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Sorry, I'm not seeing exactly how quotienting down to a multigraph on one vertex informs the automorphisms of the given LPS graph. I will look into how the LSV graphs connect, thank you.
Thank you, this resolves the first and third versions. Towards the second version, as I understand it, Weierstrass' theorem only guarantees existence. Is there a version which allows one to compute the specific approximation, with guarantees relating the uniform precision to the degree, or does that require other machinery?
