diff --git a/docs/PSH_STATUS.md b/docs/PSH_STATUS.md
index d4ff0a5..7dad969 100644
--- a/docs/PSH_STATUS.md
+++ b/docs/PSH_STATUS.md
@@ -1,3 +1,4 @@
-PSH is used only in rank-bounded form PSH_{k,Δ,r}.
-Rank-bounded only: PSH_{k,\Delta,r}. No unbounded-round pebble game, no full FO^k, no global k-WL stabilization.
-is assumed anywhere in this repository.
+PSH is used only in rank-bounded form PSH_{k,Δ,r} (r-round k-pebble / FO^k rank ≤ r).
+No unbounded-round pebble game, no full FO^k, and no global k-WL stabilization is assumed.
+
+