A citizen-mathematics experiment
Quiver Quest
A quiver is a handful of dots joined by arrows. Mutating a dot reverses its arrows and reroutes the paths through it. Every dot starts green. Your goal is a maximal green sequence: mutate only green dots, until every dot has turned red.
Small quivers are puzzles. Wild ones are open mathematics: nobody knows all their sequences, or exactly which beginnings can never be finished. Find sequences nobody else has, propose rules about which beginnings are doomed, and break other people's rules with counterexamples.
Three modes
Photo by Abhishekgowda28, CC0 1.0 Dynkin
Curious Kitten
Finite type. Learn the moves.
8 quivers
Photo by TechnoKittyCat, CC0 1.0 Tame
House Cat
Euclidean type. Compare routes and hunt for patterns.
4 quivers
Photo by Dominique Bérubé (berdom on iNaturalist), CC0 1.0 Wild
Wild Cat Researcher
Wild type. Open questions live here.
13 quivers
How scoring works
MGS Hunter: finding sequences
- A maximal green sequence of length n (the number of mutable vertices) earns 5 points.
- Any other maximal green sequence earns 5 + ⌈100 ÷ √f⌉ points, where f is the number of distinct players who have found that exact sequence on that quiver. It goes down as more players find it.
- The first player to find a sequence keeps a permanent 25-point first-discovery bonus.
- You earn each sequence once per quiver. Submitting it again changes nothing.
- Sequences are distinct when their ordered lists of mutated vertices differ, even if they end at the same quiver.
Theorem Hunter: conjectures, counterexamples and proofs
A counterexample is credited by name on the conjecture board, and the conjecture it breaks stays on the record. The published policy sets 50 points for a verified counterexample, 200 for an accepted proof and 300 for an accepted generalisation, but the leaderboards don't add these points yet: today they rank maximal green sequences only.
Exploring is free and private: only the sequences you submit are checked and recorded. Every sequence is verified on our server; a sequence that isn't a genuine maximal green sequence earns nothing.