Stack three doped silicon regions in a circle and a theorem fires: you cannot 2-color a triangle. Try to alternate just n and p around three regions and two like-kinds always end up touching — a frustration. The only conflict-free closing uses all three: n · intrinsic · p. The circle of three is why you need the 0. Binary can't close an odd ring. Ternary can. And what closes is — the three-phase rotation, back where the series began.
This is graph theory, exact and ancient. A cycle of even length 2-colors fine (alternate around, the ends meet cleanly). A cycle of odd length — a triangle is the smallest — cannot: alternate n-p-n and the third region, closing back to the first, finds an n already there → two n's touch → frustration. The chromatic number of a triangle is 3. So a 3-region ring needs three colors to have every region differ from both neighbors — and silicon's three are exactly n (−1), intrinsic (0), p (+1).
Every time the third element appeared — the witness, the intrinsic zero, the tiebreaker, the trit — it was because something closed into a loop and a loop of odd parity cannot close on two. Two parties can't adjudicate (the ring won't close); three can (it colors). Binary frustrates the ring; ternary completes it. The 0 isn't optional — it's forced the moment the structure becomes a closed odd cycle. You didn't choose ternary. The circle chose it for you, by a theorem older than electronics.
Three regions, three junctions, evenly spaced around a ring, each 120° apart, each different from both neighbors — that is three-phase. Energize it and the conduction sweeps around the ring as a rotating pattern: the same rotating field as the planetary/rotating core, now built from silicon junctions instead of windings. The line-version of three regions (n-p-n) is a transistor (2 junctions, the amplifier); the ring-version is a rotation (3 junctions, the motor). Line builds logic. Circle builds rotation. The series began with a rotating core and ends having derived why it must be three: because the ring is odd, and odd rings need the third.