mirror of https://github.com/zcash/zips.git
Adjust Founders' Reward payment.
Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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Daira Hopwood
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b934946949
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5e5413f536
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@ -1248,6 +1248,8 @@ electronic commerce and payment, financial privacy, proof of work, zero knowledg
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\newcommand{\FounderAddressChangeInterval}{\mathsf{FounderAddressChangeInterval}}
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\newcommand{\FoundersFraction}{\mathsf{FoundersFraction}}
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\newcommand{\BlockHeight}{\mathsf{height}}
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\newcommand{\FounderAddressAdjustedHeight}{\mathsf{FounderAddressAdjustedHeight}}
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\newcommand{\FoundersRewardLastBlockHeight}{\mathsf{FoundersRewardLastBlockHeight}}
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\newcommand{\Halving}{\mathsf{Halving}}
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\newcommand{\FounderAddress}{\mathsf{FounderAddress}}
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\newcommand{\FounderAddressList}{\mathsf{FounderAddressList}}
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@ -9104,29 +9106,29 @@ and $\FoundersFraction$ are instantiated in \crossref{constants}.
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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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\item $\Halving(\BlockHeight \typecolon \Nat) := \notblossom{\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}}}
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\notbeforeblossom{\begin{cases}
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\floor{\hfrac{\BlockHeight - \SlowStartShift}{\PreBlossomHalvingInterval}},\hspace{1em}\blossom{\caseif \text{not } \IsBlossomActivated(\BlockHeight)} \\[1.4ex]
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\blossom{\floor{\hfrac{\BlossomActivationHeight - \SlowStartShift}{\PreBlossomHalvingInterval} + \hfrac{\BlockHeight - \BlossomActivationHeight}{\PostBlossomHalvingInterval}},}&\blossom{\caseotherwise}
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\end{cases}}$
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\vspace{0.5ex}
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\item $\BlockSubsidy(\BlockHeight) := \begin{cases}
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\item $\BlockSubsidy(\BlockHeight \typecolon \Nat) := \begin{cases}
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\SlowStartRate \mult \BlockHeight,&\caseif \BlockHeight < \hfrac{\SlowStartInterval}{2} \\[1.4ex]
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\SlowStartRate \mult (\BlockHeight + 1),&\caseif \hfrac{\SlowStartInterval}{2} \leq \BlockHeight \\[1.4ex]
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&\text{ and } \BlockHeight < \SlowStartInterval \\[1.4ex]
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\floor{\hfrac{\MaxBlockSubsidy}{2^{\Halving(\BlockHeight)}}},&\notblossom{\caseotherwise}\notbeforeblossom{\caseif \SlowStartInterval \leq \BlockHeight} \\
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\floor{\hfrac{\MaxBlockSubsidy}{2^{\Halving(\BlockHeight)}}}\!\!,&\notblossom{\caseotherwise}\notbeforeblossom{\caseif \SlowStartInterval \leq \BlockHeight} \\
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\notbeforeblossom {
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&\blossom{\text{ and not } \IsBlossomActivated(\BlockHeight}) \\[1.4ex]
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\blossom{\floor{\hfrac{\MaxBlockSubsidy}{\BlossomPoWTargetSpacingRatio \mult 2^{\Halving(\BlockHeight)}}},}&\blossom{\caseotherwise}
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&\blossom{\text{ and not } \IsBlossomActivated(\BlockHeight)} \\[1.4ex]
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\blossom{\floor{\hfrac{\MaxBlockSubsidy}{\BlossomPoWTargetSpacingRatio \mult 2^{\Halving(\BlockHeight)}}}\!\!,}&\blossom{\caseotherwise}
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} %notbeforeblossom
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\end{cases}$
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\item $\FoundersReward(\BlockHeight) := \begin{cases}
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\item $\FoundersReward(\BlockHeight \typecolon \Nat) := \begin{cases}
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\BlockSubsidy(\BlockHeight) \mult \FoundersFraction,&\caseif \Halving(\BlockHeight) = 0 \\
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0,&\caseotherwise
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\end{cases}$
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\item $\MinerSubsidy(\BlockHeight) := \BlockSubsidy(\BlockHeight) - \FoundersReward(\BlockHeight)$.
