Topology of the Polar Vortex and Montana Weather

The paper and the model align on methodology and phenomena but both leave key gaps. The paper specifies sliding-window delay embeddings with M=7, tau=1 and 30-point windows for 2015–2020 and uses VR persistent homology, reporting a single winter peak per year and the largest signal in early 2016; it also shows H1 snapshots on 2016-02-01 (two prominent features) and 2016-02-03 (one feature) consistent with a merge event (figures described in the text) . However, the paper does not formalize the persistence-norm time series, uniqueness criteria, or margins, and it contains a small inconsistency between the SW formula (vectors in R^{M+1}) and the phrase “vectors of 7 daily observations” when M=7 . The model proposes an executable pipeline that would confirm exactly these claims and dates (including 2016-02-01 vs 2016-02-03) but remains unexecuted due to missing data and also introduces a mis-specified top-2 count that mixes H0 and H1, whereas the paper’s discussion is explicitly H1-centric; the paper’s abstract even frames “vortex splitting” in terms of the number of distinct persistent H1 features .