Reaching the Metallicity Floor at z about 10: Lensed Star Clusters at Cosmic Dawn and Cosmic Noon

Origins of globular clusters (GCs) are linked to the assembly of their host galaxies. We analyze star-cluster populations in two strongly lensed systems that bracket Cosmic Dawn and Cosmic Noon: the Cosmic Gems arc (GEMS) at z=9.625, among the first galaxies, and the Sparkler at z=1.378. New STARRED deconvolution photometry of GEMS provides SEDs for ten unique, doubly imaged cluster candidates, while a homogeneous Bayesian analysis places both populations on a common cosmological timeline. The GEMS clusters formed at z form about 10 -- 11 (median 10.2), consistent with halo assembly at or above the atomic-cooling scale. Their photometry requires low metallicities: individual clusters are consistent with [Z/ H] -1.2, and the data exclude [Z/ H] at least-0.5, though they cannot distinguish reliably below [Z/ H] -1.5. This conclusion is unchanged when using stellar-population models including binary evolution---important for ultraviolet emission at this age---yielding similarly low metallicities, [Z/ H]=-2.2 to-2.7. The formal estimate, [Z/ H] = -2.3 plus or minus0.3, is consistent with the Milky Way GC metallicity floor, though its value remains prior-dependent. The Sparkler clusters formed about2.5 Gyr later, at z form about 2 -- 3.5 in a Cosmic Noon dwarf galaxy, and are more enriched ([Z/ H] about-0.5). Comparison with Milky Way GCs places GEMS in an exceptionally early, metal-poor regime and the Sparkler among later, more enriched populations, though neither association uniquely determines an in-situ or ex-situ origin. Closed-box and gas-regulator calculations show both systems are compatible with limited pre-enrichment followed by rapid enrichment and accretion-regulated growth. Together, they probe distinct cluster-forming environments from Cosmic Dawn to Cosmic Noon.