Open. The site labels the problem OPEN (page last edited 29 December 2025) and notes that it cannot be resolved by a finite computation. Three partial claims settle subclasses of the question: Pólya 1929 (accepted, refereed) every function of finite order, and Biernacki 1927 (pending) and Murai 1983 (accepted, refereed) every function with $\sum1/n_k<\infty$; the question is open only for functions of infinite order with $\sum1/n_k=\infty$. The frontmatter standing derives from the claim pages and stays open, since no claim settles the whole question.