  In quantum field theory (QFT) above two spacetime dimensions, one is usually
only able to construct exact operator maps from the ultraviolet (UV) to the
infrared (IR) of strongly coupled renormalization group (RG) flows for the most
symmetry-protected observables. Famous examples include maps of chiral rings in
4d $\mathcal{N}=2$ supersymmetry. In this letter, we construct the first
non-perturbative UV/IR map for less protected operators: starting from a
particularly "simple" UV strongly coupled non-Lagrangian 4d $\mathcal{N}=2$
QFT, we show that a universal non-chiral quarter-BPS ring can be mapped exactly
and bijectively to the IR. In particular, strongly coupled UV dynamics
governing infinitely many null states manifest in the IR via Fermi statistics
of free gauginos. Using the concept of arc space, this bijection allows us to
compute the exact UV Macdonald index in the IR.
