Add initialization coverage distribution matching

1 files changed, 13 insertions, 0 deletions

diff --git a/notes/03_paper_outline.md b/notes/03_paper_outline.md
index 328871f..6055722 100644
--- a/notes/03_paper_outline.md
+++ b/notes/03_paper_outline.md
@@ -128,6 +128,19 @@ Prior-aware corollary:
 \operatorname{tr}(\Sigma_A M_\mu).
 \]
 
+Distributional validation target:
+
+\[
+A(a)=a^\top M_\mu a
+=
+\frac{\sum_i \lambda_i G_i}{\sum_i G_i},
+\qquad
+G_i\sim\chi^2_1.
+\]
+
+Use this to compare predicted target-coverage distributions for isotropic,
+subspace, axis, and anisotropic feedback initializations.
+
 ## 7. Trajectory Bridge
 
 Introduce local approximation: