Making Single-Cell Data Distillation Auditable: Traceable Real-Cell Coresets via Discrete Min-Max Selection

Single-cell datasets are increasingly costly to store, audit, and reuse for model training. Dimensionality reduction and dataset distillation can reduce this burden, but conventional distillation methods often produce synthetic expression profiles that cannot be traced to an assayed cell. We formulate traceable single-cell data distillation as retaining original cell identifiers and gene symbols under fixed cell and gene budgets. The resulting training subset remains connected to measured counts, labels, and assay metadata, so unexpected predictions can be checked against their source data. We propose two real-cell selectors. Fixed-CF uses static characteristic-function matching. Minmax-CF solves an entropy-regularized discrete min--max problem that upweights poorly preserved directions and adds only observed cells. Across donor-, technology-, and perturbation-level shifts on three datasets, Minmax-CF retains 96.52% of Full balanced accuracy on MS, approximately matches Full on average on hPancreas with a median $2.55\times$ GPU speedup in the all-gene setting, and obtains the lowest pathway error among compressed methods on Norman. Performance remains weaker for rare states, some technology shifts, unseen perturbation components, and settings where fidelity is weakly associated with downstream utility. Because the selected IDs refer to measured cells, these cases can be investigated by inspecting the corresponding training support, labels, and assay metadata. Minmax-CF consistently reduces worst-direction discrepancy, while downstream utility and cost vary across datasets and tasks.