Fourth-order regularization of nonlinear drift-diffusion equations with focusing drift

This record is a non-public technical dataset prepared solely for the purpose ofobtaining a stable DOI. It is not a published article, and it does not constitutea public release of the scientific content. The document contains intermediatederivations, numerical notes, and model formulations related to the fourth-orderregularized drift–diffusion equation (SC-PDE), which stabilizes focusing-drivenblow-up phenomena via degenerate mobility and fourth-order dissipation. The material summarizes the internal development of a phenomenological surrogatemodel for gravitational focusing, kinematic caustics, and finite-core saturation,but it is not the final peer-reviewed version. Mathematical details, figures, andfull theoretical discussions will appear only in future public releases or in thejournal submission currently under review. This dataset is archived under closed access to ensure that no part of themanuscript is considered publicly disclosed prior to journal publication. Thecontent is provided exclusively as a private research record to establish DOI-basedtimestamping during ongoing development.