The problem is that we do not have any processes converging on a 100% accurate model for any field of scientific research. Every model currently in existence has problems and these problems are becoming thornier.

Simulation is a model and as such is not a "completely separate property". You raise the "mathematically proven" Solomonoff induction process. Yet you do not state the limitations to such a process and the simple fact that it is about computability and for all intents and purposes completely impractical for any study of reality.

There are many simulations that are not computable.

You have a belief that a model is possible to be 100% accurate. You will need to demonstrate that belief. Every model and theory makes some assumption and simplifications about the subject matter for which it is applicable.

You make an assumption that mathematics is capable of describing the universe accurately. Yet mathematics is an idealised system with its own assumptions as to what is true.

This is no way means that the universe itself is mathematical, nor does it mean that mathematics can describe the universe. I have no problem with models and theories being useful but all fail in some area of applicability.

The fundamental error you are making is the assumption that humans can understand. We can gain some understanding but we do not understand. There is a big difference here.

I'll say it again, science (even mathematics) is not about finding the "truth" but is about creating workable models and theories that we can use. If you want "truth" then study philosophy and religion.

Every experiment performed in the search for a more workable model and theory always gives rise to more questions. Many times, those questions can be "swept under the carpet" because those questions lead to question the firmly held belief in the model and theory being investigated.

You cannot declare that the OP's claim is simply false since he talking about the universe and not a "mathematical universe". Your claim that the universe is a mathematical universe is supposition on your part.

When you claim that a model or theory is capable of being 100% accurate then you are making the claim that the model or theory is correct.

It is interesting that you recognise that we don't know the fundamental structure of reality, yet you make the claim that it is mathematical. Please take a step back and also recognise that mathematics is a useful tool to help develop useful models and theories. Don't give authority to mathematics and the theories and models that come out of it. Keep in mind that they are useful "tools" only.

The discussion is about physics and philosophy and the interaction between the two. Those who have claimed that physics doesn't need philosophy have forgotten or have never looked at the specific philosophical underpinnings involved in the current crop of models and theories in use across every field of scientific study and investigation. Those philosophical viewpoints have dictated where the various models and theories have gone.

Have a look at your own fundamental belief system and ask yourself "How would I look at the universe around me if my basic belief was different?" Understand that your philosophical and religious viewpoint colours how you interpret the results of experiments, colours what experiments you will perceive and how you will develop your theories and models. If you are an Atheist, you will see things in a variety of ways. If you are a Buddhist, you will see things differently. This will happen whether you are a Hindu, a Daoist, a Moslem, a Christian, a Wiccan, or any of the various religious or philosophical systems.