ON THE SMALL BOUNDARY PROPERTY, Z-ABSORPTION, AND BAUER SIMPLEXES

The paper proves SBP and Z-absorption for the two classes via approximate divisibility on traces and Bauer-simplex arguments, culminating in Theorems 4.6 (dynamical systems) and 4.9 plus Proposition 4.10 (AH-diagonal), with the local neighborhood-zero-boundary form captured by Lemma 2.1 and the trace-norm characterization Theorem 2.9. The candidate solution follows essentially the same program but mislabels “approximate divisibility” as a “weak restricted property Γ,” and cites older numbering; it also routes Z-stability for crossed products via Kerr–Szabó rather than the paper’s URP/COS route. With these caveats (naming/numbering and an implicit URP hypothesis for general amenable Γ), the logical spine matches the paper and yields the same conclusions.