How to modify a final draft to reflect that a conjecture in its preprint was refuted?
up vote
19
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?
publications mathematics preprint
edited 1 hour ago
Nat
5,25531338
asked 15 hours ago
David Harris
31817
add a comment |
up vote
19
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?
publications mathematics preprint
edited 1 hour ago
Nat
5,25531338
asked 15 hours ago
David Harris
31817
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
8 hours ago
add a comment |
up vote
19
down vote
favorite
up vote
19
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?
publications mathematics preprint
edited 1 hour ago
Nat
5,25531338
asked 15 hours ago
David Harris
31817
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
publications mathematics preprint
edited 1 hour ago
Nat
5,25531338
asked 15 hours ago
David Harris
31817
edited 1 hour ago
Nat
5,25531338
asked 15 hours ago
David Harris
31817
edited 1 hour ago
Nat
5,25531338
edited 1 hour ago
Nat
5,25531338
edited 1 hour ago
Nat
5,25531338
5,25531338
asked 15 hours ago
David Harris
31817
asked 15 hours ago
David Harris
31817
asked 15 hours ago
David Harris
31817
31817
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
8 hours ago
add a comment |
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
8 hours ago
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
8 hours ago
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
8 hours ago
add a comment |
3 Answers
3
active
oldest
votes
up vote
25
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:
- Describe the conjecture in the special case
- Prove or make the convincing case in the special case
- 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.
answered 14 hours ago
Designerpot
1,934213
add a comment |
up vote
16
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.
answered 15 hours ago
allo
1,415214
add a comment |
up vote
3
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.
answered 15 hours ago
user2768
9,86422543
“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
15 hours ago
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
15 hours ago
3
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
14 hours ago
@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
14 hours ago
5
@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
13 hours ago
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
25
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:
- Describe the conjecture in the special case
- Prove or make the convincing case in the special case
- 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.
answered 14 hours ago
Designerpot
1,934213
add a comment |
up vote
25
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:
- Describe the conjecture in the special case
- Prove or make the convincing case in the special case
- 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.
answered 14 hours ago
Designerpot
1,934213
add a comment |
up vote
25
down vote
up vote
25
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:
- Describe the conjecture in the special case
- Prove or make the convincing case in the special case
- 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.
answered 14 hours ago
Designerpot
1,934213
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:
- Describe the conjecture in the special case
- Prove or make the convincing case in the special case
- 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.
answered 14 hours ago
Designerpot
1,934213
answered 14 hours ago
Designerpot
1,934213
answered 14 hours ago
Designerpot
1,934213
answered 14 hours ago
Designerpot
1,934213
1,934213
add a comment |
add a comment |
up vote
16
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.
answered 15 hours ago
allo
1,415214
add a comment |
up vote
16
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.
answered 15 hours ago
allo
1,415214
add a comment |
up vote
16
down vote
up vote
16
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.
answered 15 hours ago
allo
1,415214
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.
answered 15 hours ago
allo
1,415214
edited 13 hours ago
answered 15 hours ago
allo
1,415214
answered 15 hours ago
allo
1,415214
answered 15 hours ago
allo
1,415214
1,415214
add a comment |
add a comment |
up vote
3
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.
answered 15 hours ago
user2768
9,86422543
“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
15 hours ago
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
15 hours ago
3
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
14 hours ago
@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
14 hours ago
5
@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
13 hours ago
add a comment |
up vote
3
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.
answered 15 hours ago
user2768
9,86422543
“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
15 hours ago
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
15 hours ago
3
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
14 hours ago
@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
14 hours ago
5
@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
13 hours ago
add a comment |
up vote
3
down vote
up vote
3
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.
answered 15 hours ago
user2768
9,86422543
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.
answered 15 hours ago
user2768
9,86422543
edited 13 hours ago
answered 15 hours ago
user2768
9,86422543
answered 15 hours ago
user2768
9,86422543
answered 15 hours ago
user2768
9,86422543
9,86422543
“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
15 hours ago
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
15 hours ago
3
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
14 hours ago
@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
14 hours ago
5
@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
13 hours ago
add a comment |
“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
15 hours ago
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
15 hours ago
3
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
14 hours ago
@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
14 hours ago
5
@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
13 hours ago
“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
15 hours ago
“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
15 hours ago
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
15 hours ago
@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
15 hours ago
3
3
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
14 hours ago
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
14 hours ago
@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
14 hours ago
@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
14 hours ago
5
5
@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
13 hours ago
@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
13 hours ago
add a comment |
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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
8 hours ago