papers/lux-warp-messaging/sections/05-optimistic-delivery.tex

\section{Optimistic Delivery}
\label{sec:optimistic}

\subsection{Protocol Description}

For latency-sensitive applications, LWM supports optimistic delivery where messages are executed before source finality:

\begin{algorithm}[H]
\caption{Optimistic Warp Delivery}
\label{alg:optimistic}
\begin{algorithmic}[1]
\Require Message $\mathcal{M}$ in preferred (unfinalized) block $B$
\Require Relayer economic bond $\beta \geq 2 \cdot \mathcal{M}.\mathsf{gasLimit} \cdot \text{gasPrice}$
\State Relayer posts $(\mathcal{M}, H(B), \beta)$ to destination
\State Destination executes $\mathcal{M}.\mathsf{payload}$ provisionally
\State Open dispute window: $\Delta_d = 100$ blocks ($\approx 20$ min)
\If{valid fraud proof received within $\Delta_d$}
    \State Revert provisional execution
    \State Slash $\beta$; distribute 50\% to challenger, 50\% burned
\Else
    \State Finalize execution; refund $\beta$ plus relay fee
\EndIf
\end{algorithmic}
\end{algorithm}

\subsection{Fraud Proof Construction}

\begin{definition}[Fraud Proof]
A fraud proof against optimistic message $\mathcal{M}$ claiming inclusion in block $B$ at height $h$ consists of:
\begin{equation}
    \mathsf{FP} = (B', h, \Pi_{B'})
\end{equation}
where $B' \neq B$ is a finalized block at height $h$ on the source appchain and $\Pi_{B'}$ is a valid warp proof (BLS aggregate) of $B'$'s finality.
\end{definition}

\begin{theorem}[Optimistic Safety]
If honest stake $\geq 2W/3$ and $\Delta_d$ exceeds the network synchrony bound, then undetected fraud occurs with negligible probability.
\end{theorem}

\begin{proof}
If $B$ is not finalized, then a different block $B'$ is finalized at the same height (by consensus safety, at most one block is finalized per height under $2/3$ honesty). Honest validators can produce $\Pi_{B'}$ and submit the fraud proof within $\Delta_d$ under synchrony assumptions.
\end{proof}

\subsection{Latency Comparison}

\begin{table}[H]
\centering
\caption{End-to-end latency: standard vs.\ optimistic delivery.}
\label{tab:latency}
\begin{tabular}{lrr}
\toprule
\textbf{Phase} & \textbf{Standard (ms)} & \textbf{Optimistic (ms)} \\
\midrule
Source finality & 1{,}000--3{,}000 & 0 \\
Signature collection & 200--500 & 0 \\
Aggregation & 5--20 & 5--20 \\
Destination submission & 100--500 & 100--500 \\
On-chain verification & 2--5 & 2--5 \\
\midrule
\textbf{Total} & \textbf{1{,}307--4{,}025} & \textbf{107--525} \\
\bottomrule
\end{tabular}
\end{table}