In a UTxO architecture, centralizing the pool state into one UTxO (as in a traditional AMM) would constrain the DEX to one transaction per block. To achieve high throughput, the DEX must take advantage of the inherent parallelism properties made possible by UTxOs. For this reason, the pool state is divided along two dimensions (e.i. price ticks and liquidity providers), enabling parallel processing of UTxOs within the same block (Fig. 13). In addition to increased throughput, fragmentation also minimizes memory requirements. Since each transaction is only dependent on a local state, this results in lower transaction sizes and thereby lower fees. Another desirable property of fragmented liquidity is the emergence of arbitrary liquidity curves. Instead of predefining a fixed curve like in an AMM, the liquidity distribution is dynamic, decentralized, and governed by market sentiment, resulting in more efficient asset allocation.