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 <noreply@anthropic.com>

1 files changed, 259 insertions, 0 deletions

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
+        },
+        {
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+          "best_text_overlap": 0.7105187496542062
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+        {
+          "index": 5,
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+        },
+        {
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+          "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
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+        {
+          "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,
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+        0.96,
+        0.95,
+        0.938,
+        0.928,
+        0.907,
+        0.903
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+      "spectrum_profile": [
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+          "index": 0,
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+        {
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+        {
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+        {
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+          "best_text_overlap": 0.501988106773722
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+        {
+          "index": 4,
+          "best_text_overlap": 0.783113379169079
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+        {
+          "index": 5,
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+        {
+          "index": 6,
+          "best_text_overlap": 0.4801278579299998
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+        {
+          "index": 7,
+          "best_text_overlap": 0.383298070449205
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+        {
+          "index": 8,
+          "best_text_overlap": 0.47046163940920954
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+        {
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+          "best_text_overlap": 0.4732632962224147
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+        {
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+        {
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+        {
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+          "best_text_overlap": 0.3098353728024743
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+        {
+          "index": 14,
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+        {
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+      ]
+    },
+    {
+      "label": "scenes-1024",
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+      "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
+        },
+        {
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+          "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