Somewhere below a few thousandths of solar metallicity, the universe stops providing examples. Surveys of gas and stars keep finding a metallicity floor: a lower bound, around 10^-4 to 10^-3 of solar, that even the most metal-poor systems rarely undercut, in dwarf galaxies, in high-redshift absorbers, and in the Galactic halo's most ancient stars (Kunth and Ostlin 2000; Wise et al. 2012). Truly metal-free stars, the Population III objects every standard simulation requires, have never been observed.
In ΛCDM the floor must be manufactured: the first stars form from pristine BBN-composition gas, and their supernovae must then enrich essentially every future star-forming environment above the floor, quickly and uniformly. Making that work requires assumptions about Population III initial mass functions, supernova yields, and metal mixing efficiencies that remain deeply uncertain, and in practice many simulations simply impose the floor by hand to avoid producing the metal-free stars observation refuses to supply (Wise et al. 2012; Jaacks et al. 2018). The universality is the hard part: enrichment by scattered first-generation supernovae should be patchy, leaving pristine pockets, yet the floor appears everywhere.
The standing rests on a powerful null result that deepens annually: decades of dedicated searches through the most metal-poor halo stars keep finding iron-poor but carbon-enhanced compositions, never zero metals. Extremely large telescopes will push the search orders of magnitude further.