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Is the following two-dimensional graph likely to be globally rigid?

The test for local rigidity boils down to checking the rank of the rigidity matrix (the Jacobian of the length function), which can in turn be interpreted as checking whether a certain polynomial is zero … We also go through some analysis for global rigidity, but it's for whether the check for generic global rigidity works, not whether the particular framework is actually globally rigid. …
Dylan Thurston's user avatar