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math.GT2026
Hard unknots are often easy from a different perspective
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
Recent attempts to train AI models to recognize knots have produced millions of "hard" unknot diagrams resistant to simplification by Reidemeister moves, pass moves, or random walk…
math.GT2025
New Upper Bounds for Stick Numbers
Jason Cantarella, Andrew Rechnitzer, Henrik Schumacher +1
We use a version of simulated annealing with knot-type preserving moves to find polygonal representatives of various knot types with low stick number. These give better bounds on s…