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# 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.
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