Follow the knot.
See each verified move. Amber marks the changing strands; gaps show underpasses.
Find a sequence of moves
The local move
The small drawing isolates this kind of move. The large panels show the actual knot.
Change the knots and search settings
Signed Gauss words use O1+ and U1+. Each crossing appears twice.
Verification and search details
Every displayed full-knot drawing follows the signed planar diagram, with no extra intersections. Moves are checked by Reidemeister replay. The trefoil test also has an independent Python verifier. Playback shows discrete before-and-after diagrams.
Search details will appear here.
Failure within finite move and crossing limits leaves equivalence unknown. The search sees only point capacities and opaque seam values. It uses no coloring invariant, crossing-reduction heuristic, pretrained policy, or precomputed failure labels. Markings start empty and update during search after unmarked exhaustive probes prove a candidate impossible under these exact bounds. Budget stops never create failure markings. Online search contract and limits ↗