We present a closed-form product representation for SU(2) 3nj recoupling coefficients associated with trivalent graphs. The expression is constructed by cutting edges and computing matching-number-derived ratios; the 3nj symbol is expressed as a product of hypergeometric factors parameterized by these ratios. Readers should consult the paper for definitions, assumptions, and derivations.

## Repository Contents

- `index.md` — Paper landing page (Jekyll)
- `<paper>.tex` and `<paper>.pdf` — LaTeX source and rendered PDF
- `scripts/` — Analysis scripts (see below)
- `data/` — Generated outputs for reproducing figures and tables

## Analysis Scripts

### `scripts/coefficient_calculator.py`

Computes 3nj coefficients using the closed-form formula and produces analysis outputs. Use for reproducing numerical experiments from the paper.

Usage (research-only):
```bash
python scripts/coefficient_calculator.py --out data/3nj_analysis.csv

scripts/symmetry_checker.py

Checks symmetry properties (e.g., reflection) for selected 3nj configurations and produces data/reflection_symmetry.csv.

Usage:

python scripts/symmetry_checker.py --out data/reflection_symmetry.csv

Requirements

• mpmath, numpy, pandas (install via pip install -r requirements.txt)

Scope, Validation & Limitations

Scope

• Audience: mathematical physicists and numerical analysts interested in SU(2) recoupling and hypergeometric representations.
• Purpose: provide reproducible derivations and computational tools to evaluate and analyze the closed-form expressions.

Validation & Reproducibility

• Repro artifacts: include data/*, the approximate commit id, and the command-line arguments used for runs when citing numeric results.
• For UQ: if sampling or stochastic methods are used, include seeds and diagnostic outputs (convergence checks, error bounds).

Limitations

• The formulas and numeric examples are derived under the assumptions stated in the paper; applicability outside those assumptions should be validated by readers.

Citing

If you use these results, cite the paper and include the commit id of this repository and any generated data artifacts.