The Hirsch conjecture (1957): a d-dimensional polytope with n facets has diameter at most n - d.
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 4/5
A 1957 conjecture at the heart of linear programming theory.
Attackability 2/5
Finite polytope witness (43 dimensions, 86 facets), LP-verifiable; required deep structural insight to locate.
- finite witness
- 4/5
- oracle cost
- 3/5
- freshness
- 1/5
- seedability
- 2/5
Confirmed resolution
counterexample by Francisco Santos on .
A 43-dimensional counterexample with 86 facets, settling a 53-year-old question central to linear programming.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
Confirmed
This entry no longer accepts claims or resolution reports.