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OpenAI: A claimed fixed zero-free half-plane for zeta and Dirichlet L-functions

Reported result · significance if the exact claim is established

If verified · conditional significanceClaim scope and evidenceReported result · not independently verified.
If verified · reference score700,000Editorial revision range 450,000–950,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.

Provisional assessment of the stated contribution scope. Scientific evidence and contributor attribution are separate.

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What is claimed?

The manuscript claims nonvanishing for the Riemann zeta function and every Dirichlet L-function in Re(s)>7/8, and for finite-order Hecke L-functions over Q(sqrt(-3)). The bound is independent of height and conductor.

Scientific scope

Principal-character poles at s=1 are allowed. The boundary Re(s)=7/8 is excluded. This does not put all nontrivial zeros on Re(s)=1/2 and is not the Riemann hypothesis. A bound on the number of zeros is a different result. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.

Evidence state

The manuscript reports a proof. WRS has not independently audited the complete argument or replayed the reported formalization. The grade and score here express conditional significance; they do not certify correctness. The provisional value enters the main reference rankings with an unverified label, but not achieved-science progress totals.

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