Generic injectivity conjecture for three-dimensional stiffness tensors

Let $E(3)$ be the space of three-dimensional stiffness tensors, let $F$ map a stiffness tensor to its slowness polynomial, and write the target as $\mathbb{R}[p_1,p_2,p_3]$. The slowness polynomial is the polynomial associated to the slowness surface of the tensor. Generic injectivity conjecture. The slowness polynomial associated to a generic stiffness tensor in dimension $n=3$ determines the stiffness tensor; equivalently, the map

$$F\colon E(3)\to\mathbb{R}[p_1,p_2,p_3]$$

is generically injective. The paper proves generic injectivity in dimension two and gives partial results for orthorhombic and monoclinic tensors in dimension three, while noting that the full three-dimensional statement remains unresolved in the supplied text.