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zeekay fc9b2e03e1 papers: fix LaTeX/ref/typo errors from swarm review (42 papers)
Auto-fixes from the paper accuracy swarm: unambiguous build-breakers, broken
\ref/\cite/\input targets, and prose typos. Substantive accuracy findings
(dates, contradictory numbers, LP numbering) reported separately for review.
2026-06-27 02:02:47 +00:00

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\section{Background}
\label{sec:background}
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\subsection{Lux Network Architecture}
Lux employs a three-chain primary network:
\begin{itemize}[leftmargin=1.5em]
\item \textbf{P-Chain} (Platform Chain): tracks validator sets, manages staking, creates
appchains.
\item \textbf{X-Chain} (Exchange Chain): UTXO-based chain for asset issuance and trading.
\item \textbf{C-Chain} (Contract Chain): EVM-compatible chain for smart contracts.
\end{itemize}
Validators post a minimum 2,000 LUX stake on the P-Chain and run all three primary chains.
Appchain validation is opt-in: a primary validator may additionally validate any subset of
registered appchains by running the appchain's VM and advertising participation on the P-Chain.
Historically, appchain validators received no direct remuneration from appchains, creating a
mismatch between the security provided and the incentive to provide it~\cite{lux2020platform}.
\subsection{Beacon Consensus}
Lux's Beacon consensus achieves probabilistic finality in $\mathcal{O}(\log n)$ rounds
under the honest-majority assumption, with sub-second finality observed in practice. The
key property relevant to restaking is that conflicting transactions are identified and
rejected rapidly: any equivocating validator (one who votes for two conflicting blocks) can
be detected within one consensus epoch. This property enables efficient slashing without
requiring extended unbonding periods~\cite{rocket2019wave}.
\subsection{EigenLayer and Prior Work}
EigenLayer~\cite{eigen2023restaking} pioneered restaking on Ethereum, enabling ETH stakers
to opt into securing additional Actively Validated Services via delegation to operators who
run AVS-specific software. Key characteristics of EigenLayer:
\begin{itemize}[leftmargin=1.5em]
\item Ethereum-native: operates through beacon chain withdrawal credentials and LST
(Liquid Staking Token) deposits.
\item Slashing is coordinated through EigenLayer's \texttt{SlasherManager} contract.
\item AVSs register their slashing conditions as smart contracts.
\item Operators choose which AVSs to serve; restakers delegate to operators.
\end{itemize}
Limitations include: long unbonding periods (7 days on Ethereum), high gas costs for
slashing coordination, and the absence of native primitives for appchain-level security
(since Ethereum has no equivalent to Lux appchains).
\subsection{Related Work}
Cosmos Hub's Interchain Security (ICS)~\cite{cosmos2022ics} provides a different approach:
consumer chains lease the entire validator set of the Hub rather than individual validators.
This is simpler but less flexible, requiring all Hub validators to participate. Polkadot's
shared security model~\cite{wood2016polkadot} assigns parachains to relay-chain validator
subsets through an auction mechanism. Neither model enables the granular, operator-chosen
service selection that LRP provides.
Babylon~\cite{babylon2023bitcoin} explores restaking Bitcoin security to PoS chains via
UTXO timestamping. While complementary, it addresses a different threat model (long-range
attacks) rather than Byzantine fault tolerance in execution environments.
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