  We initiate the systematic study of flux scalar potentials and their vacua by
using asymptotic Hodge theory. To begin with, we consider F-theory
compactifications on Calabi-Yau fourfolds with four-form flux. We argue that a
classifications of all scalar potentials can be performed when focusing on
regions in the field space in which one or several fields are large and close
to a boundary. To exemplify the constraints on such asymptotic flux
compactifications, we explicitly determine this classification for situations
in which two complex structure moduli are taken to be large. Our classification
captures, for example, the weak string coupling limit and the large complex
structure limit. We then show that none of these scalar potentials admits de
Sitter vacua at parametric control, formulating a new no-go theorem valid
beyond weak string coupling. We also check that the recently proposed
asymptotic de Sitter conjecture is satisfied near any infinite distance
boundary. Extending this strategy further, we generally identify the type of
fluxes that induce an infinite series of Anti-de Sitter vacua, thereby
generalizing the well-known Type IIA settings. Finally, we argue that also the
large field dynamics of any axion in complex structure moduli space is
universally constrained. Displacing such an axion by large field values will
generally lead to severe backreaction effects destabilizing other directions.
