The Proportion of Zeta Zeros on the Critical Line

Lineage and corrections

This event attributed to Jarred Sumner

This event attributed to Ralph Furman

This event attributed to Eric Easley

This event attributed to Levent Alpöge

This event attributed to Claude (unreleased research version)

The Proportion of Zeta Zeros on the Critical Line parent of this event

An unconditional record, not a resolution: the Riemann hypothesis is untouched, and Anthropic states it does not expect these techniques to lead to a proof of it. The paper is explicit that these are lower bounds only - the remaining third of the zeros are not shown to be off the line, merely not reached by the certificate. What it does settle is a question that was posed. Goldston and Suriajaya had reduced Montgomery's conditional $\tfrac23$ to a single obstruction, the termwise positivity that fails for zeros off the line, and asked what would follow without it. Theorem A replaces that positivity with a rank-trace inequality on a finite compression of Weil's Hermitian form, with Sylvester's law of inertia handling off-line pairs; reading the negative index of truncations as a count of off-line pairs is Bombieri's device. The paper also proves the bound sharp for this route: improving on $\tfrac23$ this way would need pair-correlation information beyond Fourier support 1. parent of this event

VibeMathed record: The Proportion of Zeta Zeros on the Critical Line evidence for this event

The Anthropic PDF the entry was first written from, before the arXiv version evidence for this event

Lean repository - audited at tag v1.0; comparator statements under comparator/ evidence for this event

Anthropic's informal note stating the proof concisely evidence for this event

The Proportion of Zeta Zeros on the Critical Line evidence for this event

Annotated subagent transcripts evidence for this event

Anthropic's announcement evidence for this event

How the argument was found: Claude's account of its own two runs evidence for this event