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Add missing forward slashes before mathbfs
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jamesray1 authored Jan 30, 2018
1 parent 5b60d75 commit 34b9991
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions Paper.tex
Original file line number Diff line number Diff line change
Expand Up @@ -1108,7 +1108,7 @@ \subsection{Reward Application}
\\ \nonumber
\Omega(B, \boldsymbol{\sigma}) & \equiv & \boldsymbol{\sigma}': \boldsymbol{\sigma}' = \boldsymbol{\sigma} \quad \text{except:} \\
\qquad\boldsymbol{\sigma}'[{B_H}_c]_b & = & \boldsymbol{\sigma}[{B_H}_c]_b + (1 + \frac{\lVert B_\mathbf{U}\rVert}{32})R_b \\
\qquad\forall_{mathbf{U} \in B_\mathbf{U}}: \\ \nonumber
\qquad\forall_{\mathbf{U} \in B_{\mathbf{U}}}: \\ \nonumber
\boldsymbol{\sigma}'[U_c] & = & \begin{cases}
\varnothing &\text{if}\ \boldsymbol{\sigma}[U_c] = \varnothing\ \wedge\ R = 0 \\
\mathbf{a}' &\text{otherwise}
Expand Down Expand Up @@ -1383,7 +1383,7 @@ \section{Modified Merkle Patricia Tree}\label{app:trie}

When considering such a sequence, we use the common numeric subscript notation to refer to a tuple's key or value, thus:
\begin{equation}
\forall_{mathbf{I} \in \mathfrak{I}} I \equiv (I_0, I_1)
\forall_{\mathbf{I} \in \mathfrak{I}} I \equiv (I_0, I_1)
\end{equation}

Any series of bytes may also trivially be viewed as a series of nibbles, given an endian-specific notation; here we assume big-endian. Thus:
Expand Down Expand Up @@ -1421,7 +1421,7 @@ \section{Modified Merkle Patricia Tree}\label{app:trie}
\begin{equation}
c(\mathfrak{I}, i) \equiv \begin{cases}
\texttt{\small RLP}\Big( \big(\texttt{\small HP}(I_0[i .. (\lVert I_0\rVert - 1)], true), I_1 \big) \Big) & \text{if} \quad \lVert \mathfrak{I} \rVert = 1 \quad \text{where} \; \exists I: I \in \mathfrak{I} \\
\texttt{\small RLP}\Big( \big(\texttt{\small HP}(I_0[i .. (j - 1)], false), n(\mathfrak{I}, j) \big) \Big) & \text{if} \quad i \ne j \quad \text{where} \; j = \arg \max_x : \exists \mathbf{l}: \lVert \mathbf{l} \rVert = x : \forall_{mathbf{I} \in \mathfrak{I}}: I_0[0 .. (x - 1)] = \mathbf{l} \\
\texttt{\small RLP}\Big( \big(\texttt{\small HP}(I_0[i .. (j - 1)], false), n(\mathfrak{I}, j) \big) \Big) & \text{if} \quad i \ne j \quad \text{where} \; j = \arg \max_x : \exists \mathbf{l}: \lVert \mathbf{l} \rVert = x : \forall_{\mathbf{I} \in \mathfrak{I}}: I_0[0 .. (x - 1)] = \mathbf{l} \\
\texttt{\small RLP}\Big( (u(0), u(1), ..., u(15), v) \Big) & \text{otherwise} \quad \text{where} \begin{array}[t]{rcl}
u(j) & \equiv & n(\{ I : I \in \mathfrak{I} \wedge I_0[i] = j \}, i + 1) \\
v & = & \begin{cases}
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