Summary: Suppose that \(M\) is a tracial von Neumann algebra embeddable into \(\mathcal{R}^{\omega}\) (the ultraproduct of the hyperfinite \(\text{II}_{1}\)-factor) and \(X\) is an \(n\)-tuple of selfadjoint generators for \(M\). Denote by \(\Gamma (X ; m, k, \gamma)\) the microstate space of \(X\) of order \((m, k,\gamma)\). We say that \(X\) is tubular if for any \(\epsilon > 0\) there exists \(m \in \mathbb{N}\) and \(\gamma > 0\) such that if \((x_{1},\dots, x_{n}), (y_{1}, \dots, y_{n}) \in \Gamma(X;m,k,\gamma)\), then there exists a \(k \times k\) unitary \(u\) satisfying \(|ux_iu^* - y_i|_2 < \epsilon\) for each \(1 \leq i \leq n\). We show that the following conditions are equivalent: \(M\) is amenable (i.e., injective); \(X\) is tubular; any two embeddings of \(M\) into \(\mathcal{R}^{\omega}\) are conjugate by a unitary \(u \in \mathcal {R}^{\omega}\).