A piecewise map is honest only when the branch choices are checked. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A branch choice is part of the source

Starting at three quarters uses the high branch and lands at one half.

2(134)=122\left(1-\frac{3}{4}\right)=\frac{1}{2}
Tent branch ledgerThe first branch is checked as high.mapId=tentparameter=nonestates=3/4,1/2,1,0stepCount=3branchRoles=high,low-or-equal,high

The equality boundary is explicit

At one half the low-or-equal branch gives 1, then the high branch gives 0.

1210\frac{1}{2}\mapsto 1\mapsto 0
Boundary branch ledgerThe equality rule is validated rather than narrated.mapId=tentparameter=nonestates=3/4,1/2,1,0stepCount=3branchRoles=high,low-or-equal,high