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There are two types of Fee Market Cap Schedulers:
  1. Linear (Mode 3)
  2. Exponential (Mode 4)

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Math Formula

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Step 1: Calculate Passed Periods

The number of periods passed is determined by how much the sqrt price has increased from the initial price:
Passed Period=(Current Sqrt Price−Initial Sqrt Price)×10,000Initial Sqrt Price×Sqrt Price Step Bps\text{Passed Period} = \frac{(\text{Current Sqrt Price} - \text{Initial Sqrt Price}) \times {10,000}}{\text{Initial Sqrt Price} \times \text{Sqrt Price Step Bps}}
Where:
  • current_sqrt_price: The current sqrt price of the pool
  • initial_sqrt_price: The initial sqrt price when the pool was created
  • sqrt_price_step_bps: The sqrt price increase (in bps) required to advance one period

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Step 2: Calculate Current Fee

There are two modes for fee calculation:

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Linear Fee Market Cap Scheduler (Mode 3)

Current Fee=Cliff Fee Numerator−(Passed Period×Reduction Factor)\text{Current Fee} = \text{Cliff Fee Numerator} - (\text{Passed Period} \times \text{Reduction Factor})
The fee decreases by a constant amount (reduction_factor) for each period passed.

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Exponential Fee Market Cap Scheduler (Mode 4)

Current Fee=Cliff Fee Numerator×(1−Reduction Factor10,000)Passed Period\text{Current Fee} = \text{Cliff Fee Numerator} \times \left(1 - \frac{\text{Reduction Factor}}{10,000}\right)^{\text{Passed Period}}
The fee decreases by a percentage of the current fee for each period passed.

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Scheduler Expiration

The scheduler has an expiration mechanism to ensure fees eventually reach the minimum: 
Expiration Point = Activation Point + Scheduler Expiration Duration
  • If current_point > expiration_point, the scheduler expires
  • When expired, the fee defaults to the minimum fee (fee calculated at number_of_period)
  • This prevents fees from staying high indefinitely if the price doesn’t increase

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Edge Cases

ConditionBehavior
current_sqrt_price <= init_sqrt_pricepassed_period = 0 (fee stays at cliff fee)
passed_period > number_of_periodpassed_period = number_of_period (fee at minimum)
Scheduler expiredFee defaults to minimum fee
Alpha Vault buying (before activation)Fee at minimum fee

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Example Calculations

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Linear Mode Example

Given:
  • cliff_fee_numerator: 500,000,000 (50% fee)
  • number_of_period: 100
  • sqrt_price_step_bps: 100 (1% sqrt price step)
  • reduction_factor: 4,950,000
  • init_sqrt_price: 1,000,000
  • current_sqrt_price: 1,050,000 (5% increase)
Step 1: Calculate passed period 
Passed Period = (1,050,000 - 1,000,000) × 10,000 / (1,000,000 × 100)
             = 50,000 × 10,000 / 100,000,000
             = 5 periods
Step 2: Calculate fee 
Fee = 500,000,000 - (5 × 4,950,000)
    = 500,000,000 - 24,750,000
    = 475,250,000 (≈ 47.5% fee)

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Exponential Mode Example

Given:
  • cliff_fee_numerator: 500,000,000 (50% fee)
  • number_of_period: 100
  • sqrt_price_step_bps: 100 (1% sqrt price step)
  • reduction_factor: 390 (3.9% reduction per period)
  • init_sqrt_price: 1,000,000
  • current_sqrt_price: 1,050,000 (5% increase)
Step 1: Calculate passed period 
Passed Period = 5 periods (same as above)
Step 2: Calculate fee 
Fee = 500,000,000 × (1 - 390/10,000)^5
    = 500,000,000 × (0.961)^5
    = 500,000,000 × 0.8154
    = 407,700,000 (≈ 40.8% fee)

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Fee Numerator Conversion

To convert fee numerator to percentage: 
Fee Percentage = Fee Numerator / 10,000,000
Examples:
  • 500,000,000 = 50% fee
  • 10,000,000 = 1% fee
  • 100,000,000 = 10% fee