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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>
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A rank-truncation ladder from four to full rank returns chance accuracy
at the natural-data correlation of 0.656, as does full-rank spectral
initialisation with refinement. Coarse-to-sharp smoothing widens basins
and thins decoys, and recovers nothing, so below the polynomial
threshold the deficit is information the algorithm class cannot use
rather than a basin it cannot find. Solver-side candidates should wait
on the correlation instead of competing with it.
Co-Authored-By: Claude <noreply@anthropic.com>
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The natural-data obstruction decomposes into field correlation, landscape
shape, search strength, problem size, and orthogonal signal, and every
candidate attacks exactly one. Records what is measured, what is running,
and what is specified but unstarted, so branches can be eliminated in
cost order rather than by preference.
Co-Authored-By: Claude <noreply@anthropic.com>
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