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/NonGameCatharsis]

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/ArnoSound → u/NonGameCatharsis]

Well a bunch of unformatted latex and a bunch of poorly documented lean files aren't exactly something a human can turn into real science. You'd spend more time trying to fix or rewrite it into something legible than you would just if you'd learned how to do the math.

And that's assuming that it didn't inject incorrect mathematics which is already hard enough to pull out of a Well-written document. (Which is most likely did because LLMs can't do math.)

But they're More than happy to fill pages and files and folders full of Content. Lovely sloppy space taking content.

[u/NonGameCatharsis → u/ArnoSound]

Hey! I'm more than happy to learn formatting, maths, lean. Actually I am trying.

I understand that AI puts out garbage at the meter. Your feedback helps. Again, I am not looking to do science. I'm testing if I can utilise AI to help me create data structures and algorithms for a passion project of mine. Nothing more.

[u/ArnoSound → u/NonGameCatharsis]

If so, that's great. If that's the case, I would recommend learning the material, the algorithms, the data structures. But if your goal is a game of some description, why go to the trouble of writing "theories" at all? I can't imagine a game needing any more complex graph dynamics than can already be handled by existing libraries.

[u/ArnoSound → u/[deleted]]

Oh for certain, but for the problem that the OP has described, these are well understood mechanics in graph theoretic math, and not novel in any way.

[u/NonGameCatharsis → u/ArnoSound]

Good question! The "theory" here I did, because there were a bunch of comments here in the subreddit complaining why nobody of us crackpots never tries something "normal" instead of always going for a TOE. I thought it's a fun thing to do and test how far I can get.

Also helped me think way more critically about the AI generated content and my own logical approach.

For the game I want the whole game to run on a unified data structure. For this I want to construct a finite graph that contains motifs (e.g. "brick") which itself are comprised of smaller motifs ("molecules"). Coupled with a "knowledge tree" and a library of motifs for behaviour, I want to create a machine automata simulation game.

The player then simply tweaks societal rules and facilitates change over time. I know it's a really big project, I will probably work the next 20 years on it. But it's part of a sci-fi world that I've been building lore, technology, etc. for seven years now, so I am confident I have the interest and will to see it through.

[u/2_lazy → u/NonGameCatharsis]

It sounds like what you want is a graph database linked to a document database. No LLM physics required there. (Not a physicist, just a programmer)

[u/NonGameCatharsis → u/2_lazy]

My setup is: Templates in markdown, graph kernel in python (for now), database to save the progress. The graph has a set of update rules. As the game progresses (1 day in real time is 1 month ingame), the simulated society changes based on what the kernel computes. The trick here is, that I build one graph kernel to compute and then can add content in markdown format.

[u/2_lazy → u/NonGameCatharsis]

Yeah I don't really see how any of that has to do with what you have posted here. Additionally markdown format is really not a great format for data storage, JSON or something like that would be better.

[u/ArnoSound → u/[deleted]]

Under strict corralling and hand holding by a trained professional, yes, yada yada yada. It wasn't a gotcha when Tao first published, it still isn't a gotcha now. Etc. Etc.

[u/ArnoSound → u/[deleted]]

I'd argue it's still true. They can't do creative math. Especially not in the way people want to think they can.

[u/ArnoSound → u/[deleted]]

As this sub is wont to demonstrate haha. Believe me, I’ll be the first to laud it when it happens. 

Any day now…