Do you mean hop ß acids? If so I am sure the answer is 0 as beer pH is usually sufficient to preserve the beer for a good long time if it is kept cold and was put up free from exposure to spoilage bacteria.
"Besides the formation of insoluble complexes with proteins and polypeptides, contributing to the colloidal stability of beer, hops sterilize the wort solution, which takes care of the bacteriological stability of beer."
It's is my understanding that the beta acids are what provide this....and there has to be some minimum quantity to achieve that effect...
Things in nature are seldom on/off. Thus we need to ask what you mean by "bacteriologically stable". Does this mean that 99.99% of samples stored at room temperature for a period of a month do not show signs of infection? Or does it mean 99.99% of samples stored at 40 °F for a month do not show signs of infection. Or is your definition 3 nines or 5 nines? What you want is a nines vs mg/L table and I haven't got one. Clearly the more mg/L ß acids the more nines you will get but you can also got to more nines by storing colder for shorter periods of time at lower beer pH etc., etc. This is, I suppose, a long winded way of saying "I haven't a clue" but I wanted to explain a bit why I haven't and why I don't think you will be able to get a simple answer to your question.
There is doubtless material in the literature concerning the bacteriostatic properties of hops acids and you will probably have to consult it to at least gain some insight into your question.
