Doubly Discordant SH0ES NGC4258 Cepheid Relations (HVI), and Impactful Extinction Laws

S$H_0$ES 2016-2022 $HVI$ data for classical Cepheids in the keystone galaxy NGC4258 yield doubly discordant Wesenheit Leavitt functions:~$\Delta W_{0,H-VI} = -0.13\pm0^{m}.02$ ($-0^{m}.17$ unweighted) and that is paired with a previously noted $\Delta W_{0,I-VI}\simeq-0^{m}.3$, which in concert with complimentary evidence suggest the 2016 S$H_0$ES NGC4258-anchored $H_0 \pm \sigma_{H_0}$ warrants scrutiny (i.e., $\sigma_{H_0}/{H_0}\gtrsim 6$\%). Cepheid distance uncertainties are further exacerbated by extinction law ambiguities endemic to such Leavitt relations (e.g., NGC4258), particularly for comparatively obscured variables (e.g., $\Delta d \gtrsim 4$\%, reddened Cepheid subsamples in the Milky Way, M31, NGC2442, NGC4424, NGC5643, NGC7250). Lastly, during the analysis it was identified that the 2022 S$H_0$ES database relays incorrect SMC Cepheid photometry.