Other forms: suppositiously
Something you assume to be true without having any real proof is suppositious. If there's no evidence that your brother stole your favorite sweatshirt, it's suppositious to accuse him of the deed.
When you use supposition, or an unproven belief, to decide something, that's suppositious. Both words come from suppose and its root, which means "to assume." This adjective is uncommon today — you're more likely to say "unfounded" or "based on an assumption." Still, feel free to pull out suppositious for situations such as the suppositious evidence a substitute teacher uses to punish the whole class for passing notes.