The dots are the multiplication clock (orange = full-tour numbers, blue = squares, black = laps); the colors are the Möbius "shadow" of how each number factors. Spin to a lock: try sides 125, p 5. The landing dots snap into crisp spokes sitting right on the shadow's own spokes, both pinned to the same grid, and for that spiral they're fully predictable: the orange full-tour lines are essentially projections of the black laps. So one clock lays a prime's × structure bare. What it can't show is how that shifts from prime to prime, whether a number is full-tour depends on which clock you're on, and "how often, across all primes?" is a question no single clock answers. So we stacked them → Prime-Field Census.