Unbounded normalized gaps between zeta zeros

Prove the conjecture that the limsup of the normalized gaps between consecutive ordinates of the non-trivial zeros of the Riemann zeta function is infinite, namely λ=∞.

Background

The paper defines λ as the limsup of the consecutive zero gaps γ_{n+1}−γ_n normalized by the average local spacing 2π/log γ_n. It records only conditional or partial evidence for the extreme-gap behavior predicted by random-matrix heuristics.

The conjecture is presented as a consequence of the stronger Gaussian Unitary Ensemble hypothesis, which predicts that the appropriately normalized zeta-zero ordinates have the same local statistics as eigenvalues of large random matrices from the Gaussian Unitary Ensemble.

References

The conjecture $\lambda=\infty$ is a consequence of the stronger GUE Hypothesis which asserts that the statistics of the ordinates of the non-trivial zeros of the zeta function, appropriately normalized, behave like the statistics of eigenvalues of large random matrices from the Gaussian Unitary Ensemble (GUE).

— Isolated zeros of the Riemann zeta function and zeros of linear combinations of Dirichlet $L$-functions  (2610.26841 - Lamzouri, 19 Oct 2026) in Section 1, Introduction