A rejected balance claim can still be an exact checked ledger. 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 wrong rate breaks the flow match

The two directed flows are six and three.

ΦAB=6,ΦBA=3\Phi_{A\to B}=6,\quad \Phi_{B\to A}=3
Rejected balance flowsA rejected case still renders as a checked ledger.populations=A=6|B=3rates=AB=1|BA=1flowAB=6flowBA=3acceptedBit=0 bit

The rejected bit is zero

The balance claim fails, but the arithmetic remains exact.

acceptedBit=0\hbox{acceptedBit}=0
Rejected balanceThe failed claim is explicit.populations=A=6|B=3rates=AB=1|BA=1flowAB=6flowBA=3acceptedBit=0 bit