All information that exists is physical, encoded in a physical substrate. Beads in an abacus, holes in a punched card, distributions of charge in a computer memory. Hypothetical information that is not encoded physically cannot be causal. A book or computer program that have not been written can have no effects. Only information that exists in a physical encoding can be causal, by virtue of it’s physicality.
Not sure where you are going with this. What is causality? Is there a non-mathematical way of making it precise? And if I have found some way to make it precise, does it matter if I write it down here in this HN comment, or on a piece of paper, or just think it? Is the mathematical content different depending on how it is expressed in physical reality?