Longitudinal recovery is introduced as an exact finite remaining-gap ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Recovery starts from the remaining gap

The equilibrium index is 16. From start 0, the remaining gap is 16.

160=1616\mathbin{-}0=16
NMR recoveryLongitudinal magnetization recovers by a checked remaining-gap fraction.start 0gap 16final 8

A half step lands at 8

Recovering one half of the gap adds 8, so the final magnetization index is 8.

0+1216=80+\frac{1}{2}\cdot16=8
NMR recoveryLongitudinal magnetization recovers by a checked remaining-gap fraction.start 0gap 16final 8