mirror of https://github.com/zcash/zips.git
Cosmetics.
Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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@ -9039,8 +9039,9 @@ Define:
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\item $\MedianTime(\BlockHeight) := \median(\listcomp{\nTime(i) \for i \from
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\maximum(0, \BlockHeight - \PoWMedianBlockSpan) \upto \BlockHeight - 1})$
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\item $\ActualTimespan(\BlockHeight) := \MedianTime(\BlockHeight) - \MedianTime(\BlockHeight - \PoWAveragingWindow)$
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\item $\ActualTimespanDamped(\BlockHeight) := \\
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\AveragingWindowTimespan\blossom{(\BlockHeight)} + \trunc{\scalebox{0.98}{\hfrac{\ActualTimespan(\BlockHeight) - \AveragingWindowTimespan\blossom{(\BlockHeight)}}{\PoWDampingFactor}}}$
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\item $\ActualTimespanDamped(\BlockHeight) :=$
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\vspace{-0.5ex}
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\item \tab $\AveragingWindowTimespan\blossom{(\BlockHeight)} + \trunc{\scalebox{0.98}{\hfrac{\ActualTimespan(\BlockHeight) - \AveragingWindowTimespan\blossom{(\BlockHeight)}}{\PoWDampingFactor}}}$
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\item $\ActualTimespanBounded(\BlockHeight) := \bound{\MinActualTimespan\blossom{(\BlockHeight)}}{\MaxActualTimespan\blossom{(\BlockHeight)}}(\ActualTimespanDamped(\BlockHeight))$
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\item $\MeanTarget(\BlockHeight) := \begin{cases}
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\PoWLimit, \hspace{16em}\text{if } \BlockHeight \leq \PoWAveragingWindow \\
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@ -9111,20 +9112,24 @@ in its \blockHeader is defined as $\floor{\hfrac{2^{256}}{\ToTarget(\nBits) + 1}
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\crossref{subsidyconcepts} defines the \blockSubsidy, \minerSubsidy,\blossom{ \fundingStreams,} and
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\foundersReward. Their amounts in \zatoshi are calculated from the \blockHeight using
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the formulae below. The constants $\SlowStartInterval$, $\PreBlossomHalvingInterval$,
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\blossom{$\PostBlossomHalvingInterval$, $\BlossomActivationHeight$, }$\MaxBlockSubsidy$,
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and $\FoundersFraction$ are instantiated in \crossref{constants}.
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\blossom{The per-\fundingStream constants $\FundingStreamFraction{i}$, $\FundingStreamStartHeight{i}$,
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the formulae below.\notbeforeblossom{
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}The constants $\SlowStartInterval$, $\MaxBlockSubsidy$, $\FoundersFraction$,\notblossom{ and} $\PreBlossomHalvingInterval$,
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\blossom{$\MaxFundingStreams$, $\PostBlossomHalvingInterval$, and $\BlossomActivationHeight$} are instantiated in \crossref{constants}.