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\item $\MinerSubsidy(\BlockHeight \typecolon \Nat) := \BlockSubsidy(\BlockHeight) - \FoundersReward(\BlockHeight)$.
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\end{formulae}
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\introsection
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@ -9211,39 +9213,54 @@ Each address representation in $\FounderAddressList$ denotes a \transparent
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P2SH multisig address.
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\introlist
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Let $\SlowStartShift$ be defined as in the previous section.
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Let $\SlowStartShift$ and $\Halving$ be defined as in the previous section.
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Define:
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\begin{formulae}
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\item $\FounderAddressChangeInterval := \ceiling{\hfrac{\SlowStartShift + \PreBlossomHalvingInterval}{\NumFounderAddresses}}$
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\item $\FounderAddressIndex(\BlockHeight) := 1 + \floor{\hfrac{\BlockHeight}{\FounderAddressChangeInterval}}$.
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\blossom{
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\item $\FounderAddressAdjustedHeight(\BlockHeight \typecolon \Nat) :=$
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\vspace{-0.5ex}
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\item \tab $\begin{cases}
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\BlockHeight, &\caseif \BlockHeight < \BlossomActivationHeight, \\
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\BlossomActivationHeight + \hfrac{\BlockHeight - \BlossomActivationHeight}{\BlossomPoWTargetSpacingRatio}, &\caseotherwise
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\end{cases}$
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}
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\item $\FounderAddressIndex(\BlockHeight \typecolon \Nat) := 1 + \floor{\hfrac{\blossom{\FounderAddressAdjustedHeight(}\BlockHeight\blossom{)}}{\FounderAddressChangeInterval}}$
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\item $\FoundersRewardLastBlockHeight :=
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\notblossom{\SlowStartShift + \PreBlossomHalvingInterval - 1}
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\blossom{\maximum\Of{\setof{\BlockHeight \typecolon \Nat \suchthat \Halving(\BlockHeight) < 1}}}$\,.
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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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Let $\RedeemScriptHash(\BlockHeight \typecolon \Nat)$ be the standard redeem script hash, as defined in
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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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A \coinbaseTransaction for \block $\BlockHeight \in \range{1}{\SlowStartShift + \PreBlossomHalvingInterval - 1}$
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A \coinbaseTransaction for \blockHeight $\BlockHeight \in \range{1}{\FoundersRewardLastBlockHeight}$
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\MUST include at least one output that pays exactly $\FoundersReward(\BlockHeight)$ \zatoshi
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with a standard P2SH script of the form \ScriptOP{HASH160} \;$\RedeemScriptHash(\BlockHeight)$\; \ScriptOP{EQUAL}
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as its $\scriptPubKey$.
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}
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\begin{pnotes}
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\item No \foundersReward is required to be paid for $\BlockHeight \geq$
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\notblossom{$\SlowStartShift + \PreBlossomHalvingInterval$
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(i.e.\ after the first halving)}\blossom{$\BlossomActivationHeight$},
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or for $\BlockHeight = 0$ (i.e.\ the \genesisBlock).
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\item No \foundersReward is required to be paid for $\BlockHeight > \FoundersRewardLastBlockHeight$
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(i.e.\ after the first halving), or for $\BlockHeight = 0$ (i.e.\ the \genesisBlock).
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\item The \foundersReward addresses are not treated specially in any other way, and
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there can be other outputs to them, in \coinbaseTransactions or otherwise.
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In particular, it is valid for a \coinbaseTransaction with
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$\BlockHeight \in \range{1}{\SlowStartShift + \PreBlossomHalvingInterval - 1}$ to have
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$\BlockHeight \in \range{1}{\FoundersRewardLastBlockHeight}$ to have
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other outputs, possibly to the same address, that do not meet the criterion
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in the above consensus rule, as long as at least one output meets it.
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\item The assertion $\FounderAddressIndex(\FoundersRewardLastBlockHeight) \leq \NumFounderAddresses$
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holds, ensuring that the \foundersReward address index remains in range for the
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whole period in which the \foundersReward is paid.
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\end{pnotes}
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\blossom{\todo{\Blossom is not intended to change the total \foundersReward or the effective period over
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which it is paid; ensure that this is the case.}}
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\subsection{Changes to the Script System} \label{scripts}
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