Three reaction rows show why charge, baryon number, and lepton families must all close. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Muon decay closes both family ledgers

The accepted muon row keeps scaled charge -3, electron-family total 0, and muon-family total 1 on both sides.

3011-3\quad0\quad1\Rightarrow1
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

Electron to photons fails lepton number

The electron row starts with scaled charge -3 and electron-family number 1, while two photons total 0 and 0.

3010-3\ne0\quad1\ne0
Rejected particle ledgerThe visible status is rejected because ledgers do not close.electronphotonphotonQ3=-3B3=0Le=1Lmu=0Q3=0B3=0Le=0Lmu=0Q3=0B3=0Le=0Lmu=0rejected

Proton decay closes charge but not baryon number

The proton row keeps scaled charge 3 on both sides, but scaled baryon number changes from 3 to 0.

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