Add functional capacity overlap simulation

1 files changed, 27 insertions, 0 deletions

diff --git a/scripts/README.md b/scripts/README.md
index 94f9fff..f24c117 100644
--- a/scripts/README.md
+++ b/scripts/README.md
@@ -84,3 +84,30 @@ The prior-free minimax theorem says:
 \]
 
 with equality for isotropic feedback. Outputs are written under `outputs/minimax_initialization/`.
+
+## Functional Capacity Overlap
+
+Run:
+
+```bash
+python scripts/functional_capacity_overlap.py --parameters 96 --task-rank 24 --constraint-ranks 0 24 48 72 84 96 --trials 100 --seed 5 --plot
+```
+
+This samples a task-sensitive subspace \(S\) of dimension \(d\) and an alignment
+constraint subspace \(E\) of dimension \(k\) inside \(\mathbb R^P\). It validates:
+
+\[
+\Delta d_{\mathrm{hard}}
+=
+\max(0,k-(P-d))
+\]
+
+and:
+
+\[
+\mathbb E[\operatorname{tr}(P_E P_S)]
+=
+\frac{kd}{P}.
+\]
+
+Outputs are written under `outputs/functional_capacity_overlap/`.