Orbital

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.