This may be somewhat tangential, and if it is too much so, then ignore this and move along.
Isn't the key axiom - preservation of information - a presupposition, and not a formally evidenced law? As best I can tell, it's mostly been assumed as a required premise for a larger axiom - the eternality of matter.
In quantum mechanics, breaking unitarity (which implies conservation of information) is akin to breaking the rule in statistics that probabilities have to add up to 100%. You get things like a 300% chance of rain or a 90% chance of [null reference exception]. It's hard to overstate how deep down it is and how many things depend on it.
Isn't the key axiom - preservation of information - a presupposition, and not a formally evidenced law? As best I can tell, it's mostly been assumed as a required premise for a larger axiom - the eternality of matter.