Catalyst has released a whitepaper detailing how it will further utilize the Uniswap and Balancer AMM equations. The official summary explains how and why it will become a catalyst for cross-chain applications.
Uniswap v2 and Balancer are the gold standards for trader and LP ease of use, and they have and will continue to make it easy for the protocol to maintain liquidity for its ecosystem. So far, no other protocol has replicated the one-to-one cross-chain user experience. Either they must deal with intermediary tokens, rely on cross-chain bridges, or move their assets to specific liquidity chains. With Catalyst, this will change.
Through independent evaluation of swaps, we can execute swaps on Uniswap v2, Balancer, and even stablecoin cross-chain without changing underlying performance. How to achieve this? Through the Unit of Liquidity. Catalyst is designed based on an independent price curve rather than a constant function. Uniswap v2 uses a constant function: x * y = k, which means that the product of the pre-swap balances must equal the post-swap balances. This equation is difficult to cross-chain expand because the constant k depends on x and y, which will be stored on different chains in a native cross-chain environment – without a clever solution, access to k is impossible.
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Instead, Catalyst quotes the value of liquidity within the treasury. Since this comparison depends only on the local state, it can be asynchronously completed independently of the rest of the system’s state. By mirroring swaps at the target end, swaps are executed cross-chain using native assets only. The intermediate is called Units, and users never “touch” them. If the swap fails, the original input is returned to the user. By cleverly choosing the price curve, Catalyst can create an invariant that: 1) can mimic Balancer invariants; 2) can produce flatter invariants that can facilitate stablecoin swaps; 3) can enable cross-chain liquidity auctions, etc.
Reference: https://twitter.com/CatalystAMM/status/1666839952972300288
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