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Small fix
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saltiniroberto committed Dec 17, 2024
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Expand Up @@ -27,7 +27,7 @@ \section{Basic 3SF concepts}\label{sec:3sf}

\paragraph{Checkpoints.}
In the protocol described in~\cite{d20243}, a \emph{checkpoint} is a tuple $(\chain, c)$, where \(\chain \) is a chain and \( c \) is a slot signifying where \( \chain \) is proposed for justification (this concept is introduced and explained below).
However, for efficiency reasons, in the specification targeted by this project, a \emph{valid} checkpoint $\C$ is a triple $(H, c, p)$ where $H$ is the hash of a chain $\chain$, $c$ is as per the definition above and $p = \chain.p$.
However, for efficiency reasons, in the specification targeted by this project, a \emph{valid} checkpoint $\C$ is a triple $(H, c, p)$ where $H$ is the hash of a chain $\chain$, $c$ is the slot at which chain $\chain$ is proposed for justification, as per the definition above, and $p = \chain.p$.
The total pre-order among checkpoints is defined:
$\C \leq \C'$ if and only if either \(\C.c < \C'.c\) or, in the case where \(\C.c = \C'.c\), then \(\C.p \leq \C'.p\).
Also, $\C < \C'$ means $\C \leq \C' \land \C \neq \C'$.
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