purely
Only for one reason, with nothing else involved.
Purely means completely or only, without anything else mixed in. When something exists purely by chance, luck is the only reason it happened. When a decision is made purely for fun, enjoyment is the sole purpose, with no other motives involved.
The word emphasizes that one thing, and only that one thing, is responsible for a situation. If you watch a documentary purely out of curiosity, you're not watching because someone assigned it or because you need information for a project. You're watching for one reason alone: you want to know more.
Scientists might describe something as purely theoretical, meaning it exists only as an idea and hasn't been proven through experiments yet. A musician playing purely for personal enjoyment isn't concerned with impressing an audience or earning money. A gift given purely from kindness has no expectation of getting anything in return.
The word often appears when someone wants to be clear about their intentions or when distinguishing between mixed motivations and singular ones. If your friend says they invited you to their party purely because they enjoy your company, they're reassuring you that no other calculation went into the invitation. They just wanted you there.