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papers/lux-quasar-consensus/sections/13-appendix-a-consensus-parameter-tuning.tex
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\section{Appendix A: Consensus Parameter Tuning}
\subsection{Safety vs. Liveness Trade-offs}
Increasing $\alpha$ and $\beta$ improves safety at the cost of latency:
\begin{table}[h]
\centering
\begin{tabular}{@{}llll@{}}
\toprule
$\alpha$ & $\beta$ & \textbf{Safety} & \textbf{Finality Latency} \\
\midrule
13 & 8 & 99.9999\% & 8ms (GPU) / 80ms (CPU) \\
15 & 10 & 99.99999\% & 10ms (GPU) / 100ms (CPU) \\
18 & 12 & 99.999999\% & 12ms (GPU) / 120ms (CPU) \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Network Size Scaling}
Optimal K grows with network size:
\begin{align}
K_{opt} &\approx \sqrt{N} \\
\alpha &\approx 0.6 \times K \\
\beta &\approx 0.4 \times K
\end{align}