How to modify a final draft to reflect that a conjecture in its preprint was refuted?
up vote
26
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 Nov 29 at 3:13
Nat
5,25431338
asked Nov 28 at 12:39
David Harris
35337
add a comment |
up vote
26
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 Nov 29 at 3:13
Nat
5,25431338
asked Nov 28 at 12:39
David Harris
35337
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
add a comment |
up vote
26
down vote
favorite
up vote
26
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 Nov 29 at 3:13
Nat
5,25431338
asked Nov 28 at 12:39
David Harris
35337
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 Nov 29 at 3:13
Nat
5,25431338
asked Nov 28 at 12:39
David Harris
35337
edited Nov 29 at 3:13
Nat
5,25431338
asked Nov 28 at 12:39
David Harris
35337
edited Nov 29 at 3:13
Nat
5,25431338
edited Nov 29 at 3:13
Nat
5,25431338
edited Nov 29 at 3:13
Nat
5,25431338
5,25431338
asked Nov 28 at 12:39
David Harris
35337
asked Nov 28 at 12:39
David Harris
35337
asked Nov 28 at 12:39
David Harris
35337
35337
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
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
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
add a comment |
3 Answers
3
active
oldest
votes
up vote
36
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 Nov 28 at 14:16
Designerpot
2,621415
add a comment |
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.
answered Nov 28 at 13:06
allo
1,455214
add a comment |
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.
answered Nov 28 at 13:06
user2768
11k22949
“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
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
36
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 Nov 28 at 14:16
Designerpot
2,621415
add a comment |
up vote
36
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 Nov 28 at 14:16
Designerpot
2,621415
add a comment |
up vote
36
down vote
up vote
36
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 Nov 28 at 14:16
Designerpot
2,621415
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 Nov 28 at 14:16
Designerpot
2,621415
answered Nov 28 at 14:16
Designerpot
2,621415
answered Nov 28 at 14:16
Designerpot
2,621415
answered Nov 28 at 14:16
Designerpot
2,621415
2,621415
add a comment |
add a comment |
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.
answered Nov 28 at 13:06
allo
1,455214
add a comment |
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.
answered Nov 28 at 13:06
allo
1,455214
add a comment |
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.
answered Nov 28 at 13:06
allo
1,455214
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 Nov 28 at 13:06
allo
1,455214
edited Nov 28 at 14:48
answered Nov 28 at 13:06
allo
1,455214
answered Nov 28 at 13:06
allo
1,455214
answered Nov 28 at 13:06
allo
1,455214
1,455214
add a comment |
add a comment |
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.
answered Nov 28 at 13:06
user2768
11k22949
“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
add a comment |
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.
answered Nov 28 at 13:06
user2768
11k22949
“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
add a comment |
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.
answered Nov 28 at 13:06
user2768
11k22949
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 Nov 28 at 13:06
user2768
11k22949
edited Nov 28 at 14:37
answered Nov 28 at 13:06
user2768
11k22949
answered Nov 28 at 13:06
user2768
11k22949
answered Nov 28 at 13:06
user2768
11k22949
11k22949
“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
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
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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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