The first pdf says this:
"An additional factor favoring the use of denitrification is its ability to stabilize the buffering capacity of culture water. Acidification is often observed in nitrifying recirculating systems (e.g. Kaiser and Wheaton, 19831, where alkalinity decreases by 6.0-8.6 mg HCO; for each milligram of ammonium oxidized to nitrate (Sharma and Ahlert, 1977; Grady and Lim, 1980). However, release of hydroxyl ions by denitrification raises alkalinity; it was estimated that each mg of nitrate reduced to N, causes alkalinity to increase by 3.57 mg (Jeris and Owens, 1975). The overall effect of denitrification in stabilizing the pH in recirculating systems has been described (Otte and Rosenthal, 1979; Kaiser et al., 1989). "
While I do not have a good handle on the odd units of measure for alk they are using without seeing more detail in the original papers (which I cannot get past page 1; see below), they are showing what I am claiming: ammonia conversion to nitrate consumes alk and denitrification adds it back.
The main confusion (aside from strange units of measure for alk) may be coming that they write it as ammonium converted to nitrate, and then nitrate to N2.
First some conversion math.
1 mg ammonium becomes 3.44 mg nitrate
So they claim 1 mg ammonium (we'll come back to the ammonium ammonia issue) to nitrate decreases alk by 6.0-8.6 units of alk (let's call this an average of 7.3)
and that 1 mg of nitrate adds back 3.57 mg of alk when denitrified.
Thus, 1 mg of ammonium to 3.44 mg nitrate then denitrified removes 7.3 - 3.57 *3.44 = 7.3 - 12.2 = -4.9 units of alk
Ignoring the confusing units, this seems to roughly match my claim, taking into account that ammonium is not what we are concerned with being produced, it is ammonia!
Ammonia may rapidly get protonated, but that itself is an alk impacting process.
NH3 --> NH4+ + OH-
That adds alk. One cannot ignore that process and it must be added to the above equation. Of course, how much one adds back will depend on whether one is actually starting with ammonia (adds nothing more) or ammonium (adds 3.57 in their units?) and that is dictated by pH. the above numbers are measurements, not calculations from equations, and so one cannot assume that all ammonia/ammonium is in one form or the other. It is something in between.
The denitrification numbers are attributed to:
Jeris, J.S. and Owens, R.W., 1975. Pilot-scale, high rate biological denitrification. J. Water Pollut. Control Fed., 47: 2043-2057. Kaiser, G.E. and Wheaton.
I cannot see past page 1, but they show the exact reaction that I assume at the bottom of page 1, which shows 1 unit of alk produced for each unit of nitrate consumed.
If you can get past page 1 of the Jeris paper above, we can perhaps see what numbers they actually showed and what the units of measure mean.