The existence conjecture for data-compressing effective ad hoc descriptions

A number is compressed by a non-constructive unique effective description when the validity of the description can be checked effectively given the number, but the number cannot be constructed effectively from the description except by systematic search. Existence conjecture. There exist numbers compressed by non-constructive unique effective descriptions. This conjecture concerns a distinction between effectively verifying a description once a number is supplied and effectively constructing the number from that description; the supplied text does not state whether it has been resolved.