There is a paper (not accepted for publication yet) that contains several conjectures. Some of these conjectures were proven recently.

The referee of the original paper requires to substitute the proven "Conjectures" with the "Results". However, there are several papers that cite these conjectures, so I feel it would be wrong to rename them. 

What is the best (or standard) way to indicate in the original paper that the conjectures were proven in the subsequent papers? Are there any good examples of doing that?

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    $\begingroup$ With the amount of time between preprint posting and final journal publishing being often considerable, this is common (or at least not uncommon) and personally I think it's fine to state the conjectures as Conjectures (while of course explaining that they have subsequently been proven). $\endgroup$ – Sam Hopkins Jun 23 at 2:50
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    $\begingroup$ I would indicate it in footnotes. $\endgroup$ – auniket Jun 23 at 3:07
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    $\begingroup$ My opinion is that this question is opinion-based. More seriously, my personal viewpoint is that the title must be maximally informative. If you say "Conjectures" in the title, this will be misleading if the conjectures are resolved already. And if you say "Results", this will conceal the fact that the paper is mostly about the conjectures which have been later resolved. Is not it possible to avoid both words "Conjectures" and "Results" in the title and just say something like "About those or these properties of this or that"? $\endgroup$ – მამუკა ჯიბლაძე Jun 23 at 4:41
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    $\begingroup$ Check out page 7 of the latest version of arxiv.org/abs/0708.2632 to see a pretty extreme example of discussion of "subsequent developments" since the first posting of a paper. $\endgroup$ – Sam Hopkins Jun 23 at 13:58
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    $\begingroup$ I wonder whether the conventional name of the Riemann Hypothesis will change if a proof is published? $\qquad$ $\endgroup$ – Michael Hardy Jun 23 at 17:20

The standard way is to leave the conjectures as they are, and add a remark, or a footnote, saying that "after this paper was written (or after it was submitted for publication) this conjecture was proved" and give a reference.


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