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OpenAI · 003-02 · 2026-10-05 · Number theory

The Quasi-Riemann Hypothesis (alternate 11/12 proof)

preprints/The-Quasi-Riemann-Hypothesis-October-5-2026

Family 003. The quasi-Riemann hypothesis.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Vacuum energy. A zero-free statement or a vacuum phrase is not an explanation of vacuum-energy smallness and not a swampland test. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. Em02-E · XI-A · XVI-P

Proves that every Dirichlet -function, including , is zero-free in , resolving the quasi-Riemann hypothesis. The same half-plane is zero-free for every finite-order Hecke -function over . A companion gives a different proof of the zero-free half-plane .

We establish the quasi-Riemann hypothesis by proving that every Dirichlet L-function, including Riemann's zeta function, has no zeros in the half-plane . More generally, we prove the same zero-free half-plane for every finite-order Hecke L-function over . In particular, this rules out the existence of Landau–Siegel zeros.

Preprint source and Lean scope

The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.

A Lean scope note is stored for family 003, but it does not name this preprint. It names 003-01, 003-03. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.

  • Vacuum energy

    A zero-free half-plane is not vacuum energy

    Family 003 records a quasi-Riemann zero-free half-plane. That half-plane is not an explanation of vacuum-energy smallness and not a swampland test. The authors are OpenAI. The companion does not verify those proofs.

    Vacuum energyEm02-E exponential potentialXVI-P two-point loop