A Stern–Gerlach magnet doesn't read a hidden label off a particle — it forces a choice. Along its axis the spin comes out only up or down, never in between.
Feed it a beam already spin-up along vertical, then turn the magnet by angle θ. The up-fraction is exactly cos²(θ/2) — all of it at 0°, half at 90°, none at 180°. Turn the dial and watch the two ports trade weight.
Chain three magnets for the punchline. The first purifies the beam to up. The second, turned sideways, splits it — and erases what the first one decided. A third magnet back along vertical splits again, its down port full of the very spins the first magnet threw away.
That's why measurement isn't readout: each magnet prepares a fresh state along its own axis. Stern and Gerlach saw the beam split in 1922 — before anyone knew what spin was.
Something in the simulation stopped unexpectedly — the lesson continues without it. Nothing you did was wrong; you can move on.