Add spaces

Paper.tex

@@ -1404,7 +1404,7 @@ \section{Signing Transactions}\label{app:signing}
 \mathtt{\small ECDSARECOVER}(e \in \mathbb{B}_{32}, v \in \mathbb{B}_{1}, r \in \mathbb{B}_{32}, s \in \mathbb{B}_{32}) & \equiv & p_u \in \mathbb{B}_{64}
 \end{eqnarray}
 
-Where $p_u$ is the public key, assumed to be a byte array of size 64 (formed from the concatenation of two positive integers each $< 2^{256}$) and $p_r$ is the private key, a byte array of size 32 (or a single positive integer in the aforementioned range). It is assumed that $v$ is either the `recovery identifier' or `chain identifier doubled plus 35 or 36'. The recovery identifier is a 1 byte value specifying the sign and finiteness of the curve point; this value is in the range of $[27, 30]$, however we declare the upper two possibilities, representing infinite values, invalid. The chain identifier is a constant natural number.
+Where $p_u$ is the public key, assumed to be a byte array of size 64 (formed from the concatenation of two positive integers each $< 2^{256}$) and $p_r$ is the private key, a byte array of size 32 (or a single positive integer in the aforementioned range). It is assumed that $v$ is either the `recovery identifier' or `chain identifier doubled plus 35 or 36'. The recovery identifier is a 1 byte value specifying the sign and finiteness of the curve point; this value is in the range of $[27, 30]$, however we declare the upper two possibilities, representing infinite values, invalid. The chain identifier $\mathtt{\tiny chain\_id}$ is a constant natural number.
 
 \newcommand{\slimit}{\ensuremath{\text{s-limit}}}
 
@@ -1428,8 +1428,8 @@ \section{Signing Transactions}\label{app:signing}
 The message hash, $h(T)$, to be signed is the Keccak hash of the transaction. Two different flavors of signing schemes are available. One operates without the latter three signature components, formally described as $T_r$, $T_s$ and $T_w$. The other operates on nine elements:
 \begin{eqnarray}
 L_S(T) & \equiv & \begin{cases}
-(T_n, T_p, T_g, T_t, T_v, \mathbf{p}) & \text{if} \; v \in \{27, 28\}\\
-(T_n, T_p, T_g, T_t, T_v, \mathbf{p}, \mathtt{\tiny chain\_id}, (), ()) & \text{otherwise}\\
+(T_n, T_p, T_g, T_t, T_v, \mathbf{p}) & \text{if} \; v \in \{27, 28\} \\
+(T_n, T_p, T_g, T_t, T_v, \mathbf{p}, \mathtt{\tiny chain\_id}, (), ()) & \text{otherwise} \\
 \end{cases} \\
 \nonumber \text{where} \\
 \nonumber \mathbf{p} & \equiv & \begin{cases}