Theseus's Thread

↗ Daedalus — where this labyrinth was carved

Daedalus builds the labyrinth; here Theseus walks out of it — provably. A perfect maze is a tree, so its one path is trivially shortest. So we braid it (open dead-ends → loops → many routes) and weight the corridors (some slow, some quick) until the route that looks shortest is no longer the one that costs least. Then we don’t trust the picture — we prove the thread minimal with three unrelated witnesses.

The labyrinth

Size 22

Braiding 0.55

The thread-finder

show the flood (settled cells) tint corridors by terrain cost

The proof

the thread A* settled Dijkstra settled entrance heart

Three witnesses must agree on the cost, or the badge above goes red: A* (heuristic = Manhattan × cheapest corridor ⇒ admissible), Dijkstra (the heuristic-free optimum), and an independent Bellman–Ford relaxation that shares no code with the heap search. The thread is also re-summed step-by-step through real open passages: the drawing cannot lie. · a workshop cross — Pathfinder × Daedalus.

Theseus’s Thread