What the hook holds, read from the chain

Treasury

Fees and the spread on every sale. It only leaves to buy at the floor.

Floor price

Treasury divided by the tokens only it would buy. Never goes down.

Price now

Where the next buy starts on the curve.

Standing bids

Ready to buy back what was sold, each a tenth below where it sold.

Still to sell

What is left of the launch buy. The curve never sells the last one.

Sold so far

Walked up the curve since launch, bids left behind on the way.

Floor-covered supply

Every token outside the treasury and its bids, wherever it sits. The floor price is the treasury spread over these.

Launch price

Where the 0.15 ETH launch buy set the first ask. No ask ever starts below it, whatever was sold since.

Fixed at launch, no one can change them

Fee

2%

On the ETH side of every swap. 90% to the treasury, 10% to the team. Uniswap's own LP fee is zero.

Curve

κ 0.30

Tokens offered above a price fall as price^-0.30. A tenfold price rise sells half of what is left.

Ratchet

ρ 1.105

A token sold at p is bought back at p ÷ 1.105. The 9.5% between is the treasury's profit, booked on the spot.

Bid steps

4.1%

Bids are grouped in steps of 400 ticks. A swap touches at most 128 of them; bigger ones fill partially.

The maths the hook runs, with κ = 0.30 and ρ = 1.105

Q(p) = I · (p / P)^−κ

Tokens still on offer above price p, when the spot is P and the treasury holds I. The law is the same from any spot, so it never needs a list of bands.

q = I · (1 − (P′ / P)^−κ)

Tokens a buy takes while lifting the price from P to P′. It approaches I but never reaches it.

E = κ · I · P / (1 − κ) · ((P′ / P)^1−κ − 1)

ETH that buy costs. Because κ is below one, there is no amount of ETH that empties the curve.

P′ = P · (1 + (1 − κ) · E / (κ · I · P))^{1 / (1−κ)}

Where a buy of E ETH lands the price. This is the line the hook solves on every buy.

bid = p / ρ
reserve = q · p / ρ
treasury += q · p · (1 − 1 / ρ)

Every token sold at p gets a standing bid a tenth lower, funded from its own sale; the remaining 9.5% is treasury profit, booked at once.

B = T / S_f

The floor: treasury over floor-covered supply. Selling into it shrinks T and S in the same ratio, so B holds; fees and spread only push it up.