diff --git a/hash_const.tex b/hash_const.tex
index 5a2b023..16ab97f 100644
--- a/hash_const.tex
+++ b/hash_const.tex
@@ -65,7 +65,9 @@ Using the same argument as in $\gIJ$ yields
 \end{equation*}
 Setting $T_3 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 0}\kMapParam{\wVec}$, $T_4 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 1}\kMapParam{\wVec}$ gives an exact calculation for each term given a fixed $\buck$:
 \begin{equation*}
-T_3 = \gVt{(k \cdot)} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(0)}, \kMapParam{\wVec} =  \gVt{(k) }1\}\rightarrow T_3 \in [0, 2^{\numTup - rank(\matrixH')}]
+T_3 = \gVt{\sum_{\substack{k \in \{\wVec \st \\
+				\matrixH \cdot \wVec = \buck^{(0)},\\
+				\kMapParam{\wVec} = k\}}}k} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(0)}, \kMapParam{\wVec} =  \gVt{(k) }1\}\rightarrow T_3 \in [0, 2^{\numTup - rank(\matrixH')}]
 \end{equation*}
 \begin{equation*}
 T_4 = \gVt{(k \cdot)} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(1)}, \kMapParam{\wVec} = \gVt{(k) 1}\}\rightarrow T_4 \in [0, 2^{\numTup - rank(\matrixH')}]