From 7c2eaaa5ae6f9bc5b61de1f7f86b1cc0896b5596 Mon Sep 17 00:00:00 2001
From: YurenHao0426 <Blackhao0426@gmail.com>
Date: Thu, 28 May 2026 22:49:27 -0500
Subject: Add static alignment beta validation

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 scripts/README.md | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 scripts/README.md

(limited to 'scripts/README.md')

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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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