When a message from Laura appears on your screen, how do you know it was really Laura who wrote it? On a local network anyone can start a program and call it Laura. The new BeeBEEP answers that question with cryptography, not with trust.
A key that never leaves your device
The first time BeeBEEP starts, it creates a pair of keys for your installation and keeps the private one in your system's keyring. It never travels on the network. Every time two BeeBEEPs connect, each one proves that it holds its own key, so the name on your screen is tied to a key, not to a word anyone can type.
Remembered at the first meeting
The first time you meet someone, BeeBEEP remembers their key. If one day someone shows up with the same name but a different key, BeeBEEP does not quietly accept it: it tells you, and you decide. For the same reason, if your own key cannot be read, BeeBEEP stays off the network instead of making up a new one: a key that changed at every restart would teach everyone to click "accept" without thinking, and then an impostor would look exactly like you.
A signature on what matters
From the same key comes a signing key (Ed25519). It signs what others must be able to believe even when it reaches them second-hand: your presence on the network, your identity card, your answer to a group invitation. Anyone can check the signature; nobody can forge it.
Messages that others carry but cannot read
Sometimes two colleagues cannot reach each other directly, say on two parts of a network that do not see each other. Another BeeBEEP in between can carry the message. It is encrypted end to end, from your device to the recipient's, so whoever carries it sees only a sealed envelope.