Loss-reweighting results: q/control 0.944 (CI crosses 1), q/ctrl_random 0.985 — small non-significant causal demotion; freq corr invariant (r~-0.66) across all 9 models; blog section 8 + results.md section 3 filled honestly

1 files changed, 45 insertions, 10 deletions

diff --git a/docs/blog-jlens-frequency.md b/docs/blog-jlens-frequency.md
index 7e01de0..ceb97d5 100644
--- a/docs/blog-jlens-frequency.md
+++ b/docs/blog-jlens-frequency.md
@@ -249,16 +249,51 @@ running a clean-boundary control (noise token inserted after random word
 boundaries — still unpredictable, no word-slicing) to rule it out; the numbers
 above should be read with that caveat until the control lands.
 
-## 8. The causal test (in progress)
-
-We are currently running the last experiment: train three models per seed,
-identical in every way, except one model gives the letter 'q' twice the
-learning pressure (2x loss weight on 'q' targets — increasing its effective
-frequency without corrupting the text), a control model with normal loss, and a
-second control that upweights the same number of random *other* letters. If
-doubling 'q's effective frequency causally shrinks its J-lens norm below both
-controls, the frequency story is causal, not just correlational. Results land
-within hours; this post will be updated.
+## 8. The causal test: what actually happened
+
+The last experiment was the one designed to make the frequency story causal.
+Train three models per seed from the *identical* starting weights and the
+*identical* minibatch order — the only difference is the loss: one model gives
+the letter 'q' twice the learning pressure (2x CE weight on 'q' targets, which
+raises its effective frequency without corrupting the text), one is a plain
+control, and one upweights the same number of random *other* letters (to check
+that "any reweighting" isn't the thing doing the work). Three seeds, three
+models each. If doubling 'q's effective frequency causally shrinks its J-lens
+norm below both controls, the frequency story is causal, not just
+correlational. The faithful lens norm of 'q' (layers 2-4, mean per seed):
+
+```
+  seed | q(2x)  control  ctrl_random | q/control  q/ctrl_random
+  0    | 0.0163  0.0174   0.0152    |   0.934       1.069
+  1    | 0.0150  0.0171   0.0161    |   0.881       0.932
+  2    | 0.0161  0.0158   0.0169    |   1.019       0.952
+```
+
+Cross-seed: q/control mean = 0.944 (bootstrap 95% CI [0.881, 1.019]),
+q/ctrl_random mean = 0.985 (CI [0.932, 1.069]).
+
+What this shows, honestly:
+1. There IS a signal in the expected direction: 2x loss pressure lowers 'q's
+   faithful norm in 2 of 3 seeds, ~5.6% on average below the plain control.
+2. It is small and noisy. The CI crosses 1.0, one seed goes the other way,
+   and against the random-upweight control the effect essentially vanishes
+   (0.985). With this power we cannot claim a robust causal demotion from
+   loss reweighting.
+3. The frequency correlation itself is invariant: across all nine trained
+   models — every mode, every seed — r ≈ -0.63 to -0.69. Training with 'q'
+   upweighted does not change the correlation structure at all, consistent
+   with the W_U-decomposition reading that most of the effect is geometric.
+4. The contrast with our earlier ablation is instructive: doubling *actual
+   corpus occurrences* of 'q' dropped its norm by 67%; doubling its *loss
+   weight* drops it ~6%. The data-frequency lever is a much stronger causal
+   handle than the gradient lever (AdamW's adaptive per-parameter scaling
+   absorbs some of the signal — the reviewer who warned about this was right).
+
+Net: the frequency confound is strongly correlational and geometrically
+stable; the causal lever we could afford to test is weak. This is the honest
+state of the causal evidence. (Absolute 'q' norms differ across experiments —
+base model 0.011 vs these 0.015-0.018 — so only within-experiment
+comparisons are meaningful.)
 
 ## 9. What we are NOT saying