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\blossom{The per \fundingStream constants $\FundingStreamFraction{i}$, $\FundingStreamStartHeight{i}$,
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and $\FundingStreamEndHeight{i}$ are instantiated in \crossref{fundingstreams}.}
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\vspace{1ex}
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\begin{formulae}
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\item $\SlowStartShift \typecolon \Nat := \hfrac{\SlowStartInterval}{2}$
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\item $\SlowStartRate \typecolon \Nat := \hfrac{\MaxBlockSubsidy}{\SlowStartInterval}$
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\vspace{0.5ex}
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\item $\Halving(\BlockHeight) := \notblossom{\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}}}
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\notbeforeblossom{\begin{cases}
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\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}},\hspace{1em}\blossom{\caseif \text{ not } \IsBlossomActivated(\BlockHeight}) \\
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\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}},\hspace{1em}\blossom{\caseif \text{not } \IsBlossomActivated(\BlockHeight)} \\[1.4ex]
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\blossom{\floor{\hfrac{\BlossomActivationHeight - \SlowStartShift}{\PreBlossomHalvingInterval} + \hfrac{\BlockHeight - \BlossomActivationHeight}{\PostBlossomHalvingInterval}},}&\blossom{\caseotherwise}
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\end{cases}}$
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\vspace{0.5ex}
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\item $\BlockSubsidy(\BlockHeight) := \begin{cases}
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\SlowStartRate \mult \BlockHeight,&\caseif \BlockHeight < \hfrac{\SlowStartInterval}{2} \\[1.4ex]
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\SlowStartRate \mult (\BlockHeight + 1),&\caseif \hfrac{\SlowStartInterval}{2} \leq \BlockHeight \\[1.4ex]
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@ -9137,8 +9142,10 @@ and $\FundingStreamEndHeight{i}$ are instantiated in \crossref{fundingstreams}.}
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\end{cases}$
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\blossom {
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\item $\FundingStreamValue{i}(\BlockHeight) := \\[1.4ex]
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\begin{cases}
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\vspace{0.5ex}
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\item $\FundingStreamValue{i}(\BlockHeight) :=$
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\vspace{-0.5ex}
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\item \tab $\begin{cases}
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0,&\caseif \BlockHeight < \BlossomActivationHeight \\
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\floor{\BlockSubsidy(\BlockHeight) \mult \FundingStreamFraction{i}},&\caseif \FundingStreamStartHeight{i} \leq \BlockHeight \\
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&\text{ and } \BlockHeight < \FundingStreamEndHeight{i} \\
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@ -9154,7 +9161,10 @@ and $\FundingStreamEndHeight{i}$ are instantiated in \crossref{fundingstreams}.}
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0,&\caseotherwise
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\end{cases}$
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\item $\MinerSubsidy(\BlockHeight) := \BlockSubsidy(\BlockHeight) - \FoundersReward(\BlockHeight) \blossom{- \sum_{i = 0}^\text{streams} \FundingStreamValue{i}(\BlockHeight)}$.
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\item $\MinerSubsidy(\BlockHeight) :=$
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\vspace{-1.5ex}
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\item \tab $\BlockSubsidy(\BlockHeight) - \FoundersReward(\BlockHeight)
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\blossom{\,- \ssum{i = 1}{\MaxFundingStreams} \FundingStreamValue{i}(\BlockHeight)}$.
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\end{formulae}
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\introsection
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@ -9249,7 +9259,7 @@ Define:
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\end{formulae}
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Let $\RedeemScriptHash(\BlockHeight)$ be the standard redeem script hash, as defined in
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\cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check representation
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\cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check form
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given by $\FounderAddressList_{\,\FounderAddressIndex(\BlockHeight)}$.
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\consensusrule{
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@ -9293,8 +9303,9 @@ Define:
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\begin{formulae}
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\item $\FundingStreamAddressChangeInterval := \PostBlossomHalvingInterval / 48$
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\item $\FundingStreamAddressPeriod(\BlockHeight) := \floor{\hfrac{\BlockHeight + \PostBlossomHalvingInterval - \HeightForHalving(1)}{\FundingStreamAddressChangeInterval}}$
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\item $\FundingStreamAddressIndex{i}(\BlockHeight) := \\
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1 + \FundingStreamAddressPeriod(\BlockHeight) - \FundingStreamAddressPeriod(\FundingStreamStartHeight{i})$.
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\item $\FundingStreamAddressIndex{i}(\BlockHeight) :=$
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\vspace{-0.5ex}
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\item \tab $1 + \FundingStreamAddressPeriod(\BlockHeight) - \FundingStreamAddressPeriod(\FundingStreamStartHeight{i})$.
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\end{formulae}
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The number of \transparent addresses per \fundingStream is therefore:
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@ -9308,7 +9319,7 @@ Each address representation in $\FundingStreamAddressList{i}_{\oneto{\FundingStr
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denotes a \transparent P2SH multisig address.
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Let $\RedeemScriptHash_i(\BlockHeight)$ be the standard redeem script hash, as defined in
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\cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check representation
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\cite{Bitcoin-Multisig}, for the P2SH multisig address with Base58Check form
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given by $\FundingStreamAddressList{i}_{\,\FundingStreamAddressIndex{i}(\BlockHeight)}$.
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Recall from \crossref{subsidies} the definition of $\FundingStreamValue{i}$.
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