How much of persistent homology is topology? A quantitative decomposition for spin model phase transitions

ArXi:2603.29072v1 Announce Type: cross Point-cloud persistent homology (PH) -- computing alpha or Rips complexes on spin-position point clouds -- has been widely applied to detect phase transitions in classical spin models since Donato, with subsequent studies attributing the detection to the topological content of the persistence diagram. We ask a simple question that has not been posed: what fraction of the PH signal is genuinely topological? We