Yes, provenance is the basics with these things; providing such (provenance) is not fabricated. Anyone can tell you that the specimen was brought out by a diver when collecting stuff from a wreck ... or the like.
The ball posted, with its circa 4" diameter, should weigh about, say, 3 pounds and,
if it were an artillery item, would fit in a XIV-XVI century small bombard, or a falcon. I guess too small for catapults, though... like those in Sant'Angelo.
Also i realize that, their construction being too regular, doesn't help supporting their genuinity
.
.