Orbswap Litepaper

TL;DR

Orbswap is a simplified superellipse version of Paradigm's “Orbital” research paper for a high-dimensional automated market maker (AMM) specifically for a massive multi‑stablecoin pool.

Problems

There are going to be thousands of stablecoins and today's AMM infrastructure was not designed with this in mind.

Every time a new stablecoin is launched, the issuer must attract liquidity to inherit stability from other assets and ensure the price stays pegged in the market. This is extremely expensive and limits the scale of new stables.

Routing between stablecoins becomes more complex and further fragments liquidity over time, lowering capital efficiency of using each.

Solution

Orbswap consolidates stablecoin liquidity in a single n‑dimensional pool with concentrated geometry—now optimized using superellipse invariants—to tighten slippage, reduce de‑peg impact of trades that are close to 1:1 in price, and massively increase capital efficiency.

A spherical AMM consisting of 2 assets can be expressed as a circular invariant as follows:

To extend it for stablecoin use, we convert the invariant to a superellipse:

Where u is equal to:

You can test how these operate in a simulation here: https://www.desmos.com/calculator/mbohmvmytg

And simulate an AMM swap example here: https://www.desmos.com/calculator/2t4evqjqjj

Stablecoin liquidity does not need to be linear across the full price curve when it is behaving normally, and liquidity can be super concentrated around equal prices. If one of the stablecoins depegs, the others can all trade at efficient prices, while the depegged one will become worthless much faster than a traditional AMM curve.

Inspiration

• Orbital paper by Dave White, Dan Robinson, and Ciamac Moallemi from Paradigm.
• Multiple asset n-dimensional AMM first proposed by Eric Forgy and Leo Lau.
• Concentrated Circular and Superelliptical Market Maker by Vasily Tolstikov.

We thank them all for publishing their unique designs and research.

Implementation

Superellipse‑shaped invariant: replaces the perfect sphere from the Paradigm paper with a superellipse contour, which more precisely models 1:1 stablecoin relationships—concentrating capital density and reducing wasted depth.

The Paradigm paper suggests using ticks to improve capital efficiency, by allowing LPs to supply liquidity centrated around equal prices of tokens. However, we can have the same effect by flattening the orbital into a superellipse instead. The trade-off being that users can no longer customize their exposure. We will improve this in V1 and allow each LP to have their own unique asymetric exposure with ticks on the superellipse.

An execution price is chosen as the average of the prices before and after a trade executes, the same as most other AMMs, like Uniswap.

Novelty

The superellipse invariant optimizes the high‑dimensional pool geometry, better aligning to stablecoin behavior than pure spheres.

It’s the first working implementation demonstrating these theoretical ideas in practice.

It enables massive n‑coin pools with capital‑efficient, low‑slippage liquidity surfaces.

Releases:

Version 0 features (live on Arbitrum today)

• A single orbital liquidity pool with support for n number of stablecoins (currently with ~10)
• Only a centralized administrator can add a new stableoin type to the pool.
• Anyone can add liquidity for all supported stablecoins in the pool, but liquidity must be balanced at the current prices for each. This limitation will be removed in V1.
• A single ERC-20 LP token for the pool.
• Swaps between any 2 stablecoins in the pool. Limited to a single type of token in, and a single type of token out.
• MIT licensed code fully available.
• No audits completed.

Version 1 (early 2026)

• Supported stablecoin selection will be more decentralized.
• Unbalanced liquidity deposits.
• Multi-coin swaps. Example: sell stablecoin-A, receive output in 25% of stablecoin-B and 75% in stablecoin-C.
• Superellipse ticks for concentrated liquidity.
• ERC-6909 support for LP tokens.
• Multiple security audits.

Why deploy on Arbitrum?

With over $3.5B in stablecoins on the chain, Arbitrum is a liquidity hub for stables between Ethereum and other chains like Hyperliquid. The low cost and reliability of Arbitrum makes it the perfect place for experimenting with our new AMM designs quickly. We spend no time at all worrying about the chain's underlying architecture, and all our time focusing on making better products and pushing the limits of AMM capital efficiency. Other chain deployments, and better crosschain liquidity management, will come in the long term.

In the next (full) version of Orbswap, we anticipate needing to rely on more intense trigonometry calculations which are unsuitable to do in Solidity. However, using Arbitrum Stylus we can write EVM smart contracts in Rust and access more advanced existing trig libraries.