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Sharp Bounds on the Ground State Energy of the SYK Model

Mathematical physics · posed by Feng, Tian and Wei; predicted by Garcia-Garcia, Jia and Verbaarschot, 2019 · solved

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Statement

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

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Arpon Basu, Pravesh K. Kothari and Siddhant Midha, using GPT-5.5 Pro, GPT-5.6 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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.

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