Shafarevich-Tate 2-parity conjecture for elliptic curves

Let $K$ be a number field and $E$ an elliptic curve over $K$, and let \cyrr Sh$(E/K)$ denote its Shafarevich-Tate group. Shafarevich-Tate 2-parity conjecture. For every elliptic curve $E/K$,

$$\dim_{\mathbf{F}_2}\text{\cyrr Sh}(E/K)[2]$$

is even. If the $2$-primary subgroup \cyrr Sh$(E/K)[2^\infty]$ is finite, the Cassels pairing implies this parity, so the conjecture concerns the general case where that finiteness is not known; the source gives no resolution.