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If you trust your previous advisor, I would:

  1. Talk to your him (or his co-authors) to figure out whether you are really correct about that mistake. Also state that (if correct) you would like to get a publication out of this due to the effort you put into this. If he accepts the mistake, you may then benefit from having him on your side (be it as a co-author, reviewer, etc.). If it turns out that you were wrong about this, you save a lot of time. If he doesn’t agree, but also cannot convince you otherwise, you can still to have an open scientific debate about this.

At least in my fields, contacting the authors is the common first step when noticing potential mistakes in papers, independent of the relationship to the authors. This is less to give them a chance to correct it, but to give them a chance and use their capabilities to dispel potential wrong arguments.

If you do not trust your advisor and pre-prints are a thing in your field, consider having a pre-print ready for submission when talking to your supervisor, so you can outrun them (or use any of the other methods to prove priority). At least in any reasonable journal, you shouldn’t be able to correct a fundamental mistake just like that. Corrections need to undergo at least some review as well.

Finally, if you think that your field may be so corrupt that corrections of mistakes can be completely suppressed, you should seriously ponder whether you want any reputation in that field anyway. If your answer is no, you have nothing to lose, and may as well try to publish about the mistake. Either you succeed or you can make a fuss about the way you were rejected.

If you trust your previous advisor, I would:

  1. Talk to your him (or his co-authors) to figure out whether you are really correct about that mistake. Also state that (if correct) you would like to get a publication out of this due to the effort you put into this. If he accepts the mistake, you may then benefit from having him on your side (be it as a co-author, reviewer, etc.). If it turns out that you were wrong about this, you save a lot of time. If he doesn’t agree, but also cannot convince you otherwise, you can still to have an open scientific debate about this.

At least in my fields, contacting the authors is the common first step when noticing potential mistakes in papers, independent of the relationship to the authors. This is less to give them a chance to correct it, but to give them a chance and use their capabilities to dispel potential wrong arguments.

If you do not trust your advisor and pre-prints are a thing in your field, consider having a pre-print ready for submission when talking to your supervisor, so you can outrun them (or use any of the other methods to prove priority). At least in any reasonable journal, you shouldn’t be able to correct a fundamental mistake just like that. Corrections need to undergo at least some review as well.

Finally, if you think that your field may be so corrupt that corrections of mistakes can be completely suppressed, you should seriously ponder whether you want any reputation in that field anyway. If your answer is no, you have nothing to lose, and may as well try to publish about the mistake. Either you succeed or you can make a fuss about the way you were rejected.

If you trust your previous advisor, I would:

  1. Talk to him (or his co-authors) to figure out whether you are really correct about that mistake. Also state that (if correct) you would like to get a publication out of this due to the effort you put into this. If he accepts the mistake, you may then benefit from having him on your side (be it as a co-author, reviewer, etc.). If it turns out that you were wrong about this, you save a lot of time. If he doesn’t agree, but also cannot convince you otherwise, you can still to have an open scientific debate about this.

At least in my fields, contacting the authors is the common first step when noticing potential mistakes in papers, independent of the relationship to the authors. This is less to give them a chance to correct it, but to give them a chance and use their capabilities to dispel potential wrong arguments.

If you do not trust your advisor and pre-prints are a thing in your field, consider having a pre-print ready for submission when talking to your supervisor, so you can outrun them (or use any of the other methods to prove priority). At least in any reasonable journal, you shouldn’t be able to correct a fundamental mistake just like that. Corrections need to undergo at least some review as well.

Finally, if you think that your field may be so corrupt that corrections of mistakes can be completely suppressed, you should seriously ponder whether you want any reputation in that field anyway. If your answer is no, you have nothing to lose, and may as well try to publish about the mistake. Either you succeed or you can make a fuss about the way you were rejected.

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If you trust your previous advisor, I would:

  1. Talk to your him (or his co-authors) to figure out whether you are really correct about that mistake. Also state that (if correct) you would like to get a publication out of this due to the effort you put into this. If he accepts the mistake, you may then benefit from having him on your side (be it as a co-author, reviewer, etc.). If it turns out that you were wrong about this, you save a lot of time. If he doesn’t agree, but also cannot convince you otherwise, you can still to have an open scientific debate about this.

At least in my fields, contacting the authors is the common first step when noticing potential mistakes in papers, independent of the relationship to the authors. This is less to give them a chance to correct it, but to give them a chance and use their capabilities to dispel potential wrong arguments.

If you do not trust your advisor and pre-prints are a thing in your field, consider having a pre-print ready for submission when talking to your supervisor, so you can outrun them (or use any of the other methods to prove priority). At least in any reasonable journal, you shouldn’t be able to correct a fundamental mistake just like that. Corrections need to undergo at least some review as well.

Finally, if you think that your field may be so corrupt that corrections of mistakes can be completely suppressed, you should seriously ponder whether you want any reputation in that field anyway. If your answer is no, you have nothing to lose, and may as well try to publish about the mistake. Either you succeed or you can make a fuss about the way you were rejected.