An LSST-DESC Precursor Project: Hyper Suprime-Cam Year 1 $3\times 2$pt in Harmonic Space

We present the first fully photometric joint analysis of weak gravitational lensing and galaxy clustering (3$\times$2pt) in harmonic space with LSST-DESC analysis pipelines applied to Hyper Suprime-Cam Year 1 (HSC Y1) data. The HSC Y1 dataset, with imaging depth and galaxy number density similar to those expected for the first year of LSST observations, is an ideal testbed for validating DESC measurement and inference tools. We measure the full set of angular power spectra - cosmic shear, galaxy clustering, and galaxy-galaxy lensing - perform null tests, and correct for the impact of observing conditions on both the galaxy density and shear fields via mode deprojection. We validate our likelihood pipeline by reproducing the official HSC Y1 cosmic shear cosmological constraints with the DESC inference code. Jointly analysing all three two-point functions, we constrain $\mathrm{\Lambda }$CDM and $w$CDM cosmologies, reporting results for cosmic shear, the combination of galaxy clustering and galaxy-galaxy lensing (2$\times$2pt), and the full 3$\times$2pt. From the joint 3$\times$2pt $\mathrm{\Lambda }$CDM analysis we find ${\mathrm{\Omega }}_m=0.249_{-0.051}^{+0.061}$, ${\sigma }_8=0.904_{-0.091}^{+0.098}$, and $S_8\equiv {\sigma }_8\sqrt{{\mathrm{\Omega }}_m\mathrm{/}0.3}=0.821_{-0.021}^{+0.018}$. This analysis validates the complete DESC 3x2pt infrastructure on survey data, providing the foundation for the forthcoming LSST Year 1 cosmological analysis.