  We introduce a deterministic SO(3) invariant dynamics of classical spins on a
discrete space-time lattice and prove its complete integrability by explicitly
finding a related non-constant (baxterized) solution of the set-theoretic
quantum Yang-Baxter equation over the 2-sphere. Equipping the algebraic
structure with the corresponding Lax operator we derive an infinite sequence of
conserved quantities with local densities. The dynamics depend on a single
continuous spectral parameter and reduce to a (lattice) Landau-Lifshitz model
in the limit of a small parameter which corresponds to the continuous time
limit. Using quasi-exact numerical simulations of deterministic dynamics and
Monte Carlo sampling of initial conditions corresponding to a maximum entropy
equilibrium state we determine spin-spin spatio-temporal (dynamical)
correlation functions with relative accuracy of three orders of magnitude. We
demonstrate that in the equilibrium state with a vanishing total magnetization
the correlation function precisely follow Kardar-Parisi-Zhang scaling hence the
spin transport belongs to the universality class with dynamical exponent z=3/2,
in accordance to recent related simulations in discrete and continuous time
quantum Heisenberg spin 1/2 chains.
