How to modify a final draft to reflect that a conjecture in its preprint was refuted?

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I am currently in the process of trying to publish a mathematics paper. A draft of this paper had been posted on arxiv, which contained an interesting conjecture.



In the intervening time, this conjecture has been refuted by another group of authors. I am not sure how I should edit my paper to reflect this.



One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.



What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.



Note that most of my paper is unaffected by this refutation, and in fact I still believe that the conjecture could hold for the special case I need



Is there a better way of handling this situation?










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  • AFAIK, arxiv stores every version as separate paper. So your original work is more or less cast in stone and cited already, you can only follow-up
    – aaaaaa
    Nov 28 at 20:20










  • Where have they published? If it's an easily-editable format (e.g. arXiv and not print) you could always contact them and ask them to cite a specific version, because you're editing the paper and don't want their citation to become difficult to trace.
    – Nic Hartley
    Nov 29 at 19:48














up vote
25
down vote

favorite












I am currently in the process of trying to publish a mathematics paper. A draft of this paper had been posted on arxiv, which contained an interesting conjecture.



In the intervening time, this conjecture has been refuted by another group of authors. I am not sure how I should edit my paper to reflect this.



One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.



What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.



Note that most of my paper is unaffected by this refutation, and in fact I still believe that the conjecture could hold for the special case I need



Is there a better way of handling this situation?










share|improve this question























  • AFAIK, arxiv stores every version as separate paper. So your original work is more or less cast in stone and cited already, you can only follow-up
    – aaaaaa
    Nov 28 at 20:20










  • Where have they published? If it's an easily-editable format (e.g. arXiv and not print) you could always contact them and ask them to cite a specific version, because you're editing the paper and don't want their citation to become difficult to trace.
    – Nic Hartley
    Nov 29 at 19:48












up vote
25
down vote

favorite









up vote
25
down vote

favorite











I am currently in the process of trying to publish a mathematics paper. A draft of this paper had been posted on arxiv, which contained an interesting conjecture.



In the intervening time, this conjecture has been refuted by another group of authors. I am not sure how I should edit my paper to reflect this.



One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.



What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.



Note that most of my paper is unaffected by this refutation, and in fact I still believe that the conjecture could hold for the special case I need



Is there a better way of handling this situation?










share|improve this question















I am currently in the process of trying to publish a mathematics paper. A draft of this paper had been posted on arxiv, which contained an interesting conjecture.



In the intervening time, this conjecture has been refuted by another group of authors. I am not sure how I should edit my paper to reflect this.



One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.



What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.



Note that most of my paper is unaffected by this refutation, and in fact I still believe that the conjecture could hold for the special case I need



Is there a better way of handling this situation?







publications mathematics preprint






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share|improve this question








edited Nov 29 at 3:13









Nat

5,25531338




5,25531338










asked Nov 28 at 12:39









David Harris

34837




34837











  • AFAIK, arxiv stores every version as separate paper. So your original work is more or less cast in stone and cited already, you can only follow-up
    – aaaaaa
    Nov 28 at 20:20










  • Where have they published? If it's an easily-editable format (e.g. arXiv and not print) you could always contact them and ask them to cite a specific version, because you're editing the paper and don't want their citation to become difficult to trace.
    – Nic Hartley
    Nov 29 at 19:48
















  • AFAIK, arxiv stores every version as separate paper. So your original work is more or less cast in stone and cited already, you can only follow-up
    – aaaaaa
    Nov 28 at 20:20










  • Where have they published? If it's an easily-editable format (e.g. arXiv and not print) you could always contact them and ask them to cite a specific version, because you're editing the paper and don't want their citation to become difficult to trace.
    – Nic Hartley
    Nov 29 at 19:48















AFAIK, arxiv stores every version as separate paper. So your original work is more or less cast in stone and cited already, you can only follow-up
– aaaaaa
Nov 28 at 20:20




AFAIK, arxiv stores every version as separate paper. So your original work is more or less cast in stone and cited already, you can only follow-up
– aaaaaa
Nov 28 at 20:20












Where have they published? If it's an easily-editable format (e.g. arXiv and not print) you could always contact them and ask them to cite a specific version, because you're editing the paper and don't want their citation to become difficult to trace.
– Nic Hartley
Nov 29 at 19:48




Where have they published? If it's an easily-editable format (e.g. arXiv and not print) you could always contact them and ask them to cite a specific version, because you're editing the paper and don't want their citation to become difficult to trace.
– Nic Hartley
Nov 29 at 19:48










3 Answers
3






active

oldest

votes

















up vote
35
down vote













If you can prove or at least make a convincing case for the conjecture in the special case you need, I'd do the following:



  1. Describe the conjecture in the special case

  2. Prove or make the convincing case in the special case

  3. Write "in a previous draft, we expected this conjecture to hold generally. However, it has subsequently been shown ..."

