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/field_anatomy_w64.json | 40 ++++++++++++++++++++++++++++++++++ 1 file changed, 40 insertions(+) create mode 100644 artifacts/vg_5k/field_anatomy_w64.json (limited to 'artifacts/vg_5k/field_anatomy_w64.json') diff --git a/artifacts/vg_5k/field_anatomy_w64.json b/artifacts/vg_5k/field_anatomy_w64.json new file mode 100644 index 0000000..1e023eb --- /dev/null +++ b/artifacts/vg_5k/field_anatomy_w64.json @@ -0,0 +1,40 @@ +{ + "protocol": "Both fields split into an additive row/column-mean model and its residual, then correlated component by component. Hidden pairs are read only to align the two fields.", + "label": "natural-weighted64", + "size": 256, + "rows": [ + { + "component": "raw field", + "correlation": 0.6922159706308013 + }, + { + "component": "degree model only", + "correlation": 0.09663282041737035 + }, + { + "component": "residual after degree", + "correlation": 0.7052697077805243 + }, + { + "component": "residual after top-1 eigen", + "correlation": 0.542199919037366 + }, + { + "component": "residual after top-2 eigen", + "correlation": 0.37481036694327863 + }, + { + "component": "residual after top-5 eigen", + "correlation": 0.3855465012648901 + }, + { + "component": "residual after top-10 eigen", + "correlation": 0.18341225740386502 + } + ], + "visual_degree_variance_share": 0.01546868013212138, + "text_degree_variance_share": 0.026806936723177938, + "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." +} \ No newline at end of file -- cgit v1.2.3