I don't think it exists. We can't even seem to agree on a standard criteria for "intelligence" when assessing humans let alone a rigorous mathematical definition. In turn, my understanding of the commonly accepted definition for AGI (as opposed to AI or ML) has always been "vaguely human or better".
Unless the marketing department is involved in which case all bets are off.
It can exist for the purpose of the paper. As in "when I write AGI, I mean ...". Otherwise what's the point in any rigour if we're just going by "you know what I mean" vibes.