If you can't or don't want to argue for the conjecture in your special case, then your formulation works as well.






share|improve this answer



























    up vote
    20
    down vote













    When you believe, that your special case still holds, you can keep the conjecture and mention that you believe it holds for your special case and that it does not hold in the general case with a citation of the other paper.




    We conjecture X for all cases in which Y holds. Note that X does not hold in the general case, as shown by Name [42].




    So the other paper even improves on the revision of your paper and you can acknowledge this by adding this information and the citation. It would be way more complicated when the conjecture would be totally wrong. But when it is correct for a special case, both papers are useful.






    share|improve this answer





























      up vote
      4
      down vote














      One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.




      This isn't pulling the legs out, since the subsequent paper cites a published arxiv draft. Indeed, Tyszka published 152 drafts (of one work) over almost six years and any version can be cited.




      What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.




      That's certainly a nice touch.




      I still believe that the conjecture could hold for the special case I need




      Prove this result, at least partially.






      share|improve this answer






















      • “Prove this result.” Presumably the OP has already thought seriously about this and can’t yet see how, otherwise they would have included it as a theorem not a conjecture.
        – PLL
        Nov 28 at 13:09







      • 2




        @PLL The OP believes the conjecture holds for a special case, even though the conjecture has been disproved in the general case. So, I presume the OP has a significant basis for their belief. At the very least, they can surely prove part of the special case, thereby reducing the leap of faith required to accept it.
        – user2768
        Nov 28 at 13:12







      • 4




        I believe it COULD hold for the special case (i.e. it is still a relevant, interesting, and open, conjecture). I have no evidence that it DOES hold.
        – David Harris
        Nov 28 at 14:04










      • @DavidHarris Without any evidence, I personally wouldn't call it a conjecture. But, the definition of conjecture is rather vague, so your usage is correct. I tried searching for a mathematician's definition: I couldn't find one. (I did stumble upon Guido's book of conjectures, which is quite nice.)
        – user2768
        Nov 28 at 14:21







      • 6




        @user2768: I’d say mathematicians typically use conjecture for a statement we have some heuristic evidence of — e.g. various particular cases we know hold, or perhaps some numerical evidence — but no proof, and usually not even anything we’d call a partial proof, at the point where we first present it as a conjecture (since if we had a partial proof, we’d usually then isolate what was missing to complete it and present that statement as the conjecture instead).
        – PLL
        Nov 28 at 14:49











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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

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      up vote
      35
      down vote













      If you can prove or at least make a convincing case for the conjecture in the special case you need, I'd do the following:



      1. Describe the conjecture in the special case

      2. Prove or make the convincing case in the special case

      3. Write "in a previous draft, we expected this conjecture to hold generally. However, it has subsequently been shown ..."

      If you can't or don't want to argue for the conjecture in your special case, then your formulation works as well.






      share|improve this answer
























        up vote
        35
        down vote













        If you can prove or at least make a convincing case for the conjecture in the special case you need, I'd do the following:



        1. Describe the conjecture in the special case

        2. Prove or make the convincing case in the special case

        3. Write "in a previous draft, we expected this conjecture to hold generally. However, it has subsequently been shown ..."

        If you can't or don't want to argue for the conjecture in your special case, then your formulation works as well.






        share|improve this answer






















          up vote
          35
          down vote










          up vote
          35
          down vote









          If you can prove or at least make a convincing case for the conjecture in the special case you need, I'd do the following:



          1. Describe the conjecture in the special case

          2. Prove or make the convincing case in the special case

          3. Write "in a previous draft, we expected this conjecture to hold generally. However, it has subsequently been shown ..."

          If you can't or don't want to argue for the conjecture in your special case, then your formulation works as well.






          share|improve this answer












          If you can prove or at least make a convincing case for the conjecture in the special case you need, I'd do the following:



          1. Describe the conjecture in the special case

          2. Prove or make the convincing case in the special case

          3. Write "in a previous draft, we expected this conjecture to hold generally. However, it has subsequently been shown ..."

