On emergence and consciousness I don't know why you think that or where you got that from. You think properties can be exhausted, you think functions can be exhausted, I think you've invented this whole idea of exhausting properties, I don't think it comes from anybody who knows what they're talking about when it comes to emergence.
Think about a turing complete system. You can write any program technically in any Turing complete system - the limitation to the size and capabilities of that program are limited by the number of units in your turing complete system, but if you increase the units (like individual logic gates and storage capacity), you increase the number of things it can do.
Even though a particular logic gate may have a remarkably few set of properties, when you combine many logic gates, the number of new possible programs - with new possible system level properties - increases rapidly. "Exponentially" is probably an understatement. More rapidly than that.
So the number of possible system level properties isn't just limited by the number of properties of the components, but also increases exponentially with the number of those components as well. You seem to think that if you count the properties of the components, you can somehow figure out a specific number of properties any system made of those components can have, without taking into account this fact about turing complete systems. There's genuinely no hard limit from just the properties of the components - add more components in the right ways, and the higher level systems can have more and more properties. There's genuinely no limit once you have turing completeness.
So where are you getting these ideas about exhausting properties from? Did you just make it up?