How a v4 Pairs coin works

Launch

launch(name, symbol, uri, choice, creator, acknowledgeUnchecked) is payable. It checks the hook route, deploys the coin (fixed supply S = 10⁹ × 10¹⁸, minted once to the factory), creates the pool keyed (ETH, coin, fee, 200, hook), initializes it at tick₀, and in one unlock adds the position and runs the optional dev buy.

Stack route: the factory calls the hook stack's createDam with base fee 10,000 pips and the dynamic-fee flag, and becomes the pool's stack owner. Other routes call PoolManager.initialize.

Curve

Position [tick_min, tick₀] with L = ⌊(S − 10⁹) · 2⁹⁶ / (√P₀ − √P_min)⌋. At tick₀ the position is entirely coin. A buy of Δx ETH (after fees) moves √P to √P′ = L·√P / (L + Δx·√P/2⁹⁶) and pays out L·(√P − √P′)/2⁹⁶ coins.

Dev buy cap: the swap's price limit is √P₀ − (0.05·S)·2⁹⁶/L, so the creator receives at most 5% of the supply.

Fees

Invariants

• Factory liquidity per coin never decreases.
• Split sums to 100%: creator + stakers + burn + protocol = collected ETH, checked by a fuzz test.
• Coin supply is constant; burns move coins to 0x…dEaD.
• Stack royalty ≤ 30 bps.
• uncheckedHook never flips back.

State machine

Per coin: Launched, then (StackProposed, then StackApplied or Cancelled) any number of times on the stack route, then optionally Frozen. A standalone hook or no hook stays Launched.

Live parameters