  The perturbative approach to quantum field theories has made it possible to
obtain incredibly accurate theoretical predictions in high-energy physics.
Although various techniques have been developed to boost the efficiency of
these calculations, some ingredients remain specially challenging. This is the
case of multiloop scattering amplitudes that constitute a hard bottleneck to
solve. In this paper, we delve into the application of a disruptive technique
based on the loop-tree duality theorem, which is aimed at an efficient
computation of such objects by opening the loops to nondisjoint trees. We study
the multiloop topologies that first appear at four loops and assemble them in a
clever and general expression, the N$^4$MLT {\it universal topology}. This
general expression enables to open any scattering amplitude of up to four
loops, and also describes a subset of higher order configurations to all
orders. These results confirm the conjecture of a factorized opening in terms
of simpler known subtopologies, which also determines how the causal structure
of the entire loop amplitude is characterized by the causal structure of its
subtopologies. In addition, we confirm that the loop-tree duality
representation of the N$^4$MLT universal topology is manifestly free of
noncausal thresholds, thus pointing towards a remarkably more stable numerical
implementation of multiloop scattering amplitudes.
