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The user-facing statement still carried the retired correlation
threshold. Adds the correction, the joint condition that replaces it,
the width diagnosis, and the closure of the shrink-N route.
Co-Authored-By: Claude <noreply@anthropic.com>
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Four tests around today's additions. Two failed on first run and both
were worth having.
The degree decomposition left an O(1/n) residual on a field that is
purely additive: excluding the diagonal makes the two-way design
unbalanced, so one pass of row and column means does not remove a pure
degree effect. Swept to convergence instead. At N=256 the correction
moves the reported variance shares by under 0.001, so the refutation of
the hubness hypothesis stands unchanged -- but the instrument that
produced it now does what it claims.
The other failure was the test's own scale: two random 16-dimensional
subspaces of R^64 overlap above 0.7 by chance, which is why the real
measurements are made at N=256 where the null sits at 1.0.
Co-Authored-By: Claude <noreply@anthropic.com>
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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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Four random resized crops per Visual Genome image, segmented
independently with their fields averaged, leave the correlation at
0.6559. Closed-world re-renders resample layout, which is nuisance by
construction, so averaging removes modality-private variation; random
crops perturb framing that self-supervised patch features already
absorb, leaving nothing to cancel.
Co-Authored-By: Claude <noreply@anthropic.com>
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identifiability
Method: scene states are sets of part states; relation fields are built
within each modality and are invariant to how each side labels its own
features; the cross-modal bridge is a coupling searched under an energy
that is a closed-form functional of one matrix; solving is spectral
initialisation followed by exact local refinement.
Evidence: in a procedurally generated closed world, blind recovery of a
hidden image-caption correspondence reaches 95.3% at 256 scenes against
0.39% chance, and the recovered pairs transfer to 200 held-out scenes at
93.0% exact retrieval with random-pair and shuffled-image controls at or
near chance. Cross-modal value correspondence is derived from disjoint
corpora rather than declared. On Visual Genome the field correlation
reaches 0.656 against the 0.9 that polynomial recovery needs, with the
deficit attributed away from segmentation and discretisation.
Protocol: no image-text pair enters any objective, optimiser,
initialisation, or model selection; hidden pairs score orderings only.
Co-Authored-By: Claude <noreply@anthropic.com>
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