An ideal echo restores a recoverable bucket but not irreversible loss. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
An echo separates recoverable and lost dephasing
Before the echo, coherent signal is 6. The recoverable bucket is 4 and irreversible loss is 2.
6+4+2=12
The echo cannot recover irreversible loss
Without the echo, visible signal is 6. The ideal echo restores the recoverable 4 and reaches 10; the lost 2 stays lost.