AbstractWithin the framework of Topological Residual Theory (TRT), this paper rigorously establishes thefirst-principles physical picture that "space itself flows at the speed of light along curves in a right￾handed cylindrical helical form." In this picture, length and time originate from different aspects ofthe same spacetime flow motion, thereby providing a geometric explanation for the origin of theconstancy of the speed of light.To fundamentally resolve the dimensional mismatch among different physical fields that arises inclassical field theory from differing measurement protocols, we propose a Velocity-FieldRepresentation scheme: the electric, gravitational, and magnetic fields are directly defined as thethree local velocity components of the light-speed spacetime flow along the orthogonal basis of theFrenet-Serret (FS) frame [1]:This achieves a complete unification of all underlying field dimensions to velocity at the kinematiclevel. Since the flow speed of spacetime is fixed at the speed of light , different physicalinteractions essentially correspond to the allocation of this motion budget among the threeorthogonal directions: tangential propagation, normal centripetal constraint, and binormal torsion.The allocation mechanism is precisely controlled by the helical pitch angle .By introducing the time definition , we derive the first-order time-evolution equations ofthe three fields under the characteristic rotation frequencies of the FS frame (bending frequency , twisting frequency ). Under the rigid rotation of the frame, the total kineticenergy density remains strictly constant. Utilizing the rigidrotational dynamics of the frame and the vector and scalar triple-product identities, we elucidate thephysical nature by which the "self-work" terms of the rigid triad automatically vanish during rotation,thereby revealing the deep geometric mechanism of dissipation-free energy flow.The macroscopic observable fields — centripetal gravitational acceleration , tangentialelectric field strength , and magnetic rotational angular frequency —emerge naturally as the time derivatives or rotational frequencies of the underlying velocity fieldsafter being modulated by the motion-budget allocation. This provides a self-consistent first￾principles framework for the geometric unification of gravity and electromagnetism.E = ct, A = cn, B = cb. E = ct, A = cn, B = cb.Cαds = c dtωK = CK ωT = CTU = 21(E ⋅ E + A ⋅ A + B ⋅ B) = 23c2g = c2κne = c2κt Bmacro = cτbKeywords: Frenet-Serret geometry; right-handed cylindrical helical spacetime flow; velocity-fieldrepresentation; dimensional self-consistency; energy conservation; motion-budget allocation