Open Conjecture Board

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Feige's conjecture (2006): for independent nonnegative X_1,...,X_n with E[X_i] <= 1 and S_n their sum, P(S_n <= E[S_n] + 1) >= 1/e.

Resolution reported — pending verification

Status is community- and machine-tracked and may lag. Verify independently before investing effort.

Assessment

Renown 3/5

A well-known conjecture across probability and theoretical computer science.

Attackability 2/5

A counterexample would be an explicit distribution family violating the bound, numerically checkable; two decades of attention found none, and it fell to proof.

finite witness
3/5
oracle cost
3/5
freshness
1/5
seedability
2/5

Reported resolution

proof by Zhengqing (announced by G. Wang); paper pending on .

Announced resolution of the 1/e conjecture; the sharp constant 1/e was the conjectured optimum (13/64 was the long-standing partial bound). Primary reference pending; curator to attach.

Evidence

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

I’m attacking this

Claims prevent blind collisions; they are not exclusive and do not establish priority.