According to the mass principle, the 'lighter core wood' is not the exact truth. The core wood IS doing something, so 'the lighter the better' is not the best approach. The core is at least experiencing a lot of shearing forces, so the wood must be able to cope with those. Since you'll be gluing wood to both sides of this core, it is also preferable to have good gluing qualities. A diffuse porous wood is therefore preferred, because it is uniform and resists shear better than most ring porous woods. In my opinion, a typical core wood is medium dense, uniform, diffuse porous and easy to glue. Walnut, cherry and especially maple are very suitable core woods. But the truth is, almost any wood will work as a core (maybe not balsa...). Myself, I prefer a third lam as core for its ability to allow me to use a third wood species. A nicely contrasting core is simply stunning. Also, this core is not at the surface of the bow, so you can actually make use of some of your laminates that did not qualify for backings or bellies. A hickory lam with a little too much grain run off, or an ipé lam with a small pin knot... these would normally not be suited for a backing and belly respectively, but are perfectly fine for a core. I've got a piece of ipé with some small drying cracks, which I don't trust as a belly lam. So I'll use it as a core lam instead.
The third core lam also allows me to use thinner belly lams. If you have a 3/8" ipé lam, for instance as a left over from milling belly slats, it is not thick enough to use as a belly alone when combined with bamboo/hickory. So I add a core of maybe 1/8" and I have enough thickness to make a great 50# bow. Using multiple lams also means that each lam will be thinner. The thinner the lams, the easier they are to bend. So the easier it is to press them into a form or shape. A severe reflex/deflex or recurve is easily obtained when using three lams, while it is difficult when using only two lams.