Testing residual-symmetry-fixed columns of $U_{\rm PMNS}$ at DUNE and T2HK with initial JUNO constraints

We study fixed-column predictions of the lepton mixing matrix that arise from residual symmetries originating in a class of discrete flavour and modular symmetries. While the recent high-precision determination of $\sin^{2}\theta_{12}$ by JUNO already constrains part of these predictions, the remaining ones are primarily characterized by non-trivial correlations between $\sin^{2}\theta_{23}$ and the Dirac CP phase $\delta_{\rm CP}$, which are currently only weakly constrained. This motivates a detailed investigation using next-generation long-baseline neutrino experiments. For the viable scenarios, we derive precise $\sin^{2}\theta_{23}$-$\delta_{\rm CP}$ correlations and use them to generate test-event samples, marginalising over the remaining oscillation parameters. We perform detailed simulations for DUNE and T2HK, presenting allowed regions in the $\sin^{2}\theta_{23}$-$\delta_{\rm CP}$ plane and evaluating the CP-violation fraction as a function of exposure. Our results show that the combined sensitivity of DUNE and T2HK provides a robust test of fixed-column lepton-mixing predictions.