The live-fraction check is source-bound to the dead-time budget. 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 live fraction cites the dead-time source
The live-fraction check cites 3 fields from the dead-time budget: clock, live time, and rate.
3source fields
A same-valued fraction from another budget is not enough
The source contract keeps the 4 second live time tied to this 12 second clock.