  To study the chemical evolution across cosmic epochs, we investigate Ne, S,
Cl, and Ar abundance patterns in the COS Legacy Archive Spectroscopic SurveY
(CLASSY). CLASSY comprises local star-forming galaxies (0.02 < z < 0.18) with
enhanced star-formation rates, making them strong analogues to high-z
star-forming galaxies. With direct measurements of electron temperature, we
derive accurate ionic abundances for all elements and assess ionization
correction factors (ICFs) to account for unseen ions and derive total
abundances. We find Ne/O, S/O, Cl/O, and Ar/O exhibit constant trends with
gas-phase metallicity for 12+log(O/H) < 8.5 but significant correlation for
Ne/O and Ar/O with metallicity for 12+log(O/H) > 8.5, likely due to ICFs. Thus,
applicability of the ICFs to integrated spectra of galaxies could bias results,
underestimating true abundance ratios. Using CLASSY as a local reference, we
assess the evolution of Ne/O, S/O, and Ar/O in galaxies at z>3, finding no
cosmic evolution of Ne/O, while the lack of direct abundance determinations for
S/O and Ar/O can bias the interpretation of the evolution of these elements. We
determine the fundamental metallicity relationship (FMR) for CLASSY and compare
to the high-redshift FMR, finding no evolution. Finally, we perform the first
mass-neon relationship analysis across cosmic epochs, finding a slight
evolution to high Ne at later epochs. The robust abundance patterns of CLASSY
galaxies and their broad range of physical properties provide essential
benchmarks for interpreting the chemical enrichment of the early galaxies
observed with the JWST.
