Conjecture · version 2

classical RH fails

Statement

There exists a nontrivial zero ρ of ζ(s) with Re(ρ) ≠ 1/2.

Assumptions

  • The same classical meromorphic zeta function and critical strip.

Scope

The logical negation of the all-zero classical target, not a failure of a broader GRH variant.

Evidence

Source reports

Connections

In this problem · publication v12 · Selected context

Riemann hypothesis →

Alternative answer · Open

An off-line nontrivial zero would refute the same classical RH assertion.

Relationship not independently reviewed. This concerns its use in this problem.

In this problem · publication v13

Riemann hypothesis →

Alternative answer · Open

An off-line nontrivial zero would refute the same classical RH assertion.

Relationship not independently reviewed. This concerns its use in this problem.

Sources

Bombieri · official RH description →

  • §I, PDF page 1 → · Original passage ↗
    Recorded wording

    Do all nontrivial zeros of the Riemann zeta function have real part 1/2?

    paraphrase · No upstream full text or code is republished by this record.

Enrico Bombieri · Published

Official Clay exposition. Historical results and approaches must not be read as current record bounds.

Revision & attribution

Source revision: official-description. Observed Oct 10, 2026.

The cited work does not report AI involvement; absence of attribution is not evidence of absence.

Official description PDF: official-description. External source evidence; no OpenMath execution or independent reproduction is attached.

History

Statement versions

Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.

Assessment history · 1

Assessments retained in these publication records. Earlier statement versions retain their own source histories.

Record details
Claim ID
claim-rh-fails
Statement version
2
SHA-256
ad9213af95b6bde34a7fa14ab3b68858cd927f65102ffc59947230971cb21d34

Publication records