Alpha, beta-minus, and gamma rows close different count ledgers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Alpha carries four mass and two protons
In the alpha row, parent A 20 closes as daughter A 16 plus emitted A 4. Parent Z 10 closes as daughter Z 8 plus emitted Z 2.
A:20=16+4Z:10=8+2
Beta-minus keeps mass and raises daughter Z
In the beta-minus row, parent A 14 closes as daughter A 14 plus emitted A 0. Parent Z 6 closes as daughter Z 7 plus emitted Z -1.
A:14=14+0Z:6=7−1
Gamma carries energy without count change
In the gamma row, parent A 12 closes as daughter A 12 plus emitted A 0. Parent Z 6 closes as daughter Z 6 plus emitted Z 0.