Matrix synthesis

The off-diagonal memory Hamiltonian $\Omega (t)$ is part of the construction, not an omitted cross-coupling error. The underlying bosonic evolution is not treated as a bounded full-oscillator Hamiltonian.

Figure fig:port is the shared-port synthesis. One scalar input $u(t)$ drives both memories because $\lambda (t)$ is a vector. The generator $C(t)$ contains the memory mixing required by passivity. Two separate window approximations are not this joint port.