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.
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.