You are located outside of two rooms which have a door between them. Each room has one or more computers whose total power is unknown, so they cannot be reliably used as proof-of-work to compare times, however they are not strong enough to break cryptographic secrets. You cannot see who is in the rooms.
There are only two options:
there are two different people in the rooms: in each room there is a different, honest person who stays in their room, or
there is one dishonest person who pretends to be two different people, by moving between the rooms.
You and the person in each room can verbally communicate with each other only through a computer network. You can also send stuff back and forth between you and the rooms, e.g. cards, balls — in order to find out if these are two different people or one person who pretends to be two. However there is a random delay of up to one minute in all methods of communication due to limits of the communication infrastructure.
The people in the rooms can communicate with each other through you, assuming they are two different people.
However, you cannot do anything that would reveal the actual identity of a person, e.g. check their DNA, take their fingerprints, take their photo, collect a sample of their handwriting, ask to see their ID card, listen to their voice, etc.
What strategy would you devise in order to make the dishonest person reveal their pretension, if indeed there is only one person in the rooms?
P.S. It's always possible to send to each room a different secret number, and if a person can tell me both numbers, then they have proven that they have access to both rooms. However to achieve this, I will probably have to reward the dishonest person e.g. by paying them, or by threatening to punish honest people who cannot prove having access to both rooms. Which is exactly the opposite of what a good solution would achieve. A good solution would make a dishonest person expose their pretension without punishing (or punishing too severely) honest people.