[gizmo686]

Do we have solid evidence (theoretical or otherwise) that space is not continuous.

My understanding is that the only fully accepted implication of the plank length is that it is the smallest measurable unit of length. Attempts to probe smaller regions result in black holes (do to the increasing energy necessary to probe small units of length; and the fact that energy is mass, and therefore exerts gravity).

[T-A]

Correct. And to date, all data remains consistent with space being continuous. This was big a couple of years ago:

https://phys.org/news/2015-03-einstein-scientists-spacetime-...

(the news piece focuses on foam, but the constraint applies generally to any kind of discrete structure where derivatives get replaced by stencils).