What would proof-by-gathering be, mathematically speaking?

Maybe something with an initial NULL_TERMINATOR_EVENT_#ID advertised, and the proof being that people actually gather because they're that ready for imagination to take control of their life.

I know proof-by-consensus but I want to make a governance style that is purely 'proof-by-observation' via tech implants for those that want the analog data to be relevant and 'proof-by-proximity/presence/permissiveness'.