papers/lux-cross-chain-security/sections/07-security-inheritance-for-application-cha.tex

\section{Security Inheritance for Application Chains}


\subsection{Inheritance Model}

An application chain $C$ with validator set $V_C \subseteq V_P$ (where $V_P$ is the primary network validator set) inherits the following security properties:

\begin{enumerate}[leftmargin=2em]
\item \textbf{Consensus safety}: If $>2/3$ of $V_P$ is honest, $>2/3$ of $V_C$ is honest (since $V_C \subseteq V_P$).
\item \textbf{Finality}: $C$'s epoch proofs are included in the primary network's epoch proof via Warp \texttt{FINALITY\_PROOF} messages.
\item \textbf{Post-quantum security}: $C$ inherits triple-proof quantum finality from the primary network validators' ML-DSA and Pulsar keys.
\item \textbf{Cross-chain communication}: $C$ can send/receive Warp messages to/from any other chain in the network with the same security guarantees.
\end{enumerate}

\subsection{Chain Isolation}

Despite sharing validators, chains are isolated in execution:

\begin{invariant}[State Isolation]
A transaction on chain $C_1$ cannot read or modify the state of chain $C_2$ except through the Warp message protocol.
\end{invariant}

This means a bug in one application chain's VM cannot corrupt another chain's state. The worst case for a compromised application chain is that it produces invalid Warp messages, which are rejected by the destination chain's verification rules.