solely
Only, with nothing and no one else involved.
Solely means only, exclusively, or entirely. When something depends solely on you, it depends on you alone and nobody else. If you're solely responsible for feeding your family's dog, you can't blame your brother if the dog doesn't get fed because that job belongs entirely to you.
The word emphasizes that one thing, and only that one thing, is involved. A scientist might discover that a plant's survival depends solely on a particular kind of bee for pollination: no other insect will do the job. When a student succeeds solely through natural talent without studying, it means talent alone carried them through.
You'll often see solely used to make crystal clear that nothing else matters or contributes. If a judge rules solely on the facts presented in court, she's ignoring everything else: rumors, personal feelings, or outside pressure. When your teacher says your grade depends solely on your final project, you know that one assignment determines everything.