diff --git a/Paper.tex b/Paper.tex
index 139debb3..92f83fd3 100644
--- a/Paper.tex
+++ b/Paper.tex
@@ -239,7 +239,7 @@ \subsection{The Transaction} \label{ch:transaction}
 \item[gasLimit] A scalar value equal to the maximum amount of gas that should be used in executing this transaction. This is paid up-front, before any computation is done and may not be increased later; formally $T_g$.
 \item[to] The 160-bit address of the message call's recipient or, for a contract creation transaction, $\varnothing$, used here to denote the only member of $\mathbb{B}_0$ ; formally $T_t$.
 \item[value] A scalar value equal to the number of Wei to be transferred to the message call's recipient or, in the case of contract creation, as an endowment to the newly created account; formally $T_v$.
-\item[v, r, s] Values corresponding to the signature of the transaction and used to determine the sender of the transaction; formally $T_w$, $T_r$ and $T_s$. This is expanded in Appendix \ref{app:signing}.
+\item[w, r, s] Values corresponding to the signature of the transaction and used to determine the sender of the transaction; formally $T_w$, $T_r$ and $T_s$. This is expanded in Appendix \ref{app:signing}.
 \end{description}
 
 Additionally, a contract creation transaction contains:
@@ -760,7 +760,7 @@ \section{Message Call} \label{ch:call}
 \boldsymbol{\sigma} & \text{if} \quad \boldsymbol{\sigma}^{**} = \varnothing \\
 \boldsymbol{\sigma}^{**} & \text{otherwise}
 \end{cases} \\
-(\boldsymbol{\sigma}^{**}, g', \mathbf{s}, \mathbf{o}) & \equiv & \begin{cases}
+\qquad (\boldsymbol{\sigma}^{**}, g', A, \mathbf{o}) & \equiv & \begin{cases}
 \Xi_{\mathtt{ECREC}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 1 \\
 \Xi_{\mathtt{SHA256}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 2 \\
 \Xi_{\mathtt{RIP160}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 3 \\
@@ -843,9 +843,9 @@ \subsection{Execution Environment}
 \item $I_e$, the depth of the present message-call or contract-creation (i.e. the number of {\small CALL}s or {\small CREATE}s being executed at present).
 \end{itemize}
 
-The execution model defines the function $\Xi$, which can compute the resultant state $\boldsymbol{\sigma}'$, the remaining gas $g'$, the suicide list $\mathbf{s}$, the log series $\mathbf{l}$, the refunds $r$ and the resultant output, $\mathbf{o}$, given these definitions:
+The execution model defines the function $\Xi$, which can compute the resultant state $\boldsymbol{\sigma}'$, the remaining gas $g'$, the transaction substate $A$, and the resultant output $\mathbf{o}$, given these definitions:
 \begin{equation}
-(\boldsymbol{\sigma}', g', \mathbf{s}, \mathbf{l}, r, \mathbf{o}) \equiv \Xi(\boldsymbol{\sigma}, g, I)
+(\boldsymbol{\sigma}', g', A, \mathbf{o}) \equiv \Xi(\boldsymbol{\sigma}, g, I)
 \end{equation}
 
 \subsection{Execution Overview}
@@ -953,7 +953,7 @@ \subsection{The Execution Cycle}
 
 Stack items are added or removed from the left-most, lower-indexed portion of the series; all other items remain unchanged:
 \begin{eqnarray}
-O\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I)\big) & \equiv & (\boldsymbol{\sigma}', \boldsymbol{\mu}', A', I) \\
+O\big(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I\big) & \equiv & (\boldsymbol{\sigma}', \boldsymbol{\mu}', A', I) \\
 \Delta & \equiv & \mathbf{\alpha}_w - \mathbf{\delta}_w \\
 \lVert\boldsymbol{\mu}'_\mathbf{s}\rVert & \equiv & \lVert\boldsymbol{\mu}_\mathbf{s}\rVert + \Delta \\
 \quad \forall x \in [\mathbf{\alpha}_w, \lVert\boldsymbol{\mu}'_\mathbf{s}\rVert): \boldsymbol{\mu}'_\mathbf{s}[x] & \equiv & \boldsymbol{\mu}_\mathbf{s}[x+\Delta]