Generalised model-independent characterisation of strong gravitational
  lenses VI: the origin of the formalism intrinsic degeneracies and their
  influence on $H_0$
  We give a physical interpretation of the formalism intrinsic degeneracies of
the gravitational lensing formalism that we derived on a mathematical basis in
part IV of this series. We find that all degeneracies occur due to the
partition of the mass density along the line of sight. Usually, it is
partitioned into a background (cosmic) density and a foreground deflecting
object. The latter can be further partitioned into a main deflecting object and
perturbers. Weak deflecting objects along the line of sight are also added,
either to the deflecting object or as a correction of the angular diameter
distances, perturbing the cosmological background density. A priori, this is an
arbitrary choice of reference frame and partition. They can be redefined
without changing the lensing observables which are sensitive to the integrated
deflecting mass density along the entire line of sight. Reformulating the time
delay equation such that this interpretation of the degeneracies becomes easily
visible, we note that the source can be eliminated from this formulation, which
simplifies reconstructions of the deflecting mass distribution or the inference
of the Hubble constant, $H_0$. Subsequently, we list necessary conditions to
break the formalism intrinsic degeneracies and discuss ways to break them by
model choices or including non-lensing observables like velocity dispersions
along the line of sight with their advantages and disadvantages. We conclude
with a systematic summary of all formalism intrinsic degeneracies and
possibilities to break them.
