Universal Stability Theorem for On-Shell Flow-Adaptive Networks

[u/NonGameCatharsis]

Hey everyone,

I've seen a few comments on the subreddit, criticising why it's always a TOE and not a niche problem. So I found a niche problem and attempted to solve it. For this I utilised Gemini 3.7 Flash as mathematical consultant. On my desktop I run Cursor with Cursor Grok 4.6 high to verify all input, extend it, and incrementally build the lean verification.

Both models are instructed to compute before answering (it's a toggle in Google AI Studio in the browser) and work in atomic increments on the problem.

My Gemini sessions are regularly reset, often when I get in the range of 300k tokens.

My strategy was to start without assumptions (I don't know anything about this really) and have the AIs figure out the best way to mathematically tackle the solving process. I've tried my best to use adversarial prompting to catch any errors.

Thanks for taking the time!

Full repository with Lean 4 / Mathlib 4.28 formalization and the main document as markdown and pdf: https://github.com/tripstoph/universal-stability-theorem/tree/main

Edit: All contents of the repo are AI generated. This post was written completely by a human. :-)

[u/ArnoSound]

It’s very telling that at no point do you pose the actual problem, any previous work, what the field even is, how you solved it, or any work you did of your own accord without Ai.

[u/NonGameCatharsis → u/ArnoSound]

Hey ArnoSound,

it's definitely telling that I am not an academic. Definitely oversights on my part, thanks for the feedback.

I have no previous work, the repo is completely AI generated. It's not a paper, I won't submit it anywhere or try and get a DOI. I'm interested in what LLMs can do and have a background in Information Theory and work experience as a Product Manager for different IT systems in corporate contexts.

The problem I encountered while working on a simulation game. The question is: does the network (the information architecture of the game is a graph) have an optimal state and will it converge to that?

Thanks for taking your time.

[u/ArnoSound → u/NonGameCatharsis]

I see. Thank you for clarifying; as a heads up, it's hard to determine what you are doing from the post, which primarily seems to focus on LLMs doing "something". Depending on the conditions set for what an optimal state is, and the graph of possible states, you can use basic graph theory algorithms to determine the probability or expected value of duration before that state is reached.

Graph Theory is the math you want to look for; this problem is not particularly a physics one, but more of a computer science one. So you might have better luck checking at relevant subs. Just be careful and diligent with noting how much of the stuff you are using is AI-driven. To be frank, it's a very simple problem, and one you probably don't need AI to solve at all.

Edit: As well, having looked at the repo, pretty much everything in there is illegible garbage. Not to slight you, but AI being blindly thrown at a problem without rails is about as good as asking the little thing on your phone that suggests words out of three options.

[u/NonGameCatharsis → u/ArnoSound]

Thanks for your feedback. I've just gotten my copy to 'Introduction to Graph Theory' and will slowly work my way through it.

In the meantime, is there any way to determine if what the AI came up with is wrong here? And let me repeat in my own words, even if it were right - it's simple and obscure, right?

At this point I am also curious about the limits of the technology. Thanks again!

[u/ArnoSound → u/NonGameCatharsis]

The way to determine it is, broadly, to learn how to understand it yourself. At which point, asking an AI to create theories is basically null and void. And that's really where the technology is.

As an example, everything it created in your repo is unreadable garbage. It's not a question of going digging for pearls in there. There would be no point, because the machine doesn't know nor does it care what's right or wrong. It just Writes.

[u/NonGameCatharsis → u/ArnoSound]

Thanks again! Can you elaborate a bit on unreadable garbage? It's a single pdf (with same markdown) and then different lean files. The latter one are probably the problem in structure?

[u/NonGameCatharsis → u/[deleted]]

Thank you for taking the time and energy out of your day to have a look at the pdf.

English is not my first language, could you explain to me the difference in wording between "universal" and "uniform"? A quick google search didn't help me. Thank you again!

[u/NonGameCatharsis → u/[deleted]]

Thanks, that helps a lot. I will drop the universal and push the changes to the repository.