A normalized two-pentagon network

We now construct a genuine two-tensor network, rather than appending an unrelated register to a region label.

Take two copies of the same six-leg perfect tensor. Join boundary leg $5$ of the left tensor to boundary leg $1$ of the right tensor. The two logical inputs are $C_L,C_R$. The open boundary has eight qubits:

For four-bit strings $a,d$ and bits $b,c$, define

The internal edge is contracted, not made available to the decoder.