papers/lux-teleport-protocol/sections/10-bridge-accounting-and-auditing.tex

\section{Bridge Accounting and Auditing}
\label{sec:audit}

\subsection{On-Chain Accounting}

The bridge contract maintains transparent accounting:

\begin{table}[H]
\centering
\caption{Bridge accounting entries.}
\label{tab:accounting}
\begin{tabular}{lrl}
\toprule
\textbf{Metric} & \textbf{Access} & \textbf{Description} \\
\midrule
$\mathsf{totalLocked}[T]$ & On-chain & Total token $T$ locked on source \\
$\mathsf{totalMinted}[T]$ & On-chain & Total wrapped $T$ minted on destination \\
$\mathsf{totalBurned}[T]$ & On-chain & Total wrapped $T$ burned (returns) \\
$\mathsf{totalReleased}[T]$ & On-chain & Total token $T$ released on source \\
\bottomrule
\end{tabular}
\end{table}

\begin{definition}[Solvency Invariant]
At all times:
\begin{equation}
    \mathsf{totalLocked}[T] - \mathsf{totalReleased}[T] = \mathsf{totalMinted}[T] - \mathsf{totalBurned}[T]
\end{equation}
This is verified on-chain at every bridge operation and can be audited by any observer.
\end{definition}

\subsection{Proof of Reserves}

The bridge publishes Merkle proofs of its locked balances:

\begin{algorithm}[H]
\caption{Proof of Reserves}
\label{alg:reserves}
\begin{algorithmic}[1]
\Procedure{ProveReserves}{token $T$, block $h$}
    \State $\mathsf{balance} \gets$ vault balance of $T$ at block $h$
    \State $\pi \gets$ Merkle state proof of vault balance at block $h$
    \State $\mathsf{wrapped} \gets$ total supply of wrapped $T$ on destination
    \State Publish $(\mathsf{balance}, \pi, \mathsf{wrapped}, h)$
    \State Anyone can verify $\mathsf{balance} \geq \mathsf{wrapped}$
\EndProcedure
\end{algorithmic}
\end{algorithm}