General antonyms:
* Fact: A statement that is known to be true.
* Certainty: Absolute assurance or conviction.
* Proof: Evidence that establishes the truth of something.
* Reality: The state of things as they actually exist.
Antonyms focusing on the idea of speculation:
* Evidence: Something that provides proof or support for a claim.
* Confirmation: Verification or proof of something.
* Truth: A statement or belief that is in accordance with reality.
Antonyms focusing on the idea of guesswork:
* Knowledge: Information or understanding acquired through experience or study.
* Understanding: The ability to comprehend something.
* Clarity: The state of being easily understood.
The best antonym for conjecture will depend on the specific context of your sentence.