Intelligence is a computational property of a system that can be measured (both directly and indirectly), not something that exists independent of it. There is no more implied intelligence in or behind any "thing" than that which is intrinsic to that thing itself. Predictive error complexity does (with caveats) allow the measure of intelligence (among other things) of systems whose state we cannot fully observe. I do not want to get into the details of it because it is way too technical, but all I can say is that it does not get you where you want to go -- quite the opposite.
Which is what I've been restating over and over. Given some pattern in nature, one cannot assert any more intelligence than that allowed given the algorithmic information content of that pattern. Given some quantity of algorithmic information content, we can assert an upper bound on intelligence. You are trying to invent additional algorithmic information that is entirely unnecessary to generate the observed pattern.
I would have questions as to how the abstractions of math can be accurately applied to physical objects, and how accurately intelligence can be assessed through the algorhythmic calculations engaged. For example, if these calculations, or this definition of intelligence, can be applied to an object that is known to be the product of human intelligence, how much does it tell us, and how accurate is the telling? Has anyone tried it?