Chowla-type correlation conjecture for omega sequences

Let ${\cal O}$ denote the omega sequence, and let $C_k({\cal O},N)$ be its correlation measure of order $k$ for the first $N$ terms.

Omega correlation conjecture.

$$C_k({\cal O},N)=o(N).$$

The paper describes this as essentially Chowla's conjecture. No proof or resolution is supplied in the given text.