> For the complete documentation index, see [llms.txt](https://docs.shellprotocol.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.shellprotocol.io/deep-dive/primitives/proteus-amm-engine.md).

# Proteus AMM Engine

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This is a developer's guide to building with Proteus. For a complete introduction, check out the [Proteus wiki page](https://wiki.shellprotocol.io/how-shell-works/proteus-amm-engine).
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## What is Proteus

Proteus is an AMM (Automated Market Maker) engine that is capable of approximating any bonding curve, enhancing Shell Protocol's market-making strategies. It is capable of extremely precise liquidity concentration across multiple price ranges, but still uses fungible LP tokens.

There are two implementations of Proteus: Static Proteus and Evolving Proteus.

## Static Proteus implementation details

It turns out that in order to create any bonding curve and achieve extremely precise liquidity concentration, all you need is 4 parameters: list of slopes of the radial lines in order to create slices, list of values representing relative scale factors of each slice, a list of a values, and a list of b values representing price points of the particular slice.

Those params are labeled as lists of:

1. ms - representing a list of slopes of the radial lines
2. \_as - list of price points of the particular slice
3. bs - list of price points of the particular slice
4. ks - list of values representing relative scale factors of each slice

## Determining ms, \_as, bs and ks values

Determining `ms`, `_as`, `bs` and `ks` values is not an easy task to do. In order to understand them better you may want to spend some time going through the files in `scripts/params` directory of our [public repo](https://github.com/Shell-Protocol/Shell-Protocol/tree/main/scripts/params). You will find examples of different type of pools in that folder, like well known constant product and stablepool.

## Evolving Proteus

Evolving Proteus is an advanced version of the Proteus AMM engine, with which the bonding curve can change every block (or "evolve") during a specified time frame.\
\
Evolving Proteus also differs from Static Proteus in that Evolving Proteus only has one slice. Evolving Proteus is good for liquidity bootstrapping, or any use case that requires a [Dutch auction](https://en.wikipedia.org/wiki/Dutch_auction). It is also good for creating managed pools.

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For a thorough understanding of Proteus, it is advisable to first read the initial version of the [Proteus White Paper](https://shellprotocol.io/static/Proteus_AMM_Engine_-_Shell_v2_Part_1.pdf), followed by the [updated (second version) White Paper](https://github.com/cowri/Proteus/blob/main/Proteus_white_paper_UPDATED.pdf), and finally, the [Update 3 document](https://shell-protocol.notion.site/Proteus-AMM-Engine-Update-3-7f33b7e1561347b696874a8ba02b9782). The actual implementation of the Ocean can be accessed in our public repository, located within the Proteus.sol file at the [provided link](https://github.com/Shell-Protocol/Shell-Protocol/blob/main/src/proteus/Proteus.sol).
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