I can't tell anything from that pic.

is the right side of it blurry or is my right lens blurry? lol!

Hi,
there are any number of clever ways to anchor these panels. Regrettably, your installer could not even come up with one such.
1) a cleat of 1x1 stock screwed to the floor and to the panel on the inside of the box. It's held short of the front edge so it's less conspicuous.
2) an angle iron under the front corner, screwed to the floor so the bottom of the ell is under the panel. The business end of the angle get hidden under baseboard. You have to plan on baseboard or this won't work.
3) a dowel pin(s) drilled in to the floor below the panel. The panel fits with corresponding hole(s). Probably the most tricky method.
Any of these re going to call for some molding, small or larger to hide the gap at the bottom.
Casey

You are absolutely right. That picture stinks.

Here is one of the amazing panels that is suspended from above. A ruler slides under it easily.

{{!gwi}}

Here is an even larger gap. This post is completely unconnected to the floor, and the gap is 1/2 inch. The neighboring cabinets are also 1/2 inch off the floor on this side. No shims. Should there be shims? The soapstone is already in place.

{{!gwi}}

Anyone with ideas on how to fix the posts? Can shims still be added under the cabinet?

I am wondering - do y'all think the posts should be replaced with ones that touch the floor? What fix would you want? Would it be good enough to put a block of wood under the post and wrap it with molding?