Sebastien Tchitchek and co-authors, in a paper submitted to arXiv on 2026-09-01, introduce the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. ^[1] The paper reports that experiments on 12 scientific collections comprising 227 diagrams show a median per-collection speedup of d_SK over state-of-the-art approximations of W_2 of 626x, with an aggregate speedup of 2100x. ^[2] The authors claim that the encoded point sets are matched via one-dimensional optimal assignment in O(N log N) steps, yielding an explicit diagonal-aware point assignment. ^[3] The paper asserts that the SK-Wasserstein distance controls the classical 2-Wasserstein distance, admits an explicit isometric embedding into a Hilbert space, and induces a positive-definite Gaussian kernel. ^[4] The Sierpiński--Knopp Wasserstein Distance is intended for applications involving 2-Wasserstein approximation. ^[5] The authors suggest that this new distance metric addresses limitations in existing methods for analyzing persistence diagrams. ^[6] The research paper associated with this metric has been assigned the identifier 2609.01528. ^[7]