Hidden quantum $R$-matrix in the discrete-time classical Heisenberg magnet

We construct local $M$-operators for an integrable discrete-time version of the classical Heisenberg magnet by convoluting the twisted quantum trigonometric $4\times4$ $R$-matrix with certain vectors in its “quantum” space. Components of the vectors are identified with $\tau$-functions of the model. Hirota's bilinear formalism is extensively used. The construction generalizes the known representation of $M$-operators in continuous-time models in terms of Lax operators and the classical $r$-matrix.