2 problems

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Fast mixing conjecture for face flips on the triangle lattice
Fast mixing conjecture. The mixing time of the face-flip Markov chain on $T_{m,n}$ is $O(mn \log(mn))$ .
Conjectureopenmarkov-chains mixing-times origamiarXiv posted 2 days ago
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Conjecture on foldability of concentric convex smooth crease patterns
Foldability conjecture. The circular pleat folds, and every similar crease pattern consisting of a concentric series of convex smooth curves also folds.
Conjectureopencurved-folding developable-surfaces origamiarXiv posted 2 days ago

Fast mixing conjecture for face flips on the triangle lattice