Conjecture · version 1
For the standard Chernoff density f, satisfies for every real x.
This is stronger than inf κ > 0. The selected 2026 theorem does not prove that the origin minimizes curvature, and this curation does not assert a comprehensive current-status assessment.
Not assessed
The 2014 conjecture is recorded as a distinct quantitative target. The selected 2026 result does not establish its sharp constant; no current resolution is inferred from the older source.
Chernoff’s density is log-concave · Introduction; Section 3, Conjecture 3.1 →
Source dated Feb 5, 2014 · Observed Oct 14, 2026
In this problem · publication v8
Different statement · related variant · Open
The qualitative question asks for some uniform positive constant; the sharper 2014 conjecture specifies the origin curvature as the best constant.
The selected strong-log-concavity proof gives no origin-minimum conclusion. The old conjecture alone is not a current literature assessment.
Proved · version 1
For , with W two-sided standard Brownian motion and density f, .
Scope: The lower bound is uniform over the whole real line. Strict positivity at each point alone would not establish this infimum bound.
Open · version 1
For the standard Chernoff density f, satisfies for every real x.
Scope: This is stronger than inf κ > 0. The selected 2026 theorem does not prove that the origin minimizes curvature, and this curation does not assert a comprehensive current-status assessment.
Relationship not independently reviewed.
Connection in Strong log-concavity of the Chernoff density →Relationship not independently reviewed. This concerns its use in this problem.
The sharper original conjecture requires κ(x) ≥ κ(0) for every x. Its reported numerical value κ(0) ≈ 3.4052 is not established as a uniform lower bound by the selected 2026 theorem.
paraphrase · Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.
Ordinary log-concavity is established, and uniform positive negative log-curvature is proposed as a stronger property of the same Chernoff density.
paraphrase · Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.
Fadoua Balabdaoui · Jon A. Wellner · Published · Publication date Feb 5, 2014
Source-reported results and external checks are separate from independent OpenMath assessment.
Source revision: v2. Observed Oct 14, 2026.
No AI contribution is reported in this selected source.
The paper establishes v(x) > 0 and v(x) ≥ 4x for the normalized one-sided factor, hence κ(x) > 4|x| and inf κ > 0 for the Chernoff density.
paraphrase · Linked proof prose is not republished. Any copied graph data is CC0, as specified by its archive.
Xianyang Zhang · Quan Zhou · Preprint · Publication date Jul 21, 2026
Source-reported results and external checks are separate from independent OpenMath assessment.
Source revision: v1. Observed Oct 14, 2026.
The authors attribute the proof to GPT-5.6 Sol, describe an initial algebraic failure and later corrected approaches, and report carefully checking the argument and revising the exposition.
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.
Not assessed
The 2014 conjecture is recorded as a distinct quantitative target. The selected 2026 result does not establish its sharp constant; no current resolution is inferred from the older source.
Source dated Feb 5, 2014 · Observed Oct 14, 2026 · Source passage →