Proposed
Full sharp deviation formula proposed by Ling ↗
Corollary 1.3 covers every δ > 0 via the proposed proof of Samuels’ conjecture; independent assessment is pending.
Source dated Aug 18, 2026 · Observed Oct 13, 2026
Bound · version 1
The later proposal for every positive deviation
Statement
For every n ≥ 1 and δ > 0, the infimum of P(S < E S + δ) over independent nonnegative integrable variables with E Xᵢ ≤ 1 equals . This infimum is attained. Taking the infimum over n gives .
Assumptions
- Strict threshold, fixed positive finite n and positive δ.
- The optimization ranges over all admissible distributions.
Scope
Ling’s later Corollary 1.3 proposes the fully sharp formula; it is not part of the linked unit-slack Lean proof.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Evidence
Source reports
Connections
In this problem · publication v5 · Selected context
Feige’s probability conjecture →
Different statement · related variant · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v7
Feige’s probability conjecture →
Different statement · related variant · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
Sources
On Samuels’ Conjecture →
- Theorem 1.1 and Corollary 1.3; arXiv submitted 18 August, manuscript dated 19 August → · Original passage ↗
Recorded wording
Claims Samuels’ sharp mean-vector formula and the full sharp Feige formula for every δ > 0.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Zhi Ling · Preprint · Publication date Aug 18, 2026
Revision & attribution
Source revision: 2026-08-18. Observed Oct 13, 2026.
No specific AI contribution is attributed by this source record.
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.
Proposed
Full sharp deviation formula proposed by Ling ↗
Corollary 1.3 covers every δ > 0 via the proposed proof of Samuels’ conjecture; independent assessment is pending.
Source dated Aug 18, 2026 · Observed Oct 13, 2026 · Source passage →
Record details
- Claim ID
- claim-feige-all-deviations-sharp
- Statement version
- 1
- SHA-256
- 36f6717e74a6c68ecbf32c900d68208e29fcbe4c800172a9e63336300b2d4c98