Paradigm's Orbital AMM — multi-asset stablecoin pool with concentrated liquidity & institutional settlement
Paper · Solana · Anchor · StableHacks 2026
Orbital is a next-generation multi-asset stablecoin AMM designed by Paradigm. It combines the best of Curve (multi-asset pools) and Uniswap V3 (concentrated liquidity) while adding a novel depeg isolation mechanism.
This repository is the first Solana-native implementation of the Orbital AMM, extended with a permissioned institutional settlement layer for regulated entities.
| Feature | Description |
|---|---|
| Sphere Invariant | ||r - x||² = r² — geometric invariant enabling N-asset pools on a hypersphere |
| Nested Ticks | Spherical cap-based concentrated liquidity with per-tick reserves |
| Depeg Isolation | When an asset depegs, its tick flips to Boundary — isolating risk from other LPs |
| Trade Segmentation | Multi-tick swap execution with boundary detection and automatic tick crossing |
| Institutional Settlement | Policy engine, allowlists, daily volume limits, and on-chain audit trails |
| KYC/AML Compliance | On-chain KYC registry, risk scoring, jurisdiction filtering, FATF Travel Rule |
Single Anchor program with 4 bounded contexts as Rust modules:
orbital/
├── math/ # Core math engine
│ ├── sphere.rs # Sphere invariant, price, equal-price point
│ ├── torus.rs # Tick crossing detection, delta-to-boundary
│ ├── tick.rs # k bounds, x_min/x_max, capital efficiency
│ ├── newton.rs # Analytical swap solver (quadratic)
│ ├── fixed_point.rs # Q64.64 fixed-point arithmetic (i128)
│ └── reserve_state.rs # O(1) invariant verification
│
├── domain/ # Business logic
│ ├── core/ # Pool operations, swap math
│ ├── liquidity/ # LP position management
│ ├── settlement/ # Institutional settlement orchestration
│ └── policy/ # Access control, compliance
│
├── instructions/ # On-chain instruction handlers
│ ├── initialize_pool # Create N-asset pool with sphere invariant
│ ├── execute_swap # Multi-segment swap with tick crossing
│ ├── create_tick # Deploy concentrated liquidity tick
│ ├── add_liquidity # Deposit to full-range or tick position
│ ├── remove_liquidity # Withdraw with boundary-aware logic
│ ├── create_policy # Define settlement policy
│ ├── update_policy # Modify policy parameters
│ ├── manage_allowlist # Add/remove institutional participants
│ ├── manage_kyc_entry # KYC/KYT/AML registry per member
│ ├── execute_settlement # Policy-checked institutional swap
│ └── close_pool # Authority-only pool shutdown
│
├── state/ # Account definitions (PDA)
│ ├── pool, position, tick
│ ├── policy, allowlist, kyc_entry
│ └── settlement, audit_entry
│
├── errors.rs # Program error codes
└── events.rs # CPI event definitions
Based on the Paradigm Orbital paper:
| Formula | Description | Implementation |
|---|---|---|
Σ(r - xᵢ)² = r² |
Sphere invariant | sphere.rs |
(r - xⱼ) / (r - xᵢ) |
Marginal price | sphere.rs |
q = r(1 - 1/√n) |
Equal price point | sphere.rs |
α = Σxᵢ / √n |
Alpha (torus coordinate) | torus.rs |
k_min = r(√n - 1) |
Minimum tick bound | tick.rs |
k_max = r(n-1) / √n |
Maximum tick bound | tick.rs |
D = √(k²n - n((n-1)r - k√n)²) |
Tick discriminant | tick.rs |
x_min = (k√n - D) / n |
Lower reserve bound | tick.rs |
x_max = min(r, (k√n + D) / n) |
Upper reserve bound | tick.rs |
s(α) = √(r² - (α - r√n)²) |
Boundary sphere radius | torus.rs |
d_out = -b + √(b² + 2ad - d²) |
Analytical swap output | newton.rs |
Precision: Q64.64 fixed-point (i128 backing, 64 fractional bits) for all on-chain math.
