  We consider the Sudakov form factor in N=4 SYM in the off-shell kinematical
regime, which can be achieved by considering the theory on its Coulomb branch.
We demonstrate that up two three loops both the infrared-divergent as well as
the finite terms do exponentiate, with the coefficient accompanying
$\log^2(m^2)$ determined by the octagon anomalous dimension $\Gamma_{oct}$.
This behaviour is in strike contrast to previous conjectural accounts in the
literature. Together with the finite terms we observe that up to three loops
the logarithm of the Sudakov form factor is identical to twice the logarithm of
the null octagon $\mathbb{O}_0$, which was recently introduced within the
context of integrability-based approaches to four point correlation functions
with infinitely-large R-charges. The null octagon $\mathbb{O}_0$ is known in a
closed form for all values of the 't Hooft coupling constant and kinematical
parameters. We conjecture that the relation between $\mathbb{O}_0$ and the
off-shell Sudakov form factor will hold to all loop orders.
