  Phenomenological rules that govern the collective behaviour of complex
physical systems are powerful tools because they can make concrete predictions
about their universality class based on generic considerations, such as
symmetries, conservation laws, and dimensionality. While in most cases such
considerations are manifestly ingrained in the constituents, novel
phenomenology can emerge when composite units associated with emergent
symmetries dominate the behaviour of the system. We study a generic class of
active matter systems with non-reciprocal interactions and demonstrate the
existence of true long-range polar order in two dimensions and above, both at
the linear level and by including all relevant nonlinearities in the
Renormalization Group sense. We achieve this by uncovering a mapping of our
scalar active mixture theory to the Toner-Tu theory of dry polar active matter
by employing a suitably defined polar order parameter. We then demonstrate that
the complete effective field theory -- which includes all the soft modes and
the relevant nonlinear terms -- belongs to the (Burgers-) Kardar-Parisi-Zhang
universality class. This classification allows us to prove the stability of the
emergent polar long-range order in scalar non-reciprocal mixtures in two
dimensions, and hence a conclusive violation of the Mermin-Wagner theorem.
