Remark: Fermionic sign and representation

For residual creators ${e_1}^{†},{e_2}^{†}$ and bath creators ${b_1}^{†},{b_2}^{†}$, expand

Putting bath creators before residual creators gives the minus sign in (eq:Vone). Both logical basis vectors have even total fermionic parity. The reference is an abstract logical register, not another occupation mode.

All partial traces and entanglement cuts below refer to the declared tensor representation. No basis-independent fermionic mode-entanglement identification is asserted.