  The Swampland Distance Conjecture (SDC) states that, as we move towards an
infinite distance point in moduli space, a tower of states becomes
exponentially light with the geodesic distance in any consistent theory of
Quantum Gravity. Although this fact has been tested in large sets of examples,
it is fair to say that a bottom-up justification that explains both the
geodesic requirement and the exponential behavior has been missing so far. In
the present paper we address this issue by making use of the Covariant Entropy
Bound as applied to the EFT. When applied to backgrounds of the Dynamical
Cobordism type in theories with a moduli space, we are able to recover these
main features of the SDC. Moreover, this naturally leads to universal lower and
upper bounds on the 'decay rate' parameter $\lambda_{\text{sp}}$ of the species
scale, that we propose as a convex hull condition under the name of Species
Scale Distance Conjecture (SSDC). This is in contrast to already proposed
universal bounds, that apply to the SDC parameter of the lightest tower. We
also extend the analysis to the case in which asymptotically exponential
potentials are present, finding a nice interplay with the asymptotic de Sitter
conjecture. To test the SSDC, we study the convex hull that encodes the
(asymptotic) moduli dependence of the species scale. In this way, we show that
the SSDC is the strongest bound on the species scale exponential rate which is
preserved under dimensional reduction and we verify it in M-theory toroidal
compactifications.
