u/JimPeebles

I've been experimenting with a different flavor of LLM physics: instead of asking an LLM to invent a new theory, use it to attack a narrow mathematical question in an existing theory, then keep pushing the result through adversarial review and formal verification.

Repo:

https://github.com/jimpeebles/emd-coupling-identifiability

The question is about Einstein-Maxwell-dilaton theory and its coupling constant a:

Can a^2 be recovered locally from a finite metric jet, and if so, at what order?

The result we ended up with is:

At metric order 3, there is an exact one-parameter ambiguity. Different values of a can produce the same metric three-jet on an explicit active family.

So a^2 cannot be recovered from that three-jet. In particular, a = sqrt(3) and a = 1 collide.

At order 4, the missing information becomes recoverable and the ambiguity collapses to just a vs -a.

The part I think is most relevant here: after a lot of LLM-assisted derivation, criticism, and rewriting, the surviving claim was formalized in Lean.

The repo contains 75 Lean modules, builds with no sorry, admit, or project axioms, and includes an explicit claim ledger spelling out what is not being claimed.

This is not "LLM discovers new theory of gravity." It's a much narrower finite-jet identifiability result, and novelty is explicitly not claimed yet.

I'd especially love criticism on whether:

this is already known in the EMD/Rainich literature under different language;

the order-3/order-4 threshold is actually mathematically interesting;

the physical interpretation overreaches the formal result; or

there's an assumption/theorem in the chain where the whole thing breaks.

Given this subreddit, I fully expect someone to try to murder it. That's partly why I'm posting it here. :)

If you think it's wrong, pointing to the first theorem or assumption that fails would be especially useful.

I’ve been using LLMs as an adversarial research partner to revisit an old gravity/EM unification thread through Kaluza, Rainich, Einstein-Maxwell-dilaton theory, and modern rotating KK black-hole solutions.

The most interesting surviving idea is a possible critical amplification mechanism: instead of brute-forcing spacetime curvature with absurd EM field strengths, a light geometric scalar could sit near a finite-volume instability and be parametrically pumped by the Lorentz invariant \(F_{\mu\nu}F^{\mu\nu}\sim B^2-E^2\).

In a reduced simulation, the system was kept below the ordinary static scalarization threshold at all times, yet a resonant \(F^2\) pump produced exponential Floquet growth and nonlinear saturation. Detuned, below-threshold, and \(F^2=0\) controls did not grow. Coupling the amplified mode to a heavier radion-like degree of freedom then produced the expected geometric displacement.

What makes this exciting, if the physics survives, is the implication: EM-to-geometry coupling might behave less like “generate a gigantic gravitational field” and more like a high-Q transducer near criticality, where coherence, topology, resonance, and mode overlap matter more than brute power. In the strongest version, that opens the door to experimentally controllable scalar/geometric fields, resonant spacetime sensing, EM-to-geometry conversion, and eventually some form of metric engineering.

I’m not claiming this proves a new physical effect; the PDF separates established physics, our derived/simulated results, and speculation. The main question is whether a realistic higher-dimensional EFT and realizable Maxwell cavity modes can produce the required parameter window.

Would especially welcome criticism from people familiar with KK/EMd, scalarization, Floquet systems, moduli/radion EFTs, or cavity searches. The goal is to find the quickest reason this fails—or the narrow version worth developing further.

Link: Research Draft