Same phase, opposite phase, and a blocked arm are three different checked routing ledgers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Same phase routes all eight counts bright
The first split is 4 upper plus 4 lower. Same phase recombines to 8 bright and 0 dark.
4+4=8,B=8,D=0
Opposite phase routes all eight counts dark
The input and first split remain 8 to 4 plus 4, but opposite phase sends 8 counts dark.
4+4=8,B=0,D=8
A blocked arm turns interference into a loss ledger
Blocking the lower arm loses 4 counts. The surviving 4 counts split into 2 bright and 2 dark.