If you want to do a co-op RSG run without using a LAN Server, how do you show the world creation and prove that it was generated randomly? Is it just done on trust?

Since it's a LAN world and not a server, the admin (or the person hosting) must show in their video the random generation of the world, them entering the server, opening to lan, etc... Basically the only difference is that instead of showing the player enter the server from the menu screen, it has to show the generation of the world (and the blank seed generation input) from the menu screen, similar to the requirements of a solo speedrun.

what about if its on a server?