Spectral Edge of the Quartic SYK Model

Precise statement

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

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.6

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

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

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

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-22

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

   VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• The source status is candidate and must not be represented as solved.
• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.