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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.

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Here's a relevant blog post: https://scottaaronson.blog/?p=3327 'Is “information is physical” contentful?'

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.

The article does say it’s “experimentally extremely well confirmed”.

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