Time Quantum from Internal Symmetry: When the Minimum Temporal Resolution Equals the Group Order

It is proved that for any statistical mechanical system with Z_q internal symmetry and all-or-nothing matching, the minimum time quantum equals the group order q. The generalized block-level binary mapping (Theorem 3') yields a critical coupling J_t^c(q) = (q-1)N_b/(qN_b-1) · (h_y - h_d) that increases monotonically with q, with universal (q-independent) inter-block coupling and q-dependent effective field. The all-or-nothing condition forces a first-order phase transition. Empirical validation using 141 years of CUG-CMA climate data confirms both the q=5 and q=6 predictions: the Z_5 > Z_6 effect size ordering matches the J_t/J_t^c depth ratio for all three climate variables, the correlation length ratio ξ_5/ξ_6 = 0.984 confirms bond universality, TMAX_std shows a 15.6-fold autocorrelation drop between 5-year and 6-year blocks (time-quantum resonance), and the 1984 boundary exhibits AC1 elevation without variance enhancement (first-order signature). The Z_11 test (solar cycle) shows no resonance, establishing three necessary conditions for time-quantum resonance. The result establishes a structural principle: the discrete time quantum is determined by internal symmetry, not by external parameters.