Analytical transport controls and horizon-dependent execution

For deterministic emissions,

The last lower bound follows because mandatory later delivery forces consumption of the earlier message qubit.

For constant $r$,

For pure input $|0⟩$, all rails remain zero, so $S(C_t)=S(D_{\le t}{F}_{\le t})=H({\pi }_t)$.

At $K=t=3,r=1/2,\gamma =3/4$, the following values are analytical, not solver outputs:

The common sector vector is $(1,3,3,1)/8$, ordered $3,2,1,0$. Its entropy is $3-\frac{3}{4}{\log }_{2}3$.

warning. At two opportunities, “emit then vacuum” and “vacuum then emit” can share the same final core and reflected configuration. For constant $r$, perfect transmission, and zero rails, their temporal off-diagonal element is $r(1-r)$. A mixture of simulator trajectories would incorrectly remove it.