Introduction

Orbital Pool isn’t just another AMM, it’s a paradigm shift. The future holds a million stablecoins. Today's infrastructure isn't ready.

Orbital is an automated market maker for pools of 2, 3, or 10,000 stablecoins. It unlocks capital efficiency by bringing concentrated liquidity to higher dimensions.

By bending liquidity into a torus-shaped universe, Orbital unlocks concentrated liquidity for three or more stablecoins at once. This isn’t your usual 2D liquidity grid—it’s an entirely new dimension where LPs can laser-focus around the $1 mark, while still guaranteeing fair prices even if an entire stablecoin depegs.

It’s like Uniswap V3’s surgical precision colliding head-on with Curve’s bulletproof stability, and the result is something that shouldn’t even exist, but somehow, it does.

Orbital is the AMM where capital efficiency doesn’t just scale, it warps!

Mathematical Visualization

Key Features

• Multi-Token Stability Engine: Seamlessly trade across three or more stablecoins in a single pool with no more fragmented liquidity.
• Warped Concentrated Liquidity: Liquidity providers can laser-focus capital around $1, achieving maximum efficiency while still keeping markets resilient.
• Torus Invariant Model: A breakthrough mathematical invariant that curves liquidity across dimensions, ensuring fair pricing even in extreme scenarios.
• Boundary-Aware Swaps: Swaps automatically handle transitions between interior and boundary regions, ensuring correct pricing even at the edge of the liquidity surface.
• Fusion of Giants (Uniswap × Curve): Orbital takes Uniswap V3’s precision and Curve’s stability, merging them into a next-generation AMM.
• Powered by Arbitrum Stylus + Rust: Our entire mathematical engine runs in Rust via Stylus, unlocking performance and gas efficiency for complex calculations.

Mathematical Foundation

The Orbital Model

The Orbital AMM is built on the mathematical foundation described in the Paradigm Orbital Whitepaper. The core innovation lies in extending concentrated liquidity to higher dimensions using spherical geometry.

Core Mathematical Concepts

1. Sphere AMM Formula

Where:

• r(vector) = (r, r, ..., r) vector is the center of the sphere
• xᵢ is the AMM's reserve of asset i
• r is the radius of the sphere

2. Torus Invariant

The pool uses a torus (donut-shaped) invariant that combines:

• Interior Ticks: Behave like spheres for normal trading
• Boundary Ticks: Behave like circles when reserves hit boundaries

3. Newton's Method

Implementation of newton's method in Stylus contract to solve torus invariant with multiple fallback strategy.

4. Q96X48 Implementation We utilize the Q96X48 fixed-point arithmetic format, where the lower 48 bits represent the fractional component and the upper 96 bits represent the integer component.

5. Tick Geometry

Each tick is defined by:

• k: Plane constant (tick identifier)
• r: Radius of the tick
• Status: Interior or Boundary

Architecture & User Flow

🚀 Quick Start

Prerequisites

• Foundry installed
• Node.js 16+ (for testing)
• Git

Installation

# Clone the repository
git clone https://github.com/agrawalx/orbital-pool-organized.git
cd orbital-pool-organized
cd contracts
cd solidity 

# Install dependencies
forge install

# Build the project
forge build

# Run tests
forge test

Steps to configure your own pool

# Deploy pool and the mock tokens
forge script script/DeployAndConfig.s.sol --rpc-url $RPC_URL --private-key $PRIVATE_KEY --broadcast

# Command to add liquidity
cast send $POOL_ADDRESS "addLiquidity(uint256,uint256[5])" 3000000000000000 "[1000000000000000000000,1000000000000000000000,1000000000000000000000,1000000000000000000000,1000000000000000000000]" --rpc-url $RPC_URL --private-key $PRIVATE_KEY

# Command to swap 
cast send $POOL_ADDRESS "swap(uint256,uint256,uint256,uint256)" 0 1 20000000000000000000 0 --rpc-url $RPC_URL --private-key $PRIVATE_KEY

Youtube Link

• Video Demo

Documentation

Whitepaper Reference

This implementation is based on the Paradigm Orbital Whitepaper, which provides the mathematical foundation for the Orbital AMM model.

Key Concepts from Whitepaper

1. Sphere AMM: Base mathematical model using spherical geometry
2. Torus Invariant: Combined interior and boundary tick behavior
3. Tick Consolidation: Efficient aggregation of similar ticks
4. Global Trade Invariant: Method for calculating large trades across multiple ticks

📄 License

This project is licensed under the MIT License.

Built with ❤️ by the Orbital