The facts

  1. The 49-page manuscript dated 5 October claims that every Dirichlet L-function, including the Riemann zeta function, has no zeros with real part greater than 11/12. Its argument uses mean-square estimates, large sieves and metaplectic theta-series techniques. [1]

  2. A separate 199-page manuscript dated 30 September claims the stronger boundary 7/8. Quanta reports that this version was formally verified in Lean, while the shorter 11/12 version had not been formally verified at the time of its report. [2][3]

  3. Quanta interviewed specialists including Maksym Radziwiłł and Alexander Dunn. It reports human efforts to clarify the argument and substantial criticism of the manuscripts’ exposition; formal verification and expert mathematical understanding are distinct checks. [3]

Relevant context

The full Riemann hypothesis would place all nontrivial zeta zeros on the line with real part 1/2. Both manuscripts concern weaker zero-free regions; the full conjecture remains open. [1][2][3]

Still unconfirmed

  • Journal acceptance and subsequent complete checking of both manuscripts have not been established in the checked sources.

Sources

References support the numbered facts above. Source checks: 29 Oct 2026, 02:05 UTC.

Catch-up coverage of the 19 October expert assessment. No claim is made that the full Riemann hypothesis has been proved.

  1. The Quasi-Riemann Hypothesis, 5 October manuscript

    OpenAI · Primary source · 5 Oct 2026

    Original PDF retrieved; theorem, scope, prior work and argument outline read. This is a preprint, not a verified journal-publication claim.

  2. A Zero-Free Half-Plane Re(s) > 7/8

    OpenAI · Primary source · 30 Sept 2026

    Original PDF retrieved; abstract and introduction read. Same institution as source 1, not independent corroboration.

  3. AI Proved the Quasi-Riemann Hypothesis. What Happens Now?

    Quanta Magazine · Reporting · 19 Oct 2026

    Independent specialist reporting with named mathematicians. Its formal-verification and expert-assessment descriptions are attributed, not a claim that this newsroom audited the proof.

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