I hate to say this given all the trouble you've gone to already but it's rarely a good call to sand wood up to ultra-fine grits*.
If you're looking to get a gloss on wood you can get it much more efficiently by going to a finish of some sort (including simply waxing directly onto the bare wood, although I'm not a fan of this myself).
In addition to giving you the surface gloss that you want, faster and with less effort, a finish adds protection to the wood which can obviously be very desirable for anything that won't just sit in a glass case and never be touched. Wax will resist minor handling and help ease dusting but it doesn't provide much more protection than this in the long term which is why I'm not a fan of it used by itself.
A short while ago there was a flurry of interest on one or two of the woodworking forums in a very finely sanded and buffed/burnished finish on wood with no actual finish applied, the gloss purely down to the super-smooth surface of the wood. I suppose it's something that everyone with access to fine sanding and/or buffing materials thinks to try at some point. In my case at least it became evident very quickly that for most hardwoods moisture or grease on the fingertips was enough to make the surface go matt! That certainly convinced me that finish was the way to go most of the time.
*Exceptions would be very dense, naturally oily or resinous woods. The kind of woods that don't float in water. But I must mention that most of these are from the tropics and many are now restricted because of rarity and in an attempt to curb illegal logging.