Water under concrete?
So what are the long term issues in relation to mould and fungus growth under the slab and a haven for tree roots to feed and undermine the slab. I didn't notice any reinforcement rods in that slab either. Nice idea but I owuld want to see how it resolves a few practical issues. A cracked slab will let water through without all the nice filtration benefits. Meanwhile the slab acts as a pollutant concentrator. It doesn't answer the issue of run off either.
Nice idea, needs more work.