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<title>World-Alignment.git/worldalign/rho_at_full_width.py, branch main</title>
<subtitle>Unnamed repository; edit this file 'description' to name the repository.
</subtitle>
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<entry>
<title>Test the new instruments; fix an O(1/n) bias in the degree decomposition</title>
<updated>2026-08-01T21:20:35+00:00</updated>
<author>
<name>YurenHao0426</name>
<email>Blackhao0426@gmail.com</email>
</author>
<published>2026-08-01T21:20:35+00:00</published>
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<id>735f9c7fd202d0eaed9183094d84d365e0e5404d</id>
<content type='text'>
Four tests around today's additions. Two failed on first run and both
were worth having.

The degree decomposition left an O(1/n) residual on a field that is
purely additive: excluding the diagonal makes the two-way design
unbalanced, so one pass of row and column means does not remove a pure
degree effect. Swept to convergence instead. At N=256 the correction
moves the reported variance shares by under 0.001, so the refutation of
the hubness hypothesis stands unchanged -- but the instrument that
produced it now does what it claims.

The other failure was the test's own scale: two random 16-dimensional
subspaces of R^64 overlap above 0.7 by chance, which is why the real
measurements are made at N=256 where the null sits at 1.0.

Co-Authored-By: Claude &lt;noreply@anthropic.com&gt;
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<pre>
Four tests around today's additions. Two failed on first run and both
were worth having.

The degree decomposition left an O(1/n) residual on a field that is
purely additive: excluding the diagonal makes the two-way design
unbalanced, so one pass of row and column means does not remove a pure
degree effect. Swept to convergence instead. At N=256 the correction
moves the reported variance shares by under 0.001, so the refutation of
the hubness hypothesis stands unchanged -- but the instrument that
produced it now does what it claims.

The other failure was the test's own scale: two random 16-dimensional
subspaces of R^64 overlap above 0.7 by chance, which is why the real
measurements are made at N=256 where the null sits at 1.0.

Co-Authored-By: Claude &lt;noreply@anthropic.com&gt;
</pre>
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</content>
</entry>
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