SDSS-V Local Volume Mapper (LVM): Dithered Data Cube Reconstruction with 3dcubegen

The Sloan Digital Sky Survey V (SDSS-V) Local Volume Mapper (LVM) is conducting an unprecedented wide-field integral field spectroscopic survey of the Milky Way, the Magellanic Clouds, and nearby galaxies using a strategy based on multiple dithered observations to achieve full spatial coverage, improved spatial sampling, and enhanced spectral depth. However, the scientific exploitation of these observations requires a robust methodology to combine the individual row-stacked spectra (RSS) into homogeneous three-dimensional data cubes. In this work, we present 3DCubeGen, a flexible and scalable reconstruction tool designed to combine multiple LVM dithers while preserving flux and propagating uncertainties. The method enables the coaddition of large datasets, improving the signal-to-noise ratio, enhancing spatial resolution, and increasing sensitivity to faint emission features, following and extending approaches previously implemented in integral field surveys such as CALIFA. We apply 3DCubeGen to a large set of LVM observations, including the Large and Small Magellanic Clouds and nearby galaxies, combining thousands of dithers corresponding to millions of spectra. The resulting data products demonstrate significant improvements in spatial sampling and spectral depth, enabling detailed studies of the ionised gas, stellar populations, and kinematics across extended regions. 3DCubeGen provides a robust and scalable solution for LVM data cube reconstruction and represents a key tool for exploiting the scientific potential of the SDSS-V Local Volume Mapper.