Doubly Discordant S$$\boldsymbol{H_{0}}$$ES NGC 4258 Cepheid Relations ($$\boldsymbol{HVI}$$) and Impactful Extinction Laws

S $$H_{0}$$ ES (Supernovae and $$H_{0}$$ for the Equation of State of dark energy) 2016–2022 $$HVI$$ data for classical Cepheids in the keystone galaxy NGC 4258 yield doubly discordant Wesenheit Leavitt functions: $$\Delta W_{0,H-VI}=-0\overset{\textrm{m}}{.}13\pm 0\overset{\textrm{m}}{.}02$$ ( $$-0\overset{\textrm{m}}{.}17$$ unweighted) and that is paired with the previously noted $$\Delta W_{0,I-VI}\simeq-0\overset{\textrm{m}}{.}3$$ , which in concert with complimentary evidence suggest the 2016 S $$H_{0}$$ ES NGC 4258-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., NGC 4258), particularly for comparatively obscured variables (e.g., $$\Delta d\gtrsim 4\%$$ , reddened Cepheid subsamples in the Milky Way, M 31, NGC 2442, NGC 4424, NGC 5643, NGC 7250). Lastly, during the analysis it was identified that the 2022 S $$H_{0}$$ ES database relays incorrect SMC Cepheid photometry.