Polish per review: results.md GPT-2 -0.18 demoted to do-not-cite footnote; blog section 10 adds W_U-at-init scale prediction (one-line GPT-2 unembedding check)

2 files changed, 12 insertions, 4 deletions

diff --git a/docs/blog-jlens-frequency.md b/docs/blog-jlens-frequency.md
index dec1edf..8ab2e46 100644
--- a/docs/blog-jlens-frequency.md
+++ b/docs/blog-jlens-frequency.md
@@ -385,6 +385,12 @@ regime where Anthropic's claims live) with proper statistical power, and to run
 the occupancy test their capacity claim is actually about. That's the next
 post.
 
+The learned-geometry finding makes one piece of that cheap and decisive: if
+the W_U row-norm anti-correlation is a general property of softmax-output
+models trained on Zipfian data, it should appear in GPT-2's unembedding matrix
+directly — no Jacobian computation at all. One line of code at scale, and it
+either generalizes or it doesn't.
+
 ## 11. How to reproduce everything
 
 All code, data-prep scripts, experiment scripts, tests, and this analysis live
diff --git a/results.md b/results.md
index 692ce03..7acbc56 100644
--- a/results.md
+++ b/results.md
@@ -186,7 +186,9 @@ Reading:
 
 - Original proxy finding (r = -0.65, `jlens_v2`): superseded by the faithful
   implementation; kept only for the both-ways comparison.
-- GPT-2 correlation (r = -0.18, `gpt2_jlens.py`): UNDER-POWERED (96 token
-  positions, n=100 sampled tokens) and computed a different quantity
-  (norm-per-batch vs norm-of-mean). Directionally consistent but not
-  publishable evidence on its own.
+- GPT-2 correlation: an early directional probe on GPT-2 small
+  (`gpt2_jlens.py`) gave avg r = -0.18 across layers — UNDER-POWERED
+  (96 token positions, n=100 sampled tokens) and a different quantity
+  (norm-per-batch vs norm-of-mean). Kept here only as a reproducibility
+  warning: **do not cite the -0.18 as evidence**; the at-scale test with the
+  faithful lens is future work.