Signed longitudinal starts still recover by a fraction of the remaining gap. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Signed starts use the same remaining-gap rule

Equilibrium stays at 16. The start value can be signed, but the gap is still equilibrium minus start.

gap=MMs\text{gap}=M_{\infty}-M_s
Signed recovery rowSigned starts still recover by a checked fraction of the remaining gap.start -8gap 24increment 12final 4

Three starts give three exact half-gap landings

The half-step changes because each signed start leaves a different remaining gap.

MsgapincrementMf163216082412401688\begin{array}{c|c|c|c}M_s&\text{gap}&\text{increment}&M_f\\-16&32&16&0\\-8&24&12&4\\0&16&8&8\\\end{array}

The middle row lands at four

Starting at -8 leaves gap 24; a half-step adds 12 and lands at 4.

8+12=4-8+12=4
Signed recovery rowSigned starts still recover by a checked fraction of the remaining gap.start -8gap 24increment 12final 4