Sharp Bounds on Ground State Energy of the SYK Model

Arpon Basu, Pravesh K. Kothari, Siddhant Midha

GPT-5.6 Pro suggested a twisted-boson moment identity and an isometric embedding and intertwining identity that transfer a bosonic witness into a lower-bound certificate. These steps support the authors’ E||H_SYK||=(1−o(1))√(2n)/k result for even k growing to infinity with k=o(√n), with a stated sparse extension.

Sources for this record

What was already known

Before this work, general bounds left a factor-k gap for growing k; physics heuristics predicted the √(2n)/k leading scale. The authors first found the decisive deterministic operator.

AI involvement AI-centered

Basu, Kothari and Midha credit GPT-5.6 Pro with Lemma 4.6 and Propositions 4.14–4.15. They developed the operator and the rest of the spectral argument.

The authors explicitly attribute three central retained mathematical statements to GPT-5.6 Pro while crediting themselves with the overall operator insight and full proof development.

Importance Notable

The model-suggested bridge helps close the spectral-edge gap in a specialized SYK regime.

Limitations

Basu, Kothari and Midha supplied the operator insight, complete proof and parameter analysis. No completed claim-specific human or machine check of the three suggested statements is documented. Fixed-even-k results and the spin-glass theorem are separate.

Technical verification Reported

The paper supplies proofs and reports model-assisted verification of technical proofs, but does not document a named completed human review or rigorous machine check of Lemma 4.6, Proposition 4.14 and Lemma 4.15. Reported is the missing-check default.

Human understanding Full

The human authors explain the pairing identity, the isometric embedding and the intertwining map, and trace how the resulting bosonic witness yields the SYK lower bound.

Correction and publication history

2026-10-18 · publication

The model-suggested bridge helps close the spectral-edge gap in a specialized SYK regime.

Read this published revision