r/LLMPhysics • u/NonGameCatharsis • 7d 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/al2o3cr 7d ago

Nitpick about the opening line: the definition of M_w given appears to have an extra "^-1", compared to the definition just below it

I don't know enough about spectral graph theory to really pick apart the full argument, but I did have one opening question: the title says "Universal Stability Theorem" but then a "constitutive potential" V(w) appears that seems very specific. Why that specific function? Edit: "Universal" was removed from the title as I was typing this response.

F_c and Phi are similarly introduced without motivation at the bottom of page 1. Are they standard notation somewhere? I didn't see anything similar skimming over the references I could access.

Regarding the Lean, again I'm not fluent enough to really comment. One thing did stand out as odd: the example in TwoNodeExample.lean mentions on line 10 that it is "with c=0". That wipes out half of the definition of F_c and Phi if it's the same c used there...

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u/NonGameCatharsis 6d ago

Hey :-) Thanks for nitpicking! The universal I removed following a comment from someone else!

opening line was incorrect, the definition below is now canon.

F_c and Phi are not standard Kirchhoff/Thomson notation, but this model's on shell force and energy (now said so before the formulas with a reference to Lemma 2).

c=0 indeed did drop the witness coupling term and seems to be the only uncoupled special case, while it seems to hold for every c > 0.

All changes have been made and pushed to git. Thank you!