Title: A Cepheid systematics-free test of $H_0$ to $\lesssim2.5\%$ accuracy using SH0ES photometry

Abstract: The recent SH0ES determination of the Hubble constant, $H_0=73.04\pm1.04$ km/s/Mpc, deviates significantly by $\approx5\sigma$ from the \textit{Planck} value, stimulating discussions on cosmological model extensions. To minimize statistical uncertainty and mitigate sensitivity to systematic errors in any single anchor distance determination, SH0ES combines Cepheids from various observations, including those from Type Ia supernova (SNe Ia) host galaxies, NGC 4258, and closer galaxies (MW, LMC, SMC, and M31), although this mixed sample may introduce unknown or subtle systematic errors due to comparing distant and closer Cepheids. To address this, we propose a subset excluding Cepheids from the closer galaxies, retaining only the NGC 4258 water megamasers as a single anchor, circumventing potential systematic errors associated with observational methods and reduction techniques. Focusing solely on these Cepheids yields competitive statistical errors, approximately $2.5\%$, sufficient to identify a $\approx3\sigma$ tension with the \textit{Planck} $H_0$ value. Our approach offers an opportunity to utilize optical photometry with systematic uncertainty smaller than the statistical uncertainty, potentially achieving higher precision than NIR photometry, given the lower optical background. However, currently the optical photometry sample's fidelity does not match that of NIR photometry. The significant Hubble tension obtained is unrelated to Cepheids and we discuss other options.