The Andoni-Naor-Neiman family of quadratic metric inequalities does not characterize isometric embeddability into CAT(0) spaces, as demonstrated by the Lebedeva 6-point space.
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The Andoni-Naor-Neiman inequalities and isometric embeddability into a CAT(0) space
The Andoni-Naor-Neiman family of quadratic metric inequalities does not characterize isometric embeddability into CAT(0) spaces, as demonstrated by the Lebedeva 6-point space.