Fee conversion model
The math that turns a permanent-liquidity contribution into locked liquidity.
Model, not a forecast
This page explains the mechanism with real constant-product math. It says nothing about how much will actually be contributed or what the pool will look like.
Permanent liquidity is added to a constant-product pool (x · y = k) using only SOL. To add liquidity from one asset, the program first swaps part of the SOL for the memecoin, then deposits both sides at the pool's ratio. This is a single-sided deposit (a "zap").
Inputs
| Symbol | Meaning |
|---|---|
F | SOL contributed to the fee receiver |
x | Pool SOL reserve |
y | Pool token (memecoin) reserve |
fee | Pool swap fee, in basis points |
r | Share of a swap that remains after the fee: r = 1 − fee / 10000 |
The six steps
Split the contribution
80% goes to permanent liquidity, the rest to the restricted reserve.
P = F × 80%
reserve = F − PFind the optimal swap for a single-sided deposit
Swap just enough SOL that what is left over matches the post-swap pool ratio.
s = ( √( x²(1+r)² + 4·r·x·P ) − x(1+r) ) / 2rTokens received from the swap
Δy = r·s·y / (x + r·s)Add liquidity (locked forever)
Deposit (P − s) SOL plus Δy memecoin at the post-swap ratio. This position is permanently locked.
New permanent share of the pool
q = (P − s) / (x + P)Price impact of the swap leg
The swap moves the price slightly. With price p = x / y before (p₀) and after (p₁) the swap:
impact = p₁ / p₀ − 1Repeated deployments
Each deployment adds a new slice of permanent liquidity, so the permanent share of the pool grows as contributions repeat. After each deployment the existing permanent share is diluted by the new liquidity and then the new slice is added:
share_next = share × (1 − q) + qThis simplified curve ignores trading and other LP flows, which would change the result in practice.
See permanent liquidity contributions for where F comes from, and permanent liquidity for what locking means.