Multiplicity-free bumpless pipe dream conjecture for the tablet

Let $\mathfrak X_w$ denote the relevant combinatorial object, let $\prec'$ be the chosen term order, and let $\mathcal T(\mathfrak X_w,\prec')$ be its tablet; let the support of a hieroglyph mean the positions occupied by its marked entries. Multiplicity-free bumpless pipe dream conjecture. The tablet $\mathcal T(\mathfrak X_w,\prec')$ is in natural bijection with the bumpless pipe dreams for $w$: the support of each hieroglyph gives the positions of the blank tiles of a bumpless pipe dream. This is presented as a multiplicity-free version of the preceding component-counting conjecture. The preceding statement is known for some diagonal term orders, but the tablet bijection asserted here is not established in the supplied text.