Universal Helical Geometry, E8-G3 Saturation, and Helicity-Constrained Earth Dynamics

This paper develops a unified geometric framework linking canonical helical motion, representation-theoretic saturation in exceptional Lie algebras, and rigorous helicity constraints in geophysical fluid dynamics.Part I establishes the canonical angular velocity of the standard helix and proves a chiral saturation result for the restriction E 8 → G 3 = SU(3) 3 × U(1).Part II introduces a mathematically precise helicity theorem for incompressible flows, frames SU(3) 3 as a structural consequence of E 8 saturation, and maps helix parameters to Earth's radius, oblateness, and axial convection.