We present a joint cosmological analysis of the two-point correlation function and the aperture-mass skewness measured from the Year 3 data of the Hyper Suprime-Cam Subaru Strategic Program. The aperture-mass skewness is a compressed representation of three-point shear information, designed to capture non-Gaussian features while keeping the data vector computationally tractable. We find that including the aperture-mass skewness improves the $S_8\text{−}{\mathrm{\Omega }}_m$ figure of merit by 80% compared to the two-point-correlation-function-only case, primarily due to the breaking of degeneracies. Our joint analysis yields a constraint of $S_8=0.736\pm 0.020$, which is slightly lower than the two-point-only result and increases the tension with Planck 2018 to $3.2\sigma$ in the $S_8\text{−}{\mathrm{\Omega }}_m$ plane. The two- and three-point statistics are found to be internally consistent across redshift bins and angular scales, and we detect no significant intrinsic alignment signal. We also explore extensions to the $w$ cold dark matter model and find no evidence for deviations from a cosmological constant. This work demonstrates the feasibility and scientific value of incorporating third-order shear statistics into weak lensing cosmology and provides a practical pathway for similar analyses in future Stage-IV surveys such as LSST, Euclid, and Roman.

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• Cosmological parameters
• Gravitational lenses
• Large scale structure of the Universe