Abstract: The Lorentz factor γ = 1/√(1-v²/c²) is one of the most central mathematical objects in special relativity. In standard physics, it is derived from the principles of constancy of the speed of light and relativity, but its physical essence—why moving clocks run slower—has never been directly explained. Within the framework of the Self-Construction Theory (SCT), this paper rigorously derives the inevitable emergence of the Lorentz factor from the dynamics of constructive renormalization. The core mechanism is relaxation diversion: the motion of a carrier in the relational network requires consumption of the relaxation gap to support spatial displacement, and this consumption can only spill over from its internal relaxation share. The “mutual exclusivity” between internal relaxation and kinetic relaxation—the same set of time-body and time-surface connections can serve only one purpose within the same relaxation period—is the central physical premise of this paper. The time-body (3‑simplex) is the fundamental unit of three‑dimensional spatial extension; both the reconfirmation of a carrier’s internal weaving and its spatial displacement must be realized through time-body–time-surface combinations. The same set of time-body–time-surface connections cannot simultaneously maintain old connections and establish new ones within the same renormalization step—this mutual exclusivity is rooted in the indivisibility of the time-body as the fundamental unit of three‑dimensional extension. This exclusivity leads the allocation of the relaxation gap in two orthogonal directions to satisfy the quadratic constraint Δτ² = Δt² - Δx²/c², from which the Lorentz factor naturally emerges: γ = Δt/Δτ = 1/√(1-v²/c²). The rigorous derivation that the kinetic relaxation share β = v²/c² is given in Lemma 1 of the paper “Emergence of the Relaxation Equation”. On this basis, this paper focuses on how, starting from β = v²/c², the Lorentz factor is derived through the exclusivity of relaxation diversion. This paper further proves that the speed of light c is the limit where kinetic relaxation occupies the entire relaxation gap—when v = c, the internal relaxation share drops to zero and the carrier’s internal constructive renormalization comes to a complete halt. This is the dynamical origin of “the speed of light is the maximum signal speed”. Uniform motion is physically equivalent to rest because neither changes the net distribution relation between internal and overall degrees of freedom—only acceleration can break this balance. Keywords: Lorentz factor; relaxation diversion; internal relaxation; kinetic relaxation; speed of light limit; constructive renormalization; Self-Construction Theory