That's not how the integers work!
Count variables are not left cens ored at zero!

Also, sometimes count variables are indeed left censored. Say I measure corporate creativity using # of patents in a given time period. I'm really after creativity, not patents. Patents can only be 0 or positive, but it's reasonable to assume that those 0's in the patent measure could be negative on the creativity scale, and that our creativity measure is hence leftcensored.

Meh whatever. Look up the damn tobit model and see how it deals with count data.
Yes, why don't we look up the damn tobit model and see how it deals with count data?
https://www.statalist.org/forums/forum/generalstatadiscussion/general/1339852tobitmodel
"Your situation is a lower bound of zero patents. If I understand it, it is not the case that these observations represent firms that really do have patents, but the number of them is too small to ascertain precisely, so you use 0 as a shorthand for "too small to pin down." If I have that right, these zeroes do not represent censoring of the data. They are actual zero outcomes.
My guess is that you would be better off analyzing these data with a countoutcome model such as Poisson or nbreg. It doesn't sound like a tobit to me."
Wow, just wow. Zero counts are _not_ censoring of the data, they are ACTUAL ZERO OUTCOMES. Count variables should be analyzed with counting models. Wow!

If you are using them as a proxy for research quality they are.
The assumption is that all papers below a certain quality will have zero citations.
So if, say, male papers have higher variance in quality, you're going to bias your mean by counting the catastrophically bad maleauthored papers as the same "quality" as mediocre femaleauthored papers.
There are problems with that paper, but OP is still an idiot

What are the problems?
If you are using them as a proxy for research quality they are.
The assumption is that all papers below a certain quality will have zero citations.
So if, say, male papers have higher variance in quality, you're going to bias your mean by counting the catastrophically bad maleauthored papers as the same "quality" as mediocre femaleauthored papers.
There are problems with that paper, but OP is still an idiot 
Also, sometimes count variables are indeed left censored. Say I measure corporate creativity using # of patents in a given time period. I'm really after creativity, not patents. Patents can only be 0 or positive, but it's reasonable to assume that those 0's in the patent measure could be negative on the creativity scale, and that our creativity measure is hence leftcensored.
Sounds like some voodoo bulls**t

Also, sometimes count variables are indeed left censored. Say I measure corporate creativity using # of patents in a given time period. I'm really after creativity, not patents. Patents can only be 0 or positive, but it's reasonable to assume that those 0's in the patent measure could be negative on the creativity scale, and that our creativity measure is hence leftcensored.
It's more reasonable to think that model consists of a mixture between people below a latent creativity threshold who have zero patents, people who are creative but lazy (hence zero patents too) or people who are creative and active (hence zero or more patents, with the number depending both on creativity and levels of activity. People who are in this category can have truly zero patents, e.g. if they are just starting).
As the answer in the Statalist forum implies, you have censoring when you should be seeing the full range of your dependent variable, but aren't because of some measurement restriction. A count variable, as the name says, is literally a count  it cannot be negative.
Of course, the implication that citations are a measure of quality can also be questioned. A controversial and/or low quality paper could get plenty of citations, mostly consisting in rebuttals. Is a citation here something flattering?