That becomes an interesting question as the answer is really relative. If you are asking at what level in the average tank does nitrification essentially cease. One could argue that about 6.0 is the number. And in fact for most tanks the effective number may be closer to 6.5. The standard advice is to try to hold the pH over 7.0 during cycling. How high it sould be is a different discussion.
However, what is going on and what may or may not happen over time is a completely different issue relevant to acid pH levels. There is ample scientific information of nitrification happing at pH levels as low as 4.0. But at these levels, unionized ammonia (NH3) pretty much doesn't exist. The research I have seen was not sure of what the AOB would be using as a substrate. It postulates, but that is far from knowing.
I know in the waste water treatment industry nitrfifcation at acid pH levels is a necessity and there exists strains of bacteria that do it. I know a waste water expert who is very big on keeping wild caught acid water fish and has the most eloaborite water system I have seen in a ptrivate home can get such bacteria. Yes it is commercially available if you know where to go.
I know there are some very talented folks in Europe actually spawning wild altums angels and this takes acid water and cycled tanks. I have seen the pictures and vids and read reports of etc. witnesses who are qualified to know (Ph.D. in biochcemistry and teaching professor).
I have also read instructions for how to get a tank cycled to function in pH levels under 6.0. I think I posted them somewhere on this site. I used them but only needed to keep the cycle at a 6.5 pH so it wasn't as big a deal. But how do you think folks whose tap water is in the low 6s keep fish if they can't get their tank cycled?
Basically, the process involved cycling the tank at 7.0 pH. Once there you drop the pH by 0.2 pH and then dose ammonia. Some of the bacteria will be adversely affected by the drop but others will be fine. The dosing and the waiting allow the resistent ones to multiply. Once you are processing all the ammonia (the bacterial colony has returned to full strength) you drop it again by 0.2 pH and repeat. When heading to pH 6.0 and below, this process can take a long time as each drop may require 2-3 weeks and you may need more than the standard test kits. But it does work.
So as you can see, when you ask that question in the scientific forum, the answer may not be quite the same on the general forums where folks will usually answer between 6.0 and 7.0.
And that is only half the story. Just because nitification may stop in your filter at 6.0 and slow precipitously on the way down there, this does not mean that the bacteria are dead. They are inhibited and raising the pH back up will result in a resumption of nitrifying activity.
References:
Long-term storage and subsequent reactivation of aerobic granules- http
/www.sciencedi...960852408002009 you can see the abstract free, read the whole thing but not copy if for $0.99.
Nitrification in a Biofilm at Low pH Values: Role of In Situ Microenvironments and Acid Tolerance- http
/aem.asm.org/content/72/6/4283.full - full research report available- click either fulltext or pdf to the right of the abstract