The Kontsevich tetrahedral flow revisited

We prove that the Kontsevich tetrahedral flow Ṗ=Qa:b(P), the right-hand side of which is a linear combination of two differential monomials of degree four in a bi-vector P on an affine real Poisson manifold Nn, does infinitesimally preserve the space of Poisson bi-vectors on Nn if and only if the two monomials in Qa:b(P) are balanced by the ratio a:b=1:6. The proof is explicit; it is written in the language of Kontsevich graphs.