This question has been asked before. I asked it, quite a number of years ago. I don't believe there is a simple answer.

I know the thread size, profile, and pitch are shared on some 1903 Springfield, U.S. Krag, and 'trap-door' Springfield screws.

I would not be surprised if some of our arsenal dies copied the components of French Arms that our Federal Arsenals first copied, in the early days of our Country.

Years ago, '5MadFarmers' shared a list of the contents of a 1902 - Standard Frankford Arsenal tap and die set. They called them "United States Form". The set had taps & dies for "U.S.F. Special" and "W.&S. Standard" threads.

The items that caught my eye, were: .187" X 26 tpi ( which is probably Krag side-plate and barrel-band screws) and .156" X 30 tpi (which is probably 1873 Springfield and Krag rear-sight screws).