Is Korea the origin of fermented sauce culture?

‌I asked an AI, and it said that Goguryeo, Balhae, and the Korean Peninsula were actually the origin, and it spread to China and Japan after that. It also mentioned that while China acknowledges this to some extent, China was the first to define the Hanja (Chinese character) terms and definitions for it. Regarding Japan, they reportedly acknowledge the Korean origins but claim that they were the first to succeed in commercializing it. Is this true? Are there any history experts here?