%0 Journal Article %T The 8-universality Criterion is Unique %A Scott D. Kominers %J Mathematics %D 2008 %I arXiv %X Using the methods developed for the proof that the 2-universality criterion is unique, we partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh's 8-universality criterion as an application of our characterization results. %U http://arxiv.org/abs/0807.2099v1