The Quaternion Screw: Galaxy Rotation, Spiral Arms, and the Origin of Dark Matter

A Geometric Derivation Without Dark Matter Particles

Martin Scholl — Independent Researcher — 2026

Abstract

We derive the galaxy rotation curve, the formation of spiral arms, and the cosmological abundance of dark matter from the geometry of the quaternion screw — a helical structure on the unit quaternion sphere. No dark matter particles are postulated; the observed effects follow from the algebra of quaternion multiplication alone.