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A<sc>bstract</sc> We report results from a study ofB^±→ DK^±decays followed byDdecaying to theCP-even final stateK⁺K⁻and CP-odd final state$$ {K}_S^0{\pi}^0 $$ $K_S^0{\pi }^0$, whereDis an admixture ofD⁰and$$ {\overline{D}}^0 $$ ${\overline{D}}^0$states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angleϕ₃. The results are based on a combined analysis of the final data set of 772×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle experiment and a data set of 198×10⁶$$ B\overline{B} $$ $B\overline{B}$pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be$$ \mathcal{A} $$ $A$_CP+= (+12.5±5.8±1.4)% and$$ \mathcal{A} $$ $A$_CP−= (−16.7±5.7±0.6)%, and the ratios of branching fractions to be$$ \mathcal{R} $$ $R$_CP+= 1.164±0.081±0.036 and$$ \mathcal{R} $$ $R$_CP−= 1.151±0.074±0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries$$ \mathcal{A} $$ $A$_CP+and$$ \mathcal{A} $$ $A$_CP−have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5^°<ϕ₃< 16.5^°) or (84.5^°<ϕ₃< 95.5^°) or (163.3^°<ϕ₃< 171.5^°) and 0.321 <r_B< 0.465. 

A bstract We present a measurement of the Cabibbo-Kobayashi-Maskawa unitarity triangle angle ϕ 3 (also known as γ ) using a model-independent Dalitz plot analysis of B + → D ( $$ {K}_S^0 $$ K S 0 h + h − ) h + , where D is either a D 0 or $$ \overline{D} $$ D ¯ 0 meson and h is either a π or K . This is the first measurement that simultaneously uses Belle and Belle II data, combining samples corresponding to integrated luminosities of 711 fb − 1 and 128 fb − 1 , respectively. All data were accumulated from energy-asymmetric e + e − collisions at a centre-of-mass energy corresponding to the mass of the Υ(4 S ) resonance. We measure ϕ 3 = (78 . 4 ± 11 . 4 ± 0 . 5 ± 1 . 0)°, where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is from the uncertainties on external measurements of the D -decay strong-phase parameters.