Orbswap Lite-paper

Superellipse Orbital Stablecoin AMM

Every stablecoin, from every chain, in one super-concentrated pool.

TL;DR

One pool for many stables

Orbswap is a simplified superellipse version of Paradigm's Orbital research paper: a high-dimensional automated market maker for massive multi-stablecoin liquidity.

Problem

Stablecoin liquidity fragments

Thousands of stablecoins will need reliable liquidity. Today, each new issuer must attract capital to inherit stability and maintain its peg, which fragments routing and lowers efficiency.

Solution

Concentrated geometry

Orbswap consolidates stablecoin liquidity in a single n-dimensional pool with concentrated geometry, optimized through a superellipse invariant to tighten slippage and reduce de-peg impact for assets trading near 1:1.

Math

Invariant geometry

A spherical two-asset AMM begins as a circular invariant. For stablecoin liquidity, the contour flattens into a superellipse, making the most useful part of the curve denser around equal prices.

Circular invariant
(k−x)2+(k−y)2=k2(k - x)^2 + (k - y)^2 = k^2
Superellipse invariant
∣xc−1∣u(c)+∣yc−1∣u(c)=1\left|\frac{x}{c} - 1\right|^{u(c)} + \left|\frac{y}{c} - 1\right|^{u(c)} = 1
Exponent helper
u(x)=ln⁡(2)ln⁡(xx−1)u(x) = \frac{\ln(2)}{\ln\left(\frac{x}{x - 1}\right)}
Geometry simulationSwap simulation

Implementation

Flattening the orbital

The superellipse-shaped invariant replaces the perfect sphere with a contour that better models 1:1 stablecoin relationships, concentrating capital density and reducing wasted depth.

Paradigm's paper proposes ticks for concentrated exposure. Orbswap's first version gets a similar effect by flattening the orbital itself; future versions can add LP-specific exposure with ticks on the superellipse.

Execution price is chosen as the average of the prices before and after a trade executes, similar to common AMMs.

Novelty

Why it matters

  • Optimizes high-dimensional pool geometry for stablecoin behavior.
  • Turns theoretical orbital AMM designs into a practical implementation.
  • Supports massive n-coin pools with low-slippage liquidity surfaces.

Version 0

Live release

  • Single orbital liquidity pool supporting many stablecoins.
  • Admin-managed token additions for the first release.
  • Balanced deposits across supported pool assets.
  • One ERC-20 LP token representing pool liquidity.
  • Swaps between any two supported stablecoins.
  • MIT licensed code, with audits still pending.

Version 1

Next release

  • More decentralized stablecoin selection.
  • Unbalanced liquidity deposits.
  • Multi-coin swaps with split outputs.
  • Superellipse ticks for concentrated liquidity.
  • ERC-6909 support for LP accounting.
  • Multiple security audits.

Arbitrum

Why deploy there?

Arbitrum has deep stablecoin liquidity and low transaction costs, making it a practical chain for fast AMM experimentation. Future versions may use Arbitrum Stylus to run more advanced math in Rust-backed EVM contracts.

Orbital paperResearch paperOpen app