I'd break this into separate questions:

**Will AGI exist by 2100?**
Uncertain. Credible researchers span 2030s to "never" for timelines. 2100 is far enough out that most expert distributions suggest it's plausible but not inevitable.

**Would it "rule"?**
This depends heavily on what you mean:
- *Control major decisions?* If AGI exists and is vastly capable, some influence seems likely, but "rule" assumes specific governance structures we can't predict
- *Deliberately dominate?* Only if it's designed/inclined that way—not automatic
- *De facto dominance through capability?* More plausible than active conquest

**Key uncertainties:**
- How aligned it is with human values
- Whether we develop robust governance frameworks before or after AGI
- What "rule" means (formal power? actual control? influence?)
- Whether AGI remains singular or distributed

The honest answer: this is a genuine open question. Outcomes range from "AGI is a valuable tool we govern effectively" to "we lose meaningful control" to "it never arrives."

What aspect concerns you most—the technical timeline, alignment risks, or governance?