Next.js 16 app with real-time Solana devnet integration:
| Page | Features |
|---|---|
| Swap | Token selection, real-time quote with tick-aware calculator, slippage settings |
| Dashboard | Pool overview, reserve chart, LP positions, tick selector for concentrated liquidity |
| Settlement | Policy-compliant institutional swap form, Travel Rule data input, compliance preview |
| Faucet | Devnet SPL token faucet (USDC, USDT, PYUSD) |
| Admin | Policy management (KYC toggle, risk score, Travel Rule threshold), KYC registry, allowlist |
- Rust 1.75+
- Solana CLI 1.18+
- Anchor 0.31.1
- Node.js 20+
# Install dependencies
npm install
# Build Anchor program
npm run anchor-build
# Run on-chain tests
npm run anchor-test
# Start frontend dev server
npm run dev# Deploy program
npm run deploy:devnet
# Bootstrap pool + ticks with demo liquidity
npm run bootstrap:devnetBZDXfJTBpH9ZMo2dz57BFKGNw4FYFCDr1KaUUkFtfRVD
3-asset pool: USDC · USDT · PYUSD
| Parameter | Value |
|---|---|
| Pool TVL | $150M (demo tokens) |
| Fee | 1 bps (0.01%) |
| Assets | 3 (n = 3) |
| Ticks | 5 concentrated ticks (3.5× – 18× concentration) |
| Tick TVL | $49M/asset across ticks |
Comprehensive analysis against the Paradigm Orbital paper:
| Paper Concept | Status | Notes |
|---|---|---|
| Sphere invariant | ✅ Complete | Both O(n) and O(1) verification paths |
| Multi-asset pools (n ≤ 8) | ✅ Complete | Parameterized n with Q64.64 precision |
| Price formula | ✅ Complete | Marginal price, equal-price point |
| Tick math (k bounds, x_min/x_max) | ✅ Complete | All formulas verified against paper |
| Trade segmentation loop | ✅ Complete | While loop with boundary detection and tick flip |
| Analytical swap solver | ✅ Complete | Closed-form quadratic (CU-optimized) |
| Depeg isolation (tick flip) | ✅ Complete | Interior → Boundary status transition |
| Torus tick-crossing detection | Alpha-based detection works; full torus consolidation deferred | |
| Tick consolidation (r_c = Σrᵢ) | Individual tick tracking, no aggregation | |
| Virtual reserve amplification | x_min computed but not used in swap math (#36) | |
| Per-tick fee distribution | Fees tracked globally, no per-tick LP harvest | |
| KYC/KYT/AML compliance | ✅ Complete | On-chain KYC registry, risk scoring, jurisdiction filter, Travel Rule |
Note: The MVP prioritizes correctness of the sphere invariant, trade segmentation, and institutional compliance. Virtual reserve amplification (the mechanism that converts concentrated liquidity into reduced slippage) is tracked in issue #59. Per-tick fee distribution and LP fee claim are post-MVP (#48).
stablerail/
├── anchor/ # Solana program (Rust/Anchor)
│ ├── programs/orbital/ # Main program source
│ └── Anchor.toml # Anchor configuration
│
├── app/ # Next.js frontend
│ ├── components/ # React components (swap, dashboard, settlement)
│ ├── hooks/ # Custom hooks (usePool, useSwapQuote, usePoolTicks, useKycEntries, useExecuteSettlement)
│ └── lib/ # Math library, config, deserializers
│
├── scripts/ # Deployment & bootstrap scripts
│ ├── deploy-devnet.sh # Program deployment
│ ├── bootstrap-pool.ts # Pool + tick + liquidity setup
│ └── create-demo-ticks.ts # Demo tick creation
│
└── docs/ # Documentation
├── Orbital_Math_Reference.md
├── Orbital_DDD_Architecture.md
├── Orbital_Settlement_Protocol_PRD_v2.1.md
└── DESIGN_SYSTEM.md
| Layer | Technology |
|---|---|
| Smart Contract | Rust, Anchor 0.31.1 |
| Math Engine | Custom Q64.64 fixed-point (i128) |
| Frontend | Next.js 16, React 19, TypeScript |
| Styling | Tailwind CSS 4 |
| Charts | Recharts |
| Wallet | @solana/kit, Phantom |
| Network | Solana Devnet |
| Issue | Title | Priority |
|---|---|---|
| #25 | DoraHacks submission and final cleanup | P0 |
| #23 | Demo video production (3-min format) | P0 |
| #24 | README and project documentation | P0 |
| #21 | E2E integration testing | P1 |
| Issue | Title | Description |
|---|---|---|
| #59 | Virtual reserve amplification | Use x_min from concentrated ticks to amplify swap math, reducing slippage |
| #48 | LP fee claim mechanism | Per-tick fee distribution and claim_fees instruction |
| #47 | close_pool guard fix | Seed liquidity permanently locks pool closure |
| #43 | i256 precision migration | Upgrade from Q64.64 (i128) to unlimited precision |
| #42 | Decimal normalization | Production-scale deposit handling across different token decimals |
| #36 | Depeg rebalance protection | Prevent fee-free liquidity extraction during depeg events |
This project was built for StableHacks 2026. Contributions, issues, and discussions are welcome.