No net turn on a driven cage: why light cannot make the C60 quarter-turn flux

The half-filled C60 cage prefers a quarter-turn: π/2 of magnetic flux through every pentagon, nothing through the hexagons, with an exactly golden gap √5-1. Circularly polarised light is the standard way to manufacture flux in a carbon lattice without a magnet, and it is the obvious thing to reach for here. It cannot do this one. Coupling a circular drive through Peierls phases on the cage's own bonds, the induced pentagon circulation is odd under the antipodal map, so its uniform component vanishes identically — at leading order in the inverse drive frequency, for every amplitude and every propagation axis. What the light makes instead is a dipole: one hemisphere of pentagons turning one way, the other turning back, with a correlation of -0.998 to -0.9996 against k·n and a total below 3×10^-17. The reason is that inversion acts on a Peierls-coupled cage as complex conjugation, exactly, and inversion reverses orientation. The obstruction is a leading-order one and we say where it ends. The relation does not survive exponentiation: conjugating a time-ordered product flips the sign of i in each factor without reversing the ordering. Beyond leading order the cancellation leaks, and the leak enters at second order — the uniform component scales as 1/Ω^2, verified constant in Ω^2 to three figures from Ω=8 to 32, and reaching only 1.7×10^-3 of the typical circulation at the largest amplitude tried. Light is thus not merely a bad way to reach the quarter-turn; it is forbidden at leading order and parametrically suppressed beyond it. Reaching that flux needs a genuinely time-odd source. The proof uses only centrosymmetry and Peierls coupling, so it applies to any centrosymmetric cage. Includes complete verification scripts.