As I said, I have yet to read the paper to see how the Gauss´Law and the inverse N-1 law are ruled out for small space dimensions. Other references on that would be appreciated. Has it to do with those dimensions being closed?

So string theories in general state that gravity leaks through the extra dimensions. Since the leakage from other branes into ours in an invisible elf, the way to prove that would be to measure the actual leakage from our brane out to the bulk. I don´t know if it has been tried in laboratory whether it has been looked for in planetary orbits, but from your words I would imply that no such shortage in the gravity field expected has been found whithin the current error margins. Am I right?

And that the milimetre order limit in scale for the extra dimensions would be the minimum that would make the leakage detectable with ours means. Since it has not been detected, there is only room left for smaller scales.

Then coming back to the effect of other branes into our brane, I wonder how that small scale effect adds up to the candidates as observed phenomena (galaxy rotation, clusters) which happen to be extralarge scale without affecting the moderate large scale (planetary orbits and lab measurements).

I will wait to read the full paper before commenting on that, since as I said in my earlier post the abstract seems to suggest that scale makes a difference for the ability to transmit gravity.