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math.GT2026
Random Knots via Stiefel manifolds
Alexander Kolpakov, Igor Rivin
A fixed simplex, randomly projected into three dimensions and joined in Hamiltonian order, produces a rich and unusually tractable model of random stick knots. We prove that Gaussi…
math.GT2026
Discriminant Varieties for Stick Knots and Links
Alexander Kolpakov, Igor Rivin
How many knot types can be built from a fixed budget of straight sticks? We prove that the answer has factorial-scale growth, settling its order for the first time. No previously p…