What I don’t understand is why the underground lab wouldn’t join the INTERNATIONAL megaproject.
Because they don’t want to be known. That’s what the word “underground” means.
The enforcement regime of this kind is prone to abuses, so there will be a lot of distrust; also they might feel that everyone is too incapacitated, and while they would not normally have a chance against larger above-the-ground orgs, the new situation is different.
to want to take over the world
Yes, this would be their plan, to take over the world, or to pass the control to the ASI which they would presume to be friendly to them (and, if they have an altruistic mindset, to everyone else too, but even in this case, the problem is that their assumptions of friendliness might be mistaken).
Because they don’t want to be known. That’s what the word “underground” means.
The enforcement regime of this kind is prone to abuses, so there will be a lot of distrust; also they might feel that everyone is too incapacitated, and while they would not normally have a chance against larger above-the-ground orgs, the new situation is different.
Yes, this would be their plan, to take over the world, or to pass the control to the ASI which they would presume to be friendly to them (and, if they have an altruistic mindset, to everyone else too, but even in this case, the problem is that their assumptions of friendliness might be mistaken).