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Clarify dependency of H on h in BLOCKHASH instruction #298

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5 changes: 2 additions & 3 deletions Paper.tex
Original file line number Diff line number Diff line change
Expand Up @@ -2052,9 +2052,8 @@ \subsection{Instruction Set}
&&&& where $P$ is the hash of a block of a particular number, up to a maximum age.\\
&&&& 0 is left on the stack if the looked for block number is greater than the current block number \\
&&&& or more than 256 blocks behind the current block. \\
&&&& $P(h, n, a) \equiv \begin{cases} 0 & \text{if} \quad n > H_{\mathrm{i}} \vee a = 256 \vee h = 0 \\ h & \text{if} \quad n = H_{\mathrm{i}} \\ P(H_{\mathrm{p}}, n, a + 1) & \text{otherwise} \end{cases}$ \\
&&&& and we assert the header $H$ can be determined as its hash is the parent hash \\
&&&& in the block following it. \\
&&&& $P(h, n, a) \equiv \begin{cases} 0 & \text{if} \quad n > H(h)_{\mathrm{i}} \vee a = 256 \vee h = 0 \\ h & \text{if} \quad n = H(h)_{\mathrm{i}} \\ P(H(h)_{\mathrm{p}}, n, a + 1) & \text{otherwise} \end{cases}$ \\
&&&& and we assert the header $H(h)$ can be determined from its hash~$h$ unless $h$ is zero. \\
\midrule
0x41 & {\small COINBASE} & 0 & 1 & Get the block's beneficiary address. \\
&&&& $\boldsymbol{\mu}'_{\mathbf{s}}[0] \equiv {I_{H}}_{\mathrm{c}}$ \\
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