  While gravitational microlensing by planetary systems provides unique vistas
on the properties of exoplanets, observations of a given 2-body microlensing
event can often be interpreted with multiple distinct physical configurations.
Such ambiguities are typically attributed to the close-wide and inner-outer
types of degeneracies that arise from transformation invariances and symmetries
of microlensing caustics. However, there remain unexplained inconsistencies
between aforementioned theories and observations. Here, leveraging a fast
machine learning inference framework, we present the discovery of the offset
degeneracy, which concerns a magnification-matching behaviour on the lens-axis
and is formulated independent of caustics. This offset degeneracy unifies the
close-wide and inner-outer degeneracies, generalises to resonant topologies,
and upon reanalysis, not only appears ubiquitous in previously published
planetary events with 2-fold degenerate solutions, but also resolves prior
inconsistencies. Our analysis demonstrates that degenerate caustics do not
strictly result in degenerate magnifications and that the commonly invoked
close-wide degeneracy essentially never arises in actual events. Moreover, it
is shown that parameters in offset degenerate configurations are related by a
simple expression. This suggests the existence of a deeper symmetry in the
equations governing 2-body lenses than previously recognised.