          If you can't or don't want to argue for the conjecture in your special case, then your formulation works as well.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Nov 28 at 14:16









          Designerpot

          2,222214




          2,222214




















              up vote
              20
              down vote













              When you believe, that your special case still holds, you can keep the conjecture and mention that you believe it holds for your special case and that it does not hold in the general case with a citation of the other paper.




              We conjecture X for all cases in which Y holds. Note that X does not hold in the general case, as shown by Name [42].




              So the other paper even improves on the revision of your paper and you can acknowledge this by adding this information and the citation. It would be way more complicated when the conjecture would be totally wrong. But when it is correct for a special case, both papers are useful.






              share|improve this answer


























                up vote
                20
                down vote













                When you believe, that your special case still holds, you can keep the conjecture and mention that you believe it holds for your special case and that it does not hold in the general case with a citation of the other paper.




                We conjecture X for all cases in which Y holds. Note that X does not hold in the general case, as shown by Name [42].




                So the other paper even improves on the revision of your paper and you can acknowledge this by adding this information and the citation. It would be way more complicated when the conjecture would be totally wrong. But when it is correct for a special case, both papers are useful.






                share|improve this answer
























                  up vote
                  20
                  down vote










                  up vote
                  20
                  down vote









                  When you believe, that your special case still holds, you can keep the conjecture and mention that you believe it holds for your special case and that it does not hold in the general case with a citation of the other paper.




                  We conjecture X for all cases in which Y holds. Note that X does not hold in the general case, as shown by Name [42].




                  So the other paper even improves on the revision of your paper and you can acknowledge this by adding this information and the citation. It would be way more complicated when the conjecture would be totally wrong. But when it is correct for a special case, both papers are useful.






                  share|improve this answer














                  When you believe, that your special case still holds, you can keep the conjecture and mention that you believe it holds for your special case and that it does not hold in the general case with a citation of the other paper.




                  We conjecture X for all cases in which Y holds. Note that X does not hold in the general case, as shown by Name [42].




                  So the other paper even improves on the revision of your paper and you can acknowledge this by adding this information and the citation. It would be way more complicated when the conjecture would be totally wrong. But when it is correct for a special case, both papers are useful.







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited Nov 28 at 14:48

























                  answered Nov 28 at 13:06









                  allo

                  1,455214




                  1,455214




















                      up vote
                      4
                      down vote














                      One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.




                      This isn't pulling the legs out, since the subsequent paper cites a published arxiv draft. Indeed, Tyszka published 152 drafts (of one work) over almost six years and any version can be cited.




                      What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.




                      That's certainly a nice touch.




                      I still believe that the conjecture could hold for the special case I need




                      Prove this result, at least partially.






                      share|improve this answer






















                      • “Prove this result.” Presumably the OP has already thought seriously about this and can’t yet see how, otherwise they would have included it as a theorem not a conjecture.
                        – PLL
                        Nov 28 at 13:09







                      • 2




                        @PLL The OP believes the conjecture holds for a special case, even though the conjecture has been disproved in the general case. So, I presume the OP has a significant basis for their belief. At the very least, they can surely prove part of the special case, thereby reducing the leap of faith required to accept it.
                        – user2768
                        Nov 28 at 13:12







                      • 4




                        I believe it COULD hold for the special case (i.e. it is still a relevant, interesting, and open, conjecture). I have no evidence that it DOES hold.
                        – David Harris
                        Nov 28 at 14:04










                      • @DavidHarris Without any evidence, I personally wouldn't call it a conjecture. But, the definition of conjecture is rather vague, so your usage is correct. I tried searching for a mathematician's definition: I couldn't find one. (I did stumble upon Guido's book of conjectures, which is quite nice.)
                        – user2768
                        Nov 28 at 14:21







                      • 6




                        @user2768: I’d say mathematicians typically use conjecture for a statement we have some heuristic evidence of — e.g. various particular cases we know hold, or perhaps some numerical evidence — but no proof, and usually not even anything we’d call a partial proof, at the point where we first present it as a conjecture (since if we had a partial proof, we’d usually then isolate what was missing to complete it and present that statement as the conjecture instead).
                        – PLL
                        Nov 28 at 14:49















                      up vote
                      4
                      down vote














                      One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.




                      This isn't pulling the legs out, since the subsequent paper cites a published arxiv draft. Indeed, Tyszka published 152 drafts (of one work) over almost six years and any version can be cited.




