diff --git a/equivariant_jiang_su_stability_v2.txt b/equivariant_jiang_su_stability_v2.txt
index 6a8814e..7c9c1f1 100644
--- a/equivariant_jiang_su_stability_v2.txt
+++ b/equivariant_jiang_su_stability_v2.txt
@@ -46,15 +46,19 @@ very weak comparison.
 
 ./szabo-1904.10897-equivariant-property-si.pdf
 
-Szabo and Wouters prove that an action has equivariant uniform property
-Gamma exactly when it is equivariantly Jiang-Su stable, for amenable
-groups on separable unital simple nuclear Jiang-Su stable algebras. That
-equivalence supplies the final absorption step; it remains to construct
-the required invariant central trace splittings uniformly over the whole
-trace space, even when the action moves traces.
+The decisive criterion reads:
+
+Corollary C (Szabo and Wouters). Let $\alpha : G \curvearrowright A$ be
+an action of a countable amenable group on a separable unital simple
+nuclear $Z$-stable C*-algebra. Then $\alpha$ has equivariant uniform
+property Gamma if and only if $\alpha$ is equivariantly Jiang-Su stable.
 
 ./szabo-wouters-2301.12846-equivariant-property-gamma.pdf
 
+The forward implication is the absorption step; it remains to construct
+the required invariant central trace splittings uniformly over the whole
+trace space, even when the action moves traces.
+
 For a unital C*-algebra $B$ and $\tau \in \mathcal T(B)$ write
 $\|x\|_{2,\tau} = \tau(x^*x)^{1/2}$ and
 $\|x\|_{2,u} = \sup_{\tau \in \mathcal T(B)} \|x\|_{2,\tau}$. Under the
@@ -67,6 +71,9 @@ unit.
 
 ./haagerup-1403.7653-quasitraces-are-traces.pdf
 
+Theorem 5.11 (Haagerup). Quasitraces on exact unital C*-algebras are traces.
+Corollary 5.12 (Haagerup). Every stably finite unital exact C*-algebra has a trace state.
+
 Fix a free ultrafilter $\omega$ on the positive integers and form the
 uniform tracial ultrapower