Boundary and rigidity of nonsingular Bernoulli actions

The paper proves exactly the claimed statement: for a countable exact group G, a two-point nonsingular Bernoulli action satisfying Kakutani’s condition and the finiteness condition ph = pgh for all but finitely many h (for each fixed g) is solid (Theorem A) , with the intended meaning of solidity for subequivalence relations spelled out in the introduction . The model’s solution cites this theorem and outlines the same proof strategy via boundary amenability on anti-symmetric Fock spaces and an AO-type condition for the reduced crossed product, as in the paper’s abstract and strategy sections . Minor omission: the model did not explicitly state the paper’s ‘no atoms’ assumption on (Ω, μ) that appears alongside Kakutani’s condition in Theorem A and in the Kakutani criterion discussion . Apart from that, the logic and match of hypotheses are correct.