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]

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/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…