Sure, there's no authority who stamps the official definition.

I'll make my case. To me, if you look at how the phrase is usually used -- "when humans have achieved AGI...", etc -- it evokes a science fiction turning point that implies superhuman performance in more or less every intellectual task. It's general, after all. I think of Hal or the movie Her. It's not "Artifical General Just-Like-Most-People-You-Know Intelligence". Though we are not there yet, either, if you consider the full spectrum of human abilities.

Few things would demonstrate general superhuman reasoning ability more definitively than machines producing new, useful, influential math results at a faster rate than people. With that achieved, you would expect it could start writing fiction and screenplays and comedy as well as people too (it's still very far imo), but maybe not, maybe those skills develop at different paces, and I still wouldn't want to call it AGI. But I think truly conquering mathematics would get me there.

A standard term people use for what you describe is superintelligence, not AGI.

Current frontier models are better than average humans in many skills but worse in others. Ethan Mollick calls it “jagged frontier” which sounds about right.