Doubly Discordant SH₀ES NGC 4258 Cepheid Relations (HVI) and Impactful Extinction Laws

S H₀ ES (Supernovae and H₀ 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: Δ W0,H-VI=-0m.13± 0m.02 ( -0m.17 unweighted) and that is paired with the previously noted Δ W0,I-VI-0m.3 , which in concert with complimentary evidence suggest the 2016 S H₀ ES NGC 4258-anchored H₀±σ_H₀ warrants scrutiny (i.e., σ_H₀/H₀ 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., Δ d 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 H₀ ES database relays incorrect SMC Cepheid photometry.