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Spectral Edge of the Quartic SYK Model

Determine the leading asymptotic of the largest eigenvalue of the NN-Majorana quartic SYK Hamiltonian as N→∞N \to \infty. The preprint proves λ1/N→4∫0∞g0(t)4 dt≈0.32504\lambda_1/\sqrt{N} \to 4\int_0^\infty g_0(t)^4\,dt \approx 0.32504 almost surely, via the limiting free energy at every fixed positive temperature.

Result
Proved
Status
Candidate (review pending)
AI contribution
AI co-developed
Method
Argument
Field
Random matrices & quantum many-body theory
Posed by
—
Year posed
2016
Years open
10y
Solved
2026-07-22
Model
GPT-5.6
Vendor
OpenAI
Collaborators
Yukun He
Verification
Unreviewed
Publication
Preprint
Significance
15 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

Developed with GPT-5.6; the finite-bath interpolation reduces the quartic SYK pressure to a local cavity-kernel identity.

Verification

Single-author arXiv preprint; independent review pending, so this is recorded as a candidate rather than an accepted resolution.

Source

arXiv:2607.18998 - The spectral edge of the quartic SYK model

Discussion