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Correct minor inconsistency in output representation of PoW #715

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6 changes: 3 additions & 3 deletions Paper.tex
Original file line number Diff line number Diff line change
Expand Up @@ -525,7 +525,7 @@ \subsubsection{Block Header Validity}
\begin{equation}
n \leqslant \frac{2^{256}}{H_{\mathrm{d}}} \quad \wedge \quad m = H_{\mathrm{m}}
\end{equation}
with $(n, m) = \mathtt{PoW}(H_{\hcancel{n}}, H_{\mathrm{n}}, \mathbf{d})$.
with $(m, n) = \mathtt{PoW}(H_{\hcancel{n}}, H_{\mathrm{n}}, \mathbf{d})$.

\hypertarget{block_header_without_nonce_and_mixmash_h__cancel_n}{}\linkdest{H_cancel_n}Where $H_{\hcancel{n}}$ is the new block's header $H$, but \textit{without} the nonce and mix-hash components, $\mathbf{d}$ being the current DAG, a large data set needed to compute the mix-hash, and $\mathtt{PoW}$ is the proof-of-work function (see section \ref{ch:pow}): this evaluates to an array with the first item being the mix-hash, to prove that a correct DAG has been used, and the second item being a pseudo-random number cryptographically dependent on $H$ and $\mathbf{d}$. Given an approximately uniform distribution in the range $[0, 2^{64})$, the expected time to find a solution is proportional to the difficulty, $H_{\mathrm{d}}$.

Expand All @@ -543,7 +543,7 @@ \subsubsection{Block Header Validity}
\nonumber& & H_{\mathrm{i}} = {P(H)_{H}}_{\mathrm{i}} +1 \quad \wedge \\
\nonumber& & \lVert H_{\mathrm{x}} \rVert \le 32
\end{eqnarray}
where $(n, m) = \mathtt{PoW}(H_{\hcancel{n}}, H_{\mathrm{n}}, \mathbf{d})$
where $(m, n) = \mathtt{PoW}(H_{\hcancel{n}}, H_{\mathrm{n}}, \mathbf{d})$

Noting additionally that \textbf{extraData} must be at most 32 bytes.

Expand Down Expand Up @@ -1166,7 +1166,7 @@ \subsection{State \& Nonce Validation}\label{sec:statenoncevalidation}
\begin{eqnarray}
\Phi(B) & \equiv & B': \quad B' = B^* \quad \text{except:} \\
B'_{\mathrm{n}} & = & n: \quad x \leqslant \frac{2^{256}}{\hyperlink{H__d}{H_{\mathrm{d}}}} \\
B'_{\mathrm{m}} & = & m \quad \text{with } (x, m) = \mathtt{PoW}(B^*_{\hyperlink{H_cancel_n}{\hcancel{n}}}, n, \mathbf{d}) \\
B'_{\mathrm{m}} & = & m \quad \text{with } (m, x) = \mathtt{PoW}(B^*_{\hyperlink{H_cancel_n}{\hcancel{n}}}, n, \mathbf{d}) \\
B^* & \equiv & B \quad \text{except:} \quad {\hyperlink{Transaction Receipt}{B^*_{\mathrm{r}}}} = \hyperlink{r}{r}(\hyperlink{Pi}{\Pi}(\Gamma(B), B))
\end{eqnarray}

Expand Down