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Recently, new positivity constraints were suggested to constrain arbitrary tensor integrals. In this talk, we explore two variants of these positivity constraints: one built from ``open bubbles'', which are tensor-like objects found by removing a tensor from a bubble invariant, and the second built from ``color matrices'', which are matrices found by removing a color contraction from a bubble invariant. Using these positivity constraints, we find sharp bounds on tensor integrals at finite N, and explore some features of these integrals.