                      What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.




                      That's certainly a nice touch.




                      I still believe that the conjecture could hold for the special case I need




                      Prove this result, at least partially.






                      share|improve this answer






















                      • “Prove this result.” Presumably the OP has already thought seriously about this and can’t yet see how, otherwise they would have included it as a theorem not a conjecture.
                        – PLL
                        Nov 28 at 13:09







                      • 2




                        @PLL The OP believes the conjecture holds for a special case, even though the conjecture has been disproved in the general case. So, I presume the OP has a significant basis for their belief. At the very least, they can surely prove part of the special case, thereby reducing the leap of faith required to accept it.
                        – user2768
                        Nov 28 at 13:12







                      • 4




                        I believe it COULD hold for the special case (i.e. it is still a relevant, interesting, and open, conjecture). I have no evidence that it DOES hold.
                        – David Harris
                        Nov 28 at 14:04










                      • @DavidHarris Without any evidence, I personally wouldn't call it a conjecture. But, the definition of conjecture is rather vague, so your usage is correct. I tried searching for a mathematician's definition: I couldn't find one. (I did stumble upon Guido's book of conjectures, which is quite nice.)
                        – user2768
                        Nov 28 at 14:21







                      • 6




                        @user2768: I’d say mathematicians typically use conjecture for a statement we have some heuristic evidence of — e.g. various particular cases we know hold, or perhaps some numerical evidence — but no proof, and usually not even anything we’d call a partial proof, at the point where we first present it as a conjecture (since if we had a partial proof, we’d usually then isolate what was missing to complete it and present that statement as the conjecture instead).
                        – PLL
                        Nov 28 at 14:49













                      up vote
                      4
                      down vote










                      up vote
                      4
                      down vote










                      One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.




                      This isn't pulling the legs out, since the subsequent paper cites a published arxiv draft. Indeed, Tyszka published 152 drafts (of one work) over almost six years and any version can be cited.




                      What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.




                      That's certainly a nice touch.




                      I still believe that the conjecture could hold for the special case I need




                      Prove this result, at least partially.






                      share|improve this answer















                      One option that is out of the question is to simply delete the conjecture from the paper. The problem with this is that the latter paper has cited this conjecture as its motivation. If I removed the conjecture, I would be pulling the legs out from the subsequent paper.




                      This isn't pulling the legs out, since the subsequent paper cites a published arxiv draft. Indeed, Tyszka published 152 drafts (of one work) over almost six years and any version can be cited.




                      What I am leaning toward is to state something along the lines of "In an earlier draft, we had made the following conjecture:" and then include some discussion and citations about how the conjecture has subsequently been refuted.




                      That's certainly a nice touch.




                      I still believe that the conjecture could hold for the special case I need




                      Prove this result, at least partially.







                      share|improve this answer














                      share|improve this answer



                      share|improve this answer








                      edited Nov 28 at 14:37

























                      answered Nov 28 at 13:06









                      user2768

                      10.1k22644




                      10.1k22644











                      • “Prove this result.” Presumably the OP has already thought seriously about this and can’t yet see how, otherwise they would have included it as a theorem not a conjecture.
                        – PLL
                        Nov 28 at 13:09







                      • 2




                        @PLL The OP believes the conjecture holds for a special case, even though the conjecture has been disproved in the general case. So, I presume the OP has a significant basis for their belief. At the very least, they can surely prove part of the special case, thereby reducing the leap of faith required to accept it.
                        – user2768
                        Nov 28 at 13:12







                      • 4




                        I believe it COULD hold for the special case (i.e. it is still a relevant, interesting, and open, conjecture). I have no evidence that it DOES hold.
                        – David Harris
                        Nov 28 at 14:04










                      • @DavidHarris Without any evidence, I personally wouldn't call it a conjecture. But, the definition of conjecture is rather vague, so your usage is correct. I tried searching for a mathematician's definition: I couldn't find one. (I did stumble upon Guido's book of conjectures, which is quite nice.)
                        – user2768
                        Nov 28 at 14:21







                      • 6




                        @user2768: I’d say mathematicians typically use conjecture for a statement we have some heuristic evidence of — e.g. various particular cases we know hold, or perhaps some numerical evidence — but no proof, and usually not even anything we’d call a partial proof, at the point where we first present it as a conjecture (since if we had a partial proof, we’d usually then isolate what was missing to complete it and present that statement as the conjecture instead).
                        – PLL
                        Nov 28 at 14:49

















