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Recent compilations of NIRSpec emission line galaxies have shown a mildredshift evolution of the FMR at $z > 4$, indicating that the FMR alone is notfully capable of capturing the redshift evolution of the mass-metallicityrelation: $z > 4$ galaxies appear more metal-poor than the FMR predictions.There is evidence that the most metal-deficient high-redshift galaxies are alsothe most compact. In this work, we further investigate this anti-correlation byleveraging the wealth of data gathered through the first cycle of JWST. Wecompile a sample of 427 $z > 3$ galaxies covered by both the NIRSpec prism andNIRCam short-wavelength photometry, consisting of 334 galaxies from thepublicly available programs and 93 galaxies from the first data release of theJADES program. We use this sample to infer the redshift evolution of the FMRfrom $z = 3$ to $z \sim 10$, further confirming the previously reported mildredshift evolution. We measure the rest-ultraviolet (UV) sizes of $z > 4$galaxies, inferring the mass-size relation at $z = 4-10$ with a power-law slopeof $0.21 \pm 0.04$. We investigate the redshift evolution of the mass-sizerelation, finding that at a fixed stellar mass, higher redshift galaxies appearmore compact. The degree of this redshift evolution depends on the stellarmass, with the lowest mass galaxies showing the strongest redshift evolutionand the most massive galaxies ($\log(M_{\star}/M_{\odot}) > 9$) showing noredshift evolution. We investigate the anti-correlation between the compactnessof galaxies and their gas-phase metallicities, finding that the more compactgalaxies appear more metal-deficient and therefore more offset from the localcalibration of the FMR. (abridged)

Ultraviolet Compactness of High-Redshift Galaxies as a Tracer of  Early-Stage Gas Infall, Stochastic Star Formation, and Offset from the  Fundamental Metallicity Relation