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 Apr 21, 2020 · Observed Oct 10, 2026
Theorem · version 3
RH verified to height 3,000,175,332,800
Statement
Every nontrivial zero of with has .
Assumptions
- Classical Riemann zeta function.
- Positive ordinate 0 < γ ≤ 3,000,175,332,800; conjugation gives the negative counterpart.
Scope
A rigorously verified finite height range, using ball arithmetic and a count of all zeros in that range.
Explanation
Bounds & computations · 1
Compare the quantity and hypotheses within each group. A finite check, conditional theorem and proposed improvement cover different scopes.
| Result | Value | Conditions |
|---|---|---|
| RH verified to height 3,000,175,332,800 → Proved Selected source date: | Up to 3,000,175,332,800 | Every nontrivial zero with positive imaginary part up to this height; finite rigorous verification. |
Evidence
Source reports
Connections
In this problem · publication v8 · Selected context
Riemann hypothesis →
Special case · Proved
This proves a finite restriction of RH. The number is a height, not a count of checked zeros. No conclusion for all higher ordinates follows.
Scope: Every zero in the stated height range is on the line; rigorous counting excludes missed off-line zeros there.
Limit: RH still quantifies over every height. A complete check below this bound cannot exclude even one higher off-line zero.
A distinct scope, not an additive fraction of the conjecture solved.
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v13
Riemann hypothesis →
Special case · Proved
This proves a finite restriction of RH. The number is a height, not a count of checked zeros. No conclusion for all higher ordinates follows.
Scope: Every zero in the stated height range is on the line; rigorous counting excludes missed off-line zeros there.
Limit: RH still quantifies over every height. A complete check below this bound cannot exclude even one higher off-line zero.
A distinct scope, not an additive fraction of the conjecture solved.
Relationship not independently reviewed. This concerns its use in this problem.
Sources
Platt–Trudgian · rigorous finite verification →
- Theorem 1, p. 2; §2 interval/ball arithmetic and Turing counting → · Original passage ↗
Recorded wording
All nontrivial zeros with positive imaginary part at most 3,000,175,332,800 lie on the critical line.
paraphrase · No upstream full text or code is republished by this record.
Dave Platt · Tim Trudgian · Published
Published in Bulletin of the London Mathematical Society, DOI 10.1112/blms.12460. Statements here use the pinned author manuscript, Theorem 1 and Corollary 2.
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 Apr 21, 2020.
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 Apr 21, 2020 · Observed Oct 10, 2026 · Source passage →
Record details
- Claim ID
- claim-rh-finite-height
- Statement version
- 3
- SHA-256
- 924016686bad4b9013884a35e6b95095a69a6df8add52797eba191ac0dadbca2