Based on the axiom system of spiral-dimensional topological primitives, this paper establishes the spiral-dimensional unified field dynamic equation through dynamic analysis of uniaxial chiral spiral primitives and rigorous Laplace transform. The complete derivation of mass-energy relation is accomplished following first principles. By defining the radial convergence component and angular oscillation component of the spiral field, we construct a second-order differential dynamic equation describing the evolution of fundamental spacetime, and derive the time-domain general solution of the spiral field. Combined with the definitions of spiral topological field energy and topological mass, the complete mass-energy formula of spiral-dimensional theory is obtained: E equals mc squared multiplied by (1 plus omega squared divided by sigma squared). Under low-energy and non-relativistic approximation, this formula naturally reduces to Einstein's classical mass-energy equation E equals mc squared. This work reveals the in-depth physical mechanism behind mass, energy and mass-energy equivalence from the topological origin. It proves that the classical relativistic mass-energy relation is merely a low-energy approximate special case of the spiral-dimensional unified field theory, and builds a fully self-consistent unified theoretical system integrating geometric topology and relativistic physics. Keywords: Spiral dimension; Unified field equation; Topological primitive; Mass-energy equivalence; First principle; Spacetime topology
Changquan Li (Tue,) studied this question.