A reaction passes only when every required ledger closes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One reaction closes every displayed family ledger

The accepted muon case has electron-family total 0 and muon-family total 1 on both sides.

010\quad1
Muon decay ledgerLepton-family ledgers close separately.muonelectronanti-nu_enu_muQ3=-3B3=0Le=0Lmu=1Q3=-3B3=0Le=1Lmu=0Q3=0B3=0Le=-1Lmu=0Q3=0B3=0Le=0Lmu=1accepted

Another reaction closes charge but fails another ledger

The rejected proton case has scaled charge 3 on both sides, but its scaled baryon total changes from 3 to 0.

3303\quad3\ne0
Baryon rejectionCharge closes while another ledger rejects the reaction.positronphotonuudQ3=3B3=3Q3=3B3=0Le=-1Lmu=0Q3=0B3=0Le=0Lmu=0rejected