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papers/lux-fpc-consensus/sections/07-termination-conditions.tex
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\section{Termination Conditions}
\label{sec:termination}
FPC terminates when one of the following conditions is met:
\begin{enumerate}
\item \textbf{Confidence Achieved}: $\beta$ consecutive rounds with opinion above $\alpha_{\text{conf}}$
\item \textbf{Timeout}: Maximum rounds exceeded (fallback to heavier consensus)
\item \textbf{External Signal}: Higher-level protocol requests termination
\end{enumerate}
\subsection{Safety vs. Liveness Trade-off}
The parameter $\beta$ controls the trade-off:
\begin{itemize}
\item Small $\beta$ ($\approx 3$): Fast termination, lower confidence
\item Large $\beta$ ($\approx 10$): High confidence, slower termination
\end{itemize}