The implementation of TWAMM logic presents significant challenges, particularly regarding on-chain execution due to computational limitations. The original TWAMM concept, as outlined in Paradigm's foundational paper, involves breaking long-term orders into infinitely small transactions to facilitate smooth execution over time. However, traditional methods struggle to process multiple orders simultaneously on-chain, which can lead to inefficiencies and high gas costs.

To address these issues, we developed a solution that linearizes orders. Instead of treating each order as an independent trade, this approach consolidates the processing into a single transaction at the end. This method not only reduces computational overhead but also enhances efficiency by minimizing the number of transactions that need to be executed.

Furthermore, our implementation needed to accommodate operations across multiple liquidity pools. To achieve this, we opted to track earnings per token rather than per pool. This strategy allows for better management of tokens that may exist in various pools and enables functionalities such as many-to-one token trades. By focusing on earnings per token, we can streamline the process and ensure that the TWAMM can effectively handle a diverse array of tokens while maintaining efficiency in execution.

In summary, our approach not only optimizes the TWAMM's operational capacity but also enhances its adaptability across different trading scenarios and liquidity pools, paving the way for more sophisticated trading strategies in decentralized finance.