The same-phase interferometer case keeps the full count budget at the bright detector. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The first splitter creates two equal arms
The incoming count 8 first splits into 4 upper and 4 lower.
8→4+4
Same phase recombines at the bright detector
With same phase, the recombined output is 8 bright counts and 0 dark counts.