Where Spectra runs
On this machine: the simplest. Spectra keeps its ledger in ~/.local/share/spectra, and your agents on this machine connect to it.
On a server: Spectra runs elsewhere, and you, your keys and your agents stay here. On the server, set it up for your key:
spectra init --owner YOUR-KEY --name earth
It prints the server's instance key. When you connect, the extension shows the key it sees; trust it only if they match.