From 735f9c7fd202d0eaed9183094d84d365e0e5404d Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Sat, 1 Aug 2026 16:20:35 -0500 Subject: Test the new instruments; fix an O(1/n) bias in the degree decomposition 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 --- artifacts/vg_5k/field_anatomy.json | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) (limited to 'artifacts/vg_5k/field_anatomy.json') diff --git a/artifacts/vg_5k/field_anatomy.json b/artifacts/vg_5k/field_anatomy.json index 740136c..1e0f276 100644 --- a/artifacts/vg_5k/field_anatomy.json +++ b/artifacts/vg_5k/field_anatomy.json @@ -9,31 +9,31 @@ }, { "component": "degree model only", - "correlation": 0.22252881188815218 + "correlation": 0.2225288118881524 }, { "component": "residual after degree", - "correlation": 0.6709906297296612 + "correlation": 0.670990871461728 }, { "component": "residual after top-1 eigen", - "correlation": 0.4579725907578625 + "correlation": 0.45797259075786245 }, { "component": "residual after top-2 eigen", - "correlation": 0.4555001418827857 + "correlation": 0.45550014188278554 }, { "component": "residual after top-5 eigen", - "correlation": 0.3413229646188751 + "correlation": 0.3413229646188753 }, { "component": "residual after top-10 eigen", - "correlation": 0.07969017846523709 + "correlation": 0.07969017846523718 } ], - "visual_degree_variance_share": 0.009036045331312099, - "text_degree_variance_share": 0.04921092158161093, + "visual_degree_variance_share": 0.00910733535353353, + "text_degree_variance_share": 0.049599171923929736, "it_threshold_at_size": 0.29435250562886867, "residual_above_it_threshold": true, "reading": "If the residual correlation is far below the raw correlation, the headline statistic is inflated by nuisance structure that carries no matching information, and the residual is the number that should be compared against the recovery threshold." -- cgit v1.2.3