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, 44 insertions, 0 deletions

diff --git a/logs/projection_sweep.log b/logs/projection_sweep.log
new file mode 100644
index 0000000..6efda04
--- /dev/null
+++ b/logs/projection_sweep.log
@@ -0,0 +1,44 @@
+fit 1200 vision / 1200 text, evaluated 256
+linear     keep=4     shrink=0.01   rho=0.6453
+linear     keep=8     shrink=0.01   rho=0.6495
+linear     keep=16    shrink=0.01   rho=0.6471
+linear     keep=32    shrink=0.01   rho=0.6227
+linear     keep=64    shrink=0.01   rho=0.6143
+linear     keep=4     shrink=0.05   rho=0.6525
+linear     keep=8     shrink=0.05   rho=0.6559
+linear     keep=16    shrink=0.05   rho=0.6519
+linear     keep=32    shrink=0.05   rho=0.6274
+linear     keep=64    shrink=0.05   rho=0.6198
+linear     keep=4     shrink=0.2    rho=0.6607
+linear     keep=8     shrink=0.2    rho=0.6582
+linear     keep=16    shrink=0.2    rho=0.6513
+linear     keep=32    shrink=0.2    rho=0.6292
+linear     keep=64    shrink=0.2    rho=0.6231
+linear     keep=4     shrink=1.0    rho=0.6579
+linear     keep=8     shrink=1.0    rho=0.6405
+linear     keep=16    shrink=1.0    rho=0.6280
+linear     keep=32    shrink=1.0    rho=0.6142
+linear     keep=64    shrink=1.0    rho=0.6106
+weighted^0.5 keep=8     shrink=0.05   rho=0.6698
+weighted^1.0 keep=8     shrink=0.05   rho=0.6651
+weighted^0.5 keep=16    shrink=0.05   rho=0.6826
+weighted^1.0 keep=16    shrink=0.05   rho=0.6721
+weighted^0.5 keep=32    shrink=0.05   rho=0.6874
+weighted^1.0 keep=32    shrink=0.05   rho=0.6753
+weighted^0.5 keep=64    shrink=0.05   rho=0.6922
+weighted^1.0 keep=64    shrink=0.05   rho=0.6768
+weighted^0.5 keep=8     shrink=0.2    rho=0.6728
+weighted^1.0 keep=8     shrink=0.2    rho=0.6692
+weighted^0.5 keep=16    shrink=0.2    rho=0.6835
+weighted^1.0 keep=16    shrink=0.2    rho=0.6752
+weighted^0.5 keep=32    shrink=0.2    rho=0.6884
+weighted^1.0 keep=32    shrink=0.2    rho=0.6780
+weighted^0.5 keep=64    shrink=0.2    rho=0.6918
+weighted^1.0 keep=64    shrink=0.2    rho=0.6788
+kernel g=0.25 keep=8     shrink=0.05   rho=0.6239
+kernel g=0.25 keep=16    shrink=0.05   rho=0.6199
+kernel g=0.25 keep=32    shrink=0.05   rho=0.6044
+kernel g=1.0 keep=8     shrink=0.05   rho=0.5589
+kernel g=1.0 keep=16    shrink=0.05   rho=0.5472
+kernel g=1.0 keep=32    shrink=0.05   rho=0.5251
+{"variant": "weighted^0.5", "keep": 64, "shrinkage": 0.05, "correlation": 0.6922159706308013}