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We present Weak Gravitational Lensing measurements of a sample of 157 clusters within the Kilo Degree Survey (KiDS), detected with a > 5σthermal Sunyaev-Zel’dovich (SZ) signal by the Atacama Cosmology Telescope (ACT). Using a halo-model approach, we constrained the average total cluster mass,M_WL, accounting for the ACT cluster selection function of the full sample. We find that the SZ cluster mass estimateM_SZ, which was calibrated using X-ray observations, is biased withM_SZ/M_WL = (1 − b_SZ) = 0.65 ± 0.05. Separating the sample into six mass bins, we find no evidence of a strong mass dependency for the mass bias, (1 − b_SZ). Adopting this ACT-KiDS SZ mass calibration would bring thePlanckSZ cluster count into agreement with the counts expected from thePlanckcosmic microwave background ΛCDM cosmological model, although it should be noted that the cluster sample considered in this work has a lower average massM_SZ, uncor = 3.64 × 10¹⁴ M_⊙compared to thePlanckcluster sample which has an average mass in the rangeM_SZ, uncor = (5.5 − 8.5)×10¹⁴ M_⊙, depending on the sub-sample used. 

We measured the cross-correlation between galaxy weak lensing data from the Kilo Degree Survey (KiDS-1000, DR4) and cosmic microwave background (CMB) lensing data from the Atacama Cosmology Telescope (ACT, DR4) and the Planck Legacy survey. We used two samples of source galaxies, selected with photometric redshifts, (0.1 <  z B  < 1.2) and (1.2 <  z B  < 2), which produce a combined detection significance of the CMB lensing and weak galaxy lensing cross-spectrum of 7.7 σ . With the lower redshift galaxy sample, for which the cross-correlation was detected at a significance of 5.3 σ , we present joint cosmological constraints on the matter density parameter, Ω m , and the matter fluctuation amplitude parameter, σ 8 , marginalising over three nuisance parameters that model our uncertainty in the redshift and shear calibration as well as the intrinsic alignment of galaxies. We find our measurement to be consistent with the best-fitting flat ΛCDM cosmological models from both Planck and KiDS-1000. We demonstrate the capacity of CMB weak lensing cross-correlations to set constraints on either the redshift or shear calibration by analysing a previously unused high-redshift KiDS galaxy sample (1.2 <  z B  < 2), with the cross-correlation detected at a significance of 7 σ . This analysis provides an independent assessment for the accuracy of redshift measurements in a regime that is challenging to calibrate directly owing to known incompleteness in spectroscopic surveys.