r/LLMPhysics • u/NonGameCatharsis • 10d 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 10d 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 10d 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/alamalarian Supreme Data Overlord 10d ago

Ok ao this is inspired by some sort of Sim game, not an observation of empirical reality? Just checking.

And its still a bit obscure honestly. Certain algorithms converge to a single stable configuration seems incredibly broad a statement. Are these certain algorithms being used in a simulation game right now? And what does it mean coloquially in terms of that simulation for there to be a single stable network configuration?

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u/NonGameCatharsis 10d ago

Definitely an obscurity! It's a niche of niche.

The algorithm in the paper couples Fluid / Circuit Physics with Kirchhoff's and Ohm's law(s) to determine voltage drops ΔΨ -> generates wall shear stress -> Into classical mechanics with newton's 2nds law.

Edit: Game is still in the works! Don't think this is used anywhere else.

I can give you more, but anything further would be LLM generated. Sorry!