Correlated Hopping a Year Latter and LLMs in Research

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A year after (publication) I returned to it for a different project, and I naturally returned to some of the unanswered questions from that work. As brief recap (recap model).

The two questions that I want to adress are

1) Are the elements rational?

2) Do the coefficients stabilize?

Question 1. Rational entries

Question 2. Stabilizing coefficients

GPT 5.5 pro gave the key insight of expressing as a cumulat expansion, but failed to go further to what I believe humans would consider “the easy part”. My friend Antonio Acuaviva (link) recently pointed out this https://gowers.wordpress.com/2026/05/08/a-recent-experience-with-chatgpt-5-5-pro/ to me, which I think is neat.

Conclusion

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Replicating Wigner’s Insight

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I was introduced to the notion of experimental mathematics–where one uses computation (and a lot of heuristics?) to investigate and eventually derive properties of mathematical objects–by my friend Grigory Sarnitsky. Even after using it to compute infinite powers of large matrices, I remained skeptical of its usefulness in physics (sorry Grigory).