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+[
+"Now overlay every turn at once. Each position of the sphere passes through the same circle, the j k circle, so the whole family is a pencil of spheres threaded on one ring, with their centres sliding along the i axis. The plane is just the member that reaches infinity. Sweep theta all the way round and the pencil fills space: the four snapshots were slices of the hypersphere, and the ring and the axis are its two linked threads.",
+"One more piece: the gamma factor. Every prime gives zeta a ball of its own, wrapping at its own rate, log p. They are the harmonics. There is one more place, infinity, the lamp, and its ball has no period: it is the single continuous source the harmonics are sampled from. Its factor is the gamma function. Fold it in and you get xi, which lives on the sphere cleanly, with the half turn as its symmetry: the far side of the equator is the alias of the near side, folded at the Nyquist line, one half. Sphere to plane is continuation. The gamma factor is the lamp's own ball."
+]