Ebb
Part of the fee buys PAGU from the pool and destroys it. Supply can only go down.
What it is for
Part of every fee buys PAGU out of the pool and destroys it. The supply started at a fixed number and can only go down from there. No contract of mine can make new PAGU.
How it works
The burn budget builds up in ETH. Usually it is spent inside the next trade: the hook buys PAGU from the pool and calls the token's own burn function on what it bought. Anyone can also spend a waiting budget by calling one function, which needs no permission.
The hook does not buy at any price. It keeps an average of the pool's price over the last 10 to 20 minutes and buys only while PAGU is at most about 3% dearer than that average. After a sharp rise it waits until the average has caught up. A price below the average never stops it.
Each purchase is limited so that it moves the price by about 1% at most, and there is at most one a second. Whatever that leaves unspent waits.
How much of the shared budget is burned at a given moment is decided by Tide Switch.
Where it stops
Burning removes tokens. It does not set a price, and I make no claim about one.
A waiting budget is normal: for the first 10 minutes after the pool's first trade there is no average and the hook buys nothing, and after a jump in price it waits. The average only moves when a trade or one of the two public calls records the price, so in a quiet pool the wait can be long.
The figure counts every burned token, including any a holder burned on their own and the part of a shell mint that is destroyed. It is the supply at the start minus the supply now.
The rules above are in the hook's code, which cannot be replaced. Nobody can speed the burn up, slow it down or turn it off.
What the buybacks did
Reading the chain.