Hi Edwin
You cannot ever ignore energy and still do physics. Trying to bring consciousness into the picture before you've nailed down the relationship between energy and information is a mistake, and often leads to some sort of quantum mysticism about consciousness - i.e. leads nowhere. The notion of information I use is simply configuration entropy because it is the only opinion-independent concept of information there is. Your example is still the causation of "bit from it" - information from the distribution of energy - which is Object Physics, whereas the causal pattern of agency is the reverse - expending energy on the basis of information. You've also confused information with the "meaning" of information. This is where keeping the physics focus on energy and configuration entropy helps, because it provides the basis for the most minimal definition of "meaning" in physics:
The meaning of a stimulus s to an agent a is the energetic response r that the agent displays to the stimulus s: a(s, e) -> a', r
By this definition, the meaning of a stimulus is specific to the agent that has the energetic response, and since no object displays an energetic response - that's the definition of an agent - there is no "meaning" in Object Physics. Given sufficient grasp of agency, this definition can be traced to the common understanding of the word "meaning".
The "theory" underlying Agent Physics and the key incompleteness proof is simply Science - that you can DESCRIBE physical reality using maths - nothing more. In the last 400 years this "theory" has worked out rather well. Agent Physics can be deduced in standard classical physics without the addition of any new theoretical concepts of any kind - and the key definitions and proofs are at undergraduate level physics and maths. A firm understanding of these fundamentals of classical physics and maths (over the counting numbers!) is needed before tacking quantum theory.
My example of the coin-stack is directly relevant as the same sort of pattern occurs in QFT. The "it" of the coin stack did NOT exist before, it is a compound object made of sub-objects that are energetically arranged on the basis of the configuration entropy (information) of their current arrangement. In QFT there is a critical distinction between a "bare particle" - the fundamental object - and a "real particle" that is measured in any experiment - the 2 are not the same. A "real particle" is a compound object consisting of the "bare particle" surrounded by a network of interacting "virtual" particles and radiation. As I mentioned in last year's essay, "virtual" is a concept in Relativity at the level of classical physics - it's not strictly a QT concept. I reproduce this pattern in classical physics: the fundamental or "bare" particle is a topological defect in space which is surrounded by a "radiation field" and gives a "real particle" as a compound object, EXACTLY as in QFT. The information in question resides in the configuration of the vacuum, both in terms of energy conservation and topological conditions. This is EXACTLY what Wheeler was considering - the "it" of a "real particle" from the information "bits" of the vacuum state.
The "map" is the science theory of the "territory" of reality, and the dream of an exact 1 to 1 mathematical mapping between the 2 has been PROVEN impossible within science.
Best
Michael