False Floor

ohh... >.<  Then you'll need some bolts, washers, and nuts.

Attach the posts on the bottom panel and lay the top panel into place. Mark where the posts are and drill a small pilot hole through the top and into the post. To mark center, we would make a frame and/or use the rear shelf and hang plumb bobs to make sure that where we drill is as close to center as possible.

Remove the top panel and enlarge the pilot hole large enough to hold the nuts snugly and fill in the gaps with drops of Gorilla Glue. As the glue cures, it'll expand slightly and hold the nut in place better. If you want to reinforce the nut into place, before enlarging the hole, make a flat hole the size and thickness of the washer, then enlarge the pilot hole. Take a washer and sand one side with 40-60 so that the surface is scuffed for glue to hold on to it. Install the nut and then glue the washer into place. Do not use Gorilla Glue here. You'll want to use epoxy glue and coat the scuffed side with the glue and stick the washer into place.

In the top panel, the bolts and washers bolt the top panel in place without risking damage to the posts now. If the wood is thick enough, countersink a flat hole (spade bit without the side teeth) and leave at least 1/4" (absolute minimum) of wood left to let the bolt and washer sink into the panel.  Then enlarge the pilot hole to just a smidgen larger than the bolt's shaft.

Bolt back into place and you are done.

Good Luck!

They are strings with a weight at the bottom that tell you where straight vertical is.