Tick System

Across implementations, tick systems rely on several core data structures and computations:

• Tick Bitmap: A compressed mapping tracking which ticks contain liquidity.
• sqrtPriceX96: A fixed-point representation of the square root of price, stored as a Q64.96 number, used for precision in swap math.
• LiquidityNet: The net change in liquidity (denoted as L) at a specific tick when crossed.
• Tick Spacing: The minimum distance between initialized ticks, determined by the pool's fee tier (e.g., 1 bps, 5 bps, 30 bps, 100 bps).

LPs can concentrate their capital within a custom price range defined by ticks, rather than across the entire price curve (0 to ∞). This allows them to provide the same level of liquidity depth as a V2-style pool while committing significantly less capital, dramatically boosting potential fee yield on capital deployed.

• Example: An LP can provide liquidity only between $1,500 and $2,500 for ETH/USDC, ignoring prices outside that range.

The tick system enables LPs to express specific market views and manage impermanent loss risk. Strategies include:

• Narrow Range: High fee income within a tight price band, suited for stablecoins or high-conviction ranges.
• Wide Range: Lower fee density but reduced risk of the price moving outside the position.
• Passive/Active Management: LPs can manually adjust their ranges or use automated services to rebalance positions based on market conditions.

Fees are earned in a predictable, granular manner. When a swap moves the price across ticks, liquidity from the LP's position is used, and fees are accrued proportionally. LPs earn fees only when the price is within their active range, creating a direct link between provided utility and compensation. This transparency allows for precise APR calculation based on expected trading volume within the chosen price range.

Discrete, tokenized LP positions (e.g., Uniswap V3's NFTs) built on the tick system can be integrated into other DeFi protocols. This enables:

• Position Management: Automated services that optimize and rebalance ranges.
• Collateralization: LP positions can be used as collateral in lending protocols (though with specific risk considerations).
• Vault Strategies: Yield aggregators can pool user funds to manage complex, automated liquidity provision strategies across multiple tick ranges.

The tick system allows LPs to act like professional market makers by placing discrete liquidity bids and offers at specific price points. This creates a limit-order-book-like experience within a constant product AMM framework. LPs can target liquidity to areas of expected high trading volume or volatility, optimizing for the highest possible fee return relative to their risk tolerance and market outlook.

Tick spacing is the minimum distance between two allowable price ticks, set as a multiple of the base unit (e.g., 1, 10, 60). It determines price precision and liquidity concentration.

• A spacing of 1 allows prices at every 0.01% increment (1 basis point).
• A spacing of 60 allows prices only every 0.6% increment. Higher spacing reduces the number of possible price points, concentrating liquidity into fewer, larger positions, which can reduce gas costs for liquidity providers but may increase slippage for traders.

The tick system enables concentrated liquidity, where liquidity providers (LPs) allocate capital to specific price ranges (between an upper and lower tick).

• Capital is only used when the price is within the chosen range, dramatically increasing capital efficiency compared to full-range liquidity.
• LPs must actively manage their ranges based on market volatility and fee generation goals.
• The system creates a continuous order book from discrete liquidity chunks, with execution price determined by the active tick.

Each tick is identified by an integer tick index (i). The corresponding price is calculated using the formula: price = 1.0001^i.

• This creates a geometric progression where a 1-tick move represents a ~0.01% (1 basis point) price change.
• A positive index (i) represents a price >= 1.0 (e.g., i=0 → 1.0, i=6931 → ~2.0).
• A negative index represents a price < 1.0 (e.g., i=-6931 → ~0.5). This logarithmic scaling allows consistent percentage-based granularity across all price levels.

When a swap occurs, the protocol consumes liquidity from the current active tick, moving the price. A tick crossing happens when the swap exhausts all liquidity at the current tick, moving the price to the next initialized tick.

• Each crossing triggers a state update and may incur gas costs.
• The swap executes at the effective price, which is the time-weighted average price across all ticks traversed during the transaction.
• Large swaps may cross multiple ticks, incurring higher gas fees but providing better price discovery.

Different fee tiers (e.g., 0.01%, 0.05%, 0.30%, 1.00%) are paired with recommended tick spacings. This creates distinct liquidity pools for the same asset pair.

• Lower fee tiers (0.01%, 0.05%) typically use tighter tick spacing (1 or 10) for highly correlated assets (e.g., stablecoin pairs), favoring high-frequency, low-slippage trades.
• Higher fee tiers (0.30%, 1.00%) use wider spacing (60 or 200) for volatile or uncorrelated assets, concentrating liquidity to offset impermanent loss risk. This segmentation allows LPs to align their strategy with asset volatility and expected trading volume.

The tick system introduces specific gas cost considerations for users and the protocol.

• Liquidity Provision: Positioning liquidity across many ticks increases gas costs for minting, adjusting, and collecting fees.
• Swap Execution: Crossings of initialized ticks incur additional computation and storage writes (~40k gas per crossing).
• Tick Bitmap: The protocol uses a bitmap to track initialized ticks, enabling O(1) checks for liquidity. Searching for the next initialized tick during a swap is a bounded operation to prevent excessive gas consumption and potential out-of-gas errors.

A non-fungible representation of a user's provided liquidity within a specific tick range. Unlike traditional LP tokens, which are fungible, these are often represented as NFTs (e.g., Uniswap V3) or unique ledger entries, encoding the parameters of the position.

• Components: Stores the tick lower, tick upper, liquidity amount, and fee tier.
• Management: Positions can be individually modified, increased, or closed, allowing for active liquidity management strategies.
• Fee Accrual: Fees earned are tracked and accumulated within the position, claimable upon withdrawal.

The fixed distance between allowable ticks, determined by the pool's fee tier. It is a protocol-level parameter that balances granularity against gas efficiency and liquidity fragmentation.

• Determinant: Higher fee pools (e.g., 1%) typically have wider tick spacing (e.g., 200 ticks), while lower fee pools (e.g., 0.01%) have tighter spacing (e.g., 1 tick).
• Impact on Price: Defines the minimum price movement (tick size) and the precision of liquidity deployment.
• Trade-off: Tighter spacing allows more precise liquidity ranges but can increase gas costs for crossing multiple ticks.

A computational abstraction used in constant product AMMs with concentrated liquidity. Because liquidity only exists between two ticks, the protocol uses virtual reserves of token X and token Y to simulate a full-range liquidity curve, calculating swaps and prices as if the entire constant product k = x * y were maintained.

• Purpose: Enables the constant product formula (x * y = k) to function correctly within a bounded price range.
• Calculation: Derived from the real (real) reserves and the liquidity (L) concentrated in the active tick range.
• Result: Allows for seamless integration of concentrated liquidity into the established AMM math.

A pre-set swap fee percentage (e.g., 0.01%, 0.05%, 0.3%, 1%) associated with a specific pool, which determines its tick spacing. Different tiers cater to various asset volatilities and trader preferences.

• Selection: LPs choose a tier when creating a position, aligning with the expected trading volume and price stability of the asset pair.
• Incentive Alignment: Higher volatility pairs may use higher fee tiers to compensate LPs for increased impermanent loss risk.
• Market Structure: Multiple pools for the same pair can exist with different fee tiers, creating a competitive fee market for liquidity.