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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{Introduction}
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The Lux Network's appchain architecture enables developers to deploy application-specific
blockchains with full control over consensus parameters, virtual machines, gas tokens,
and validator admission policies. As of 2025, 47 appchains serve production traffic,
spanning DeFi protocols, gaming applications, institutional asset management platforms, and
enterprise supply chain systems.
Despite this proliferation, the economic layer governing appchain creation and operation
remains underspecified in the public literature. Practitioners face concrete questions
without rigorous answers: How much should an appchain spend to attract enough validators?
What fee structure maximizes long-run revenue while remaining competitive with alternative
L2 solutions? How should fee revenue be split between appchain-native validators and Primary
Network validators who provide underlying security? How can a new appchain bootstrap a
native token without creating inflationary pressure that undermines its own economics?
This paper addresses these questions through a combination of mechanism design, empirical
calibration, and simulation. Our contributions:
\begin{enumerate}[leftmargin=1.5em]
\item \textbf{Appchain cost model}: A detailed cost accounting framework for appchain
creation and operation across five throughput tiers (Section~\ref{sec:costs}).
\item \textbf{Validator incentive mechanism}: A formal model of the validator's
participation decision, including the opportunity-cost constraint relative to
Primary Network staking (Section~\ref{sec:validators}).
\item \textbf{Cross-appchain MEV analysis}: A formal treatment of MEV arising from
cross-appchain transaction ordering, with an on-chain redistribution mechanism
(Section~\ref{sec:mev}).
\item \textbf{Fee sharing protocol}: A two-tier fee-sharing mechanism balancing appchain
sovereignty with Primary Network security incentives (Section~\ref{sec:feesharing}).
\item \textbf{Token bootstrapping}: A liquidity-weighted emission schedule for appchain
native tokens that avoids inflationary oversupply (Section~\ref{sec:bootstrapping}).
\item \textbf{Elastic scaling}: A dynamic validator set sizing mechanism based on
observed demand (Section~\ref{sec:elastic}).
\end{enumerate}
\subsection{The Appchain Value Stack}
We conceptualize appchain economics as a value stack with four layers:
\begin{description}[leftmargin=2em,style=nextline]
\item[Layer 1: Infrastructure] P-Chain consensus, validator hardware, network bandwidth.
\item[Layer 2: Security] Economic collateral staked by Primary Network and appchain
validators.
\item[Layer 3: Execution] Transaction processing, VM computation, state storage.
\item[Layer 4: Application] MEV, user-level fees, protocol revenue.
\end{description}
Each layer has costs that must be covered by the value generated at that layer and the
layers above. A sustainable appchain economy requires that application-layer revenue flows
sufficiently downward to sustain infrastructure and security.
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