diff --git a/Paper.tex b/Paper.tex
index 1948eb98..903961ac 100644
--- a/Paper.tex
+++ b/Paper.tex
@@ -854,8 +854,8 @@ \subsection{Execution Overview}
 \end{eqnarray}
 \begin{equation}
 X\big( (\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \big) \equiv \begin{cases}
-\big(\varnothing, \boldsymbol{\mu}, A^0, I, ()\big) & \text{if} \quad Z(\boldsymbol{\sigma}, \boldsymbol{\mu}, I)\\
-O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \cdot \mathbf{o} & \text{if} \quad \mathbf{o} \neq \varnothing\\
+\big(\varnothing, \boldsymbol{\mu}_g, A^0, I, ()\big) & \text{if} \quad Z(\boldsymbol{\sigma}, \boldsymbol{\mu}, I)\\
+O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \boxplus \mathbf{o} & \text{if} \quad \mathbf{o} \neq \varnothing\\
 X\big(O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I)\big) & \text{otherwise}\\
 \end{cases}
 \end{equation}
@@ -863,7 +863,7 @@ \subsection{Execution Overview}
 where
 \begin{eqnarray}
 \mathbf{o} & \equiv & H(\boldsymbol{\mu}, I) \\
-(a, b, c) \cdot d & \equiv & (a, b, c, d)
+(a, b, c, d) \boxplus e & \equiv & (a, b_g, c, d, e)
 \end{eqnarray}
 
 Note that we must drop the fourth value in the tuple returned by $X$ to correctly evaluate $\Xi$, hence the subscript $X_{0,1,2,4}$.