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What are the correct terms for potential theorems and proofs before they have been affirmatively reviewed, do I use "hypthesis" or "proposition" for what would be "theorem" after peer review has confirmed correctness?

What about the proof part; are there any special keywords that could be used for what would be a proof if its correctness has been affirmed in a peer review?

As a concrete hypothetical example lets assume I think I have found a proof that general matching reduces to assignment and want to publish that on arXiv, should I formulate the result and a potential proof as a theorem/proof pair or should I use some other keyword pair until correctness has been decided upon in a review process?

The reason for asking is that I plan my first submission to arXiv and want to prevent readers from misconceptions about the reliability of the results.

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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
    – Community Bot
    Commented Apr 7 at 14:51
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    I think your usage of 'keywords' here is a bit unusual. That is often used for words used in the metadata (i.e. outside the manuscript) to tag your submission to journals and sort it among other topics. But here, it seems you're using it for what phrasing to use in the paper. On another note, why do you consider your results unreliable to the point you're unwilling to call them theorems?
    – Anyon
    Commented Apr 7 at 16:06

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If you are claiming that something is a theorem, then you should call it a theorem. You are misunderstanding the peer review process if you think that going through a formal peer review process is either necessary or sufficient for something to be a theorem (or even, which is presumably what you have in mind, for something to be accepted as a theorem within a mathematical community).

A theorem is a theorem even if it never goes through peer review. A false proof is a false proof even if it does make it through peer review (and many do).

Yes, part of the reason why peer review exists is indeed to prevent the publication of false results, but this in no way implies that you cannot call something a theorem unless it has gone through peer review.

Finally, note that "proposition" and "theorem" are roughly synonymous, the distinction being that a proposition is presumably less important or less difficult to prove than a theorem.

The reason for asking is that I plan my first submission to arXiv and want to prevent readers from misconceptions about the reliability of the results.

If you don't think your results are reliable, you should not publish them even on arXiv. By the way, if you are uncertain about whether your results hold, don't count on peer review to confirm this. If there is a mistake in your proof, a referee might spot it, if you are lucky, but it is equally possible that they will not.

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    And, to add to the last sentence, if the referee does not spot the mistake and the mistake gets published, then the readers of the paper will blame the author for the mistake, not the referee.
    – Jochen Glueck
    Commented Apr 7 at 18:40

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