Propose a conjecture

A good conjecture can be broken. The most useful kind names a quiver and a green prefix and claims that no maximal green sequence begins that way. It becomes a challenge at once: a verified counterexample disproves it automatically, with credit to whoever finds it, and the conjecture stays on the record either way.

Votes measure interest, not truth. Only a named reviewer can mark a conjecture proved, with a written reason. Before you post, check Known results: some bans are already theorems.