The most common and most likely answer to this crossword clue is the 10 letter word CONJECTURE
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Buddy explains!
The straight part
We know that "opinion without proof" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case opinion without proof = conjecture.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CONJECTURE mean?
CONJECTURE noun- A statement or an idea which is unproven, but is thought to be true; a guess.
- A supposition based upon incomplete evidence; a hypothesis.
- (philology) A statement likely to be true based on available evidence, but which has not been formally proven.
- Interpretation of signs and omens.
- To guess; to venture an unproven idea.
- To infer on slight evidence; to guess at.