arXiv:2510.03616v4 Announce Type: replace Abstract: Source apportionment, the attribution of observed multipollutant concentrations to underlying sources, can be cast as a non-negative matrix factorization (NMF) problem. Because NMF is non-unique, source apportionment imposes often unverifiable constraints such as structural sparsity or rotational tuning based on scientific knowledge, which may not be available in newer geographies or new sensor technology. Geometric NMF approaches offer a more data-driven route to identification, but many still rely on source profiles with arbitrary scalings, assume exact separability, and lack a framework for consistent estimation. We address these limitations by formally establishing statistical identifiability of the source apportionment matrix under a stochastic framework that replaces hard separability with soft probabilistic relaxations. We then present a scalable geometric algorithm to estimate this matrix and prove its consistency, to our knowledge the first such result requiring no exact sparsity, no parametric distributional assumptions, and accommodating spatio-temporal dependence. We apply this method in a setting where prior knowledge of sources is limited, so structural assumptions are challenging to impose. Over the last four decades, the Arctic has warmed four times faster than the rest of the planet, with anthropogenic aerosols among the major forcings. Greenland Summit Station has collected size-resolved particulate matter year-round since 2003, yet these records remain underutilized. Analyzing the 2003--2016 record with geometric NMF and HYSPLIT trajectories, we characterize long-range transport of anthropogenic and natural species into the Arctic.