  We conjecture that in a consistent supergravity theory with non-vanishing
gravitino mass, the limit $m_{3/2}\rightarrow 0$ is at infinite distance. In
particular one can write $M_{\mathrm{tower}} \sim m_{3/2}^\delta$ so that as
the gravitino mass goes to zero, a tower of KK states as well as emergent
strings becomes tensionless. This conjecture may be motivated from the Weak
Gravity Conjecture as applied to strings and membranes and implies in turn the
AdS Distance Conjecture. We test this proposal in classical 4d type IIA
orientifold vacua in which one obtains a range of values $\tfrac13 \le \delta
\le 1$. The parameter $\delta$ is related to the scale decoupling exponent in
AdS vacua and to the $\alpha$ exponent in the Swampland Distance Conjecture for
the type IIA complex structure. We present a general analysis of the gravitino
mass in the limits of moduli space in terms of limiting Mixed Hodge Structures
and study in some detail the case of two-moduli F-theory settings. Moreover, we
obtain general lower bounds $\delta\, \geq \, \frac{1}{3}, \, \frac{1}{4}$ for
Calabi--Yau threefolds and fourfolds, respectively. The conjecture has
important phenomenological implications. In particular we argue that low-energy
supersymmetry of order 1 TeV is only obtained if there is a tower of KK states
at an intermediate scale, of order $10^8$ GeV. One also has an upper bound for
the Hubble constant upon inflation $H \lesssim m_{3/2}^\delta
M^{(1-\delta)}_{\text{P}}$.
