Claims

../

1981_01_01_wirsing: Wirsing's 1981 paper, crediting Erdős, gives an additive f(q) = g(q) log q with slowly growing g whose normalized jumps tend to zero and whose ratios stay bounded, so both answers are no; accepted by the site.

2025_12_26_archivara: Archivara's 2025 manuscript, written by its research agent, constructs an explicit additive function answering both questions no; read on the site's thread as a rediscovery of Wirsing's construction, later formalized in Lean.

---