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_scale.json | 259 +++++++++++++++++++++++++++++++++ 1 file changed, 259 insertions(+) create mode 100644 artifacts/vg_5k/shared_rank_scale.json (limited to 'artifacts/vg_5k/shared_rank_scale.json') diff --git a/artifacts/vg_5k/shared_rank_scale.json b/artifacts/vg_5k/shared_rank_scale.json new file mode 100644 index 0000000..b0d6e98 --- /dev/null +++ b/artifacts/vg_5k/shared_rank_scale.json @@ -0,0 +1,259 @@ +{ + "protocol": "Effective rank from the participation ratio of each field's spectrum; shared directions from principal angles between the two leading eigenspaces. No pairing enters beyond the alignment the fields already carry.", + "width": 48, + "rows": [ + { + "label": "scenes-256", + "size": 256, + "correlation": 0.7157944505313559, + "visual_effective_rank": 39.69132496762981, + "text_effective_rank": 47.98422953390366, + "shared_directions_cos_gt_0.7": 23, + "principal_cosines_top8": [ + 0.992, + 0.984, + 0.971, + 0.963, + 0.962, + 0.949, + 0.94, + 0.935 + ], + "spectrum_profile": [ + { + "index": 0, + "best_text_overlap": 0.8406807387214822 + }, + { + "index": 1, + "best_text_overlap": 0.6748753041856854 + }, + { + "index": 2, + "best_text_overlap": 0.7174150319587717 + }, + { + "index": 3, + "best_text_overlap": 0.4742164704027202 + }, + { + "index": 4, + "best_text_overlap": 0.7105187496542062 + }, + { + "index": 5, + "best_text_overlap": 0.5435228035336661 + }, + { + "index": 6, + "best_text_overlap": 0.5173316630294161 + }, + { + "index": 7, + "best_text_overlap": 0.3720956303455928 + }, + { + "index": 8, + "best_text_overlap": 0.4031225977235423 + }, + { + "index": 9, + "best_text_overlap": 0.5909531802492844 + }, + { + "index": 10, + "best_text_overlap": 0.373881786434362 + }, + { + "index": 11, + "best_text_overlap": 0.2816693575587397 + }, + { + "index": 12, + "best_text_overlap": 0.21822240451244762 + }, + { + "index": 13, + "best_text_overlap": 0.3929212823566225 + }, + { + "index": 14, + "best_text_overlap": 0.4024276537497661 + }, + { + "index": 15, + "best_text_overlap": 0.2659834432053085 + } + ] + }, + { + "label": "scenes-512", + "size": 512, + "correlation": 0.720884905640894, + "visual_effective_rank": 44.16644435195353, + "text_effective_rank": 56.80473066126686, + "shared_directions_cos_gt_0.7": 20, + "principal_cosines_top8": [ + 0.99, + 0.973, + 0.96, + 0.95, + 0.938, + 0.928, + 0.907, + 0.903 + ], + "spectrum_profile": [ + { + "index": 0, + "best_text_overlap": 0.8697350573768952 + }, + { + "index": 1, + "best_text_overlap": 0.7200022519825038 + }, + { + "index": 2, + "best_text_overlap": 0.7564612333353183 + }, + { + "index": 3, + "best_text_overlap": 0.501988106773722 + }, + { + "index": 4, + "best_text_overlap": 0.783113379169079 + }, + { + "index": 5, + "best_text_overlap": 0.37328195185984525 + }, + { + "index": 6, + "best_text_overlap": 0.4801278579299998 + }, + { + "index": 7, + "best_text_overlap": 0.383298070449205 + }, + { + "index": 8, + "best_text_overlap": 0.47046163940920954 + }, + { + "index": 9, + "best_text_overlap": 0.4732632962224147 + }, + { + "index": 10, + "best_text_overlap": 0.348622185453265 + }, + { + "index": 11, + "best_text_overlap": 0.4225508394457381 + }, + { + "index": 12, + "best_text_overlap": 0.21406071363464227 + }, + { + "index": 13, + "best_text_overlap": 0.3098353728024743 + }, + { + "index": 14, + "best_text_overlap": 0.3400635764036258 + }, + { + "index": 15, + "best_text_overlap": 0.23608736474375264 + } + ] + }, + { + "label": "scenes-1024", + "size": 1024, + "correlation": 0.6922444253804424, + "visual_effective_rank": 49.142293255949674, + "text_effective_rank": 62.90043889867087, + "shared_directions_cos_gt_0.7": 19, + "principal_cosines_top8": [ + 0.988, + 0.962, + 0.949, + 0.938, + 0.922, + 0.916, + 0.908, + 0.9 + ], + "spectrum_profile": [ + { + "index": 0, + "best_text_overlap": 0.8301375686311265 + }, + { + "index": 1, + "best_text_overlap": 0.6075551782428065 + }, + { + "index": 2, + "best_text_overlap": 0.6710977881848478 + }, + { + "index": 3, + "best_text_overlap": 0.6555164924250194 + }, + { + "index": 4, + "best_text_overlap": 0.6194066121363382 + }, + { + "index": 5, + "best_text_overlap": 0.40182630965483374 + }, + { + "index": 6, + "best_text_overlap": 0.5020646929681399 + }, + { + "index": 7, + "best_text_overlap": 0.3892962240055352 + }, + { + "index": 8, + "best_text_overlap": 0.47168546897479857 + }, + { + "index": 9, + "best_text_overlap": 0.40763120184534807 + }, + { + "index": 10, + "best_text_overlap": 0.44277607795178114 + }, + { + "index": 11, + "best_text_overlap": 0.2873332187039861 + }, + { + "index": 12, + "best_text_overlap": 0.40798659732142045 + }, + { + "index": 13, + "best_text_overlap": 0.3901617780561322 + }, + { + "index": 14, + "best_text_overlap": 0.3381332001188724 + }, + { + "index": 15, + "best_text_overlap": 0.26462763928061106 + } + ] + } + ], + "reading": "The narrow modality is the one to upgrade. 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