rjh01
Gentleman of leisure
Here's an interesting question: how would you test any of the ideas put forward to explain the optical (Kepler) data?
Specifically, what telescopes (etc) would you point towards the star (or nearby)? What sorts of signatures would you look for? Would observing in something other than the electromagnetic spectrum - neutrinos, say, or cosmic rays - help to test at least some of the ideas?
In one of the links it suggests looking at the dips. Exactly how long does it take for it to dip? You could also look at the frequencies. If they dipped at slightly different times then the body may have an atmosphere.