Caio Moreira Goolsby, Christopher J. Conselice, Duncan Austin, Tom Harvey, Jose Diego, Nathan Adams, Julien Marabotto, Jordan D'Silva, Qiong Li

We leverage the strong gravitational field of Abell S1063 to identify faint, highly magnified galaxies using ultra-deep James Webb Space Telescope (JWST)/NIRCam imaging from the GLIMPSE survey and ancillary Hubble Space Telescope (HST)/ACS imaging from the Hubble Frontier Fields program. We construct a photometric catalogue of lensed high-redshift candidates and use these sources to constrain the faint end of the rest-frame UV luminosity function (UVLF) over $z\simeq6$--11. Rather than treating the UVLF turnover ($M_{\rm t}$) as a hard cutoff, we model it as a gradual quadratic suppression and explicitly account for the potential continued contribution of galaxies beyond the turnover. In a shallow-turnover scenario, up to one-third of the UV luminosity density can arise from sources fainter than $M_{\rm t}$. While we find no direct evidence for a turnover down to $M_{\rm UV}=-13.5$ at $z=6$, our analysis can only confidently exclude weak, medium, and strong turnover models down to $M_{\rm t}=-15.9$, $-15.1$, and $-14.8$, respectively. Across these models, we infer lower limits of the UV luminosity, star formation density, and the ionization rate as: $ρ_{\rm UV}\geq22\times10^{25}\,{\rm erg\,s^{-1}\,Hz^{-1}\,Mpc^{-3}}$, ${\rm SFRD}\geq25\times10^{-3}\,M_\odot\,{\rm yr^{-1}\,Mpc^{-3}}$, and $\log_{10}(\dot{n}_{\rm ion}/{\rm s^{-1}\,Mpc^{-3}})\geq51.02$. We find that galaxies fainter than the conventional $M_{\rm UV}=-17$ limit contribute more than half of the UV luminosity density and at least $\sim64\%$ of the ionizing photons produced by star-forming galaxies at $z=6$. Because our turnover model permits a suppressed, but non-zero, galaxy population beyond $M_{\rm t}$, sources fainter than the turnover remain contributors to both $ρ_{\rm UV}$ and $\dot{n}_{\rm ion}$, emphasizing the need to consider the turnover and its shape during reionization.