One way to view PropAMMs is as a next step to all the different ways we have signed a swap and sourced swap liquidity over the years. Ordinary AMM: When you sign an ordinary AMM tx, eg. uniswap app in 2021, you are agreeing to use that specific AMM pool at whatever the market price is when the block is built, but no worse price than the min you sign into the tx. The pool you're using you picked manually from the swap UI. Aggregator: When you sign an aggregator tx, like on matcha, you're agreeing to use a specific series of AMM pools and other onchain venues to achieve your swap. The specific path is quoted to you every ~10 seconds, that's why aggregators are always updating quotes-- because the specific path of onchain composability that your funds will take is snapshot into the signed tx, so it needs to be continuously refreshed. If a better funds path becomes available after you sign, too bad, you already signed. Solver: When you sign a solver tx, like cowswap, you're agreeing to exchange at whatever best rate a 3rd party marketplace of solvers finds, but no worse swap rate than your signed min rate. The main difference here vs. an ordinary AMM is that the solver marketplace is empowered to use any and all sources of liquidity that are synchronously composable. Solvers might use protocols that you've never heard of to fill your order, and indeed do all the time. Solvers do not bring any of their own money. They are fully focused on using their offchain compute/data to find you a swap solution purely from existing onchain liquidity sources, in a single synchronous tx. This competitive solver search process happens asynchronously in a batch with other cowswap txs, which is why you wait after you sign a cow order and then it moos as you when it's filled. Onchain solver: Something novel that has been attempted, but isn't very popular afaik, is do the solving synchronously onchain such that the best swap strategy is discovered during the swap's execution itself. This is only possible when onchain execution is cheap (it takes a lot more gas to to find the best swap than to execute it). It's also inherently limiting because you just can't check the entire chain for the best exotic liquidity during the swap itself, even cheap gas is too expensive and limited. PropAMMs: A PropAMM is a market maker that plugs into the MEV pipeline to fulfill your swap using the latest price as of the millisecond when the block is built. The 12 seconds between eth L1 blocks is an eternity for micro price discovery, but PropAMMs sidestep the 12 seconds entirely by quoting the very latest price as of the exact moment the block is built. This is only possible when the market maker is directly plugged into the block building process. The "prop" in PropAMM stands for "proprietary", meaning that the PropAMM is not neutral infra, it's a team risking their own money to try and make a profit fulfilling your swap. PropAMMs are a standalone liquidity source and need to be integrated into a swap workflow, such as solvers or aggregators, to become accessible to end users. What makes PropAMMs so promising for Ethereum is that they allow our capital to remain on L1 where it's safest and most productive, while sidestepping the massive downside of 12-second block time due to always quoting the freshest price at the instant the block is built in our mev pipeline. Eat your cake (better fresher prices) and have it too (stay on L1).