Three statistics failed the same way -- fields agreeing on the number and disagreeing on recovery -- because each was invented by staring at the fields rather than by asking what matching needs. The fourth asks directly: declare half the scenes anchors, hand over their correspondence, describe the rest by their field rows against the anchors, and match one-to-one by Hungarian assignment. Seconds to compute, and it upper-bounds blind recovery because blind recovery must also discover the anchor correspondence. Never violated across six fields spanning the full range of outcomes, and it separates every case the refuted statistics collapsed: synth full bound 0.989 blind 0.958 gap +0.03 synth noise 0.35 bound 0.984 blind 0.947 gap +0.04 synth omit size bound 0.997 blind 0.056 gap +0.94 synth rank 8 bound 0.930 blind 0.129 gap +0.80 Visual Genome bound 0.291 blind 0.000 gap +0.29 This corrects two claims from earlier today. Caption suppression does not destroy information -- its bound is 0.997 -- it destroys blind searchability, by making scenes interchangeable under permutation in a way given anchors break. And Visual Genome's problem was never spectral width: with the correspondence handed over, seven scenes in ten still cannot be identified. Co-Authored-By: Claude <noreply@anthropic.com>
The replacement gate proposed this morning is refuted by a control run this afternoon. Independent noise lowers the correlation to 0.828 without narrowing the underlying signal and reaches the same measured width as a field whose captions omit one factor -- 15.7 against 15.0 -- with recovery at 94.7% and 5.6%. A second instrument built specifically to fix that, counting canonical directions that generalise to held-out scenes, fails the same way and rates Visual Genome highest of the three failing fields. Established: the correlation does not govern recovery, in both directions. Corpus overlap does control it -- the caption-suppression ladder is monotone from 96.4% to 0.0%. Not established: any statistic that predicts recovery cheaply. Documents corrected accordingly rather than quietly rephrased; the refuted claim stood for four hours and is recorded as such. Co-Authored-By: Claude <noreply@anthropic.com>
DINOv2-large, twice the depth of base and wider, leaves the shared count at exactly 15 and moves the correlation by less than the segmentation noise floor. Four vision-side interventions now raise the vision field's own rank and leave the intersection alone. The cheap tier of the register is exhausted. What remains is a corpus chosen for naturally wide overlap, promoted to the central bet, and the unbalanced formulation, promoted to the critical path since such a corpus is unlikely to arrive in bijection. Co-Authored-By: Claude <noreply@anthropic.com>
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>
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>