The curve

Buying

You send MNT and receive tokens. The contract works out how many at the current point on the curve, takes its 1% fee, and sends them straight to your wallet. There is nobody on the other side of the trade and nothing to match against, so a buy either fills at the price you were quoted or better, or it does not go through.

You set a slippage tolerance before you sign. If the price moves further than that between your quote and your transaction landing, the trade reverts and you keep your MNT, minus gas.

Selling

The same thing backwards. You send tokens, the contract pays you MNT out of the reserves it is holding, and the price moves back down the curve. You can sell any amount at any time while the token is on its curve. There is no lock up and no window.

Why the price goes up

The curve is a constant product, the same idea an automated market maker uses. The contract behaves as though it holds a pool of MNT and a pool of tokens whose product stays fixed. Buying takes tokens out of that pool and puts MNT in, so each token after the first costs slightly more.

Nobody sets the price and nobody can move it except by trading. The full arithmetic, including how to reproduce our numbers exactly, is on pricing a curve.

The reserves are real

Every MNT paid into a curve stays in the contract until that token graduates. It is not lent out, not moved, and not available to anyone. You can read the figure yourself, per token, and check that the sum across every token matches the contract's balance.

This is what makes selling back possible at any point. If reserves could be spent, a sell would depend on somebody else buying first.

How far along a curve is

The progress bar on a token's page is its reserves against its threshold. At 100% the curve is full, the last 700 millionth token has been sold, and the token graduates. What happens then is graduation.