In this talk we will derive spectral bounds of 6-dimensional N=(1,0) supergravity models, focusing for concreteness on the tensor sector of F-theory compactifications on elliptic Calabi-Yau 3-folds. Geometrically, we will pursue universal constraints on the allowed base 2-folds, which result in explicit upper bounds on their Picard numbers, and hence, on the tensor spectra of the associated supergravity models. While the proposed bounding strategy manifests the boundedness both at the abstract and the explicit levels, the derived explicit bounds are still to be optimized; we will also report briefly on our on-going attempt at such an optimization, exhibiting the effectiveness of toric blowups in achieving a large number of tensors.