  High-resolution JWST observations can test confusion-limited HST observations
for a photometric bias that could affect extragalactic Cepheids and the
determination of the Hubble constant. We present JWST NIRCAM observations in
two epochs and three filters of >330 Cepheids in NGC4258 (which has a 1.5%
maser-based geometric distance) and in NGC5584 (host of SNIa 2007af), near the
median distance of the SH0ES HST SNIa host sample and with the best leverage
among them to detect such a bias. JWST provides far superior source separation
from line-of-sight companions than HST in the NIR to largely negate confusion
or crowding noise at these wavelengths, where extinction is minimal. The result
is a remarkable >2.5x reduction in the dispersion of the Cepheid P-L relations,
from 0.45 to 0.17 mag, improving individual Cepheid precision from 20% to 7%.
Two-epoch photometry confirmed identifications, tested JWST photometric
stability, and constrained Cepheid phases. The P-L relation intercepts are in
very good agreement, with differences (JWST-HST) of 0.00+/-0.03 and 0.02+/-0.03
mag for NGC4258 and NGC5584, respectively. The difference in the determination
of H_0 between HST and JWST from these intercepts is 0.02+/-0.04 mag,
insensitive to JWST zeropoints or count-rate non-linearity thanks to error
cancellation between rungs. We explore a broad range of analysis variants
(including passband combinations, phase corrections, measured detector offsets,
and crowding levels) indicating robust baseline results. These observations
provide the strongest evidence yet that systematic errors in HST Cepheid
photometry do not play a significant role in the present Hubble Tension.
Upcoming JWST observations of >12 SNIa hosts should further refine the local
measurement of the Hubble constant.
