In this, we describe how Catalyst further generalises both the Uniswap and Balancer AMM equation.
Let's go over how and why this will be a catalyst for cross-chain applications 🧵
2/ Uniswap v2 and Balancer are the gold standards for ease of use for both traders and liquidity providers.
They have enabled and continue to enable protocols to easily maintain liquidity for their ecosystem.
3/ So far, no other protocol has replicated the user experience 1-to-1 cross-chain.
You either have to be exposed to an intermediate token, rely on a bridge, or move your assets to a specific liquidity chain.
With Catalyst, this changes.
4/ By evaluating swaps independently, we can execute swaps on the Uniswap v2, Balancer, or even a stable-coin invariant cross-chain with no change to underlying performance.
How? With the Unit of Liquidity!
5/ Catalyst is designed based on independent price curves rather than a constant function.
Uniswap v2 uses the constant function: x * y = k, which states that the product of the balances before a swap needs to be equal to the balances after the swap.
6/ This equation is hard to scale cross-chain since the constant k depends on both x and y.
In a native cross-chain environment, these would be stored on different chains—making k inaccessible without clever workarounds.
7/ Instead, Catalyst quotes incoming value against the value of liquidity within a vault.
Since this comparison only depends on the local state, it can be done asynchronously, independently of the rest of the system state.
8/ By mirroring the swap on the target side, swaps are executed cross-chain using only native assets. The intermediate is called Units, and the user is *never* exposed to them.
If the swap execution fails, the original input is returned to the user.
9/ By cleverly choosing the price curves, Catalyst can create an invariant that:
- Can mimic the Balancer invariant
- Can produce a flatter invariant that can facilitate stable-coin swaps
- Can enable cross-chain liquidity auctions
- And so much more!
10/ The simplicity of the Unit of Liquidity enables developers to build never-before-seen cross-chain applications.