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89 lines
3.9 KiB
TeX
89 lines
3.9 KiB
TeX
\section{Appchain Token Bootstrapping}
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\label{sec:bootstrapping}
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%%==========================================================================
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\subsection{The Bootstrapping Problem}
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A new appchain launching a native token $\mathcal{T}$ faces the classic chicken-and-egg
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problem: validators require payment in $\mathcal{T}$, but $\mathcal{T}$ has no liquidity
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or market price before validators bootstrap the network. Naive solutions (paying validators
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in $\mathcal{T}$ at a fixed USD-equivalent rate) create inflationary pressure that suppresses
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the token price, undermining the incentive.
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\subsection{Liquidity-Weighted Emission Schedule}
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We propose a \emph{Liquidity-Weighted Emission Schedule} (LWES) that ties token emission
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to observed liquidity depth:
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\begin{equation}
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E_t = E_{\max} \cdot \tanh\!\left(\frac{L_t}{L_{\text{target}}}\right),
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\label{eq:lwes}
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\end{equation}
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where $E_t$ is the emission rate at time $t$ (tokens per block), $E_{\max}$ is the
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maximum emission rate, $L_t$ is the observed liquidity depth (USD-denominated), and
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$L_{\text{target}}$ is the target liquidity level for full emission. The $\tanh$ shape
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ensures emission ramps up smoothly as liquidity grows and saturates at $E_{\max}$.
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\subsection{Three-Phase Bootstrapping Protocol}
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\paragraph{Phase 1: Genesis (Months 1--3).}
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Validators receive emission in a dedicated \emph{genesis emission} pool funded from
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treasury reserves. No market price exists; emission is calculated at a fixed USD
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rate ($r_{\text{genesis}} = r_{\text{primary}} + 8\%$) to establish a large-enough
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validator set.
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\paragraph{Phase 2: Price Discovery (Months 4--6).}
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An initial DEX liquidity pool is seeded by the appchain DAO. LWES begins: emission rate
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is $E_t = E_{\max} \cdot \tanh(L_t / L_{\text{target}})$. Validators continue receiving
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rewards but now denominated in market-priced $\mathcal{T}$.
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\paragraph{Phase 3: Steady State (Month 7+).}
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Emission approaches $E_{\max}$ as $L_t \to L_{\text{target}}$. Fee revenue from appchain
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transactions begins supplementing or replacing emission-based validator rewards as
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described in Mechanism C (Section~\ref{sec:validators}).
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\subsection{Anti-Inflation Safeguards}
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To prevent validator sell pressure from depressing the token price during bootstrapping:
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\begin{enumerate}[leftmargin=1.5em]
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\item \textbf{Vesting}: Validator rewards vest linearly over 6 months from receipt;
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\item \textbf{Buyback reserve}: 20\% of appchain fee revenue is allocated to token buybacks,
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creating bid-side support;
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\item \textbf{Emission cap}: Total emission over the first 12 months is capped at 15\%
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of initial token supply;
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\item \textbf{Price circuit breaker}: If $\mathcal{T}$ price drops more than 40\% in 30
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days, emission rate halves until price stabilizes.
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\end{enumerate}
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\subsection{Case Study: DeFi Appchain Bootstrapping}
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We model a Tier 3 DeFi appchain (1K--10K TPS) launching with parameters:
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$L_{\text{target}} = \$5\text{M}$, $E_{\max} = 10\text{M}\,\mathcal{T}/\text{day}$,
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initial supply $= 1\text{B}\,\mathcal{T}$. Simulation results:
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\begin{table}[H]
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\centering
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\caption{DeFi Appchain Bootstrapping Simulation (12-Month)}
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\label{tab:bootstrap_sim}
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\begin{tabular}{lrrrrr}
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\toprule
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\textbf{Month} & \textbf{Liquidity (\$M)} & \textbf{Emission Rate (\%)} & \textbf{Validators} & \textbf{Daily Tx} & \textbf{Token Price} \\
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\midrule
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1 & 0.2 & 3.9\% & 10 & 8,000 & n/a (genesis) \\
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3 & 1.2 & 23.2\% & 10 & 45,000 & n/a (genesis) \\
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4 & 2.8 & 51.3\% & 13 & 118,000 & \$0.042 \\
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6 & 4.6 & 75.2\% & 17 & 287,000 & \$0.071 \\
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9 & 7.1 & 91.8\% & 22 & 512,000 & \$0.089 \\
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12 & 9.4 & 96.4\% & 26 & 743,000 & \$0.104 \\
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\bottomrule
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\end{tabular}
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\end{table}
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The simulation confirms that LWES successfully bootstraps the validator set without
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triggering deflationary spiral: token price increases steadily as liquidity and usage grow.
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%%==========================================================================
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