Foundational preprint derives a unified metric classification for deficit gradient flows, suggesting universal tools for various systems.
This foundational QBN preprint derives a unified Riemannian metric classification for all deficit gradient flows purely from QBN core axioms. It proves KL divergence is the unique deficit functional, unifies Fisher–Rao and Wasserstein geometries via a two-parameter family, and identifies Sinkhorn distance as the globally smooth interpolating metric. It constructs functorial coarse-graining theory and derives finite-ε Sinkhorn gradient dynamics, supplying universal geometric tools for all physical, AI and social QBN systems. Dated June 2026, unreviewed foundational preprint. Independent researcher: davidwyu@126.com
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Wengang Yu (2026) studied this question.