papers/lux-economics/sections/11-security-analysis.tex

\section{Security Analysis}

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\subsection{Validator Incentive Alignment}

The proposed mechanisms are incentive-compatible in the following sense:

\begin{theorem}[Validator Truthfulness]
Under Mechanism C with the SSF protocol, it is a dominant strategy for validators to
truthfully report their capacity $K$ and honestly participate in appchains they have opted into.
\end{theorem}

\begin{proof}[Proof Sketch]
Overstating $K$ leads to accepting more appchains than the validator can serve, triggering
liveness faults and reputation slashing. Understating $K$ forgoes positive-value
opportunities. Hence truthful reporting maximizes expected utility. Dishonest participation
(agreeing to validate but not validating) triggers liveness slash penalties that exceed
the validator's potential gain from saved resources.
\end{proof}

\subsection{Collusion Resistance}

A coalition of validators might coordinate to extract MEV without sharing proceeds
through the CSMO mechanism. The CSMO is resistant to such collusion because:

\begin{enumerate}[leftmargin=1.5em]
  \item Lux Teleport bridges emit on-chain events visible to the CSMO oracle;
  \item Any cross-appchain arbitrage that bypasses the CSMO auction is detectable by
    comparing Lux Teleport event timestamps with block production timestamps;
  \item Detected collusion triggers a reputation slash of 50 points per incident.
\end{enumerate}

\subsection{Economic Attack Resistance}

We consider an attacker who creates many low-cost appchains to manipulate the SSF
distribution (collecting SSF revenue by artificially inflating appchain transaction counts).
The SSF formula (Eq.~\ref{eq:surcharge}) ties surcharge amounts to observed security
$\Pi(s)$, which requires real staked capital. An attacker cannot inflate transaction
count without also posting economic collateral proportional to their claimed security,
making the attack unprofitable.

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