Organizers, cashiers and station managers, before the event

1. A seller with its key: the online shop, each cashier and each promoter sign their vouchers with the key agreed on before the event.
2. A station that trusts it: the station always hands out what was signed by a seller whose key it has, within its range, for this event and this station, and that this same phone hasn't already handed out. It doesn't ask anyone.
3. One inventory per station: each station subtracts from what it has; it doesn't hand out what it doesn't have.
4. What's at risk shows up when syncing: a copy of a voucher shown at two stations or on two phones that can't see each other can go through at both. It's found on upload, with station, time, phone and value.

No way of working requires the phones to see each other. Sharing between phones is an extra: it only helps when a station has several phones accepting the same vouchers.