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In this paper, we outline a theory of referential accessibility called Veins Theory (VT). We show how VT addresses the problem of" left satellites", currently a problem for stack-based models, and show that VT can be used to significantly reduce the search space for antecedents. We also show that VT provides a better model for determining domains of referential accessibility, and discuss how VT can be used to address various issues of structural ambiguity.