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.
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