Correction, same session: the width statistic does not survive its control

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>

1 files changed, 35 insertions, 21 deletions

diff --git a/EXTENDED_ABSTRACT.md b/EXTENDED_ABSTRACT.md
index 1e96cae..7dec8f8 100644
--- a/EXTENDED_ABSTRACT.md
+++ b/EXTENDED_ABSTRACT.md
@@ -86,11 +86,18 @@ The theory said so in advance and we misread it. Matching thresholds are
 derived for exchangeable full-rank noise, where each of the N²/2 field
 entries constrains the pairing independently; a rank-*r* shared component
 supplies about *rN*, an eighth as many at 256 scenes with *r* near ten.
-The corrected gate is a joint condition on the correlation and on the
-width of the shared spectrum — the number of directions along which the
-two modalities agree, measured by principal angles against a
-scene-shuffled null. Neither alone suffices: 18 shared directions at
-correlation 0.508 fails, and 11 at 0.902 fails.
+
+What replaces the correlation is an open question, and we report two
+failed answers rather than one plausible one. The obvious candidate is
+the width of the shared spectrum, and it does not survive its own
+control: independent noise that lowers the correlation to 0.828 without
+narrowing the underlying signal 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% respectively. A second instrument built to fix that,
+counting canonical directions that generalise to held-out scenes, rates
+the three failing fields at 16.6 to 17.2 and ranks the worst of them
+highest. **What is established is that the correlation is not the
+governing statistic; what is not established is what is.**
 
 ## A closed world settles the mechanism
 
@@ -132,9 +139,9 @@ frequency rankings diverge in the tail.
 
 Ported to Visual Genome under the same recipe — DINOv2 patch features,
 spectral segmentation, distributional word statistics — the field
-correlation reaches 0.716 and the shared spectrum 15 directions, against
-0.928 and 26 for the synthetic world that recovers. The trajectory that
-got there is more informative than either number.
+correlation reaches 0.731 against 0.928 for the synthetic world, and
+blind search returns 0.0000 against a chance rate of 0.0039. The
+trajectory that got there is more informative than the number.
 
 Discretisation cost more than half the signal: hard class codes give
 0.166 where continuous states give 0.489, because fields need only
@@ -149,19 +156,26 @@ underperform corpus-fitted statistics, 0.19 against 0.656, so in-context
 features beat isolated crops and corpus-specific vectors beat a language
 model's pooled states.
 
-The width diagnosis localises the remaining gap somewhere the correlation
-alone never pointed. Both modalities are individually rich on
-photographs — vision effective rank 40, text 48 — and they agree on 15
-directions, so **each side is rich about something and they are rich
-about different things.** That intersection barely moves under anything
-tunable on the vision side: near-tripling the segments costs one shared
-direction, and handing the pipeline annotated boxes instead of
-unsupervised segmentation buys one. The text side moves it from 10 to 17
-and saturates. Enlarging the population does not help either, 23 to 19
-shared directions from 256 to 1024 scenes. The ceiling behaves like a
-property of what the two corpora are about rather than of how either is
-encoded, which makes corpus choice a first-class variable: the closed
-world reaches 26 because its captions state exactly the world state.
+What does localise the gap is an intervention rather than a statistic.
+In the closed world the caption is encoded in separate factor blocks, so
+one can be suppressed — the caption stops stating a property while vision
+still sees it, and nothing else changes. Deleting a single word class
+takes recovery from 96.4% to 5.6% at a correlation of 0.830, higher than
+anything we reach on photographs, and the full ladder is monotone in how
+much the caption states. **Corpus overlap controls recovery**, whatever
+the mediating quantity turns out to be.
+
+Encoder-side changes do not. Five interventions on the vision side —
+near-tripling the segments, substituting annotated boxes for unsupervised
+segmentation, third-order moments in the set kernel, and doubling the
+backbone to DINOv2-large — each raise the vision field's own effective
+rank and leave both the correlation and every width measure where they
+were. The gains that did arrive came from the projection, the text
+vectors and the phrase encoding, and total 0.075 in correlation. This
+makes corpus choice a first-class variable rather than a fallback: a
+region description does not say as much about a photograph as the closed
+world's captions say about their scenes, and no vision encoder repairs
+that.
 
 ## What is not shown