We can describe Solomonoff-based agents like AIXI. None of them are fully sufficient for true general AI, but you could probably accomplish quite a bit with an AIXI-like agent.
As fas as I know, the only thing existing AIXI implementations have demonstrated, is to learn to play Pac-man at a somewhat reasonable, but not in any way stellar level.
I don't consider this mathematical model of induction/prediction to be an accurate description of "intelligence" in the sense of "True AI" (which itself is open to interpretation).
This is the cake: human intelligence. Right now we have pieces of it, but even the end goal isn't well defined.
We know the human mind makes predictions, recognizes patterns, can formulate plans, works with both concrete and fuzzy information, and so on. But we still don't understand what human intelligence really is, overall.
We figured out how to make icing, but we still don't really know what a cake is.