Price
One curve, from a $5,000 open.
The position runs from the opening price out across the ticks above it. That is the same shape as a constant-product pool whose quote side starts at a virtual $5,000 and whose token side starts at the full supply. Nothing is special about the arithmetic. It is what a one-sided Uniswap v3 or v4 position does.
Call the virtual quote P and the supply S. P is $5,000. S is 1,000,000,000 tokens. After buyers have paid a net quote q into the pool, the tokens still in the pool and the market cap are:
tokens in pool = P × S / (P + q) market cap = (P + q)² / P
q is quote after the pool fee. At q = 0 the market cap is P, about $5,000. The same open is used for every quote. On Robinhood, P is the ETH amount that was worth about $5,000 at launch, using the ETH dollar reference. The page shows that open in dollars.
A few points on the curve
Before fees. “Sold” is the share of supply that has left the pool.
| Net quote in | Market cap | Supply sold |
|---|---|---|
| $0 | $5,000 | 0% |
| $5,000 | $20,000 | 50% |
| $20,000 | $125,000 | 80% |
| $45,000 | $500,000 | 90% |
A sell moves q back down. It cannot move the launch position below the open, because that is where q returns to zero.
Several pools, one cap
A multi launch splits the supply across the pools and gives each pool its own slice of the virtual quote. Each book opens at the same price. The token page shows one price and one market cap. A stock launch is a single book against that stock, opened at the same $5,000.
A quote token is accepted when it has a price. On Robinhood that price can come from a hookless pool, or from a hooked pool that is registered for pricing only. A hooked price pool is not itself a Parabolarc sell route. The launch pool is still hookless.