papers/lux-quasar-benchmarks/sections/03-benchmark-1-finality-time.tex

\section{Benchmark 1: Finality Time}

\label{sec:finality}
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Finality time is measured as wall-clock elapsed time from transaction broadcast to the
point at which the transaction is irreversibly committed and cannot be reverted without
violating the protocol's safety assumptions.

\subsection{Definitions}

Protocols define ``final'' differently:
\begin{itemize}
\item \textbf{Quasar}: Block has both valid BLS aggregate certificate and valid Pulsar
      threshold certificate ($\geq 2n/3$ contributors each).
\item \textbf{Tendermint}: Block committed after \texttt{Precommit} phase with $\geq 2n/3$
      signatures~\cite{tendermint}.
\item \textbf{HotStuff}: Block finalized after 3-chain rule (propose, pre-commit,
      commit, decide)~\cite{hotstuff}.
\item \textbf{Narwhal+Tusk}: DAG vertex committed after Tusk's zero-message-overhead
      commit rule~\cite{narwhal-tusk}.
\item \textbf{Casper FFG}: Checkpoint finalized after two consecutive justified
      epochs~\cite{casper-ffg}. Each epoch = 32 slots $\times$ 12\,s = 384\,s.
\item \textbf{Tower BFT}: 32 layers of exponentially increasing vote lockout
      periods~\cite{solana-wp}.
\item \textbf{Snow}: Probabilistic finality after $\beta$ consecutive successful
      sampling rounds~\cite{snow-paper}.
\end{itemize}

\subsection{Results ($n = 100$ validators)}

\begin{table}[h]
\centering
\begin{tabular}{@{}lrrr@{}}
\toprule
\textbf{Protocol} & \textbf{Median (ms)} & \textbf{p99 (ms)} & \textbf{Max (ms)} \\
\midrule
\textbf{Quasar}        & \textbf{204}  & \textbf{347}    & 512 \\
Narwhal+Tusk           & 464           & 890             & 1{,}340 \\
Snow (Avalanche)       & 920           & 1{,}850         & 3{,}100 \\
Tendermint (CometBFT)  & 1{,}180       & 2{,}410         & 4{,}200 \\
HotStuff (Aptos)       & 1{,}640       & 3{,}200         & 5{,}800 \\
Tower BFT (Solana)     & 12{,}800      & 13{,}400        & 14{,}200 \\
Casper FFG (Ethereum)  & 768{,}000     & 768{,}000       & 768{,}000 \\
\bottomrule
\end{tabular}
\caption{Time to irreversible finality at $n=100$ validators, 3-datacenter WAN.}
\label{tab:finality}
\end{table}

\begin{figure}[h]
\centering
\begin{tikzpicture}
\begin{axis}[
    ybar,
    bar width=12pt,
    width=0.95\textwidth,
    height=7cm,
    ymode=log,
    log ticks with fixed point,
    ylabel={Finality time (ms, log scale)},
    symbolic x coords={Quasar, Narwhal, Snow, Tendermint, HotStuff, Tower BFT, Casper FFG},
    xtick=data,
    xticklabel style={rotate=30, anchor=east, font=\small},
    ymin=100,
    ymax=2000000,
    nodes near coords,
    nodes near coords style={font=\tiny, above},
    every node near coord/.append style={rotate=45, anchor=south west},
    enlarge x limits=0.1,
    legend style={at={(0.02,0.98)}, anchor=north west, font=\small},
]
\addplot[fill=luxpurple] coordinates {
    (Quasar, 204)
    (Narwhal, 464)
    (Snow, 920)
    (Tendermint, 1180)
    (HotStuff, 1640)
    (Tower BFT, 12800)
    (Casper FFG, 768000)
};
\addplot[fill=luxblue!40] coordinates {
    (Quasar, 347)
    (Narwhal, 890)
    (Snow, 1850)
    (Tendermint, 2410)
    (HotStuff, 3200)
    (Tower BFT, 13400)
    (Casper FFG, 768000)
};
\legend{Median, p99}
\end{axis}
\end{tikzpicture}
\caption{Finality time comparison (log scale). Quasar achieves 204\,ms median
finality---3.8$\times$ faster than the next DAG-based competitor.}
\label{fig:finality-bar}
\end{figure}

\subsection{Analysis}

Quasar's finality advantage stems from two design decisions:

\begin{enumerate}
\item \textbf{Parallel certificate collection}: BLS and Pulsar signatures are collected
      concurrently. The critical path is the slower of the two (BLS aggregation at
      $\sim$195\,ms over WAN), not their sum.
\item \textbf{Responsive finality}: Like HotStuff, Quasar finalizes at actual network
      speed, not at a fixed timer. With 38\,ms median intra-cluster RTT, finality
      completes well under the block time.
\end{enumerate}

\textbf{GPU BLS acceleration}: When validators use GPU-accelerated BLS aggregation
(Metal or CUDA shaders), the BLS round completes in $\sim$10\,ms instead of
$\sim$195\,ms. In single-datacenter deployments with sub-millisecond RTT, this
yields \textbf{10\,ms finality}---the primary target for co-located validator sets.
CPU BLS remains available as a 100\,ms fallback on commodity hardware.

Ethereum's Casper FFG is architecturally incapable of sub-minute finality: two full
epochs (12.8\,min) are required by design~\cite{casper-ffg}. Solana's Tower BFT
requires 32 layers of exponentially locked votes, producing $\sim$12.8\,s irreversible
finality regardless of network conditions~\cite{solana-wp}.

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