Decoder B: one retained qubit

Retain the first observed occupied rail as memory. For every later occupied rail $a$, apply ${\mathrm{CX}}_{b\to a}$, then $H_a$, measure $a$ as $z$, consume it, and apply ${Z_b}^z$. Vacuum dummy rails are consumed. Return $b$ after the horizon; if no memory exists, prepare $I/2$. The peak is at most $q_A+1$.