When a company refuses to disclose the fully diluted number of shares, what do you do? Assume it is the number of shares authorized (which you can find for $20 at https://delecorp.delaware.gov/tin/GINameSearch.jsp)?
You walk. You don't want to work with a founder/company that isn't forthcoming and truthful.
That is the upper bound that is generally much higher than the fully diluted count, so not a good proxy. However, it would be a fair assumption on your part since you are not given the right level of transparency. At any rate, probably best to be firm about the ask and just walk away if you dont get it, since it is not a good sign for things to come. Unless, of course, you would be okay to work there if they dont disclose you a salary (salary? dont worry about it...)
Is it an absolute upper bound? Is there a legal prohibition against creating derivative instruments (options, contracts secured by issuance of stock, etc.) in excess of authorized-at-time-of-execution?
in practice, it is set very high to cover all conversions and future capital needs and then some. however, it can be increased if needed, with a sharedholder vote.
Authorized shares is a pretty much irrelevant number. Companies typically have millions more shares of common stock authorized than they have actually issued to anyone. The relevant number is the number of shares actually issued and outstanding. You might also care about how many options have been issued and could in theory become outstanding shares, so in that case you'd want what is called the total fully diluted number of shares.
You don't want to work for someone like that. If they won't tell you that, what else are they hiding?
As others have said, walk away. Also, if convertible debt is involved, ask for the total number of outstanding shares after the debt converts.