book is the cistern divided by supply, in wei per whole token. it is what a burn pays before the fee.
gross = amount × cistern / totalSupply fee = gross × 40 / 10000 pay = gross − fee
the fee stays in the cistern, so every burn raises book for every remaining holder. position does not move on a burn. the curve is only ever advanced by mints. the site draws this as the wedge: the marginal price above, book below, and the region between them that a burn can never reach into.
a mint adds c plus r to the cistern and adds q(e plus c) minus q(e) tokens to the supply. the eth per token of what it adds is at least the marginal price at e, which is at least book, so the average cannot fall. a burn removes tokens and removes proportionally less eth than their share, because of the fee, so the average cannot fall. there is no third operation.