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We present an analysis of the complete singular phase space of a jet when multiple measurements have been made about the jet structure. Using Soft-Collinear Effective Field Theory, strict factorization theorems are found only for the boundaries of physical phase space in these multi-differential cross-sections. These theorems have incompatible evolution equations, but nonetheless, a resummation ansazt can be found that interpolates between the boundaries. While logarithmic accuracy cannot be guaranteed in the bulk of phase space, the ansazt reproduces the correct resummation exactly at any boundary. Aside from jet physics, applications to more exclusive PDF's and Drell-Yan event shapes are indicated.
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