Equivalence · version 3
For the classical de Bruijn–Newman constant, RH is equivalent to 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.
The equivalence is a theorem; whether the constant is zero remains the unresolved target.
Proved
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
Rodgers–Tao · Newman constant is nonnegative · §1: RH iff Λ ≤ 0; Theorem 1.1: Λ ≥ 0 →
Observed Oct 10, 2026
Replaces an earlier source assessment. Earlier assessment ↓
In this problem · publication v12 · Selected context
Supporting result · Proved
The equivalence is proved. Its two target assertions remain open; proving an equivalence does not prove either target.
RH gives Λ ≤ 0; the proved Λ ≥ 0 turns this into the target Λ = 0.
Λ ≤ 0.2 and a proposed smaller positive upper bound do not reach zero.
Open · version 3
Every nontrivial zero of the meromorphic continuation of has .
Scope: Every zero at every height; negative-even trivial zeros and the pole at 1 are excluded.
Open · version 2
Λ = 0 for the classical de Bruijn–Newman heat-flow family H_t and Riemann kernel defined in Rodgers–Tao §1.
Scope: A heat-flow target equivalent to classical RH; positive upper bounds leave this target open.
Relationship statement · Proved · version 3
For the classical de Bruijn–Newman constant, RH is equivalent to 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.
Scope: The equivalence is a theorem; whether the constant is zero remains the unresolved target.
Relationship not independently reviewed.
Connection in Riemann hypothesis →Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v13
Supporting result · Proved
The equivalence is proved. Its two target assertions remain open; proving an equivalence does not prove either target.
RH gives Λ ≤ 0; the proved Λ ≥ 0 turns this into the target Λ = 0.
Λ ≤ 0.2 and a proposed smaller positive upper bound do not reach zero.
Open · version 3
Every nontrivial zero of the meromorphic continuation of has .
Scope: Every zero at every height; negative-even trivial zeros and the pole at 1 are excluded.
Open · version 2
Λ = 0 for the classical de Bruijn–Newman heat-flow family H_t and Riemann kernel defined in Rodgers–Tao §1.
Scope: A heat-flow target equivalent to classical RH; positive upper bounds leave this target open.
Relationship statement · Proved · version 3
For the classical de Bruijn–Newman constant, RH is equivalent to 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.
Scope: The equivalence is a theorem; whether the constant is zero remains the unresolved target.
Relationship not independently reviewed.
Connection in Riemann hypothesis →Relationship not independently reviewed. This concerns its use in this problem.
After the nonnegativity theorem, RH is equivalent to Λ = 0.
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.
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.
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.
Source revision: official-description. Observed Oct 10, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proved
Only the cited assertion with its exact assumptions. This report does not resolve the canonical Problem or establish independent OpenMath mathematical review.
Observed Oct 10, 2026 · Source passage →
Open · Superseded in an indexed context
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 Jul 3, 2021 · Observed Oct 10, 2026 · Source passage →