New sequential dynamics

Set the injection unitary to

The leftmost ${\mathrm{CZ}}_{2,3}$ cancels the last chronological gate of $J$. Thus injection uses twelve elementary gates.

After injection:

1. $W_1$ emits position $1$, leaving $C_1=(2,3,4,5)$;

2. $W_2$ applies ${\mathrm{CZ}}_{2,3}$ on the remnant, then emits position $2$, leaving $C_2=(3,4,5)$;

3. $W_3$ emits position $3$, leaving $C_3=(4,5)$.

Emission itself is a tensor-factor reassignment, not an allocation. The dimensions are

At the third step the joint message encoding is $V$.

There is a nontrivial gate during the emission sequence, acting only on not-yet-emitted carriers. The process has a fixed remnant and does not assert complete evaporation.