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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 wa…
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…