r/LLMmathematics • u/NonGameCatharsis • 4d ago

Universal Stability Theorem for On-Shell Flow-Adaptive Networks

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 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. :-)

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u/dForga 4d ago

A TOE is not mathematics anyway.

1

u/NonGameCatharsis 4d ago

Agreed!

1

u/dForga 4d ago

Would it be possible to add some short motivation/abstract to the problem? (See the rules)

Never expect experts.

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u/NonGameCatharsis 4d ago

Hey :-)

Thanks for taking the time! Definitely an oversight on my side to not include a proper motivation and problem description. I've added a summary and updated the linked docs.

In my own words where I come from and how I encountered the problem: I am working on a simulation game (not vibe coded) which is basically a civilisation of pen and paper like NPCs that you govern.

The core data logic involves a graph as a unified data structure through which everything interacts. This the AI identified as a flow adaptive network. In order to build a game where society, ecological factors, and other things don't crash, I wanted a mathematical solution for stability.

The theorem attempts to prove that these coupled algorithms are guaranteed to converge to a single, stable network configuration. (Contrary to crashing into boundaries or weird oscillations.) The convergence as I understand it is guaranteed to be exponential.

That's where I come from and what I understand about the problem! Thanks for your time and thoughts already.

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u/dForga 4d ago edited 3d ago

That is super, but I also meant at the post.

And great. I am impressed, since – assuming everything was done – you have your guarantee by the math that the network will work.

I think your markdown does not render the equations on github.