High-precision numerical framework for the time-varying solar neutrino flux with full Earth matter oscillation corrections for global underground laboratories

Solar neutrinos have been studied for over half a century to test both the Standard Solar Model and the electroweak sector of the Standard Model of particle physics. Contemporary experiments are now entering an era of high-precision measurements, demanding corresponding theoretical predictions with sub-percent accuracy to enable meaningful comparison. In this paper, we identify and analyze the essential physical and computational components required to compute solar neutrino fluxes with high fidelity, and present a unified, computationally efficient framework. This framework incorporates: (i) the time-varying Earth-Sun distance; (ii) Earth matter effects modeled using both one-dimensional (1D) and three-dimensional (3D) Earth electron-density profiles; and (iii) a fast, Strang-splitting-based implementation of the Mikheyev-Smirnov-Wolfenstein (MSW) neutrino propagation formalism, enabling rapid, large-scale scans over neutrino trajectories and energy grids. We deliver site-specific predictions for the China Jinping Underground Laboratory (CJPL) and other underground laboratories actively engaged in solar neutrino programs.