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, 40 insertions, 0 deletions

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