Motivated by questions related to the landscape of flux compactifications, we combine new and existing techniques into a systematic, streamlined approach for computing vertical fluxes and chiral matter multiplicities in 4D F-theory models. A central feature of our approach is the conjecturally resolution-independent intersection pairing of the vertical part of the integer middle cohomology of smooth elliptic CY fourfolds, relevant for computing chiral indices and related aspects of 4D F-theory flux vacua. We illustrate our approach by analyzing vertical flux backgrounds for F-theory models with simple, simply-laced gauge groups and generic matter content, as well as models with U(1) gauge factors. We explicitly analyze resolutions of these F-theory models in which the elliptic fiber is realized as a cubic in $mathbb P^2$ over an arbitrary (e.g., not necessarily toric) smooth base, and confirm the resolution-independence of the intersection pairing of the vertical part of the middle cohomology. In each model we study, we find that vertical flux backgrounds can produce nonzero multiplicities for all anomaly-free chiral matter field combinations, suggesting that F-theory geometry imposes no additional linear constraints beyond those implied by anomaly cancellation.
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