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A paper contains three theorems. After submitting the paper, the author finds out that one of their theorems was already published by someone else with stronger result. Although their result is not as strong, the author’s method is much simpler.

They have two choices:

  1. Keep the theorem and mention the result already done, and state that the method in current paper is simpler.
  2. Just drop the theorem from the paper, and keep 2 theorems instead.

Given that they have already submitted the paper, the author just has to wait for referee's report. So their choice will come after the decision of the referee.

What would be the best choice?

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    You should definitely inform the editor ASAP, rather than waiting for the referee report. One reason is to avoid wasting the referee's time: they may vaguely remember having seen such a theorem but waste time trying to locate it for you when you already know. A second reason is to avoid looking like you are trying to influence the decision by withholding information (in the hope that it's more likely to be accepted if the referee doesn't notice that one theorem is already known). Sep 19 '15 at 21:28
  • I can't be the only one thinking - if the referee says nothing, then do nothing. The aim of the game is to get papers published, not to keep endlessly revising and re-submitting them whenever anyone else publishes anything.
    – Simon B
    Sep 19 '15 at 22:10
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    @SimonB Regardless of what the referee notices, it's dishonest to present a result as new when you know someone else already obtained it. This is not (from my reading) a case of someone else getting a result after you, but an older result you didn't know about at first.
    – Kimball
    Sep 19 '15 at 22:31
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    @SimonB The aim is to increase the sum of human knowledge. That this gets turned into a game of publishing as many papers as possible is unfortunate. And I can't be the only one thinking - it's a small step from lies of omission (not admitting the existence of prior work and hoping nobody notices it) to lies of commission (submitting things one knows to be false and hoping nobody notices). Sep 20 '15 at 0:58
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Choice 1 seems pretty clear. It is honest about prior work (existing theorem) and the contribution (new proof).

You could also inform the editor that you have found a theorem that someone else has done, but that you believe your proof to be novel. This will allow the editor to better judge your work.

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    +1 for informing the editor who can in turn inform the referees who don't have to guess about the reason you didn't cite that other paper. Sep 19 '15 at 16:18
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    "You could also inform the editor that you have found a theorem that someone else has done, but that you believe your proof to be novel." Readers will want to know this, as well as the editor; so I'd suggest saying this in the abstract and/or introduction. Sep 19 '15 at 21:00
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Whenever you can, include the reference and specifically explain the differences of both approaches, including the shortcomings of your method. It is a related work after all :)

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