Add static alignment beta validation

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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.
+