A reaction must close every conservation ledger at once, so a single failing budget rejects the whole reaction even if the others match. The accepted muon case closes electron-family 0 and muon-family 1 on both sides, while the rejected proton case keeps charge 3 but lets baryon number drop from 3 to 0 exactly for the stated toy ledgers; real measurements carry particle-identification error, missing-energy resolution, and detector efficiency limits.
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.
01
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.