Struggle for Project Purity

If a player has fewer cards remaining in their library than the number of rad counters they have when the triggered ability resolves, they’ll mill as many cards as they can.

Any effects (such as proliferate) that interact with counters a player gets, has, or loses can interact with rad counters.

Rad counters are a kind of counter that a player may have. They’re not associated with any specific permanents.

The cards are milled all at once, which means abilities that trigger “whenever one or more nonland cards are milled” will trigger exactly once as long as at least one nonland card was milled.

If you somehow control Struggle for Project Purity and no choice was made for it (perhaps because another permanent on the battlefield became a copy of it), it has neither of the two triggered abilities.

In a game using the shared team turns option, such as an Archenemy or Two-Headed Giant game, the inherent triggered ability associated with rad counters triggers once for each player on the active team that has rad counters. Each instance of that ability is controlled by one of those players.