VibeMathedMath problems solved by AI
All problems

Sharp Bounds on the Ground State Energy of the SYK Model

For the Sachdev-Ye-Kitaev Hamiltonian on nn Majorana modes with kk-body interactions, the paper proves EHop=(1o(1))2n/k\mathbb{E}\|H\|_{op} = (1-o(1))\sqrt{2n}/k for super-constant ko(n)k \le o(\sqrt{n}), confirming predictions of Garcia-Garcia, Jia and Verbaarschot and answering a question of Feng, Tian and Wei.

Result
Proved
Status
Resolved
AI contribution
AI co-developed
Method
Argument
Field
Mathematical Physics, Random Matrices
Posed by
Feng, Tian and Wei; predicted by Garcia-Garcia, Jia and Verbaarschot
Year posed
2019
Years open
7y
Solved
2026-07-29
Model
GPT-5.5 Pro / GPT-5.6 Pro
Vendor
OpenAI
Collaborators
Arpon Basu, Pravesh K. Kothari, Siddhant Midha
Verification
Unreviewed
Publication
Preprint
Significance
20 / 100
Disclosed cost
Wikipedia
No dedicated article

What the AI did

The authors analysed a preliminary version of their explicit deterministic operator with GPT-5.5 Pro and GPT-5.6 Pro, and credit GPT-5.6 Pro with suggesting Lemma 4.6, Proposition 4.14 and Lemma 4.15. They also used it to search related literature and to assist with verifying technical proofs.

Verification

No independent check. The disclosure is unusually specific, naming the three results the model contributed, which is what makes the co-developed tier defensible here. Preprint, not refereed.

Source

arXiv

Discussion