  In Kontsevich's graph calculus, internal vertices of directed graphs are
inhabited by multi-vectors, e.g., Poisson bi-vectors; the Nambu-determinant
Poisson brackets are differential-polynomial in the Casimir(s) and density
$\varrho$ times Levi-Civita symbol. We resolve the old vertices into subgraphs
such that every new internal vertex contains one Casimir or one Levi-Civita
symbol${}\times\varrho$. Using this micro-graph calculus, we show that
Kontsevich's tetrahedral $\gamma_3$-flow on the space of Nambu-determinant
Poisson brackets over $\mathbb{R}^3$ is a Poisson coboundary: we realize the
trivializing vector field $\smash{\vec{X}}$ over $\smash{\mathbb{R}^3}$ using
micro-graphs. This $\smash{\vec{X}}$ projects to the known trivializing vector
field for the $\gamma_3$-flow over $\smash{\mathbb{R}^2}$.
