From 08fd63b8fee62ccdc284380c9832900ee83f9ede Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Sat, 1 Aug 2026 16:15:41 -0500 Subject: Retire the correlation gate: the shared spectrum governs recovery A controlled truncation refutes the project's central go/no-go rule. Projecting the recovering synthetic fields to rank r holds the field correlation at 0.902-0.929 while recovery moves 6.2% -> 12.9% -> 95.6% across ranks 4, 8, 16. A field past the supposed 0.9 threshold recovers 13%, so correlation neither predicts nor forbids recovery and the width of the shared spectrum is what moves it. The gate becomes a joint condition on correlation and shared width, measured by principal angles against a scene-shuffled null. Neither suffices alone: 18 shared directions at 0.508 fails, 11 at 0.902 fails. With the old gate retired, natural data was finally searched: 0.0000 against 0.0039 chance. The old verdict was right, its reasoning was not. Also closes route D by measurement. rho_IT ~ sqrt(4 log N / N) rises as N falls, and at N = 16 through 96 the deepest state a strong searcher reaches is deeper than the truth in 3/3 replicates at every size. Free gains: eigenvalue-weighted projection over a wide basis with 128-dim text vectors takes the correlation 0.656 -> 0.716 and shared width 10 -> 16. Hubness refuted as an inflation hypothesis. Moving the per-image segmentation eigendecomposition onto the GPU cut batch time from 130s to 1.9s. Co-Authored-By: Claude --- artifacts/vg_5k/shared_rank_segments.json | 343 ++++++++++++++++++++++++++++++ 1 file changed, 343 insertions(+) create mode 100644 artifacts/vg_5k/shared_rank_segments.json (limited to 'artifacts/vg_5k/shared_rank_segments.json') diff --git a/artifacts/vg_5k/shared_rank_segments.json b/artifacts/vg_5k/shared_rank_segments.json new file mode 100644 index 0000000..7408bd4 --- /dev/null +++ b/artifacts/vg_5k/shared_rank_segments.json @@ -0,0 +1,343 @@ +{ + "protocol": "Effective rank from the participation ratio of each field's spectrum; shared directions from principal angles between the two leading eigenspaces. 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A shared count far below both effective ranks means each side is rich but they are rich about different things." +} \ No newline at end of file -- cgit v1.2.3