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According to Stack project, when referring to them I should use the Tag system https://stacks.math.columbia.edu/tags since

“The tag system provides stable references to definitions, lemmas, propositions, theorems”

and

“The place of the lemma in the document may change, the lemma may be moved to a different chapter, but its tag always keeps pointing to it.”

Is it really true though? The stack project has many corrections every day so what happens if I refer to a Lemma whose hypothesis or conclusion suddenly change? Can we still consider this as a “reference”?

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Yes, you should cite Stack Project Tags! The conclusion of the Theorem/Lemma/etc shouldn't weaken over time.

Compare to that old reliable citation "personal communication", or, worse, to a paper that is "to appear", and is never written. At the very least, the proof is there to be examined, and indeed the entire proof tree back to elementary material.

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    $\begingroup$ I agree with you “ The conclusion of the Theorem/Lemma/etc shouldn't weaken over time” is the crucial point to consider their tag system as a reference. But is it the case? Does a Tag in Stacks project at instant T always implies the same Tag at instant T’, T’<T? $\endgroup$
    – user12770
    Apr 27, 2021 at 3:14
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    $\begingroup$ You can click on "history" on any Stacks project tag to see how it's changed over time. So if in your citation you specify the date you accessed the tag it is unambiguous. $\endgroup$
    – Dan Petersen
    Apr 27, 2021 at 3:29
  • $\begingroup$ Some tags do not have “history”...Eg: Tag of type section do not have history. Eg, Tag 0FD4 about Bertini Theorem has no history... $\endgroup$
    – user12770
    Apr 27, 2021 at 3:52
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    $\begingroup$ That's not so much of a problem, going forward, I presume. I think your concern, while reasonable, is no worse than worrying about results from the literature from 100 years ago. Theorems about manifolds, say, or algebraic topology, proved in the 1920s are not literally the same theorems we would state today. $\endgroup$
    – David Roberts ♦
    Apr 27, 2021 at 5:15
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    $\begingroup$ @user12770 If you cite a specific proposition/theorem/lemma etc then it will have a history. $\endgroup$
    – Dan Petersen
    Apr 27, 2021 at 14:32

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