Opposing flow rows show that detailed balance accepts only equality. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Reverse-flow row 1
The forward flow stays 6. Reverse rate 1 gives reverse flow 3 and accepted bit 0.
ΦB→A=3⋅1=3,accepted=0
Reverse-flow row 2
The forward flow stays 6. Reverse rate 2 gives reverse flow 6 and accepted bit 1.
ΦB→A=3⋅2=6,accepted=1
Reverse-flow row 3
The forward flow stays 6. Reverse rate 3 gives reverse flow 9 and accepted bit 0.
ΦB→A=3⋅3=9,accepted=0
Only equal opposing flows accept detailed balance
Reverse flow three is too small, six matches, and nine is too large. The accepted bit is one only at the exact match.