Proved
Scoped theorem in cited source ↗
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Source dated Mar 23, 2026 · Observed Oct 10, 2026
Bound · version 2
An explicit zero-free region near Re(s) = 1
Statement
ζ(σ + it) ≠ 0 whenever t ≥ 3 and σ > 1 − 1/(4.896 log t), with natural logarithm.
Assumptions
- Real t ≥ 3.
- Strict inequality σ > 1 − 1/(4.896 log t); classical ζ.
Scope
A height-dependent region near the right edge of the critical strip, not a fixed half-plane down to Re(s) = 1/2.
Evidence
Source reports
Connections
In this problem · publication v13 · Selected context
Riemann hypothesis →
Bound · Proved
This eliminates a specified region of possible zeros. It is not a proof of RH, nor a claim to be the strongest available region at every height.
Scope: The March 2026 preprint improves a logarithmic exclusion region near the edge of the strip.
Limit: The boundary approaches 1 as t increases. RH needs the much stronger exclusion of every zero with Re ρ > 1/2.
Excluding a region and bounding counts in a larger region are different conclusions; neither is an additive progress score.
Related results · 1
Relationship not independently reviewed. This concerns its use in this problem.
Sources
Bellotti–Trudgian–Yang · explicit zero-free region →
- Theorem 1, p. 2 (strict inequality in theorem statement) → · Original passage ↗
Recorded wording
There are no zeta zeros for t ≥ 3 and σ > 1 − 1/(4.896 log t).
paraphrase · No upstream full text or code is republished by this record.
Chiara Bellotti · Timothy S. Trudgian · Andrew Yang · Preprint
Author preprint at the cited revision; journal acceptance has not been established by this curation.
Revision & attribution
Source revision: arxiv-v1. Observed Oct 10, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Source updated Mar 23, 2026.
Guth–Maynard · zero-density estimates →
- Theorem 1.2 and equation (1.4), p. 2 → · Original passage ↗
Recorded wording
A new bound limits the number of zeros to the right of a fixed vertical line.
paraphrase · No upstream full text or code is republished by this record.
Larry Guth · James Maynard · Published
Published online 1 March 2026 in Annals of Mathematics 203, pp. 623–675, DOI 10.4007/annals.2026.203.2.6. The author manuscript was revised April 2026; the pinned theorem statement is cited here.
Revision & attribution
Source revision: arxiv-v2. Observed Oct 10, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Source updated Apr 7, 2026.
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.
Proved
Scoped theorem in cited source ↗
Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.
Source dated Mar 23, 2026 · Observed Oct 10, 2026 · Source passage →
Record details
- Claim ID
- claim-rh-explicit-zero-free-region-2026
- Statement version
- 2
- SHA-256
- 271ae11c57e630bd7ed6be861b66c948c29a166d6f294891f1ed1b86794bda15