[criddell]

I know of one other non-mainstream explanation from Max Tegmark: the mathematical universe hypothesis says reality is actually mathematics.

I'm not sure your explanation is an alternative explanation of what reality is. You've laid out some characteristics and consequences, but haven't described what's at the bottom of it.

I've heard that matter is a consequence of quantum field excitations, but what is a field? From the little bit I've read it sounds like mathematics again.

[aeternum]

The concept of a field can be described using mathematics but does that really mean mathematics is actually what the universe is made of?

Suppose for example we found that protons, neutrons, and electrons really were fundamental. Their behavior can be described with mathematics but wouldn't we say it's still the elementary particles that our compose our universe?

[criddell]

Tegmark's theory says exactly that - the particles are ultimately mathematics. Not that they can be modeled with mathematical methods, but that they are actually constructed from mathematical structures.

It's definitely not a mainstream theory.

[goatlover]

What does the mean, though? Mathematics as we understand it is an abstraction. If the universe is fundamentally abstract, what breathes fire into the models? Consciousness?

[wcoenen]

Modal realism. A mathematical structure is "real" to its conscious inhabitants (if any), and merely an abstraction from the perspective of those who are not, i.e. the inhabitants of other mathematical structures.