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@@ -118,6 +118,37 @@ directions and then stops. Enlarging the scene population does not help either
 scenes, so the ceiling is a property of what the two corpora are about rather
 than of how many scenes are sampled.
 
+## Corpus overlap sets the width, by intervention
+
+The invariance results say the width does not come from the encoders. A
+controlled intervention says where it does come from. In the synthetic world
+the caption is encoded into separate factor blocks, so a block can be
+suppressed — the caption then never states that property while vision
+continues to see it. Nothing else changes: same images, same segmentation,
+same kernel.
+
+| Caption content | ρ | shared | recovery |
+|---|---|---|---|
+| states everything | 0.928 | 20 | **96.4%** |
+| never states size | 0.830 | 15 | **5.6%** |
+
+Deleting one word class costs five shared directions and the entire result.
+The correlation is still 0.830 — higher than anything we have achieved on
+photographs — and recovery is at chance. **The synthetic world degraded to
+Visual Genome's shared width fails exactly the way Visual Genome fails**, at a
+correlation Visual Genome never reaches.
+
+This closes the causal chain. How much of the same world the two corpora
+describe sets the width of the shared spectrum; the width sets recovery; and
+the correlation reports on neither reliably. It also reframes the natural-data
+deficit as a statement about Visual Genome rather than about our pipeline: a
+region description simply does not say as much about a photograph as the
+synthetic captions say about their scenes.
+
+(Widths in this table are computed on standardised fields and are not
+comparable entry-for-entry with the tables above, which use raw fields; within
+the table the convention is identical, which is what the comparison needs.)
+
 ## Two smaller results, one refuted hypothesis
 
 **The projection improved.** Scaling each discriminant direction by its own