Other models have gradually caught up to GPT-4 while OpenAI has declined to discuss or release anything regarding their internal research and work on GPT-5. Given how far ahead they were with GPT-4, it seems odd to assume no further progress has been made and just not published yet.
The author’s assumption is based on the claim that GPT-4 Turbo “was a failed attempt at GPT-5” but I don’t see any good reason to believe this unless you take the claim that GPT-5 is impossible as a given and reason backwards.