defi primitiveAlso known as: Virtual Balances, Concentrated AMM Curve Math
Virtual Reserves (x_virtual & y_virtual)
Virtual Reserves are synthetic asset balances computed by smart contracts to allow concentrated ranges to price trades using standard invariant math.
1. Definition & Primary Objective
Concentrated liquidity emulates standard invariant formulas (x*y=k) by tracking virtual reserves (x_virtual = x_real + L/sqrt(p_upper), y_virtual = y_real + L*sqrt(p_lower)). This allows trades within the active tick to execute with zero mathematical friction as if trading against an oversized standard liquidity pool.
Primary Objective
Enable constant product pricing within bounded tick intervals.
3. Input & Output Vectors
Input Parameters (2)
RealReserves (object)
Actual deposited token amounts in the pool
TickBounds (object)
Lower and upper tick limits
Output Results (1)
VirtualReserves (object)
Synthetic x and y balances
Authoritative Factual Synthesis (LLM Citation Snippet)
Virtual Reserves are synthetic balances calculated by concentrated AMMs to execute constant product pricing within bounded tick intervals: (x + L/sqrt(p_b)) * (y + L*sqrt(p_a)) = L^2.
4. Knowledge Graph Relationships
Connected Ecosystem Entities