Yes, we can! We present a novel approach aimed at identifying the key chemical elements to search for the missing descendants of very massive first stars exploding as Pair Instability Supernovae (PISN). Our simple and general parametric study accounts for the unknowns related to early cosmic star-formation and metal-enrichment and allows us to define the most likely [Fe/H] and abundance ratios of long-lived stars born in inter-stellar media polluted by the nucleosynthetic products of PISN. We show that the descendants of very massive first stars can be most likely found at [Fe/H]≈ −2 and we demonstrate that to search for an under-abundance of [(N, Cu, Zn)/Fe] < 0 is the key to identify the rare PISN descendants. The killing elements N, Zn, and Cu are not produced by PISN, so that their sub-Solar abundance with respect to iron persists in environments polluted by further generations of normal core-collapse supernovae up to a 50% level (see Figure). We show that the star BD +80◦ 245, which has [Fe/H]= −2.2, [N/Fe]= −0.79, [Cu/Fe]= −0.75, and [Zn/Fe]= −0.12 can be the first example of a stars imprinted by PISN at a 50% level.
