# Scripts

## Static Alignment Beta Law

Run:

```bash
python scripts/static_alignment_beta.py --rows 16 --cols 16 --samples 20000 --seed 7 --plot
```

This samples independent matrix pairs \(A,B\), computes:

\[
Q =
\frac{\langle A,B\rangle_F^2}{\|A\|_F^2\|B\|_F^2},
\]

and compares the empirical distribution with:

\[
\mathrm{Beta}\left(\frac12,\frac{D-1}{2}\right),
\qquad
D=\texttt{rows}\times\texttt{cols}.
\]

Outputs are written under `outputs/static_alignment_beta/`, which is ignored by Git.