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
Bound · version 1
A cited upper bound Λ ≤ 0.2
Earlier version 1. View current version 2 →
Statement
In the classical heat-flow normalization, Λ ≤ 0.2. This is Corollary 2 of the finite-verification paper, applying Polymath15’s criterion with the verified height.
Assumptions
- Use the same classical heat-flow normalization as the lower bound.
- The rigorous finite-height verification satisfies the published Polymath15 criterion.
Scope
A published upper bound selected here as a reviewed baseline; newer proposed improvements are separately attributed below.
Evidence
Source reports
Connections
In this problem · publication v4 · Selected context
Riemann hypothesis →
Bound · Proved
Together with Λ ≥ 0 this gives 0 ≤ Λ ≤ 0.2. It does not establish Λ = 0.
Scope: The finite-height theorem and Polymath15 criterion yield Λ ≤ 0.2; newer proposed bounds remain separate.
Limit: A positive upper bound leaves Λ = 0 unresolved. This is a cited baseline, not a claim that no later improvement exists.
The upper bound depends on the same finite verification as the first result; the two heat-flow bounds constrain one constant.
Related statements
The two proved inequalities enclose the same normalized constant in [0, 0.2].
An interval containing zero is not a proof that the constant equals zero.
Details & sources
The Newman constant satisfies Λ ≥ 0 →
Proved · version 1
For the classical de Bruijn–Newman heat-flow family, Λ ≥ 0. Λ is defined by H_t(z) = ∫₀∞ exp(tu²) Φ(u) cos(zu) du, using the classical Riemann kernel Φ and normalization in the cited paper; all H_t zeros are real exactly when t ≥ Λ.
- Classical Riemann ξ heat flow and the cited normalization.
- No RH assumption.
Scope: Newman’s separate nonnegativity conjecture is proved.
A cited upper bound Λ ≤ 0.2 →
Proved · version 1
In the classical heat-flow normalization, Λ ≤ 0.2. This is Corollary 2 of the finite-verification paper, applying Polymath15’s criterion with the verified height.
- Use the same classical heat-flow normalization as the lower bound.
- The rigorous finite-height verification satisfies the published Polymath15 criterion.
Scope: A published upper bound selected here as a reviewed baseline; newer proposed improvements are separately attributed below.
Relationship not independently reviewed.
Connection in Riemann hypothesis →Relationship not independently reviewed. This concerns its use in this problem.
Sources
Platt–Trudgian · rigorous finite verification →
- Corollary 2, §3.4, p. 5; Polymath15 Table 1 applied to Theorem 1 → · Original passage ↗
Recorded wording
The finite-height verification supplies the published criterion giving Λ ≤ 0.2.
paraphrase · No upstream full text or code is republished by this record.
- 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.
Rodgers–Tao · Newman constant is nonnegative →
- Theorem 1.1; §1 normalization and RH equivalence → · Original passage ↗
Recorded wording
The de Bruijn–Newman constant Λ is nonnegative.
paraphrase · No upstream full text or code is republished by this record.
Brad Rodgers · Terence Tao · Published
Published in Forum of Mathematics, Pi (2020). The pinned 2021 author revision records a correction to Section 8; earlier manuscript history is not silently substituted.
Revision & attribution
Source revision: arxiv-v5. Observed Oct 10, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Source updated Jul 3, 2021.
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-newman-upper-bound
- Statement version
- 1
- SHA-256
- 1a57aa034a7b1e0f2875fe924bc84794fc37068789af838c1d8ecb02d771a424