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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
78 lines
2.9 KiB
TeX
78 lines
2.9 KiB
TeX
\section{Token Economics}
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\label{sec:tokens}
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\subsection{sLUX: Rebasing Token}
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sLUX implements a rebasing mechanism where the token balance of each holder increases automatically as staking rewards accrue:
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\begin{definition}[sLUX Balance]
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User $u$'s sLUX balance at time $t$ is:
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\begin{equation}
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\mathsf{balance}_u(t) = \mathsf{shares}_u \cdot \frac{\mathsf{totalPooled}(t)}{\mathsf{totalShares}(t)}
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\end{equation}
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where $\mathsf{shares}_u$ is $u$'s share count (constant between deposits/withdrawals) and $\mathsf{totalPooled}(t)$ includes accumulated rewards.
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\end{definition}
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\begin{proposition}[sLUX Value Monotonicity]
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Under honest validator operation (no slashing), the sLUX/LUX exchange rate $\rho(t) = \mathsf{totalPooled}(t) / \mathsf{totalShares}(t)$ is monotonically non-decreasing.
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\end{proposition}
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\begin{proof}
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Staking rewards increase $\mathsf{totalPooled}$ while $\mathsf{totalShares}$ remains constant (rewards do not mint new shares). Therefore $\rho(t+1) = (\mathsf{totalPooled}(t) + R_t) / \mathsf{totalShares}(t) \geq \rho(t)$ where $R_t \geq 0$ is the epoch reward.
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\end{proof}
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\subsection{wsLUX: Non-Rebasing Wrapper}
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For DeFi protocols that do not support rebasing tokens (e.g., AMM pools, lending markets), wsLUX provides a non-rebasing alternative:
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\begin{definition}[wsLUX Exchange Rate]
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\begin{align}
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\mathsf{wrap}(\mathsf{sLUX\_amount}) &: \mathsf{wsLUX\_amount} = \mathsf{sLUX\_amount} / \rho(t) \\
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\mathsf{unwrap}(\mathsf{wsLUX\_amount}) &: \mathsf{sLUX\_amount} = \mathsf{wsLUX\_amount} \cdot \rho(t)
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\end{align}
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\end{definition}
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The wsLUX token has a fixed supply relative to the underlying shares. Its value in LUX terms increases as $\rho(t)$ grows, making it suitable for yield-bearing collateral.
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\begin{table}[H]
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\centering
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\caption{Comparison of sLUX and wsLUX token properties.}
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\label{tab:token_comparison}
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\begin{tabular}{lll}
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\toprule
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\textbf{Property} & \textbf{sLUX} & \textbf{wsLUX} \\
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\midrule
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Balance changes & Yes (rebases) & No (fixed) \\
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Value accrual & Balance increases & Price increases \\
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1 LUX redeemable & Always $\geq$ 1 sLUX & Varies \\
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DeFi compatibility & Limited & Full \\
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Tax treatment & Income on each rebase & Capital gains on sale \\
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AMM suitable & No (rebase breaks LPs) & Yes \\
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Lending suitable & Limited & Yes \\
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\bottomrule
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\end{tabular}
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\end{table}
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\subsection{Fee Structure}
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\begin{table}[H]
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\centering
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\caption{LLS protocol fee schedule.}
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\label{tab:fees}
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\begin{tabular}{llr}
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\toprule
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\textbf{Fee Type} & \textbf{Collected From} & \textbf{Rate} \\
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\midrule
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Staking reward fee & Epoch rewards & 10\% \\
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\quad$\to$ Insurance pool & & 5\% \\
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\quad$\to$ Treasury/DAO & & 3\% \\
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\quad$\to$ Node operators & & 2\% \\
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Withdrawal fee & Withdrawal amount & 0\% \\
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Deposit fee & Deposit amount & 0\% \\
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\bottomrule
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\end{tabular}
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\end{table}
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The 10\% fee on staking rewards means sLUX holders receive 90\% of gross staking yield. With a gross yield of 7.3\% annually, sLUX holders earn approximately 6.6\% net.
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