A Cubic Harmonic Identity for Stationary Circular Motion: Kinematic Core, Density–Tempo Selection, and GR/Kerr Realizations.

We identify and formalize a symmetry-determined cubic harmonic identity governing stationary circular motion. The kinematic core follows from the helical Killing generator: defining $f = \Omega/(2\pi)$ and a consistently measured tangential speed $v$ yields the exact reduction $f^3/v^3 = 1/((2\pi)^3 r^3)$, independent of force-law exponent and field equations. Introducing the dimensionless monomial $i = V f^3 / v^3$ isolates a purely geometric organization, while inverse-square gravity is singled out only dynamically through a density–tempo realization for spherical sources. In stationary general relativity, the same cubic structure admits an exact operational deformation when velocity is defined locally (ZAMO/LNRF in Kerr). Finally, using dimensionless Kerr variables and any covariant macroscopic scale $V \propto M^3$, the combination becomes strictly mass-independent. This paper establishes the geometric and structural status of the cubic organization; a companion work will address first-order universality extensions tied to stability and variational dynamics (including ISCO-related constraints).