If you’re asking me to violate physics or introduce you to God, I can’t do that.

Your assertion violates physics, so that's not a good start.

I can provide some context that might expand your perspective

That's... A very arrogant way to say "let me explain what I think".

I’ll go ahead and concede that I can’t prove any of this any more than I can prove my own consciousness.

This also doesn't set a good precedent.

We’ll start with a universal language, mathematics. Since mathematics attempts to describe the universe objectively, it doesn’t have the same biases as religions and philosophies. What I’m going to try to describe is a reality that is an infinite fractal of consciousness.

Okay, sounds like an interesting idea.

We know we exist, at least I know I exist and I take it on good faith that I’m not the only conscious person. It seems reasonable that things which operate similarly and which come from the same source share attributes.

Maybe pedantic, but it depends what you mean by "share". We both share the trait of having skin, but not the same skin, for example.

Our material reality exists, at least in the same way that our individual perspectives exist. That reality seems consistent despite our perspective as individual observers.

So far, so good. Material reality exists before anything can perceive it.

The evidence so far indicates that reality is a phenomenon that exists on a higher order than our individual consciousness.

What do you mean by "higher order"? This seems a random introduction of levels of reality, apropos of nothing. I can at least concede that our subjective experience of reality is separate and not necessarily representative of actual reality, but separating them into "orders" seems to imply transcendence of some kind.

We know from our observations of reality, that infinities and paradoxes are disguised in every mundane object.

There appears to be some conflation of concepts going on here, but it would be better if you were to explain this concept itself in depth before going on to develop further theories based on such a concept. With such a vaguely phrased statement, it's hard to even know where to come at it.

The Dichotomy Paradox says you can split a candybar into infinite pieces by slicing each piece into half, but obviously that’s not the case.

The way I see it is, it is not impossible to complete an infinite number of tasks. It is merely impossible to list them. You unequivocally cannot get from A to B without getting halfway, and quarter, eighth, and so on. These infinite fractions are indeed reached, it's just impossible to keep track of.

Everything in the universe is moving, but the illusion of stillness exists due to orders of magnitude.

True but inconsequential. That's just gravity and the remnants of the initial universal expansion.

The vibration of an atom in a piece of Earth only differs from the vibration of a supernova by degrees of magnitude.

Once again, true but inconsequential.

But we’re in an infinite field that’s always expanding. What did it expand out of and what is it expanding into?

"Expanding out of" is a non-question. What does gas expand "out of" when it fills a room? Itself, if you really need an answer. As for "into", that's also a non-question. The universe is the totality of everything. IT makes no sense for there to be anything other than the universe. Therefore, the best description is simply "growth" - a growth of the universe.

I assert that it isn’t expanding into anything and it didn’t come from anywhere.

That is at least vaguely consistent with reality, yes.

It’s just a massive sine wave of a vibration so large in scale that it appears infinite.

My question to this, and everything that flows from it is:

Why? Why do you say this? This is a massive logical leap, seemingly from nowhere. Why a sine wave? A sine wave of what? What makes you say there is a universal vibration that everything is apparently tuned to? Why not a square wave, or a sawtooth?

It’s vibrating into itself like a cavitation bubble in an infinite ocean. It supports in its infinite curve smaller infinite waves that represent fundamental forces in our universe. Dimensionality, gravity, the speed of light and more are all curves on this order.

This is just pure imagination. It'd be great in a sci-fi book - genuinely, I'd love to read a sci-fi book based on an idea like this, go ahead and write it, I'll read it - but I'm really not seeing the jumping off point for this, based on your explanations beforehand. It's like, "A, therefore B, therefore Giraffe". A non sequitur.

Where they intersect, they create interference patterns, ripples, standing waves in spacetime.

Such chaotic interference in the fundamental forces of the universe would be readily apparent, especially in gravity.

These massive ripples result in universes, their ripples contain galaxies, those ripples contain solar systems.

This is another huge leap in logic, from absolutely nowhere!

Any place the intersection of curves interacts to create smaller fractals there is a refinement in complexity.

Ooookay, I guess that makes sense for worldbuilding.

The matter we’re made of reflects these intersections all the way down to the lowest level. Subatomic particles are the same shape as the universe.

Thaaaaat's a bit of a stretch, since, with the existence of gravity, you can expect such shapes to naturally form regardless. There's no meaning in the resemblance.

The “goldilocks zone” for stars is just that place in the gravity well where the intersecting curve can refract into living organisms.

...No, it's just the likely place for the right amount of heat to reach a planet...

In a biome as rich as the Earth’s thinking creatures can come into existence as long as the environment is just hostile enough to require predation and just abundant enough to allow for leisure.

Okay, another random fact thrown in to make the preceding bs sound plausible.

That’s the the whole spectrum. There’s the Light and it’s many emmenations, and there’s the darkness consuming everything that falls into it.

And... just abstract poetry to round it off.

I would like to mention that though you called this a mathematical theory, mathematics plays absolutely no role in your theory, other than mentioning sine waves, fractals and infinity - these concepts are not meaningfully explored except for their poetic and emotional weight.

Even in your life, you have to maintain that Goldilocks balance to have a healthy body and mind; what the Buddhists call, “The Middle Path,” also known as the Eternal Tau.

That is a damn stretch and a half to compare the habitable zone of a star to a philosophical doctrine, but I'll grant that it does have poetic relevance.

I’m going to get away from logic and venture into the unknown now.

My buddy, you left logic behind long ago.

With my belief that consciousness is the basis for reality

(Which you have not yet actually provided any reasoning for)

I also believe it’s the true center of the universe, the inner eye, or God’s eye. I think that from “God’s” perspective reality is like a Panopticon.

That's an interesting thought, but I see no reason to believe it, since you have provided none.

Where this central conscious gaze directs its attention, it experiences a reality.

It experiences reality the whole time, the gaze just changes which part of reality it is perceiving.

It forgets it was everything so that it can experience a small part of itself.

When was it everything - did you mention that at some point?

Like that meme, “Could God microwave a burrito so hot even He couldn’t eat it?” The answer is yes, if He forgets he’s God.

Did you establish that you have to remember reality for it to exist? I don't think you did. You must have forgotten, and that's why it doesn't exist.

I've been thinking about this a bit more, and I'd like to add that you're not totally mad, as I seem to imply. There is some logic in your claims individually, but little connecting them, and not much depth to them. Though, you seem to have stumbled upon ideas similar to Hegel, particularly the idea of quantitative change leading to qualitative change, as scattered and unrefined as the ideas are.

https://youtu.be/w85nGQ_KUgE?si=6L2hPnrKdNwhBEEo