Definition: Catalogue and host

The family $\{(M_{\mu },g_{\mu }):\mu \in I\}$ is a catalogue of prescribed backgrounds. An operational experiment additionally fixes one member $(M_{{\mu }_{\mathrm{H}}},g_{{\mu }_{\mathrm{H}}})$, called its host.

A catalogue register may change its index $\mu$. The host value ${\mu }_{\mathrm{H}}$, its metric, and its causal relation remain fixed. Whole-cone realization of a selected catalogue member in the host is asserted only when the corresponding identification has actually been supplied; in the benchmark below the direct identification is $\mu ={\mu }_{\mathrm{H}}$.