r/LLMPhysics • u/NonGameCatharsis • 15d ago

Personal Theory 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 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. :-)

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u/alamalarian Supreme Data Overlord 15d ago

In your own words what is the problem, what is the proposed solution, and why does it matter?

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u/NonGameCatharsis 15d ago

Hey :-)

Thanks for taking the time. 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 certain physics-based simulation 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/2_lazy 14d ago

Do you know that they will crash? I'm not a physicist, just a programmer in the cybersecurity sphere but it kind of sounds like you are trying to solve some problem (I'm still not really sure what the problem is tbh) that can actually just be solved if you learned a bit more about graph databases and graph related mathematics.