  Unveiling the chemical fingerprints of the first (Pop III) stars is crucial
for indirectly studying their properties and probing their massive nature. In
particular, very massive Pop III stars explode as energetic Pair-Instability
Supernovae (PISNe), allowing their chemical products to escape in the diffuse
medium around galaxies, opening the possibility to observe their fingerprints
in distant gas clouds. Recently, three z > 6.3 absorbers with abundances
consistent with an enrichment from PISNe have been observed with JWST. In this
Letter, we present novel chemical diagnostics to uncover environments mainly
imprinted by PISNe. Furthermore, we revise the JWST low-resolution measurements
by analyzing the publicly available high-resolution X-Shooter spectra for two
of these systems. Our results reconcile the chemical abundances of these
absorbers with those from literature, which are found to be consistent with an
enrichment dominated (> 50% metals) by normal Pop II SNe. We show the power of
our novel diagnostics in isolating environments uniquely enriched by PISNe from
those mainly polluted by other Pop III and Pop II SNe. When the subsequent
enrichment from Pop II SNe is included, however, we find that the abundances of
PISN-dominated environments partially overlap with those predominantly enriched
by other Pop III and Pop II SNe. We dub these areas confusion regions. Yet, the
odd-even abundance ratios [Mg,Si/Al] are extremely effective in pinpointing
PISN- dominated environments and allowed us to uncover, for the first time, an
absorber consistent with a combined enrichment by a PISN and another Pop III SN
for all the six measured elements.
