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papers/lux-fpc-consensus/sections/11-integration-with-lux.tex
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\section{Integration with Lux}
\label{sec:integration}
FPC integrates seamlessly with Lux's modular consensus architecture:
\subsection{Appchain Consensus Customization}
Different appchains can configure FPC parameters based on requirements:
\begin{lstlisting}[language=Go, caption=Appchain-specific FPC configuration]
type AppchainConfig struct {
CommitteeSize int // k: 20-50
ConfidenceRounds int // beta: 3-10
ThetaMin float64 // 0.5-0.6
ThetaMax float64 // 0.7-0.9
CoolingRate float64 // 0.8-0.95
}
// High-security appchain
secureConfig := AppchainConfig{
CommitteeSize: 30,
ConfidenceRounds: 10,
ThetaMin: 0.55,
ThetaMax: 0.85,
}
// High-performance appchain
fastConfig := AppchainConfig{
CommitteeSize: 20,
ConfidenceRounds: 3,
ThetaMin: 0.5,
ThetaMax: 0.75,
}
\end{lstlisting}
\subsection{Cross-Chain Message Finality}
FPC provides rapid finality for cross-chain messages:
\begin{enumerate}
\item Source appchain achieves FPC consensus on message
\item Message certificate includes FPC confidence score
\item Destination appchain verifies certificate threshold
\item Higher confidence messages prioritized
\end{enumerate}
\subsection{Validator Sampling Strategy}
FPC's committee sampling integrates with Lux's stake-weighted validator selection:
\begin{equation}
P(\text{validator } v \text{ selected}) = \frac{\text{stake}_v}{\sum_{i} \text{stake}_i}
\end{equation}
\subsection{Economic Incentives}
Validators earn rewards proportional to:
\begin{itemize}
\item Participation in committee queries
\item Response latency (faster responses rewarded)
\item Opinion accuracy (agreement with final consensus)
\end{itemize}