Compiled programmes and complete failure outputs

Set

The even programme consumes packet labels, holds the first rail until the second arrival, applies $B_{12}$, and reads the early pair as $t,s$. It consumes both early rails before the third arrival. On full transmission it applies $C_{ts}{R}_3$ and returns rail three; otherwise it consumes the remaining inputs and prepares $I/2$.

Indeed,

The corrected path maps intertwine logical $X,Z$ with output $X,Z$, hence have the form $|\psi ⟩\mapsto |\psi {⟩}_3\otimes |{\chi }_{ts}{⟩}_{45}$. The early pair is $I_4/4$, giving path probability $1/4$.

For odd parity,

Separate early $Y_1$ and $X_2$ measurements suffice. The $\{2,3\}$ and $\{1,3\}$ failure flags use product parity readouts and logical eigenstate preparation.

The ledgers are

They include failure preparation. For a three-packet snapshot, $Q_{\mathrm{stored},\mathrm{total}}=3q$.

Every destructive readout is part of a complete instrument. If $K_h$ are the full instruction-history maps, then ${\sum }_h{K}_h^{†}{K}_h=I$. Thus successful branches are never renormalized into a deterministic claim.