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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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