  The tadpole conjecture suggests that the complete stabilization of complex
structure deformations in Type IIB and F-theory flux compactifications is
severely obstructed by the tadpole bound on the fluxes. More precisely, it
states that the stabilization of a large number of moduli requires a flux
background with a tadpole that scales linearly in the number of stabilized
fields. Restricting to the asymptotic regions of the complex structure moduli
space, we give the first conceptual argument that explains this linear scaling
setting and clarifies why it sets in only for a large number of stabilized
moduli. Our approach relies on the use of asymptotic Hodge theory. In
particular, we use the fact that in each asymptotic regime an orthogonal
sl(2)-block structure emerges that allows us to group fluxes into
sl(2)-representations and decouple complex structure directions. We show that
the number of stabilized moduli scales with the number of sl(2)-representations
supported by fluxes, and that each representation fixes a single modulus.
Furthermore, we find that for Calabi-Yau four-folds all but one representation
can be identified with representations occurring on two-folds. This allows us
to discuss moduli stabilization explicitly and establish the relevant scaling
constraints for the tadpole.
