A next-gen AMM that supports 2, 3, or even 10,000 stablecoins in a single pool, scaling concentrated liquidity into higher dimensions.
We are building the next generation of Automated Market Makers (AMMs)—an AMM that doesn’t stop at two-token pairs, but can scale to support 2, 3, or even 10,000 stablecoins in a single pool. Inspired by Paradigm’s Orbital model, our design bends liquidity into a torus-shaped universe, extending concentrated liquidity into higher dimensions. This innovation lets liquidity providers concentrate around the $1 peg across multiple stablecoins at once, ensuring both capital efficiency and robust pricing, even if an asset collapses to zero.
Orbital combines the surgical precision of Uniswap V3 with the bulletproof stability of Curve, fusing their strengths into a single protocol. By integrating advanced mathematics like vector operations, Newton’s method for solving invariants, and high-dimensional geometry with modern blockchain tooling like Stylus Rust and Solidity, we’re pushing the boundaries of what AMMs can do.
In short, Orbital isn’t just an incremental improvement. It’s a fundamental reimagining of liquidity design in DeFi—where capital efficiency doesn’t just scale, it warps.
In the buildathon event, our first focus remained on the implementation of the swap, removeLiquidity, and addLiquidity functions by getting inspiration from Paradigm's Orbital AMM. This project gave us experience in the architecture of multi-asset stablecoin pools. By implementing such functioanlities, we developed a far greater understanding of how liquidity supply and price discovery can be generalized beyond the standard two-token AMM model. After understanding Paradigm's whitepaper on Orbital, it became clear that the key to Orbital lies in the geometry. Unlike using the standard two-dimensional price grid found in other markets, Orbital defines its invariant inside an n-dimensional sphere, in which the liquidity ticks appear as spherical caps. By virtue of symmetry, the elements fall together into a torus-shaped invariant and thus allow capital efficiency to scale among three or more stablecoins at once. The conversion of the theory into practice called for experimentation using Newton's method for solving the invariant numerically. This step was vital since Newton's method provides quick convergence and high accuracy and can be used even in the decentralized finance (DeFi) space. One among the most important technical hurdles that we faced consisted in aligning vector math using a two-dimensional decentralized finance (DeFi) architecture. Orbital's design is intrinsically high-dimensional, however, the nature of Ethereum contracts demands simplification. To overcome this challenge, we framed reserves, swaps, and movements of ticks as vector operations that can be converted to executable logic in Solidity. Apart from giving a feasible implementation to ourselves, this helped to better understand how abstruse geometry may be mapped onto real-world financial primitives. In order to handle the computational complexity and gas cost efficiently, we integrated Stylus Rust with Solidity. Heavy linear algebra and Newton iterations are handled in Rust, enabling much faster and more secure numerical computations. The outcomes are then passed back to Solidity smart contracts for verification and execution. This Solidity–Rust hybrid architecture ensures the protocol enjoys gas efficiency while retaining mathematical accuracy and thus enjoys the best of both worlds of ecosystems. In this buildathon step, we did not only recreate an Automated Market Maker (AMM) but also completely internalized the behavior of Orbital's geometric invariants, how to numerically calculate them, and how to turn such complex math into real-world coding. The work done forms the foundation of Orbital.
