Terminology

• Pool: Vessel’s AMM pool consists of two assets, the base asset and the quote asset, aligning with trading pair terminology. For example, in an ETH/USDT pool, ETH is the base asset while USDT is the quote asset.

• Tick: A tick represents discrete prices used in the AMM pool. Each pool is instantiated with a predefined set of ticks that remain unchanged throughout its lifecycle. In Vessel, ticks are defined in an arithmetic sequence, represented as a tuple $<Tick_0, TotalTicks, TickSpacing>$:

  ▪ $Tick_0=MinPrice$

  ▪ $Tick_i=Tick_0+TickSpacing \times (i-1), 0 \le i < TotalTicks$

• Interval: An interval is the minimal divisible price range in the AMM pool. $Interval_i$ covers the price range $[Tick_i, Tick_{i+1}]$, managing buy orders at $Tick_i$ and sell orders at $Tick_{i+1}$.

• Liquidity: Liquidity is the total size in base asset of orders managed by the AMM within a specific range. The liquidity of $Interval_i$ is the sum of buy order sizes at $Tick_i$ and sell order sizes at $Tick_{i+1}$. The pool's total liquidity is the sum across all intervals.

• Position: A position indicates how an LP provides liquidity within a specific range, defined by $<Tick_L, Tick_R,L>$, covering $[Tick_L, Tick_R]$, with $L$ liquidity in each interval.