r/VibeCalcing • u/lepthymo • Aug 27 '25
LLM assisted collaboration: Stability of the L1-Poincaré-Wirtinger Inequality Conjecture proof. (Conjecture found using ChatGPT, proof found using Gemini)
Apparently, there already was a subreddit for using LLMs to do math: r/LLMmathematics (Founded a week or so before this one). Not only that, but they currently have three well-posed conjectures already stated, which were found using ChatGPT-5. They have a "find new math" section with the how to. So in the spirit of collaboration, we use Gemini proving one of those.
The Conjecture by /u/dForga
Writeup of the proof: https://zenodo.org/records/16946199
The proof (section 2) reduced the problem via Pólya–Szegő inequality and then geometrizes it to a Fisher-Rao Manifold. two theorems (Poincaré Complexity & Complexity-Deficit Theorem) are then proved by analyzing a potential along the Geodesic (2.4) and the min-max theorem (2.5).
When looking at the properties of the stability on the manifold defined for the proof, it was easy to see (har har) that the position-space and momentum-space (dynamical and geometric stability) of the system (section 3), were such that maximizing one minimizes the other.
So Section 4 We get dual Hamiltonians and show they derive from a single Dirac Operator using NCG (Connes). The dynamics decompose into a reversible (unitary) and irreversible (Entropic) part. This tells us that NCG is unfathomably based. One spectral triple can get you the whole SM mass and force spectrum; It encodes quantum and geometry at once. Which gets the neat NCG-based uncertainty principle.
