Add MNIST real-data validation of e0 theorem and estimator

New script validates both no-fit claims on MNIST-subset MLPs. e0
theorem: 16 configs, hidden share 0.39-0.82, measured E_B[e0] within
0.0001-0.0089 of prediction (512 real-backward draws each). Estimator:
96 trajectories, velocity MAE 0.00196 (3.9% of mean gap), bias -0.0006,
beating fixed K(0) everywhere; kernels computed via a layerwise gram
identity self-tested against autograd at machine precision.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

1 files changed, 7 insertions, 2 deletions

diff --git a/notes/36_evidence_ledger.md b/notes/36_evidence_ledger.md
index 63e797d..14af7df 100644
--- a/notes/36_evidence_ledger.md
+++ b/notes/36_evidence_ledger.md
@@ -100,8 +100,13 @@ standard lazy approximation whose breakdown is *measured* (item 3c below).
    overprediction (+0.0026), FA near-unbiased (+0.0005); cause: drift velocity
    decays after s (alpha_t < t/s; e.g. true alpha_50 = 1.46 (BP) / 1.17 (FA)
    vs linear 2.5). Honest error story, no fitted correction.
-5. **MNIST replication (note 38)**: same protocol, width 256, depth 2,
-   N in {128,256,512}, 48 traj: see `real_data_validation_mnist/`.
+5. **MNIST replication (note 38)**: same protocol, widths {128,256} x
+   N {128,256,512} x 2 inits x 8 feedbacks = 96 traj, lazy step
+   (`eta lam_max/N = 0.05`): velocity MAE **0.00196** (= 3.9% of mean gap),
+   bias -0.0006, corr 0.911 (gap range only 0.040-0.063, so MAE/bias are the
+   operative stats); fixed K(0) MAE 0.0061 biased high — same bracket as
+   synthetic. At eta lam_max/N = 0.3 the lazy chain breaks as expected
+   (scope boundary, recorded in note 38).
 
 ### (d) The soft ramp + closed form (T7)