The empirical Constant-Lagrangian (CL) relation has previously been shown to reproduce a substantial fraction of observed galactic rotation curves, but until now it has lacked a theoretical foundation. This paper derives the CL condition from a gravitational rapidity field that generates a local Spin(1,3) rotor describing the vacuum flow surrounding a galaxy.Two independent but complementary geometric branches emerge from the same gravitational rotor. The first is a kinematic branch, in which the rapidity field generates the gravitational four-velocity and its convective acceleration. The second is a Maurer—Cartan branch, in which the differential geometry of the rotor itself is described through its Lie-algebra-valued connection. Although these branches describe different geometric objects, both converge on the same invariant isorapidity condition, expressing the conservation of the combined radial and azimuthal rapidity along the flow. In the weak-field limit, this invariant reduces directly to the Constant-Lagrangian relation governing the exterior galactic rotation curve.The construction is developed in its native BQ (biquaternion) algebra and subsequently translated into three standard mathematical languages: the Weyl representation of Clifford algebra Cl(1,3), Spacetime Algebra, and the conventional Dirac spin formalism. The agreement between these independent formulations demonstrates that the resulting isorapidity condition is a representation-independent consequence of the underlying Spin(1,3) rotor geometry rather than an artifact of a particular algebraic framework.Beyond providing a theoretical basis for the empirical Constant-Lagrangian postulate, the paper presents a unified rotor-based description in which both the kinematics of galactic vacuum flow and its Maurer—Cartan transport originate from the same gravitational rapidity field.