The zeros of the Riemann zeta function on the critical line are not evenly spaced. Some consecutive zeros are unusually close together; others are unusually far apart. Selberg proved that both extremes exist — there are arbitrarily large and arbitrarily small gaps relative to the average spacing — but said nothing about how common they are.
Zhao (arXiv:2603.17334) proves that these extremal gaps are not rare. For r-gaps — the spacing between the nth zero and the (n+r)th zero — a positive proportion of gaps exceed a specific multiple of the average, and a positive proportion fall below another. The bounds hold unconditionally with exponent α ≤ 2/3, improving to α = 1/2 under the Riemann Hypothesis.
The advance over prior work is density. Previous results established existence — at least one gap is unusually large, at least one unusually small. Zhao shows that a quantifiable fraction of all gaps are extremal. The zeros cluster and spread with measurable frequency, not just in isolated instances.
For r = 1 (consecutive zeros), this unconditionally improves results of Simonič, Trudgian, and Turnage-Butterbaugh. The method extends naturally to r > 1, giving density estimates for longer-range spacing statistics that were previously available only as existence theorems.
The gap distribution of zeta zeros is not a matter of isolated anomalies but of systematic structure. The zeros crowd and separate in patterns dense enough to measure, not just prove. The irregularity is the regularity — the density of extremal gaps is itself a structural feature of the zero distribution.