  Physics-compliant models of RIS-parametrized channels assign a
load-terminated port to each RIS element. For conventional diagonal RIS
(D-RIS), each auxiliary port is terminated by its own independent and
individually tunable load (i.e., independent of the other auxiliary ports). For
beyond-diagonal RIS (BD-RIS), the auxiliary ports are terminated by a tunable
load circuit which couples the auxiliary ports to each other. Here, we point
out that a physics-compliant model of the load circuit of a BD-RIS takes the
same form as a physics-compliant model of a D-RIS-parametrized radio
environment: a multi-port network with a subset of ports terminated by
individually tunable loads (independent of each other). Consequently, we
recognize that a BD-RIS-parametrized radio environment can be understood as a
multi-port cascade network (i.e., the cascade of radio environment with load
circuit) terminated by individually tunable loads (independent of each other).
Hence, the BD-RIS problem can be mapped into the original D-RIS problem by
replacing the radio environment with the cascade of radio environment and load
circuit. The insight that BD-RIS can be physics-compliantly analyzed with the
conventional D-RIS formalism implies that (i) the same optimization protocols
as for D-RIS can be used for the BD-RIS case, and (ii) it is unclear if
existing comparisons between BD-RIS and D-RIS are fair because for a fixed
number of RIS elements, a BD-RIS has usually more tunable lumped elements.