                      • “Prove this result.” Presumably the OP has already thought seriously about this and can’t yet see how, otherwise they would have included it as a theorem not a conjecture.
                        – PLL
                        Nov 28 at 13:09







                      • 2




                        @PLL The OP believes the conjecture holds for a special case, even though the conjecture has been disproved in the general case. So, I presume the OP has a significant basis for their belief. At the very least, they can surely prove part of the special case, thereby reducing the leap of faith required to accept it.
                        – user2768
                        Nov 28 at 13:12







                      • 4




                        I believe it COULD hold for the special case (i.e. it is still a relevant, interesting, and open, conjecture). I have no evidence that it DOES hold.
                        – David Harris
                        Nov 28 at 14:04










                      • @DavidHarris Without any evidence, I personally wouldn't call it a conjecture. But, the definition of conjecture is rather vague, so your usage is correct. I tried searching for a mathematician's definition: I couldn't find one. (I did stumble upon Guido's book of conjectures, which is quite nice.)
                        – user2768
                        Nov 28 at 14:21







                      • 6




                        @user2768: I’d say mathematicians typically use conjecture for a statement we have some heuristic evidence of — e.g. various particular cases we know hold, or perhaps some numerical evidence — but no proof, and usually not even anything we’d call a partial proof, at the point where we first present it as a conjecture (since if we had a partial proof, we’d usually then isolate what was missing to complete it and present that statement as the conjecture instead).
                        – PLL
                        Nov 28 at 14:49
















                      “Prove this result.” Presumably the OP has already thought seriously about this and can’t yet see how, otherwise they would have included it as a theorem not a conjecture.
                      – PLL
                      Nov 28 at 13:09





                      “Prove this result.” Presumably the OP has already thought seriously about this and can’t yet see how, otherwise they would have included it as a theorem not a conjecture.
                      – PLL
                      Nov 28 at 13:09





                      2




                      2




                      @PLL The OP believes the conjecture holds for a special case, even though the conjecture has been disproved in the general case. So, I presume the OP has a significant basis for their belief. At the very least, they can surely prove part of the special case, thereby reducing the leap of faith required to accept it.
                      – user2768
                      Nov 28 at 13:12





                      @PLL The OP believes the conjecture holds for a special case, even though the conjecture has been disproved in the general case. So, I presume the OP has a significant basis for their belief. At the very least, they can surely prove part of the special case, thereby reducing the leap of faith required to accept it.
                      – user2768
                      Nov 28 at 13:12





                      4




                      4




                      I believe it COULD hold for the special case (i.e. it is still a relevant, interesting, and open, conjecture). I have no evidence that it DOES hold.
                      – David Harris
                      Nov 28 at 14:04




                      I believe it COULD hold for the special case (i.e. it is still a relevant, interesting, and open, conjecture). I have no evidence that it DOES hold.
                      – David Harris
                      Nov 28 at 14:04












                      @DavidHarris Without any evidence, I personally wouldn't call it a conjecture. But, the definition of conjecture is rather vague, so your usage is correct. I tried searching for a mathematician's definition: I couldn't find one. (I did stumble upon Guido's book of conjectures, which is quite nice.)
                      – user2768
                      Nov 28 at 14:21





                      @DavidHarris Without any evidence, I personally wouldn't call it a conjecture. But, the definition of conjecture is rather vague, so your usage is correct. I tried searching for a mathematician's definition: I couldn't find one. (I did stumble upon Guido's book of conjectures, which is quite nice.)
                      – user2768
                      Nov 28 at 14:21





                      6




                      6




                      @user2768: I’d say mathematicians typically use conjecture for a statement we have some heuristic evidence of — e.g. various particular cases we know hold, or perhaps some numerical evidence — but no proof, and usually not even anything we’d call a partial proof, at the point where we first present it as a conjecture (since if we had a partial proof, we’d usually then isolate what was missing to complete it and present that statement as the conjecture instead).
                      – PLL
                      Nov 28 at 14:49





                      @user2768: I’d say mathematicians typically use conjecture for a statement we have some heuristic evidence of — e.g. various particular cases we know hold, or perhaps some numerical evidence — but no proof, and usually not even anything we’d call a partial proof, at the point where we first present it as a conjecture (since if we had a partial proof, we’d usually then isolate what was missing to complete it and present that statement as the conjecture instead).
                      – PLL
                      Nov 28 at 14:49


















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