"Then there's two roads we can take from here.  The first one is that I transmit a specification of a problem, in a simple programming language, which is too hard for our civilization to solve, but which we could easily verify a solution for.  That strategy was designed for higher-bandwidth First Contact channels than this one seems to be.  But it's the diamond standard if you do have a good way of receiving a higher-bandwidth transmission, and you have fast programming capabilities, and powerful computers."

"Speaking into my head would be interesting, but not full verification from the standpoint of greater Civilization; I'd prefer you avoided that for now.  On our own plan, there's two roads we can take from here.  The first one is that I transmit a specification of a problem, in a simple programming language, which is too hard for our civilization to solve, but which we could easily verify a solution for.  That strategy was designed for higher-bandwidth First Contact channels than this one seems to be.  But it's the diamond standard if you do have a good way of receiving a higher-bandwidth transmission, and you have fast programming capabilities, and powerful computers."