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+# Natural data under the Tier 0 recipe
+
+Run date: 2026-08-01
+
+## Question
+
+The synthetic world showed the machinery works end to end when the
+representations are good enough: 95% blind recovery, 93% transfer to
+scenes the matcher never saw. It could not show that natural data admits
+such representations. This ports the recipe to Visual Genome and measures
+the one statistic that decides whether to attempt recovery -- the
+cross-modal field correlation, which the phase diagram puts at roughly
+0.9 for polynomial matching.
+
+## Protocol
+
+Vision: DINOv2 patch features, segments from spectral clustering of the
+patch affinity graph with a spatial prior, one state per segment. No
+boxes, no labels, no text. Language: word classes and word vectors from
+positive-PMI context statistics of the 80,000 region descriptions, one
+state per phrase. Scene states are the resulting sets; relations are
+moment-kernel similarities. Annotated boxes appear only as a diagnostic
+oracle, never in the reported pipeline.
+
+## Text-side factor discovery transfers, but not the heuristic
+
+The synthetic pipeline found factor families by mutual exclusivity, since
+templated phrases carry exactly one colour word. Real language refutes
+that: colour terms are independent or better, with observed-over-expected
+co-occurrence 1.29 for black with white and 0.93 for red with blue, while
+head nouns are the genuinely exclusive family at 0.14 for car with truck.
+Run unchanged, the method returns clean noun classes and no attributes.
+
+Standard distributional word-class induction, of which exclusivity is a
+degenerate case, does transfer. Positive PMI, truncated SVD, and k-means
+over the 300 most frequent words give a colour family at 0.67 purity plus
+coherent vehicle, animal, clothing, person, and water-scene classes.
+Colour terms split into three clusters rather than one, structurally
+rather than noisily: white and blue sit with sky and clouds, because what
+a colour word modifies shapes its distribution.
+
+## What moves the field correlation
+
+| Configuration | rho |
+|---|---:|
+| Hard class codes, six segments | 0.166 |
+| Hard class codes, sixteen segments | 0.136 |
+| Continuous states, unsupervised segments | 0.489 |
+| Continuous states, oracle region boxes | 0.550 |
+| Continuous states plus content projection, unsupervised | **0.656** |
+
+The reported figure is what `worldalign.natural_pipeline` produces; an
+earlier exploratory script reached 0.664 with a wider projection-fitting
+range, and the reproducible module is cited in preference.
+| Continuous states plus content projection, oracle boxes | 0.671 |
+
+Three findings, in order of how much they overturned expectations.
+
+**Discretisation was the dominant loss.** Quantising segments and phrases
+into class codes cost more than half the signal (0.166 against 0.489).
+Relation fields need only scene-to-scene similarity, so compressing
+states into discrete classes first is pure attrition. The synthetic world
+hid this because its states are discrete by construction.
+
+**Segmentation is not the bottleneck here.** Oracle region boxes buy
+0.061 over unsupervised spectral segmentation, so the unsupervised
+segmenter captures 89% of what perfect boxes would give -- the exact
+inverse of the synthetic world, where segmentation was the entire gap.
+Flat untextured scenes are adversarial for object discovery in a way that
+photographs are not, so the synthetic measurement overstated this
+problem.
+
+**Content projection is again the largest lever.** Whitening the
+within-scene direction and keeping the eight leading between-scene
+directions lifts 0.489 to 0.656, matching its role in the earlier
+node-level battery where it took VG from 0.21 to 0.61. The protocol-legal
+configuration and the oracle-box configuration land within 0.007 of each
+other, which says the remaining deficit is not about where the objects
+are.
+
+A control worth recording: frozen general-purpose encoders do worse than
+corpus-fitted statistics. DINOv2-small CLS features of isolated region
+crops against Qwen mean-pooled phrase states reach only 0.19 in the same
+set-moment fields. In-context patch features beat isolated crops, and
+PPMI vectors fitted to this corpus beat a general language model's
+states, echoing the earlier finding that what the model layer shares is
+the mixed state rather than the isolated encoding.
+
+## Verdict
+
+The go/no-go statistic stands at 0.656 against the 0.9 that polynomial
+recovery needs, so no recovery run is warranted. The trajectory in one
+session is 0.166 to 0.656, and the remaining gap is now attributable:
+not discretisation, which is removed, and not segmentation, which costs
+0.06. What is left is the shared structure between self-supervised visual
+features and distributional language statistics at the level of single
+regions.
+
+The levers that have not been tried on natural data are the ones the
+synthetic world showed to matter most after segmentation: observation
+orbits, which VG lacks because each scene has one photograph, and richer
+per-region descriptors. Multi-view natural data -- video frames, product
+photographs, or augmentation-derived orbits -- is the next protocol
+requirement, and the synthetic result that two-sided multi-view
+observation is necessary now has a natural-data counterpart to test.
+
+## Main artifacts
+
+- `artifacts/vg_5k/natural_families{,_dist}.json`
+- `artifacts/vg_5k/natural_objects{,_16,_oracle}.pt`
+- `artifacts/vg_5k/natural_fields{,_16}.pt`